Uncategorised
Math 350H Spring 2019
01:640:350:H Linear Algebra Section

This course is a proofbased continuation of Math 250, covering Abstract vector spaces and linear transformations, inner product spaces, diagonalization, and canonical forms.
Prerequisites:
 CALC4, Math 250 and Math 300
Text: Linear Algebra (4th ed.), by Friedberg, Insel and Spence,
Prentice Hall, 2003 ISBN 0130084514. For this section, any recent edition of the textbook should be sufficient.
 Class
MW4 0140P0300 HLL009 BUS  Office Hours: Tues 23 pm, Hill 726
 Contact Information: email ctw@math.rutgers.edu
The course is strongly based on Math 250. However, we'll work axiomatically, starting from the abstract notions of vector space and of linear transformation. Much of the homework and many of the exam and quiz problems will require you to write precise proofs, building on your proofwriting experience in Math 300. From this more abstract viewpoint, we'll be developing linear algebra far beyond Math 250, with new insight and new applications.
Class attendance is very important. A lot of what we do in class will involve collective participation. We will cover the topics indicated in the syllabus below, but the dates that we cover some of the topics might be adjusted during the semester, depending on class discussion, etc. Such adjustments, along with the almostweekly homework assignments, will be announced in class and also posted on this webpage, so be sure to check this webpage regularly. Absences from a single class due to minor illnesses should be selfreported using the university system; for longer absences, students should email me with the situation. I reserve the right to lower the course grade up to one full letter grade for poor attendance.
Makeups for exams are generally not given; if a student has an extremely good reason (e.g. documented medical emergency) I may rearrange the grading scheme to accomodate.
Problem sets are due on most Tuesdays. There are no problems due on the two midtermexam Tuesdays.
Note that we will cover significant material from all the chapters in the book, Chapters 17.
Grading policy: First midterm exam: 100 points; Second midterm exam: 100 points; Problem sets and quizzes: 100 points; Final exam: 200 points (Total: 500 points).
Tentative Course Syllabus
Week  Lecture dates  Sections  topics 

1  1/23  Chapter 1  Abstract vector spaces & subspaces 
2  1/28,1/30  Chapter 1  Span of subsets, linear independence 
3  2/4, 2/6  Chapter 1  Bases and dimension 
4  2/11, 2/13  Chapter 2  Linear transformations 
5  2/18, 2/20  Chapter 2  Change of basis, dual spaces 
6  2/25, 2/27  Ch. 12  Review and Exam 1 (10/9) 
7  3/4, 3/6  Chapter 3  Rank and Systems of Linear Equations 
8  3/11, 3/13  Chapter 4  Determinants and their properties 
9  3/25, 3/27  Chapter 5  Eigenvalues/eigenvectors 
10  4/1, 4/3  Chapter 5  Diagonalization, Markov Chains 
11  4/8, 4/10  Chapter 6  Inner Product spaces 
12  4/15  Chapter 6  Unitary and Orthogonal operators 
13  4/17, 4/22  Ch.3,4,5,7  Review and Exam 2 (11/27) 
14  4/24, 4/29  Chapter 7  Orthogonal diagonalization 
15  5/1, 5/6  Chapter 7  Jordan canonical form 
17  5/14 (Tues)  123pm  Final Exam HILL 009 
Exam Dates
The exam dates are listed in the schedule above. Any conflict (such as with a religious holiday) should be reported to me at the beginning of the semester, so that the exam may be rescheduled.
Special Accommodations
Students with disabilities requesting accommodations must follow the procedures outlined at https://ods.rutgers.edu/students/applyingforservices
Academic Integrity
All Rutgers students are expected to be familiar with and abide by the academic integrity policy. Violations of the policy are taken very seriously. In particular, your work should be your own; you are responsible for properly crediting all help with the solution.
Problem Sets
The Problem Sets are available in the assignments directory on the course Sakai site.
Problem sets should be handwritten in reasonably clear writing, with an explanation of any assistance given. Typewritten assignments are allowable only by special arrangement (disability etc.) Scans of problem sets may be submitted electronically in emergencies (illness or accident) by upload to Sakai.
Some basic writing guidelines are as follows. All answers must be written in complete sentences; avoid starting each sentence with a symbol; ensure that each variable or notation is defined; number sentences or formulas as necessary so that you may refer back to them. To prove a "for all x", usually begin with "Let x be a ...". To prove an "there exists x" statement, you must construct a particular x satisfying the given property, so "Define x to be ...". To prove a that property A implies property B, begin with "Assume Property A...." Then deduce Property B. Sets are equal if they have the same elements; functions are equal if they have the same values; to prove something does not satisfy a list of axioms; it suffices to show that one of the axioms fails. On both problem sets and exams you may use properties in the text or class (referring to them by page or date) if they come before the problem you are solving in the development of the material.
Problem Sets from 2017
Problems in pdf. Solutions in pdf.)
Problems in pdf. Solutions in pdf.)
Problems in pdf. Solutions in pdf.)
Problems in pdf. Solutions in pdf.)
Practice problems in pdf for the first midterm. Last year's exam with Answers.
Problems in pdf.
Problem in pdf. Selected Answers to PS5, PS6, PS7.
(Problems in pdf)
Problems in pdf)
Problems in pdf.
Last year's second midterm with answers.
Answers and practice problems for the final. Last year's final and solutions.
More review problems for the second midterm.
Pratice problems for the second exam:
(Problems in pdf)
Recommended Practice Problems (the problem sets from 2016)
Sept. 13  1.2 #17; 1.3 #19,23; 1.4 #11,13; 1.5 #9,15 
Sept. 20  1.6 # 20,21,26,29; 1.7 #5,6 
Sept. 27  2.1 #3,11,28; 2.2 #4; 2.3 #12; 2.4 #15,17 
October 4  2.5 #3(d),7(a,b),13; 2.6 #5,10; Show that F[x]* ≅ F[[x]]. 
October 18  3.1 #6,12; 3.2 #5(b,d,h),17; 3.3 #8,10; 3.4 #8,15 If an nxn matrix A has each row sum 0, some Ax=b has no solution. 
October 25  4.1 #10(a,c); 4.2 #23; 4.3 #12,22(c),25(c); 4.4 #6; 4.5 #11,12 
Nov. 1  5.1 #3(b),20,21; 5.2 #4,9(a),12; Show that the cross product induces an isomorphism between R³ and Λ²(R³). 
Nov. 8  5.2 #18(a),21; 5.3 #2(d,f); 5.4 #6(a),13,19,25 
Nov. 15  7.1 #3(b),9(a),13; 7.2 #3,14,19(a); 7.3 #13,14; Find all 4x4 Jordan canonical forms of T satisfying T²=T³. 
Dec. 13  6.1; #6,11,12,17; 6.2 #2a,6,11; 6.8 #4(a,c,d),11 
Outreach
Welcome to the Department of Mathematics at Rutgers University, part of the School of Arts and Sciences (SAS). This page describes programs sponsored by the Department of Mathematics for teachers of mathematics and for precollege students with a strong interest in mathematics.
Programs for Students
Programs for Teachers of Mathematics
16:640:566  Axiomatic Set Theory
Math 350 Section 4 Fall 2018
01:640:350:04 Linear Algebra Section
04  11407  Woodward, Christopher  Lecture  TF2  1020 A  1140  BE250  LIV 
This course is a proofbased continuation of Math 250, covering Abstract vector spaces and linear transformations, inner product spaces, diagonalization, and canonical forms.
Prerequisites:
 CALC4, Math 250 and Math 300
Text: Linear Algebra (4th ed.), by Friedberg, Insel and Spence,
Prentice Hall, 2003 ISBN 0130084514. For this section 04, any recent edition of the textbook should be sufficient.
 Class
TF2 1020 A  1140 BE250 LIV  Office Hours: Monday 2:153:15pm, Hill 726
 Contact Information: email ctw@math.rutgers.edu
The course is strongly based on Math 250. However, we'll work axiomatically, starting from the abstract notions of vector space and of linear transformation. Much of the homework and many of the exam and quiz problems will require you to write precise proofs, building on your proofwriting experience in Math 300. From this more abstract viewpoint, we'll be developing linear algebra far beyond Math 250, with new insight and new applications.
Class attendance is very important. A lot of what we do in class will involve collective participation. We will cover the topics indicated in the syllabus below, but the dates that we cover some of the topics might be adjusted during the semester, depending on class discussion, etc. Such adjustments, along with the almostweekly homework assignments, will be announced in class and also posted on this webpage, so be sure to check this webpage regularly. Absences from a single class due to minor illnesses should be selfreported using the university system; for longer absences, students should email me with the situation. I reserve the right to lower the course grade up to one full letter grade for poor attendance.
Makeups for exams are generally not given; if a student has an extremely good reason (e.g. documented medical emergency) I may rearrange the grading scheme to accomodate.
Problem sets are due on most Tuesdays. There are no problems due on the two midtermexam Tuesdays.
Note that we will cover significant material from all the chapters in the book, Chapters 17.
Grading policy: First midterm exam: 100 points; Second midterm exam: 100 points; Problem sets and quizzes: 100 points; Final exam: 200 points (Total: 500 points).
Tentative Course Syllabus
Week  Lecture dates  Sections  topics 

1  9/4 (T)  Chapter 1  Abstract vector spaces & subspaces 
2  9/7, 9/11  Chapter 1  Span of subsets, linear independence 
3  9/14, 9/18  Chapter 1  Bases and dimension 
4  9/21, 9/25  Chapter 2  Linear transformations 
5  9/28, 10/2  Chapter 2  Change of basis, dual spaces 
6  10/5, 10/9  Ch. 12  Review and Exam 1 (10/9) 
7  10/12, 10/16  Chapter 3  Rank and Systems of Linear Equations 
8  10/19, 10/23  Chapter 4  Determinants and their properties 
9  10/26, 10/30  Chapter 5  Eigenvalues/eigenvectors 
10  11/2, 11/6  Chapter 5  Diagonalization, Markov Chains 
11  11/9, 11/13  Chapter 6  Inner Product spaces 
12  11/16  Chapter 6  Unitary and Orthogonal operators 
13  11/21, 11/27  Ch.3,4,5,7  Review and Exam 2 (11/27) 
14  11/30, 12/4  Chapter 7  Orthogonal diagonalization 
15  12/7, 12/11  Chapter 7  Jordan canonical form 
17  12/21 (Fri)  811am  Final Exam Location TBA 
Exam Dates
The exam dates are listed in the schedule above. Any conflict (such as with a religious holiday) should be reported to me at the beginning of the semester, so that the exam may be rescheduled.
Special Accommodations
Students with disabilities requesting accommodations must follow the procedures outlined at https://ods.rutgers.edu/students/applyingforservices
Academic Integrity
All Rutgers students are expected to be familiar with and abide by the academic integrity policy. Violations of the policy are taken very seriously. In particular, your work should be your own; you are responsible for properly crediting all help with the solution.
Problem Sets
The Problem Sets are available in the assignments directory on the course Sakai site.
Problem sets should be handwritten in reasonably clear writing, with an explanation of any assistance given. Typewritten assignments are allowable only by special arrangement (disability etc.) Scans of problem sets may be submitted electronically in emergencies (illness or accident) by upload to Sakai.
Some basic writing guidelines are as follows. Please write in complete sentences; avoid starting each sentence with a symbol; ensure that each variable or notation is defined; number sentences or formulas as necessary so that you may refer back to them. To prove a "for all x", usually begin with "Let x be a ...". To prove an "there exists x" statement, you must construct a particular x satisfying the given property, so "Define x to be ...". To prove a that property A implies property B, begin with "Assume Property A...." Then deduce Property B. Sets are equal if they have the same elements; functions are equal if they have the same values; to prove something does not satisfy a list of axioms; it suffices to show that one of the axioms fails. On both problem sets and exams you may use properties in the text or class (referring to them by page or date) if they come before the problem you are solving in the development of the material.
Problem Sets from 2017
Problems in pdf. Solutions in pdf.)
Problems in pdf. Solutions in pdf.)
Problems in pdf. Solutions in pdf.)
Problems in pdf. Solutions in pdf.)
Practice problems in pdf for the first midterm. Last year's exam with Answers.
Problems in pdf.
Problem in pdf. Selected Answers to PS5, PS6, PS7.
(Problems in pdf)
Problems in pdf)
Problems in pdf.
Last year's second midterm with answers.
Answers and practice problems for the final. Last year's final and solutions.
More review problems for the second midterm.
Pratice problems for the second exam:
(Problems in pdf)
Recommended Practice Problems (the problem sets from 2016)
Sept. 13  1.2 #17; 1.3 #19,23; 1.4 #11,13; 1.5 #9,15 
Sept. 20  1.6 # 20,21,26,29; 1.7 #5,6 
Sept. 27  2.1 #3,11,28; 2.2 #4; 2.3 #12; 2.4 #15,17 
October 4  2.5 #3(d),7(a,b),13; 2.6 #5,10; Show that F[x]* ≅ F[[x]]. 
October 18  3.1 #6,12; 3.2 #5(b,d,h),17; 3.3 #8,10; 3.4 #8,15 If an nxn matrix A has each row sum 0, some Ax=b has no solution. 
October 25  4.1 #10(a,c); 4.2 #23; 4.3 #12,22(c),25(c); 4.4 #6; 4.5 #11,12 
Nov. 1  5.1 #3(b),20,21; 5.2 #4,9(a),12; Show that the cross product induces an isomorphism between R³ and Λ²(R³). 
Nov. 8  5.2 #18(a),21; 5.3 #2(d,f); 5.4 #6(a),13,19,25 
Nov. 15  7.1 #3(b),9(a),13; 7.2 #3,14,19(a); 7.3 #13,14; Find all 4x4 Jordan canonical forms of T satisfying T²=T³. 
Dec. 13  6.1; #6,11,12,17; 6.2 #2a,6,11; 6.8 #4(a,c,d),11 
Michael Weingart's homepage
Michael Weingart
Associate Teaching Professor of Mathematics
weingart [at] math [dot] rutgers [dot] edu
Fall 2018 Teaching:
Math 104:01 Introduction to Probability
Math 104:03 Introduction to Probability
Courses  Calculus I  Fall 2018  draft
Courses
01:640:135  Calculus I
Textbook: For current textbook please refer to our Master Textbook List page
Math 135 provides an introduction to calculus. It is taken primarily by students interested in the biological sciences, business, economics, and pharmacy. Math 135 may be followed by Math 136.
There is another calculus sequence, Math 151152251, which is taken by students in the mathematical and physical sciences, engineering, and computer science. Although it is possible to take Math 152 after Math 135, this is not a recommended sequence. More importantly, the prerequisite for Math 251 is Math 152; Math 136 does not satifsy this prerequisite.
Students who may need to take Math 152 or 251 should start their study of calculus with Math 151, and students who decide after taking Math 135 that they may wish to take Math 251 should follow Math 135 with Math 152.
In addition to the standard 4credit format of the course, a a 5credit format has been used for some of the sections, but only the 4credit format is now being offered.
Course Materials
Previous Semesters
 Fall 2017
 Spring 2017
 Fall 2016
 Spring 2016
 Fall 2015
 Spring 2015
 Fall 2014
 Spring 2014
 Fall 2013
 Spring 2013
 Fall 2012
 Spring 2012
 Fall 2011
 Spring 2011
 Fall 2010
 Spring 2010
 Fall 2009 Instructors' web pages
 Summer 2009
 Spring 2009
Schedule of Sections
01:640:135 Schedule of Sections
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JExtBOX test
Abstract: The BianchiEgnell Stability Estimate is a stability estimate or quantitative version of the Sobolev Inequality – it states that the difference of terms in the Sobolev Inequality controls the distance of a given function from the manifold of extremals of the Sobolev Inequality with distance measured in the gradient square or \[\dot{H}^1\] norm. In this talk, we present an extension of the BianchiEgnell Stability Estimate to Bakry, Gentil, and Ledoux’s Generalization of the Sobolev Inequality to Continuous Dimensions. We also demonstrate a deep link between the Sobolev Inequality and a oneparameter family of sharp GagliardoNirenberg (GN) inequalities and how this link can be used to derive a new stability estimate on the oneparameter family of sharp GN inequalities from our stability estimate on Bakry, Gentil, and Ledoux’s Generalization of the Sobolev Inequality to Continuous Dimensions.
Here's a \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\] test equation.
Test Page iframe
Schedule of Sections
Resources for Visitors
Joomla Tips
Joomla/HTML Tips & Tricks Page 
This page is contains instructions to help faculty members with updating the Mathematics site.
HOWTOadddocument.txt
HOWTOupdatecourseinformationfilelinkinJoomla.txt
Accessing Webassign through Sakai
WebAssign  Guide for Instructors/Coordinators
test all courses fall CURRENT  MODULE
Course  Cr  Course Title  Cross Listing  

listing  credits  title  crossSectionsPrint 
test all courses fall 2016
Course  Cr  Course Title  Cross Listing  

listing  credits  title  crossSectionsPrint 
Proficiency Exams
Undergraduate Proficiency Examinations
The Mathematics Department offers proficiency examinations for selected courses. Depending on the course, and their performance on the exam, students may earn one of two types of proficiency pass:
 FullCredit proficiency. A student earning fullcredit proficiency for a course can get credit for the course as though he/she took and passed the course. The course will appear on the students university transcript with a designation such as to "By examination". The student will also receive any credits towards graduation that are normally provided for passing the course.
 Mathematics Department internal proficiency. A student earning internal proficiency for a course (referred to below as course X) is considered to have passed the course for the following purposes:
 If course X is a requirement for the math major or math minor, then that requirement is considered to have been satisfied.
 If course X is a prerequisite for another math department course (referred to below as course Y) then that prerequisite is considered to be satisfied. To register for course Y, a student who has proficiency credit for X (and has satisfied all other prerequisites for course Y) will be given a prerequisite override from the undergraduate office. (In the case that the course Y is offered by another department, the student will need a prerequisite override from the department offering course Y. A student who has received internal proficiency for course X, may request that the math advisor contact the offering department informing the department offering course Y that the student has passed a proficiency exam for course X. The offering department has the final decision whether they will accept that as satisfying the prerequisite for course Y.)
Fullcredit proficiency exams
Fullcredit proficiency exams are offered for courses 115,135, 151 and 152. Students receiving at least a grade of B on the proficiency exam can receive full credit for the course if they wish. The course will appear on the transcript as passed ``by examination''. A student getting a C on the proficiency exam will not receive full credit for the course, but will be granted Mathematics Department internal proficiency as described above. A student getting a D on the proficiency exam does not receive any type of credit and has to take the course.
Mathematics Department internal proficiency exams
The department offers internal proficiency exam for courses 025 and 026, and also for course 250. Internal proficiency exams are occasionally offered for other courses in unusual situations. To take the internal proficiency exam for 025 or 026, contact the math undergraduate office (ugoffice@math.rutgers.edu) The internal proficiency exam for 250 is offered to students who have completed the honors calculus course 291, or to other students with the approval of the math advisor or the honors committee chair (who will notify the undergraduate office of the approval). Once this approval is obtained, the student should schedule the exam through the math undergraduate office. The proficiency test for 250 may be waived for students with a grade of A in Math 291.
Evaluation of internal proficiency exams
 Course 025. A student receiving a grade of at least C will be allowed to register for 026.
 Course 026. A student receiving a grade of C will be allowed to register for 111 (Precalculus I). A student receiving a grade of B or higher will be allowed to register for 115 (Precalculus)
 Course 250. Proficiency credit for 250 requires a grade of at least B on the exam.
Restrictions
 A student must have the required prerequisites for the course in which the proficiency exam is to be taken.
 A proficiency exam may not be taken in a course in which a student has previously enrolled and received a grade.
 A proficiency exam may not be taken in a course for which a student is currently registered (at Rutgers New Brunswick) and for which classes have started.
 A student may take a proficiency exam in a given course only once.
Dates
Proficiency exams are offered at fixed times throughout the year (except near the beginning or end of a semester). A student may arrange to take the exam by contacting the Mathematics Undergraduate office, ugoffice@math.rutgers.edu The student should allow one to two weeks for scheduling the exam.
Proficiency Exams
Undergraduate Proficiency Examinations
The Mathematics Department offers proficiency examinations for selected courses. Depending on the course, and their performance on the exam, students may earn one of two types of proficiency pass:
 FullCredit proficiency. A student earning fullcredit proficiency for a course gets credit for the course as though he/she took and passed the course. The course will appear on the students university transcript with a designation such as to "By examination". The student will also receive any credits towards graduation that are normally provided for passing the course.
 Mathematics Department internal proficiency. A student earning internal proficiency for a course (referred to below as course X) is considered to have passed the course for the following purposes:
 If course X is a requirement for the math major or math minor, then that requirement is considered to have been satisfied.
 If course X is a prerequisite for another math department course (referred to below as course Y) then that prerequisite is considered to be satisfied. To register for course Y, a student who has proficiency credit for X (and has satisfied all other prerequisites for course Y) will be given a prerequisite override from the undergraduate office. (In the case that the course Y is offered by another department, the student will need a prerequisite override from the department offering course Y. A student who has received internal proficiency for course X, may request that the math advisor contact the offering department informing the department offering course Y that the student has passed a proficiency exam for course X. The offering department has the final decision whether they will accept that as satisfying the prerequisite for course Y.)
Fullcredit proficiency exams
Fullcredit proficiency exams are offered for courses 115,135, 151 and 152. To take an official proficiency exam the student should contact the office of the academic dean of their school to get prior approval, and to find out the rules for getting proficiency credit. This normally involves paying a fee to the registrar prior to taking the exam. Once this approval is obtained and the fee is paid, the student should bring the receipt from the registrar to the Math undergraduate office (Hill 303) to arrange a time to take the exam. Students receiving at least a grade of B on the proficiency exam will receive full credit for the course. It will appear on the transcript as ``by examination''. A student getting a C on the proficiency exam will not receive full credit for the course, but will be granted Mathematics Department internal proficiency as described above.
Mathematics Department internal proficiency exams
The department offers internal proficiency exam for courses 025 and 026, and also for course 250. Internal proficiency exams are occasionally offered for other courses in unusual situations. To take the internal proficiency exam for 025 or 026, contact the math undergraduate office (ugoffice@math.rutgers.edu) The internal proficiency exam for 250 is offered to students who have completed the honors calculus course 291, or to other students with the approval of the math advisor or the honors committee chair (who will notify the undergraduate office of the approval). Once this approval is obtained, the student should schedule the exam through the math undergraduate office. The proficiency test for 250 may be waived for students with a grade of A in Math 291.
Evaluation of internal proficiency exams
 Course 025. A student receiving a grade of at least C will be allowed to register for 026.
 Course 026. A student receiving a grade of C will be allowed to register for 111 (Precalculus I). A student receiving a grade of B or higher will be allowed to register for 115 (Precalculus)
 Course 250. Proficiency credit for 250 requires a grade of at least B on the exam.
Restrictions
 A student must have the required prerequisites for the course in which the proficiency exam is to be taken.
 A proficiency exam may not be taken in a course in which a student has previously enrolled and received a grade.
 A proficiency exam may not be taken in a course for which a student is currently registered (at Rutgers New Brunswick) and for which classes have started.
 A student may take a proficiency exam in a given course only once.
Dates
Proficiency exams are offered at fixed times each week throughout the year (except near the beginning or end of a semester). A student may arrange to take the exam by contacting the Mathematics Undergraduate office, ugoffice@math.rutgers.edu The student should allow one to two weeks for scheduling the exam.
01:640:350:H  Linear Algebra Honors Section
Prof. Weibel (640:350:H1) — Fall 2017
 This course is a proofbased continuation of Math 250, covering Abstract vector spaces and linear transformations, inner product spaces, diagonalization, and canonical forms.
Prerequisites:
 CALC4, Math 250 and Math 300
Text: Linear Algebra (4th ed.), by Friedberg, Insel and Spence,
Prentice Hall, 2003 ISBN 0130084514.
 Lectures MW6 (5:006:20PM) in ARC 333
 Weibel's Office hours: Monday 1:302:45 PM; Wednesday 10:30AM12 noon
Tentative Course Syllabus
Week  Lecture dates  Sections  topics 

1  9/6 (W)  Chapter 1  Abstract vector spaces & subspaces 
2  9/11 (M), 13 (W)  Chapter 1  Span of subsets, linear independence 
3  9/18, 20  Chapter 1  Bases and dimension 
4  9/25, 27  Chapter 2  Linear transformations 
5  10/2, 10/4  Chapter 2  Change of basis, dual spaces 
6  10/9, 10/11  Ch. 12  Review and Exam 1 
7  10/16, 10/18  Chapter 3  Rank and Systems of Linear Equations 
8  10/23, 10/25  Chapter 4  Determinants and their properties 
9  10/30, 11/1  Chapter 5  Eigenvalues/eigenvectors 
10  11/6, 11/8  Chapter 5  CayleyHamilton 
11  11/13, 11/15  Chapter 7  Jordan Canonical Form 
12  11/20  Chapter 7  Rational Canonical Form 
13  11/27, 11/29  Ch.3,4,5,7  Review and Exam 2 
14  12/4, 12/6  Chapter 6  Inner Product spaces 
15  12/11, 12/13  Chapter 6  Unitary and Orthogonal operators (last class) 
17  December 21 (Thursday)  47 PM  Final Exam 
Homework Assignments
td>6.3 #17,22(c); 6.5 #6,7
HW Due on:  HW Problems (due Wednesdays)  

Sept. 13  1.2 #17; 1.3 #19,23; 1.4 #11,13; 1.5 #9,15  
Sept. 20  1.6 #20,26,29; 1.7 #5,6; 2.1 #3,11,28  Show that P(X) is a vector space over F_{2}, and find a basis 

Sept. 27  2.2 #6; 2.3 #12; 2.4 #15,21; 2.5 #3(d),8,13  
Oct. 4  2.6#10; 2.7#11,14; 3.1#6,12; 3.2#9; 3.3#10  Show that F[t]* is iso. to F[[x]]  
Oct. 25  4.1 #11; 4.2 #24, 29; 4.3 #10,12,21  
Nov. 1  5.1 #3b, 20, 33a; 5.2 #4, 9a, 12  
Nov. 8  5.3 #6; 5.4 #13,17,21,27,36  
Nov. 15  7.1 #3b,9b,11; 7.2 #3,14,19a; 7.3 #13,14 
Find all 4x4 Jordan canonical forms satisfying T^{2}=T^{3}  
Dec. 13  6.1 #11,27(b,c),28; 6.2 #6,10;  6.3 #17,22(c); 6.5 #6,7  
Main 350 course page
Return to Weibel's Home Page
Schedule of Sections:
Programs for Students
This page describes programs sponsored by the Department of Mathematics for precollege students with a strong interest in mathematics and provides links to other programs.
Students interested in applying for admission to Rutgers University should consult our page for Prospective Students.
Rutgers Young Scholars Program in Discrete Mathematics is a fourweek summer residential program at Rutgers designed to provide mathematically talented high school students with an exciting experience and ultimately to encourage them to consider careers in the mathematical sciences.
Further Information
The Governor's School of New Jersey in the Sciences is a summer program for high school seniors that takes place at Rutgers. The component called the Governor's School in Engineering and Technology takes place at Rutgers.
American Mathematical Society (AMS) maintains a list of nationwide Summer Programs, Math Clubs, Magazines, Careers, and Competitions.
Programs for Teachers of Mathematics
Mathematical Outreach for K12 Teachers
Math for Teachers is an outreach program of the Department of Mathematics at Rutgers University that provides exte nded coursework to consider the mathematics you teach. As the Common Core State Standards in Mathematics (CCSSM) are implemented, you will be asked to bring students to proficiency in "mathematical practices" such as:
 Making math make sense
 Explaining and justifying mathematical work
 Strategically employing mathematical reasoning
 Organizing computational procedures
Centered at the New Brunswick campus of Rutgers University, Math for Teachers draws on the strengths of a faculty dedicated to the art of teaching and who have made major scholarly contributions to the field.
Ph.D. Recipients, 1950  Present
Mathematics Graduate Program
 42 graduates 20152019
 58 graduates 20102014
 43 graduates 20052009
 43 graduates 20002004
 72 graduates 19951999
 66 graduates 19901994
 75 graduates 19801989
 107 graduates 19701979
 39 graduates 19611969
 7 graduates 19501960
 A count of doctorates by year
Information about past Rutgers MSc. recipients can be found here.
Prehistory: Rutgers created a postgraduate study program in 1870, in order to award a certificate to people who took an extra undergraduate course after graduation. Graduate courses formally appeared in 1876. While taking such courses, graduate students were often appointed as a "Tutor in Mathematics"; this was the forerunner of the modern Teaching Assistant. About 10 people received a Masters degree in Mathematics during the era 18701906. When the Mathematics department was formally organized in 1906, it stopped admitting graduate students.
The first MSc degrees in Mathematics were awarded to James Barton (BSc 1871; Tutor 187374; MSc 1874) and Albert S. Cook (BSc 1872; Tutor 187273; MSc 1875). Other masters degrees were awarded to men who went on to become professors at Rutgers: Alfred Titsworth (MSc 1880); Robert Prentiss (MSc 1881); William Breazeale (MSc 1895); and Richard Morris (MSc 1902). The Mathematics Department had other graduate students of this type in the 1890's including: DeWitt, Scattergood (MSc 1997), VanDyck Jr. (AM 1899).
In 1929, a new Masters degree in Mathematics was created, requiring 8 courses and a written thesis. The first such degree was awarded in 1930 to Charles Eason. The first woman to receive a M.Sc. degree in Math was Eveline Stevens in 1934 (NJC '32). Professors Brasefield and Starke were the advisors for most of these students; their Masters theses may be inspected in Rutgers' Math Library. There were 9 MSc degrees granted during the 1930's, and 50 MSc degrees granted during 19401959.
The modern era: Although the Rutgers doctoral program was created in 1882, and the first PhD awarded in 1884, a doctoral program in mathematics was not organized at Rutgers until 1947. The first Ph.D. in Mathematics at Rutgers was awarded in 1951, to George Cherlin (Rutgers College '47, MSc '49). A total of 7 Ph.D.s were awarded before 1961, when the modern era began at Rutgers. Under Ken Wolfson (chair 19611975) the graduate program in mathematics gradually built up to a steady graduation rate of 13 doctorates per year in the mid1970's. It later shrank in the 1980's and then expanded again in the 1990's, reaching a high of 19 doctorates in 1995. With the economic downturn in the mid1990's, fewer students were accepted into the program, with the delayed effect that the number of doctorates has shrunk since 2000.
Number of doctorates per decade:  1950's  1960's  1970's  1980's  1990's  2000's  2010's 
5  41  107  75  138  93  100 to May 2017 
Rutgers Math Phd's 1951Present
Name  Graduated  Advisor  First job after RU  

20152019: 31 Ph.D.'s  TOP  
Semen Artamonov  May  2018  Vladimir Retakh  University of California, Berkeley, CA  
Samuel Braunfeld  May  2018  Gregory Cherlin  University, of Maryland, MD  
Hanlong Fang  May  2018  Xiaojun Huang  University of Wisconsin, Madison, WI  
Bryan Ek  May  2018  Doron Zeilberger  Space & Naval Warfare, Hanahan, SC  
Jonathan Jaquette  May  2018  Konstantin Mischaikow  Mathematical Sciences Research Institute, CA  
Andrew Lohr  May  2018  Doron Zeilberger  Microsoft, WA  
Jiayin Pan  May  2018  Xiaochun Rong  University of California, Santa Barbara, CA  
Fei Qi  May  2018  YiZhi Huang  Yale University, New Haven, CT  
Anthony Zaleski  May  2018  Doron Zeilberger  
Ruofan Yan  Jan  2018  Paul Feehan  Asset Management, NY  
Edmund Karasiewicz 
Oct  2017  Stephen Miller  University of California, Santa Cruz, CA  
Douglas Schultz  Oct  2017  Chris Woodward  TechnionIsraeli Institute of Technology, Haifa, Israel  
Thomas Sznigir  Oct  2017  M.Vogelius/H.Brezis  Applied Research Associates, Inc., Raleigh, NC  
Ross Berkowitz  May  2017  Swastik Kopparty 
Yale University, CT 

Sjuvon Chung  May  2017  Anders Buch  Ohio State University, OH  
Patrick Devlin  May  2017  Jeffry Kahn  Yale University, CT  
Michael Donders  May  2017  Jozsef Beck  Jane Street Capital, NY  
Nathan Fox  May  2017  Doron Zeilberger  The College of Wooster, Ohio  
SiaoHao Guo  May  2017  Natasa Sesum  Indiana University, Bloomington, IN  
Rachel Levanger  May  2017  Konstantin Michaikow  University of Pennsylvania, PA  
Pedro Pontes  May  2017  Henryk Iwaniec  Bloomberg, NY  
Liming Sun  May  2017  YanYan Li  Johns Hopkins University, MD  
Charles Wolf  May  2017  Shubhangi Saraf  Ben Gurion University, Israel  
Xukai Yan  May  2017  YanYan Li  Georgia Tech, GA  
Jacob Baron  Oct  2016  Jeffry Kahn  Department of Defense  
Timothy Naumovitz  Oct  2016  Michael Saks  Google, Inc., Mountainview, CA  
Bence Borda  May  2016  Jozsef Beck  
Bud Coulson  May  2016  James Lepowsky  Rutgers University, NJ  
Charles Wes Cowan  May  2016  Michael Katehakis  Rutgers University, NJ  
Brian Garnett  May  2016  Swastik Kopparty  Rutgers University, NJ  
Burak Kaya  May  2016  Simon Thomas  Middle East Technical University, Turkey  
John Kim  May  2016  Swastik Kopparty  Virtu Financial, NYC  
Howard Nuer  May  2016  Lev Borisov  Northeastern University, Boston, MA  
Matthew Russell  May  2016  V. Retakh/D. Zeilberger  Rutgers University, NJ  
Francis Seuffert  May  2016  Eric Carlen  University of Pennsylvania  
Nathaniel Shar  May  2016  Doron Zeilberger  Google, Inc., CA  
Tien Trinh  May  2016  Stephen Miller  University of Colorado Boulder, CO  
Glen Wilson  May  2016  Charles Weibel  University of Oslo, Norway  
Jianguo Xiao  May  2016  Avy Soffer  Quantitative Strategies at PeerIQ, NY  
Edward Chien  Oct  2015  Feng Luo  BarIlan University, Israel  
Manuel Larenas  Oct  2015  Avy Soffer  JRI Ingenieria Consulting Firm, Chile  
Zahra Aminzare  May  2015  Eduardo Sontag  Princeton University, Princeton, NJ  
Francesco Fiordalisi  May  2015  YiZhi Huang/ James Lepowsky 
Bloomberg LP, Princeton, NJ  
Bin Guo  May  2015  Jian Song  Columbia University, New York, NY  
Simao Herdade  May  2015  Endre Szemeredi  Clarifai, Inc., NY  
Moulik Kallupalam Balasubramanian  May  2015  Shadi Abdoire TahvildarZadeh 
Rutgers University, NJ  
Shashank Kanade  May  2015  James Lepowsky  University of Alberta, Alberta, Canada  
Vladimir Lubyshev  May  2015  Paul Feehan  Cubist Systematic Strategies, LLC, NY  
John Miller  May  2015  Henryk Iwaniec  John Hopkins University, Baltimore, MD  
Kellen Myers  May  2015  Doron Zeilberger  Farmingdale State College, Farmingdale, NY  
Ming Xiao  May  2015  Xiaojun Huang  University of Illinois at UrbanaChampaign  
Justin Bush  Jan  2015  Konstantin Mischaikow  Palantir Technologies, Inc. NY  
Jaret Flores  Jan  2015  Charles Weibel  GIS Workshop, Inc., Lincoln, NE  
Justin Gilmer  Jan  2015  Michael Saks  Bloomberg LP, NY  
Thomas Tyrrell  Jan  2015  Jerrold Tunnell  Infosys, Basking Ridge, NJ  
20102014: 58 Ph.D.'s 
TOP  
James Dibble  Oct  2014  Xiaochun Rong  Western Illinois University, Macomb, IL  
Jorge Cantillo  Oct  2014  Henryk Iwaniec  Assurant Solutions, Miami, FL  
Michael Marcondes de Freitas 
Oct  2014  Eduardo Sontag  University of Copenhagen, Denmark  
Aaron Hamm  Oct  2014  Jeffry Kahn  Winthrop University, Rock Hill, SC  
Debajyoti Nandi  Oct  2014  Robert Wilson  Chennai Mathematical Institute, India  
Kathleen Crow Craig  May  2014  Eric Carlen  UCLA, Los Angeles, CA  
Ved Datar  May  2014  Jian Song  University of Notre Dame, IN  
Knight Fu  May  2014  Charles Weibel  MediaMath, Boston, MA  
Zhan Li  May  2014  Lev Borisov  John Hopkins University, Baltimore, MD  
Robert McRae  May  2014  James Lepowsky  Beijing Int'l. Center for Math Research, China  
Yusra Naqvi  May  2014  Siddhartha Sahi  Muhlenberg College, Allentown, PA  
Eduardo Osorio Triana  May  2014  Paul Feehan  Bloomberg LP, NY  
Christopher Sadowski  May  2014  Lepowsky / YZ Huang  Ursinus College in Collegeville, PA  
Matthew Samuel  May  2014  Anders Buch  Prudential Investment Management  
Jinwei Yang  May  2014  Lepowsky / YZ Huang  University of Notre Dame, IN  
Hui Wang  Jan  2014  Haim Brezis  JP Morgan, NY  
Brandon Bate  Oct  2013  Stephen Miller  Tel Aviv University (Israel)  
Susovan Pal  Oct  2013  Feng Luo / Jun Hu  University of Paris 11  
Vijay Ravikumar  Oct  2013  Anders Buch  Tata Institute for Fundamental Research (India)  
Yu Wang  Oct  2013  Michael Kiessling  
David Duncan  May  2013  Chris Woodward  Michigan State University  
Susan Durst  May  2013  Robert Wilson  University of Arizona  
Ali Maalaoui  May  2013  Abbas Bahri  Universitat Basel (Switzerland)  
Brian Nakamura  May  2013  Doron Zeilberger  CCICADA  
Priyam Patel  May  2013  Feng Luo  Purdue University  
Ke Wang  May  2013  Van Vu  IMA (University of Minnesota)  
Yunpeng Wang  May  2013  YanYan Li  AMSS, Chinese Academy of Sciences (Beijing)  
Tian Yang  May  2013  Feng Luo  Stanford University  
Hernan Castro  Oct  2012  H. Brezis  Universidad De Talga  
Robert DeMarco  Oct  2012  J. Kahn  CCICADA  
Vidit Nanda  Oct  2012  K. Mischaikow  University of Pennsylvania  
Catherine Pfaff  Oct  2012  L. Mosher  Laboratory Analysis of Topology and Probabilities, Aix Marseille Universite/CNRS  
Susmita Venugopalan  Oct  2012  C. Woodward  Tata Institute of Fundamental Research  
John Bryk  May  2012  J. Tunnell  John Jay College (CUNY)  
Tianling Jin  May  2012  Y. Li  University of Chicago  
Elizabeth Kupin  May  2012  J. Beck  NSA  
Camelia Pop  May  2012  P. Feehan  University of Pennsylvania  
Nicholas Trainor  May  2012  M. Vogelius  Numerix LLC (NYC)  
Jay Williams  May  2012  S. Thomas  California Institute of Technology  
V.S. Padmini Mukkamala  October  2011  J. Pack and M. Szegedy  McDaniel college, Hungary; then IIT, India  
Amit Priyadarshi  October  2011  R. Nussbaum  Indian Institute of Technology, Delhi  
Andrew Baxter  May  2011  D. Zeilberger  Penn State University  
Gabriel Bouch  May  2011  E. Carlen  Freedom Church, Philadelphia  
Emilie Hogan  May  2011  D. Zeilberger  Pacific Northwest National Laboratory  
Brent Young  May  2011  M. Kiessling  Rutgers University; Cologne University (Germany)  
Linh Tran  Jan  2011  V. Vu  University of Washington  
Nan Li  Oct  2010  X. Rong  University of Notre Dame  
Jin Wang  Oct  2010  P. Feehan  Ernst & Young LLP  
Yuan Yuan  Oct  2010  X. Huang  John Hopkins University  
Sara Blight  May  2010  H. Iwaniec  National Security Agency at Fort Meade  
Goran Djankovic  May  2010  H. Iwaniec  Mathematical Institute of the Serbian Academy of Arts and Sciences  
Liviu Ilinca  May  2010  J. Kahn  Indiana University  
Hoi Nguyen  May  2010  V. Vu  University of Pennsylvania  
Wesley Pegden  May  2010  J. Beck  NYU (Courant Institute), NSF Postdoc  
Daniel Staley  May  2010  S. Ferry  Yodle, Inc.  
Paul Ellis  Jan  2010  S. Thomas  University of Connecticut  
Jawon Koo  Jan  2010  P. Feehan  South Korea  
Ming Shi  Jan  2010  P. Feehan  Ernst & Young LLP  
20052009: 50 Ph.D.'s 
TOP  
Ila Leigh Cobbs  Oct  2009  L. Carbone  Lebanon Valley College  
Paul Raff  Oct  2009  D. Zeilberger  Rutgers University  
Reza Rezazadegan  Oct  2009  C. Woodward  Aarhus University  
Thomas Robinson  Oct  2009  J. Lepowsky  Rutgers University  
Scott Schneider  Oct  2009  S. Thomas  Wesleyan University  
Biao Yin  Oct  2009  Y. Li  University of Connecticut  
Yuan Zhang  Oct  2009  X. Huang  UCSD  
Philip M. Wood  May  2009  V. Vu  NSF Postdoc, UCLA, then Stanford University  
Eric Rowland  May  2009  D. Zeilberger  Tulane University  
Luc Nguyen  May  2009  Y. Li  Univ. of Oxford  
Michael Neiman  May  2009  J. Kahn  Univ. of California  
Ian Levitt  May  2009  E. Szemeredi  Federal Aviation Administration  
Liming Wang  Oct.  2008  E. Sontag  U.C. Irvine  
Sikimeti Ma'u  Oct.  2008  C. Woodward  Massachusetts Institute of Technology  
Thotsaporn Thanatipanonda  Oct.  2008  D. Zeilberger  Dickinson College  
Ellen (Shiting) Bao  May  2008  Y. Li  University of Minnesota  
Sam Coskey  May  2008  S. Thomas  CUNY  
Colleen Duffy  May  2008  R. Wilson  U. WisconsinEau Claire  
Ren Guo  May  2008  F. Luo  University of Minnesota  
Lara Pudwell  May  2008  D. Zeilberger  Valparaiso University  
Jared Speck  May  2008  M. Kiessling/S. TahvildarZadeh  Princeton University  
Chris Stucchio  Jan.  2008  A. Soffer  Courant Institute (NSF postdoc)  
Derek Hansen  Jan.  2008  M. Vogelius  Rice University  
Kevin Costello  Oct.  2007  V. Vu  Institute for Advanced Study  
Benjamin Kennedy  Oct.  2007  R. Nussbaum  Gettysburg College  
Brian Lins  Oct.  2007  R. Nussbaum  Dickinson College  
Sujith Vijay  May  2007  J. Beck  Univ. of Illinois at UrbanaChampaign  
Michael Weingart  May  2007  F. Knop  RutgersNew Brunswick  
Haoyuan Xu  May  2007  Y. Li  Univ. of Connecticut  
Corina Calinescu  Oct.  2006  J. Lepowsky  Ohio State Univ.  
William Cuckler  Oct.  2006  J. Kahn  Univ. of Delaware  
Thuy Pham  Oct.  2006  W. Vasconcelos  Univ. of Toronto  
Moa Apagodu  May  2006  D. Zeilberger  Virginia Commonwealth Univ.  
Satadal Ganguly  May  2006  H. Iwaniec  Inst. of Mathematical Sciences, India  
Roman Holowinsky  May  2006  H. Iwaniec  The Inst. for Advanced Study  
Qinian Jin  May  2006  Y. Li  Univ. of Texas  
Rich Mikula  May  2006  Y. Li  William Paterson Univ.  
Vincent Vatter  Jan.  2006  D. Zeilberger  Univ. of St. Andrews, Scotland  
German Enciso  Oct.  2005  E. Sontag  Math Biology Inst., Ohio State Univ.  
Liang Kong  Oct.  2005  Y.Z. Huang  Max Planck Inst. & IHES (Bures)  
David Nacin  Oct.  2005  R. Wilson  William Paterson Univ.  
Sasa Radomirovic  Oct.  2005  J. Tunnell  Univ. of Trondheim, Norway  
Nick Weininger  Oct.  2005  J. Kahn  Google Inc, Mountain View  
Kia Dalili  May  2005  W. Vasconcelos  Dalhousie Univ.  
Aaron Lauve  May  2005  V. Retakh  Univ. of Quebec, Montreal  
Kai Medville  May  2005  M. Vogelius  Inst. for Math. and its Applications, Minneapolis  
Augusto Ponce  May  2005  H. Brezis  Inst. for Advanced Study & Univ. of Paris  
Yongzhong Xu  May  2005  A. Bahri  NYU (Courant Inst.)  
Laura Ciobanu  Jan.  2005  C. Sims  CRM Barcelona  
Eva Curry  Jan.  2005  R. Gundy  Dalhousie Univ.  
20002004: 43 Ph.D.'s 
TOP  
Pieter Blue  Oct.  2004  A. Soffer  Univ. of Toronto  
Jeff Burdges  Oct.  2004  G. Cherlin  Univ. Wurzburg, Germany  
Raju Chelluri  Oct.  2004  H. Iwaniec  Deceased  
Stephen Hartke  Oct.  2004  F. Roberts  Univ. of Illinois UrbanaChampaign  
Xiaoqing Li  Oct.  2004  H. Iwaniec  Columbia Univ.  
Alfredo Rios  Oct.  2004  R. Gundy  Lehigh Univ.  
Eric Sundberg  Oct.  2004  J. Beck  Whittier College  
Klay Kruczek  May  2004  J. Beck  Univ. of Western Oregon  
Aobing Li  May  2004  Y. Li  Inst. for Advanced Study and Univ. of Wisconsin  
XiaoYong Li  May  2004  L. Shepp  Industry (Contract Research Org)  
Waldeck Schutzer  May  2004  S. Sahi  U. Federal de Sao Carlos, Brazil  
Matt Young  May  2004  H. Iwaniec  American Inst. of Mathematics and Stanford Univ.  
Lin Zhang  May  2004  J. Lepowsky  Industry  
Carlo Mazza  Jan.  2004  C. Weibel  Univ. of Paris  
Rodney Biezuner  Oct.  2003  Y. Li  U. MinasGervais/Belo Horizonte, Brazil  
David Radnell  Oct.  2003  Y.Z. Huang  Univ. of Michigan  
Malka Rosenthal  Oct.  2003  M. Saks  Iona College  
James Taylor  Oct.  2003  S. Goldstein  Iowa State Univ.  
Yuka Taylor  Oct.  2003  C. Woodward  George Washington Univ.  
Madalena Chaves  May  2003  E. Sontag  RU/Industry  
Jooyoun Hong  May  2003  W. Vasconcelos  Purdue Univ.  
Liangyi Zhao  May  2003  H. Iwaniec  U.S. Military Academy (West Point)  
Louis Dupaigne  Jan.  2003  H. Brezis  Univ. of Paris VI  
Xiaodong Sun  Jan.  2003  M. Saks  Inst. for Advanced Study  
David Galvin  Oct.  2002  J. Kahn  Microsoft Corp., Seattle  
Takao Sakuraba  May  2002  G. Goldin  Rutgers  
Juan Davila  Jan.  2002  H. Brezis  Univ. de Santiago, Chile  
Brian Ingalls  Oct.  2001  E. Sontag  Waterloo Univ.  
Antun Milas  Oct.  2001  J. Lepowsky  Univ. of Arizona  
Yi Zhao  Oct.  2001  E. Szemeredi  Univ. of Illinois (Chicago)  
Bernardo Abrego  May  2001  J. Beck  California StateNorthridge  
Silvia Fernandez  May  2001  J. Beck  California StateNorthridge  
Maurice Hasson  May  2001  R. Gundy  Univ. of Arizona  
Cliff Smyth  May  2001  M. Saks  Carnegie Mellon and Inst. for Advanced Study  
Darko Volkov  May  2001  M. Vogelius  NJIT  
Steve Warner  May  2001  S. Thomas  Penn. State, Reading  
Lei Zhang  May  2001  Y. Li  Texas A&M  
Paul Dreyer  Oct.  2000  F. Roberts  Rand Corp.  
Ryan Martin  Oct.  2000  E. Szemeredi  Carnegie Mellon Univ.  
John Nahay  May  2000  R. Cohn  Monmouth Univ.  
Misha Krichman  Jan.  2000  E. Sontag  UCLA (Mech. Eng'g.)  
Yi Liu  Jan.  2000  F. Luo  Rutgers  
Michael Malisoff  Jan.  2000  H. Sussmann  Washington Univ. (St. Louis)  

TOP  
Dov Chelst  Oct.  1999  J. Lebowitz  DeVry Inst.  
Terri Girardi  Oct.  1999  J. Tunnell  Fordham Univ.  
Xin Guo  Oct.  1999  L. Shepp  Univ. of Alberta/IBM (Financial Statistics)  
Pirkko Kuusela  Oct.  1999  D. Ocone  Industry (Finland)  
Marco Lenci  Oct.  1999  J. Lebowitz  SUNY Stony Brook  
Paul O'Donnell  Oct.  1999  J. Komlos  Drew Univ.  
Sara Soffer  Oct.  1999  J. Komlos  Princeton HS  
Yang Yu  Oct.  1999  J. Kahn  Cal Tech  
Garikai Campbell  Jan.  1999  J. Tunnell  Swarthmore College  
A. Kazarnovskii Krol  Jan.  1999  I. Gelfand  Yale Univ.  
Harri Ojanen  Jan.  1999  R. Wheeden  Lumeo Software,Inc. Finland  
Senchun Lin  Oct.  1998  T. Weinstein  Industry (software)  
Jason Yuenger  Oct.  1998  J. Taylor  J. P. Morgan Stanley (Finance)  
Rita Csákány  May  1998  J. Kahn  Technical Univ. of Budapest, Hungary  
Rick Desper  May  1998  M. Farach  National Insitutes of Health  
Tor Gunston  May  1998  W. Vasconcelos  EDS (Morris Plains, NJ)  
Carol Hamer  May  1998  J. Tunnell  Airial Conseil, France  
Emanuel Kowalski  May  1998  H. Iwaniec  Princeton Univ./Inst. for Advanced Study  
Luca Mauri  May  1998  M. Tierney  Univ. of Como, Italy  
Li Sheng (OR)  May  1998  F. Roberts  Drexel Univ.  
Tong Tu  May  1998  R. Falk  Bloomberg (Financial Services Industry)  
Shaoji Xu (OR)  May  1998  F. Roberts  Bell Labs  
Amine Asselah  Oct.  1997  J. Lebowitz  ETH Zurich  
Rodica Costin  Oct.  1997  M. Kruskal  Mathematical Sciences Research Inst.  
Luke Higgins  Oct.  1997  T. Weinstein  Brigham Young Univ., Salt Lake City  
Dan Kling  Oct.  1997  F. Luo  RutgersIEEE project  
Wanglai Li  Oct.  1997  J. Lepowsky / R. Wilson  Telecommunications industry  
Richard Ng  Oct.  1997  E. Taft  Univ. of CaliforniaSanta Cruz  
Dan Radulescu  Oct.  1997  J. Lebowitz  Industry  
Luisa R. Doering  May  1997  W. Vasconcelos  Univ. Rio Grande do Sul, Brazil  
Donna Fengya  May  1997  M. Vogelius  James Madison Univ.  
Dave Reimer  May  1997  J. Beck  IAS/Trenton State  
Arpad Toth  May  1997  W. Duke  U. Michigan  
Han Zuhong  May  1997  F. Treves  Finance industry  
Y. Chitour  Jan.  1997  H. Sussmann  Univ. of Pisa, Italy  
Raika Dehy  Jan.  1997  O. Mathieu  Univ. of Strasbourg, France (ATER)  
Yi Zhang  Jan.  1997  S. Thomas  Univ. Michigan  
Katrina Barron  Oct.  1996  J. Lepowsky / Y.Z. Huang  Univ. of CaliforniaSanta Cruz  
Galin Georgiev  Oct.  1996  J. Lepowsky  Inst. for Advanced Study  
M. Losada  Oct.  1996  S. Thomas  Antonio Narino Univ. (Colombia)  
Gretchen Ostheimer  Oct.  1996  C. Sims  Tufts Univ.  
Aleksandar Pekec  Oct.  1996  F. Roberts  BRICS, Denmark  
Rosane Ushirobira  Oct.  1996  O. Mathieu  Univ. of Strasbourg, France (ATER)  
Meijun Zhu  Oct.  1996  Y. Li  U British Columbia  
Dave Anderson  May  1996  J. Taylor  West Point / ARL  
Jim Bennett  May  1996  S. Thomas  Std.Commercial Lines  
Tom Bohman  May  1996  J. Kahn  MIT/MSRI then Carnegie Mellon U.  
M.J. Kelley  May  1996  J. Taylor  Texas A&M  
Naomi Klarreich  May  1996  T. Weinstein  Case Western Reserve Univ.  
Eddie Lo  May  1996  C. Sims  NSA  
Shari Moskow  May  1996  M. Vogelius  Inst. for Math. and its Applications (Minneapolis)  
John Shareshian  May  1996  R. Lyons  Mathematical Sciences Research Inst. (Berkeley)  
JY Patrick Tai  May  1996  P. Landweber  Dartmouth  
Yansong Chen  Oct.  1995  A. Bahri  
Ovidiu Costin  Oct.  1995  J. Lebowitz / M. Kruskal  
Jason Jones  Oct.  1995  C. Weibel  
Andrew Leahy  Oct.  1995  F. Knop  
Martin Strauss  Oct.  1995  E. Allender  
Juan AlvarezPaiva  1995  T. Petrie  
WenYun Gao  May  1995  J. Tunnell / D. Rohrlich  
G. Giacomin  May  1995  J. Lebowitz  
Ying Huang  May  1995  I. Daubechies / R. Wheeden  
Susan Morey  May  1995  W. Vasconcelos  
Dale Peterson  May  1995  F. Roberts  
Claudia Polini  1995  W. Vasconcelos  
Yasmine Sanderson  May  1995  R. Wilson / O. Mathieu  
Robert Smyth  May  1995  T. Weinstein  
Maria Vaz Pinto  May  1995  W. Vasconcelos  
David W. Webb  May  1995  S. Chanillo / B. Muckenhoupt  
Jiahai Xie  May  1995  R. Goodman  
Hong Guo  Jan.  1995  J. Lepowsky  
19901994: 66 Ph.D.'s 
TOP  
A. Tuna Altınel  Oct.  1994  G. Cherlin  
Randall Fairman  Oct.  1994  R. Lyons  
Andrés Fundia  Oct.  1994  M. Saks  
Mark Kayll  Oct.  1994  J. Kahn  
Renee Koplon  Oct.  1994  E. Sontag  
Guillaume SanjeMpacko  Oct.  1994  L. Corwin / R. Goodman  
Jim Sharp  Oct.  1994  S. Thomas  
Todd Trimble  Oct.  1994  M. Tierney  
Rob Hochberg  May  1994  J. Beck  
Elizabeth Jurisich  May  1994  R. Wilson / J. Lepowsky  
Haisheng Li  May  1994  J. Lepowsky / R. Wilson  
Guotian Lin  May  1994  A. Kupiainen  
András Pluhár  May  1994  J. Beck (RUTCOR)  
András Stipzicz  May  1994  T. Petrie  
Zoltán Szabó  May  1994  T. Petrie  
Chuanfu Xie  May  1994  J. Lepowsky / R. Wilson  
Sergio Zani  Jan.  1994  R. Wheeden  
Francesca Albertini  Oct.  1993  E. Sontag  
Jeong Han Kim  Oct.  1993  J. Kahn  
Junjie Xiong  Oct.  1993  P. Hansen  
Yudi Yang  Oct.  1993  H. Sussmann  
Xin Ke  May  1993  J. Beck  
Wenzhi Luo  May  1993  H. Iwaniec  
Paolo Dai Pra  Jan.  1993  J. Lebowitz  
Tejinder Neelon  Jan.  1993  F. Treves  
Hasna Riahi  Jan.  1993  A. Bahri  
Andrew Roosen  Jan.  1993  J. Taylor  
Lin Yuandan  Oct.  1992  E. Sontag  
Wensheng Liu  Oct.  1992  H. Sussmann  
Lu Xiaoyun  Oct.  1992  J. Kahn  
Steven Sessions  Oct.  1992  P. Landweber  
Tang Guoqing  Oct.  1992  H. Sussmann  
Ed Aboufadel  May  1992  J. CroninScanlon  
Gábor Francsics  May  1992  F. Treves  
Nigel Pitt  May  1992  H. Iwaniec  
Denise Sakai  May  1992  F. Roberts (RUTCOR)  
Xueqing Tang  May  1992  A. BenIsrael (RUTCOR)  
Jianming Xu  May  1992  R. Falk  
Xiaoping Xu  May  1992  J. Lepowsky / R. Wilson  
Stephen Alessandrini  Oct.  1991  R. Falk  
Géza Bohus  Oct.  1991  J. Kahn  
Damu Cai  Oct.  1991  R. Falk  
Gustavo Comezana  Oct.  1991  J. Shaneson  
Brenda Latka  Oct.  1991  G. Cherlin  
Richard Rosengarten  Oct.  1991  G. Cherlin  
To Tzeming  Oct.  1991  N. Wallach  
Barr Von Oehsen  Oct.  1991  P. Landweber  
Xianwen Xie  Oct.  1991  R. Nussbaum  
Chua SengKee  May  1991  R. Wheeden  
Jose C. Fernandes  May  1991  R. Wheeden  
Linda Holt  May  1991  R. M. Beals  
Terry Lohrenz  May  1991  F. Treves  
Lu Guozhen  May  1991  S. Chanillo  
Chi Wang  May  1991  F. Roberts (RUTCOR)  
Sandra Caravella  Oct.  1990  T. Petrie  
YiZhi Huang  Oct.  1990  J. Lepowsky  
Seong Joo Kang  Oct.  1990  R. M. Beals  
Yuan Wang  Oct.  1990  E. Sontag  
Glenn Hurlbert  May  1990  R. Graham  
Cristiano Husu  May  1990  J. Lepowsky  
Garth Isaak  May  1990  F. Roberts (RUTCOR)  
Julio Kuplinsky  May  1990  P. Hansen  
Peter Ostapenko  May  1990  R. Goodman  
J. Asmus Petersen  May  1990  F. Treves  
Raymond Ross  May  1990  D. Rohrlich  
Zangwill Rosenbaum  Jan.  1990  F. Roberts  
19801989: 75 Ph.D.'s 
TOP  
Enriqueta Carrington  Oct.  1989  N. Wallach  
Andrzej Karwowski  Oct.  1989  J. Lebowitz  
Shari Prevost  Oct.  1989  R. Wilson  
Barry Tesman  Oct.  1989  F. Roberts  
Jan Wehr  Oct.  1989  M. Aizenman  
Krzysztof Wysocki  Oct.  1989  R. Nussbaum  
Peisen Zhang  Oct.  1989  J. Lebowitz  
Stefano Capparelli  Oct.  1988  J. Lepowsky / R. Wilson  
Carlangelo Liverani  Oct.  1988  J. Lebowitz  
Abdelhamid Meziani  Oct.  1988  F. Treves  
Jean Rynes  Oct.  1988  C. Weibel  
Haruo Tsukuda  Oct.  1988  J. Lepowsky / I. Frenkel  
SuhRyung Kim  1988  F. Roberts  
Pierluigi Frajria  Jan.  1988  N. Wallach  
Willi Schwarz  Jan.  1988  N. Wallach  
Shiferaw Berhanu  Oct.  1987  F. Treves  
Yves Crama  Oct.  1987  P. Hammer  
Beatriz de Lafferriere  Oct.  1987  W. Petryshyn  
Stefano Olla  Oct.  1987  J. Lebowitz  
David Barsky  May  1987  M. Aizenman  
Mark Hughes  May  1987  T. Petrie  
João Sampaio  May  1987  T. Petrie  
Gerardo Lafferriere  Oct.  1986  H. Sussmann  
Monica Nicolau  Oct.  1986  J. Shaneson  
Heinz Schaettler  Oct.  1986  H. Sussmann  
Carlos Videla  Oct.  1986  G. Cherlin  
Jim Maloney  May  1986  G. Cherlin  
Rafael Villareal  May  1986  W. Vasconcelos  
Leila Figueiredo  Jan.  1986  J. Lepowsky  
Marly Mandia  Jan.  1986  R. Wilson  
Abigail Thompson  Jan.  1986  J. Shaneson  
Lucilia Borsari  Oct.  1985  P. Landweber  
Paulo Cordaro  Oct.  1985  F. Treves  
Kent Orr  Oct.  1985  J. Shaneson  
YuhDong Tsai  Oct.  1985  T. Petrie  
H. Leroy Hutson  May  1985  W. Vasconcelos  
Gary Martin  May  1985  G. Cherlin  
John C.M. Nash  May  1985  M. Nathanson  
Arundhati Raychaudhuri  May  1985  F. Roberts  
Yungchen Cheng  Oct.  1984  E. Taft  
Richard J. Pfister  Oct.  1984  J. Lepowsky  
Norman Adams  May  1984  M. Tierney  
Eung Chun Cho  May  1984  T. Petrie  
Terence Lindgren  May  1984  M. Tierney  
Robert Opsut  May  1984  F. Roberts  
Dong Youp Suh  May  1984  T. Petrie  
Joan Farmer Amgott  Oct.  1983  J. Lebowitz  
Steven Chapin  Oct.  1983  R. Nussbaum  
Guillermo Ferreyra  Oct.  1983  H. Sussmann  
Robert S. Maier  Oct.  1983  J. Lebowitz  
David Mitzman  Oct.  1983  J. Lepowsky  
Steven Amgott  May  1983  B. Mitchell  
Kil Hyun Kwon  May  1983  F. Treves  
Jiang Jin Sheng  May  1983  R. Falk  
Carol Ann Keller  Jan.  1983  M. Tierney  
Peter Monk  Jan.  1983  R. Falk  
Alan Siegel  Jan.  1983  T. Petrie  
Zsu(zsanna) Kadas  Oct.  1982  H. Othmer  
Kailash C. Misra  Oct.  1982  R. Wilson  
Stephen Breen  June  1982  J. Lebowitz  
Jorge Gerszonowicz  June  1982  F. Treves  
Paul Schachter  June  1982  J. Shaneson  
Joanne Darken  Jan.  1982  H. Sussmann  
Martin Farber  Jan.  1982  P. Hell  
Ernst Adams  Oct.  1981  B. Muckenhoupt  
Dohan Kim  Oct.  1981  F. Treves  
Margaret BarryCozzens  June  1981  F. Roberts  
David Hecker  June  1981  W. Sweeney  
Arne Meurman  June  1981  J. Lepowsky  
Shirlei Serconek  Oct.  1980  R. Wilson  
Susan Szczepanski  Oct.  1980  J. Shaneson  
Michael Weiss  June  1980  G. Cherlin  
ChengShung Ko  Jan.  1980  P. Hell  
Ira L. Robbin  Jan.  1980  E. Speer  
Bernadette Tutinas  Jan.  1980  D. Gorenstein  
19701979: 107 Ph.D.'s 
TOP  
Stephen Andrilli  Oct.  1979  C. Sims  
Edward Deloff  Oct.  1979  J. D'Atri  
Stephen Davis  Oct.  1979  R. Lyons  
Regina Mladineo  Oct.  1979  N. Levitt  
Richard Watnick  Oct.  1979  J. Rosenstein  
Joseph McDonough  June  1979  J. CroninScanlon  
Max Ashkenazi  Oct.  1978  J. CroninScanlon  
Nancy H. Baxter  Oct.  1978  R. Nussbaum  
Nanhung Chen  Oct.  1978  B. Osofsky  
Karl Heinz Dovermann  Oct.  1978  T. Petrie  
Stephen Hoyle  Oct.  1978  J. CroninScanlon  
Mark Hunacek  Oct.  1978  R. Wilson  
Rochelle Leibowitz  Oct.  1978  F. Roberts  
Claude Pichet  Oct.  1978  N. Wallach  
Theodore Wilson  Oct.  1978  J. Shaneson  
Vernon Eagle Jr.  June  1978  A. Kosinski  
Douglas Kurtz  June  1978  R. Wheeden  
Susan Niefield  June  1978  B. Mitchell  
Alvany Rocha  Jan.  1978  N. Wallach  
William Heck  Oct.  1977  E. Ellentuck  
Justine Skalba  Oct.  1977  C. Sims  
Richard Stafford  Oct.  1977  M. O'Nan  
LehSheng Tang  Oct.  1977  H. Sussmann  
Adalberto Bergamasco  June  1977  J. BarrosNeto  
Ronald Dotzel  June  1977  G. Bredon  
Sarah Glaz  June  1977  W. Vasconcelos  
Charles Schwartz  June  1977  W. Hoyt  
Maria Welleda Silva  June  1977  N. Wallach  
Valdis Vijums  June  1977  J. Shaneson  
Roman WC Wong  June  1977  B. Mitchell  
Edward Conjura  Jan.  1977  W. Petryshyn  
Anna Silverstein  Jan.  1977  J.C.E. Dekker  
Edgar BecerraBertram  Oct.  1976  J. Shaneson  
Oscar Campoli  Oct.  1976  N. Wallach  
Janey Daccach  Oct.  1976  P. Landweber  
Linda Anne Grieco  Oct.  1976  C. Sims  
ShynLing Lee  Oct.  1976  S. Leader  
Walter Mallory  Oct.  1976  E. Ellentuck  
Isabel Miatello  Oct.  1976  G. Bredon  
Roberto Miatello  Oct.  1976  N. Wallach  
Sandra Brook  June  1976  S. Leader  
Letitia Seese(Korbley)  June  1976  F. Treves  
James Carrig  Jan.  1976  W. Vasconcelos  
Andrew Chermak  Jan.  1976  D. Gorenstein  
Stephen Fellner  Jan.  1976  J. Rosenstein  
Ricardo Morais  Jan.  1976  E. Ellentuck  
Luis FrotaMattos  Oct.  1975  R. Goodman  
Leslie Jones  1975  P. Landweber  
Gerard Kiernan  Oct.  1975  D. Gorenstein  
Hsiaowei Kuo  Oct.  1975  B. Muckenhoupt  
Edward Lotkowski  Oct.  1975  R. Wheeden  
Simon Aloff  June  1975  J. Shaneson  
Ítalo Déjter  June  1975  T. Petrie  
Gary Gundersen  June  1975  R. Goodman  
Russell John  June  1975  R. Wheeden  
Thomas Marlowe  June  1975  E. Taft  
Petronije Milojevic  June  1975  W. Petryshyn  
Jay Shapiro  June  1975  B. Osofsky  
Ira J. Papick  Jan.  1975  D. Dobbs  
JuiChi Chang  Oct.  1974  D. Gorenstein  
Chingan C. Cheng  Oct.  1974  B. Mitchell  
Jeffrey Dawson  Oct.  1974  W. Vasconcelos  
Edward Dougherty  Oct.  1974  J. Elliott  
Kenneth Klinger  Oct.  1974  D. Gorenstein  
Edward Boyno  June  1974  G. Bredon  
Roosevelt Gentry  June  1974  V. Williams  
Roy Goldman  June  1974  F. Treves  
Jorge Hounie  June  1974  F. Treves  
Roger Jones  June  1974  R. Gundy  
Alan Meyerhoff  June  1974  T. Petrie  
Noriko Yui  June  1974  R. Bumby  
David Kopcso  Jan.  1974  R. Wilson  
Antonio Gilioli  Oct.  1973  F. Treves  
Brian Greenberg  Oct.  1973  W. Vasconcelos  
Richard Guhl  Oct.  1973  J.C.E. Dekker  
Saroj Jain  Oct.  1973  C. Faith  
Marian Kelterborn  Oct.  1973  S. Leader  
Ana Viola Prioli  Oct.  1973  W. Vasconcelos  
Jorge Viola Prioli  Oct.  1973  B. Osofsky  
Barry J. Arnow  June  1973  S. Leader  
Wolf Iberkleid  June  1973  P. Landweber  
Northrup Fowler  June  1973  J.C.E. Dekker  
Eugene Gaydos  June  1973  S. Leader  
Sarah J. Gottlieb  June  1973  E. Taft  
Hu Sheng  June  1973  W. Vasconcelos  
Rudolf Rucker  Jan.  1973  E. Ellentuck  
Carl Bredlau  Oct.  1972  E. Ellentuck  
Robert C. Miller  Oct.  1972  D. Gorenstein  
Cristián Sánchez  June  1972  G. Bredon  
David Slater  Oct.  1972  J. Rosenstein  
Ann K. Boyle  Oct.  1971  C. Faith  
Ted Williamson  Oct.  1971  W. Petryshyn  
Reginald Luke  Oct.  1971  W. Mason  
Louie Mahony  Oct.  1971  A. Kosinski  
Ranga Rao  Oct.  1971  C. Faith  
Ralph Artino  June  1971  J. BarrosNeto  
Michael Fitzpatrick  June  1971  W. Petryshyn  
Eileen Poiani  June  1971  B. Muckenhoupt  
Ira Wolf  June  1971  M. Tierney  
John Empoliti  Oct.  1970  C. Sims  
James Roberts  Oct.  1970  S. Leader  
David Addis  Jun  1970  L. McAuley  
Peter Evanovich  Jun  1970  R. Cohn  
Jeffrey Levine  Jun  1970  B. Osofsky  
Roger Pitasky  Jun  1970  S. Leader  
Philip Zipse  Jun  1970  S. Leader  
Douglas McCarthy  Jan.  1970  J. CroninScanlon  
19611969: 39 Ph.D.'s 
TOP  
Victor Camillo  Oct.  1969  C. Faith  
John Cozzens  Oct.  1969  C. Faith  
Charles Applebaum  June  1969  J.C.E. Dekker  
Francis Christoph  June  1969  L. McAuley  
Clifton Lando  June  1969  J. CroninScanlon  
John McDonald  June  1969  J. Elliott  
William Quirin  June  1969  C. Sims  
David Wilson  June  1969  L. McAuley  
Barbara A. Lando  Jan.  1969  R. Cohn  
Harry Berkowitz  Oct.  1968  P. Roy  
Peter Fowler  Oct.  1968  J. Elliott  
Charles Hallahan  Oct.  1968  E. Taft  
Richard Munson  Oct.  1968  W. Hoyt  
Floyd B. Cole  June  1968  J.C.E. Dekker  
Richard Bauer  Jan.  1968  R. Artzy  
Robert Fraser  Oct.  1967  S. Leader  
Frode Terkelson  Oct.  1967  J. Elliott  
Herbert I. Brown  1966  V. Cowling  
William H. Caldwell  1966  C. Faith  
Matthew Hassett  1966  J.C.E. Dekker  
Gerald S. Ungar  1966  L.F. McAuley  
Avraham Ornstein  Oct.  1966  C. Faith  
Irving Bentsen  1965  R. Cohn  
V. Mancuso  Oct.  1965  B. Candless  
Joseph Barback  Oct.  1964  J.C.E. Dekker  
William R. Jones  1964  H. Zimmerberg  
William E. Kirwan  1964  M. Robertson  
Barbara Langer Osofsky  1964  C. Faith  
Fred J. Sansone  1964  J.C.E. Dekker  
ChungLie Wang  1964  R. Carroll  
Angelo Pelios  Jan.  1964  S. Leader  
Donald Ferguson  Oct.  1963  J.C.E. Dekker  
Eric S. Langford  1963  S. Leader  
Albert E. Livingston  1963  M. Robertson  
Israel Zuckerman  1963  R. Cohn  
Leonard Gewirtzman  Oct.  1962  K. Wolfson  
Michael Lodato  Oct.  1962  S. Leader  
Charles Franke  May  1962  R. Cohn  
Richard J. Libera  May  1962  M. Robertson  
19511960: 7 Ph.D.'s 
TOP  
Ronald McHaffey  1960  K. Wolfson  
Aaron Siegel  1960  V. Shapiro  
John Bender  1958  M. Robertson  
Bernard Greenspan  1958  R. Cohn  
Richard Gabriel  1955  M. Robertson  
Richard K. Brown  1952  M. Robertson  
George Y. Cherlin  1951  M. Robertson 
Number of doctorates by year:
2019  2009  12  1999  11  1989  7  1979  6  1969  9  
2018  10  2008  11  1998  11  1988  8  1978  13  1968  6  
2017  14  2007  6  1997  15  1987  7  1977  13  1967  2  
2016  15  2006  9  1996  16  1986  9  1976  15  1966  5  
2015  16  2005  12  1995  19  1985  8  1975  13  1965  2  
2014  16  2004  15  1994  17  1984  7  1974  13  1964  7  
2013  12  2003  10  1993  10  1983  11  1973  15  1963  4  
2012  11  2002  3  1992  12  1982  7  1972  4  1962  4  
2011  7  2001  10  1991  15  1981  5  1971  9  1961  0  
2010  12  2000  6  1990  12  1980  6  1970  8  1960  2 
Return to the top.
Data before 1984 compiled by M. Jablonski. Data 19842005 compiled by C. Weibel.
Special Permission System
NOTICE: Matriculated undergraduates can request special permission for closed sections of fall and spring courses only through the automated system described below. This system is available only during the special permission period, beginning shortly before the term and running through the first week of classes.
There are four kinds of special requests students may need to make to the undergraduate office to gain admittance to certain courses.
 Admission to some honors courses is by permission of the department.
 Admission to closed sections of regular courses requires a special permission number.
 Admission to courses for which the prerequisites have been filled in an unusual way may require a prerequisite override.
 Admission to Precalculus, Calculus I or Calculus II previously failed twice
Procedures
 Honors courses
 Prerequisite overrides
 Closed sections
 Retaking Precalculus, Calculus I or Calculus II previously failed twice
 Automated Web System
Honors Courses
If you are not yet registered in an honors course or an honors section of a regular course in the forthcoming semester, you need to apply for special permission by completing the appropriate Special Permission Form available online (This form is now closed). DO NOT use the Automated Web System to submit your request!
Requests for fall courses may be submitted during the previous spring or summer; requests for spring courses during the previous fall. When filling out the form, make sure you give a valid reason for your request (e.g. previous honors course, recommendation of professor, etc). Requests will be processed as they are received, so long as necessary information (current grades, references, ...) is available.
If you are already registered in an honors section for the forthcoming semester and would like to switch to another section of the SAME course, you need to use the Automated Web System to submit your request during one of the three rounds. Please see below for the dates.
Prerequisite overrides
A student who is unable to register for a course because he or she lacks the proper prerequisites should not request a special permission number. Under some circumstances – for example, if the student has taken appropriate prerequisite courses elsewhere, and these are not yet credited to his or her Rutgers transcript – please fill out a prerequisite override form.
If justification for receiving a prerequisite override is too complicated to adequately describe on the form on the online website, please go to the Advising Office of the Math Dept, room 308 of the Hill Center.
Closed Sections
Because of the high demand for many of the math department classes, many course sections are filled early in registration. Once the course is filled it is listed as Closed. However, we generally leave some spots open in the course to accomodate late registrants and transfer students. These final spots are assigned through the special permission for closed section process which starts shortly before the semester begins and continues through the first week of the semester. A student should first attempt to register through the Rutgers Web Registration System. If all sections that the student can take are closed, the student should submit a special permission form once the special permission process opens. (The schedule for the process will be listed on this web page shortly before the semester begins.)
The department makes a significant effort to accommodate as many students as possible during the process, and generally satisfies most of them, but unfortunately there is often not enough room to grant all requests.
Retaking Precalculus, Calculus I or Calculus II previously failed twice
Students who have failed Precalculus, Calculus I or Calculus II twice are not allowed by WebReg to register for the course a third time. These students should fill out the following online form and meet with the appropriate advisor. Students who have failed Precalculus twice must meet with the Basic Skills ad Precalculus advisor in LSHB room 102A, LIV. Students who have failed Calculus I or Calculus II twice must meet with the advisor in HILL 308 BUSH. Afterwards, the students have to submit a request for a special permission number following the procedure for closed sections.
Students belonging to schools other than SAS, SEBS, and RBS should see their Dean

Fall and Spring Terms
 Matriculated undergraduates should request special permission for admission to closed sections using the automated special permission system described below. While the special permission process is ongoing students should attend a section that they are trying to enter via special permission, so that no class time will be missed.
 Nonmatriculated undergraduate students and graduate students should request special permission for admission to closed sections by completing the appropriate special permission form available online. Decisions on these requests will be made during the first week of classes.
Spring 2019 Special Permission Rounds 
Rounds of Special PermissionRound 1: 
Begins: 12:01am, Wednesday, January 9 
Ends: 4:00pm, Thursday, January 17 
Decision Date: 3:00pm, Friday, January 18 
Round 2: 
Begins: 4:00pm, Friday, January 18 
Ends: 4:00pm, Thursday, January 24 Round 3: 
Begins: 4:00pm, Friday, January 25 
Ends: 4:00pm, Monday, January 28 
Decision Date: 3:00pm, Tuesday, January 29 
NOTE: 
Please be aware of the following: Last day to DROP courses without a "W" is Tuesday, January 29 Last day to ADD courses is Wednesday, January 30 Course selection for new requests will be unavailable between the end of one round and the start of the next 
If you receive an email informing you that your request has been
granted, you must login within 3 days of when the email is sent
in order to retrieve your special permission number.
Automated special permission system
For CLOSED SECTIONS – For matriculated undergraduates
Fall and Spring Semesters
Automated Web System
Enter Here
NOTE: When vieing the Special Permission login page for the first time, you may get a notice that the SSL certificate is invalid. You can disregard this and know that the site is still perfectly secure. In order to fix this, please add a permanent exception and reload the page. If you need help with this, please see our documentation regrading this issue: Certificate Errors
 Who Can Use the Online Special Permission System?
Matriculated undergraduates who wish to get special permission to enter closed sections of mathematics courses should use the mathematics department's webbased system.  How Do I Login?
Students need to use their NetID and password to access the online special permission system. Students using this system DO NOT need to have their own computer accounts or email addresses. They only need access to the web which is available on all campuses. Deans' Offices should be prepared to help disabled students with their special permission requests.
Front End Login
Graduate Courses Taken by Undergraduates
With the approval of the department, undergraduates may take graduate courses, under three conditions.
 There are no undergraduate courses in mathematics which are more appropriate for the student's program.
 Prior achievement in undergraduate or graduate mathematics courses provides a clear indication of the student's ability to do well in graduate level work.
 Admission of the student to the graduate course is consistent with the needs and desires of the graduate program.
Application Procedure
Students wishing to take graduate courses should consult the chair of the honors committee (Committee on Honors and Prizes), who will verify the first two conditions. If approved by the chair of the honors committee, the application will be reviewed by the Graduate Director in consultation with the instructor responsible for the course.
Who should take graduate courses?
Students who wish to take graduate courses should familiarize themselves with the other special opportunities available for undergraduates in the mathematics department, including the Honors Track, the Directed Reading Program, and Research Opportunities for Undergraduates. See our Undergraduate Program page for the relevant links.
Graduate courses are sometimes used to satisfy requirements for graduating with honors; specifically, a graduate course may count as an mathematics honors graduation unit. Students who wish to have a graduate course count as an honors unit must submit an application for approval of alternative honors graduation unit to the undergraduate math office.
Students in the honors track are encouraged to take some graduate courses in their senior year.
Homework  Fall 2018  Draft
Here is the official list of homework problems from the 7th edition of the Kendall Hunt text.
THE FINAL EXAM WILL ASSUME FAMILIARITY WITH THE MATERIAL COVERED BY THESE PROBLEMS. THESE HOMEWORK PROBLEMS CONSTITUTE YOUR MAIN STUDY GUIDE FOR MATH 135.
The exercises are listed by section of the book. See the Lecture Topics page to determine which sections go with which lectures.
The answers (not solutions) to the oddnumbered problems in this list are in the back of the textbook. Here is a link to the answers (prepared by Prof. Melissa Lieberman) to the evennumbered problems starting with Chapter 2 in this list. But be sure to work on the problems yourself before you check your work by looking up the answers.
SECTION  PROBLEMS 

1.2  2, 3, 5, 11, 15, 17, 19, 24, 28, 29, 33, 36. 
1.3  3, 5, 7, 10, 12, 13, 17, 20, 27, 29, 40. 
1.4  5, 9, 10, 11, 14, 17, 20, 24, 25b, 27, 28, 32, 33, 37, 38, 48. 
2.1  1, 2, 3, 4, 5, 6, 13, 15, 29. 
2.2  4, 6, 7, 11, 12, 13, 14, 15, 16, 18, 21, 22, 23, 25, 37, 38, 39, 41, 43, 49, 52, 55. 
2.3  15, 21, 25, 27, 29, 30, 37, 38, 39, 42, 43, 44, 45. 
2.4  1, 3, 6, 7, 10, 12, 19, 22, 27, 29, 32, 35, 36, 44, 47, 49. 
3.1  5, 6, 7, 8, 10, 11, 12, 14, 17, 19, 22, 23, 24, 26, 32, 33, 38, 41, 42, 43. 
3.2  7, 8, 9, 11, 13, 16, 18, 21, 24, 25, 27, 29, 33, 36, 41. 
3.3  1, 3, 4, 6, 11, 15, 17, 18, 20, 29, 37, 39, 41, 45, 52. 
3.4  3, 5, 7, 12, 13, 16, 19, 22, 34, 35. 
3.5  5, 6, 8, 9, 12, 15, 17, 19, 21, 24, 25, 27, 28, 29, 31, 32, 34, 38, 42, 46. 
3.6  1, 4, 5, 7, 8, 9, 11, 14, 26, 27, 31, 35, 36, 38, 43, 45. 
3.7  5, 8, 9, 14, 15, 21, 26, 28, 29, 30, 35, 36, 37, 38, 39, 40, 41, 46. 
3.8  3, 4, 8, 13, 19, 20, 23, 25, 28, 40, 42, 44, 45. 
4.1  4, 5, 11, 12, 17, 25, 27, 32, 36, 50. 
4.2  7, 10, 21, 22, 27, 30. 
4.3  5, 6, 11, 25, 34, 36, 40, 42, 45. 
4.4  10, 11, 12, 15, 20, 23, 27, 29, 33, 38, 47, 48. 
4.5  1, 3, 6, 7, 11, 12, 13, 17, 21, 23, 30, 37, 38, 39. Also: problems #17, 19 and 27 from Section 4.3. 
4.6  7, 8, 16, 27, 28, 34, 35, 39. 
4.7  1, 6, 13, 14, 15, 18, 25, 26. 
5.1  7, 8, 9, 10, 11, 17, 21, 23, 26, 40, 41, 43, 44. 
5.2  3, 4, 8, 25, 28. 
5.3  3, 4, 5, 6. 
5.4  2, 7, 9, 10, 11, 14, 15, 17, 23, 29, 32, 33, 35, 37, 40, 51, 52. 
5.5  1, 3, 6, 9, 10, 13, 15, 16, 21, 27, 30, 33, 40, 41, 44. 
Homework  Fall 2018  Draft with correct frame
Here is the official list of homework problems from the 7th edition of the Kendall Hunt text.
THE FINAL EXAM WILL ASSUME FAMILIARITY WITH THE MATERIAL COVERED BY THESE PROBLEMS. THESE HOMEWORK PROBLEMS CONSTITUTE YOUR MAIN STUDY GUIDE FOR MATH 135.
The exercises are listed by section of the book. See the Lecture Topics page to determine which sections go with which lectures.
The answers (not solutions) to the oddnumbered problems in this list are in the back of the textbook. Here is a link to the answers (prepared by Prof. Melissa Lieberman) to the evennumbered problems starting with Chapter 2 in this list. But be sure to work on the problems yourself before you check your work by looking up the answers.
SECTION  PROBLEMS 

1.2  2, 3, 5, 11, 15, 17, 19, 24, 28, 29, 33, 36. 
1.3  3, 5, 7, 10, 12, 13, 17, 20, 27, 29, 40. 
1.4  5, 9, 10, 11, 14, 17, 20, 24, 25b, 27, 28, 32, 33, 37, 38, 48. 
2.1  1, 2, 3, 4, 5, 6, 13, 15, 29. 
2.2  4, 6, 7, 11, 12, 13, 14, 15, 16, 18, 21, 22, 23, 25, 37, 38, 39, 41, 43, 49, 52, 55. 
2.3  15, 21, 25, 27, 29, 30, 37, 38, 39, 42, 43, 44, 45. 
2.4  1, 3, 6, 7, 10, 12, 19, 22, 27, 29, 32, 35, 36, 44, 47, 49. 
3.1  5, 6, 7, 8, 10, 11, 12, 14, 17, 19, 22, 23, 24, 26, 32, 33, 38, 41, 42, 43. 
3.2  7, 8, 9, 11, 13, 16, 18, 21, 24, 25, 27, 29, 33, 36, 41. 
3.3  1, 3, 4, 6, 11, 15, 17, 18, 20, 29, 37, 39, 41, 45, 52. 
3.4  3, 5, 7, 12, 13, 16, 19, 22, 34, 35. 
3.5  5, 6, 8, 9, 12, 15, 17, 19, 21, 24, 25, 27, 28, 29, 31, 32, 34, 38, 42, 46. 
3.6  1, 4, 5, 7, 8, 9, 11, 14, 26, 27, 31, 35, 36, 38, 43, 45. 
3.7  5, 8, 9, 14, 15, 21, 26, 28, 29, 30, 35, 36, 37, 38, 39, 40, 41, 46. 
3.8  3, 4, 8, 13, 19, 20, 23, 25, 28, 40, 42, 44, 45. 
4.1  4, 5, 11, 12, 17, 25, 27, 32, 36, 50. 
4.2  7, 10, 21, 22, 27, 30. 
4.3  5, 6, 11, 25, 34, 36, 40, 42, 45. 
4.4  10, 11, 12, 15, 20, 23, 27, 29, 33, 38, 47, 48. 
4.5  1, 3, 6, 7, 11, 12, 13, 17, 21, 23, 30, 37, 38, 39. Also: problems #17, 19 and 27 from Section 4.3. 
4.6  7, 8, 16, 27, 28, 34, 35, 39. 
4.7  1, 6, 13, 14, 15, 18, 25, 26. 
5.1  7, 8, 9, 10, 11, 17, 21, 23, 26, 40, 41, 43, 44. 
5.2  3, 4, 8, 25, 28. 
5.3  3, 4, 5, 6. 
5.4  2, 7, 9, 10, 11, 14, 15, 17, 23, 29, 32, 33, 35, 37, 40, 51, 52. 
5.5  1, 3, 6, 9, 10, 13, 15, 16, 21, 27, 30, 33, 40, 41, 44. 
Alumni and Alumnae Selected Profiles
Alumni and Alumnae of the Rutgers and Douglass Math Programs and Former Faculty
Interested in what you can do with, or in spite of, a degree in mathematics? The following are a few publiclyavailable profiles of Rutgers and Douglass math graduates and former faculty.
Selected Profiles of Alumni and Alumnae of the Rutgers and Douglass Undergraduate Math Program
Allan Borodin of the University of Toronto is "the recipient of the 2008 CRMFieldsPIMS Prize, in recognition of his exceptional achievement. Professor Borodin is a world leader in the mathematical foundations of computer science. His influence on theoretical computer science has been enormous, and its scope very broad. Jon Kleinberg, winner of the 2006 Nevanlinna Prize, writes of Borodin, "he is one of the few researchers for whom one can cite examples of impact on nearly every area of theory, and his work is characterized by a profound taste in choice of problems, and deep connections with broader issues in computer science." Allan Borodin has made fundamental contributions to many areas, including algebraic computations, resource tradeoffs, routing in interconnection networks, parallel algorithms, online algorithms, and adversarial queuing theory. Professor Borodin received his B.A. in Mathematics from Rutgers University in 1963, his M.S. in Electrical Engineering & Computer Science in 1966 from Stevens Institute of Technology, and his Ph.D. in Computer Science from Cornell University in 1969. From http://www.fields.utoronto.ca/press/0708/071206.borodin.html .
Simeon DeWitt "was the first math major at Rutgers. He became General George Washington's Chief Geographer in the Revolutionary War. His maps of Yorktown helped win the final battle of that war. Afterwards (17841834) he was the Surveyor General for New York State; he helped to plan the Erie Canal, and to develop the grid system of streets and avenues in New York City, among other things." https://www.math.uh.edu/~tomforde/famous.html
Inessa Epstein is Vice President at Morgan Stanley. She earned a Ph.D. in Mathematics at UCLA and won the Sacks Prize for recognition for the best dissertation in the field of mathematical logic worldwide in 2008. From https://www.linkedin.com/in/inessaepsteinphdb0a92914 .
Lorraine Fesq is "the Chief Technologist for the Systems Engineering and Formulation Division at the Jet Propulsion Laboratory/California Institute of Technology. She leads NASA's Fault Management Community of Practice and coleads the NASA Software Architecture Review Board. She recently spearheaded the development of the NASA Fault Management Handbook. Lorraine has contributed to over a dozen spacecraft projects and held a teaching and research position in MIT's Aeronautics/Astronautics Department. Lorraine holds two patents and has received numerous awards, including NASA's Public Service Medal and NASA's Exceptional Achievement Honor Award. She received the BA in Mathematics from Rutgers University and the MS and PhD in Computer Science from the University of California, Los Angeles." https://saturn2016.sched.org/speaker/lorraine_fesq.1uuuhx7u
Milton Friedman graduated from Rutgers University in 1932 with a bachelor degree in Mathematics. Milton Friedman was awarded the 1976 Nobel Memorial Prize in Economics "for his achievements in the fields of consumption analysis, monetary history and theory and for his demonstration of the complexity of stabilization policy." The year after, he retired from the University of Chicago to become a senior research fellow at the Hoover Institution at Stanford University. In 1988, after joining President Ronald Reagan's Economic Policy Advisory Board, he was awarded the National Medal of Science and the Presidential Medal of Freedom." From https://econwikismborg.wikispaces.com/Milton+Friedman
Ross Guberman "is the CEO of Great Forest, a leading sustainability consultancy that specializes in sustainable waste management solutions for Fortune 500 companies and organizations nationwide. Ross really does practice what he preaches, with a handson type vegan lifestyle and cycling everywhere he can. Don't be surprised if you spot him digging in the trash for a waste audit. At Great Forest Ross leads a team that specializes in assisting businesses and large commercial building operators in the development and implementation of successful sustainability programs and management systems that are customized for their specific needs. He has only stepped away from his sustainable endeavors once when he joined the Peace Corps as an environmental education volunteer in the Republic of Cape Verde in West Africa. Ross holds a B.A in mathematics from Rutgers University." http://greatforest.com/about/ourstaff/
Karla L. Hoffman received "her B.A. in Mathematics from Rutgers University in 1969, and an M.B.A. and Doctor of Science in Operations Research from George Washington University in 1971 and 1975, respectively. She is a Full Professor in the Systems Engineering and Operations Research Department and served as Chair of the department for five years ending in 2001. Previously, she worked as a mathematician in the Operations Department of the Center for Applied Mathematics of the National Institute of Standards and Technology where she served as a consultant to a variety of government agencies. Dr. Hoffman has many publications in the fields of auction theory and optimization as well as a variety of publications detailing her applied work. .... Dr. Hoffman's primary area of research is combinatorial optimization and combinatorial auction design as well software development and testing. She has developed scheduling algorithms for the airline and trucking industries, developed capital budgeting software for the telecommunications industry, and consults to the Federal Communications Commission on combinatorial auction design and software development." From https://masonspeakers.gmu.edu/speakers/
Lawrence P. Horowitz is "a Senior Advisor at Outcome Capital and brings deep corporate and strategic expertise in the medical technology space. He is also a Principal at Doremus Advisory Services where he specializes in providing valuation in support of R&D portfolio analysis and transaction structuring. His past appointments include Principal with HVA which advised private and small cap life sciences companies on their business development transactions, Vice President of Development at C.R. Bard and Senior Director Business Development at American Cyanamid Company (acquired by American Home Products and now part of Pfizer). His academic involvement includes the Rutgers Center for Management Development, Rutgers Business School, and the University of Umea (Sweden) Biotech Incubator where he has taught courses in lifescience entrepreneurship and financial analysis of R&D investment. He has an MBA in Finance from Columbia Graduate School of Business, an MS in Industrial Engineering from NYU, and a BA in Mathematics from Rutgers College where he graduated with highest honors as a Henry Rutgers Scholar. He teaches Principles of Finance and Accounting for the Professional Science Master's Program at Rutgers University." http://mbs.rutgers.edu/about/faculty
JeanMichelet JeanMichel "was born in PetitGoave, Haiti where he received his baccalaureat (high school diploma) in 1985. He then received his B.A. in Mathematics from Rutgers University in 1993 and his Ph.D. in Applied Mathematics from Brown University in 2002. His research interests are in the fields of differential equations and dynamical systems." from http://www.princeton.edu/~wmassey/NAM03/. He is now Assistant Professor at South Carolina State University.
Matt Kohut is currently teaching mathematics at A.E. Wright Middle School in Calabasas, California. After graduating with his bachelorâ€™s degree in mathematics from Rutgers University, Matt attended law school at the Rutgers School of Law  Camden. Subsequently, he clerked for the Honorable Joseph F. Lisa, Presiding Judge of the New Jersey Appellate Division, and worked as an attorney for the firm of Feintuch, Porwich and Feintuch. He then decided to return to mathematics through the Math for America fellowship program.
Carl Martin is "a pop, electronic and alternative singer/songwriter who cites George Michael and Natasha Bedingfield as his major influences. At age 17, he returned to the USA, moving to Arizona to complete his high school education. He received a BA in mathematics from Rutgers University in 2012. .... Martin is currently working with 90's Rock Music Icon Anthony Kirzan of the Spin Doctors ....." See http://www.cdbaby.com/Artist/CarlMartin and https://www.youtube.com/watch?v=ThPXVFXK268&list=PLj6N7pQVWRNCij2WMQmWAHRZkhwxUbUem&index=5"
MaryAnn Millar is "a Board Certified Gynecologist and a Fellow of the American College of Obstetricians and Gynecologists. She is Clinical Assistant Professor, Upstate University Hospital. She has a B.A. in Mathematics from Rutgers University and was awarded her M.D. from the State University of New York in Buffalo. Her residency in Ob/Gyn was completed in Syracuse at Upstate University Hospital." From http://drmaryannmillar.com/about.htm
Tom Peters is "a software engineer at Ufora, Inc. He has worked on a multiple aspects of Ufora's autoparallel, multihost, open source Python project, Pyfora. He has a PhD in mathematics from Columbia University, where he specialized in lowdimensional topology, using Heegaard Floer homology to compute invariants of manifolds, and has a BA in mathematics from Rutgers University." http://mlconf.com/mlconf2016atlanta/
Elizabeth Ricci (VirMedica) is an "accomplished global software executive with a proven track record in engineering, project management and product development, with an emphasis on quality, timeliness and customer success. In her prior engagement as VP of engineering for PHT Corporation, she was responsible for all core products and was instrumental in rolling out the company's next generation technologies. Prior positions include senior VP, products at Kadient, Inc., and senior VP, global products at Authoria, Inc. Elizabeth holds a B.A. in Mathematics from Rutgers University and a M.S. in Mathematics from Northeastern University." From http://virmedica.com/category/pressrelease/
Stephen Rosen is a "Managing Director at FTI Consulting and is based in New York. He is a member of the Insurance and Pension group in the Forensic and Litigation Consulting segment and heads the Pension practice. ..... Mr. Rosen's work includes the design, implementation, and administration of all forms of qualified employee benefit plans .... Mr. Rosen holds a B.A. in mathematics from Rutgers University. He completed coursework in business administration from the Wharton School of Business and actuarial science from the University of Iowa." from http://www.fticonsulting.com/ourpeople/stephenhrosen.
Timothy Rudderow "cofounded Mount Lucas in 1986 and is the firm's president, overseeing all of its activities. He has been in the investment business since the late 1970s, when he worked at Commodities Corporation with the late Frank Vannerson, another cofounder of Mount Lucas. Tim specializes in the design and management of technical trading systems applied to the futures, equity, and fixed income markets. He holds a B.A. in Mathematics from Rutgers University and an M.B.A. in Management Analysis from Drexel University." https://www.mtlucas.com/OurTeam.aspx?content=BioPrincipals
Jeffrey Rubin is Professor in the Department of Economics at the Institute for Health, Health Care Policy, and Aging Research New Brunswick Campus. "His research is focused on health economics including the impact of health insurance on use of care. He also has served on a subcommittee on the Governor's Commission that examined the situation facing hospitals in New Jersey, and has published papers on the costs of mental illness and the economic consequences of spinal cord injury. Rubin received his B.A. in mathematics from Rutgers College and his Ph.D. from Duke University." http://urwebsrv.rutgers.edu/experts/index.php?a=display&f=expert&id=1465.
Larry Sher is "a member of the actuarial consulting team and part of the senior leadership for October Three. Larry also is head of [their] dispute resolution practice, which provides support to clients in disputes related to their retirement plans, both in litigation and otherwise. .... Larry received a B.A. in Mathematics from Rutgers University. He has been a Board Member and ViceChair of the Actuarial Standards Board, the group that establishes actuarial standards of practice for all US actuaries. Larry has also been on the Boards of the American Academy of Actuaries and the Conference of Consulting Actuaries, and was recently President of the Conference. Larry has written several articles on cash balance and other defined benefit plan issues and is a frequent speaker at industry and professional seminars." from http://www.octoberthree.com/whoweare/larrysher
Robert L. Strawderman, joined Cornell in 2000, and previously a faculty member in the Department of Biostatistics at the University of Michigan. "His major research area is survival analysis, a branch of statistics that deals with characterizing the time until an event, such as the death of an organism or the failure of a machine, occurs. Professor Strawderman's particular research interests lie in the study of events that can recur, such heart attacks or epidemics. He collaborates extensively with subject matter specialists in applying these and other statistical methods to problems in health services, cardiology, epidemiology, demography, and veterinary medicine. Strawderman is on the faculty of two departments at Cornell, Biological Statistics and Computational Biology (BSCB) and Statistical Science..... Strawderman has a BA in Mathematics from Rutgers." https://www.orie.cornell.edu/news/index.cfm?news_id=62175&news_back=category%3D62137
Jeffrey E. Steif Professor and winner of the Eva and Lars Gardings prize in Mathematics. Department of Mathematics Chalmers University of Technology. http://www.chalmers.se/CV/steif.pdf
Michael Yatauro is on the faculty at PSUBrandywine. He earned "a B.A. in mathematics from Rutgers University, an M.A. in mathematics from the University of Pennsylvania, and a Ph.D. in mathematics from Stevens Institute of Technology. Dr. Yatauro views mathematics as a form of artistic expression and a scientific tool of great utility. His primary research is in the field of graph theory. In particular, he is interested in determining structural aspects of a graph by studying its degree sequence. ...." from http://brandywine.psu.edu/person/michaelyatauro
Tony Trongone joined Pemberton Township Schools as Superintendent [of Schools] in July, 2015. Before coming to Pemberton he served as superintendent of schools for Berlin Borough and Gibbsboro Public Schools, a post he held for five years. His previous experience includes serving as district supervisor of curriculum and instruction for Cherry Hill Public Schools, supervisor of mathematics for Gloucester City School District, and secondary mathematics teacher at Northern Burlington Regional High School in Columbus, NJ. Trongone earned his master's degree in Educational Administration from Wilmington University and his BA in Mathematics from Rutgers University. He prescribes to the theory of high challenge with high support, believing all students can learn and it is the responsibility of educators to support students in reaching their fullest potential. He is committed to providing Pemberton students with a rigorous instructional program and multiple pathways to college and career readiness. He is currently a Trustee for the New Jersey School Board Insurance Group and has served as presidentelect of the Association of Mathematics Teachers of New Jersey. His other professional memberships include the Association for Supervision and Curriculum Development, the National Staff Development Council and the New Jersey Principals and Supervisors Association, among others." From http://www.pemberton.k12.nj.us/administration/
Emily Sergel has been included in the inaugural class of winners of the Dissertation Award of the Association for Women in Mathematics. Emily completed her PhD at UCSD in 2016 and now enjoys an NSF Postdoc at the University of Pennsylvania. She graduated from SASRutgers in 2009.
Selected Alumni/Alumnae of the Graduate Program
Roy Goldman is former Chief Actuary at Humana Inc. http://press.humana.com/pressrelease/currentreleases/humananamesroygoldmanvicepresidentandchiefactuary.
William "Brit" Kirwan is Chancellor Emeritus of the University System of Maryland. He is a nationally recognized authority on critical issues shaping the higher education landscape. Prior to his 13 years as chancellor of the University System of Maryland, Kirwan served as president of Ohio State University, president of the University of Maryland, College Park, and as a member of the University of Maryland faculty. He is a soughtafter speaker on a wide range of topics, including access and affordability, cost containment, diversity, innovation, higher education's role in economic development, and academic transformation. Along with his national and international presentations on key issues, he has authored many articles on issues in higher education and has been profiled and cited in academic and mainstream publications. Currently, he chairs the National Research Council Board of Higher Education and Workforce and is past chair of the boards of the BusinessHigher Education Forum, the Association of Public and Land Grant Universities (APLU), the American Council for Education (ACE), and the American Association of Colleges and Universities (AAC&U). Among other honors, he is the recipient of the 2009 Carnegie Corporation Academic Leadership Award and the 2010 TIAA Theodore Hesburgh Leadership Excellence Award. He received his Ph.D. in Mathematics from Rutgers, The State University of New Jersey. From http://agb.org/bios/williamekirwan .
Zoltan Szabo is a Professor of mathematics at Princeton University. With Peter Ozsvath he created Heegaard Floer homology, a homology theory for 3manifolds. For this contribution to the field of topology, Ozsvath and Szabo were awarded the 2007 Oswald Veblen Prize in Geometry. They received Ph.D.'s from Rutgers University in 1994. See https://en.wikipedia.org/wiki/Peter_Ozsv%C3%A1th and https://en.wikipedia.org/wiki/Zolt%C3%A1n_Szab%C3%B3_(mathematician).
Camelia Pop "received her Ph.D. in mathematics from Rutgers University in 2012. She was a Hans Rademacher Instructor in the Department of Mathematics at the University of Pennsylvania from 2012Ã‚Â15. Her research interests are in partial differential equations and stochastic processes, including applications to population genetics and mathematical finance." From https://cse.umn.edu/r/newcollegeofscienceandengineeringfacultyfor201516/.
Emilie Purvine "completed her B.S. in Mathematics from University of Wisconsin, Madison in 2006 and Ph.D. in Mathematics from Rutgers University, New Jersey, in 2011. Emilie then joined PNNL as a Postdoc doing work on semantic knowledge systems and graph theory. She became a permanent staff scientist in November of 2012 and continues to work on graph theory and discrete math applied to cyber security and the power grid. Recently, Emilie has also begun work on applying methods from algebraic topology to information integration and evolution of cyber systems." From http://cybersecurity.pnnl.gov/principalinvestigators.stm.
Noriko Yui is "a professor of mathematics at Queen's University in Kingston, Ontario. A native of Japan, Yui obtained her B.S. from Tsuda College, and her Ph.D. in Mathematics from Rutgers University in 1974 under the supervision of Richard Bumby. Known internationally, Yui has been a visiting researcher at the MaxPlanckInstitute in Bonn a number of times and a ByeFellow at Newnham College, University of Cambridge. Her research is based in arithmetic geometry with applications to mathematical physics and notably mirror symmetry. Currently, much of her work is focused upon the modularity of CalabiYau threefolds. .... Professor Yui has been the managing editor for the journal "Communications in Number Theory and Mathematical Physics" since its inception in 2007. She has edited a number of monographs, and she has coauthored two books." from https://en.wikipedia.org/wiki/Noriko_Yui.
Select Former Faculty of the Rutgers Mathematics Department
Daniel E. Gorenstein (January 1, 1923 to August 26, 1992) was an American mathematician. He earned his undergraduate and graduate degrees at Harvard University, where he earned his Ph.D. in 1950 under Oscar Zariski, introducing in his dissertation a duality principle for plane curves that motivated Grothendieck's introduction of Gorenstein rings. He was a major influence on the classification of finite simple groups. After teaching mathematics to military personnel at Harvard before earning his doctorate, Gorenstein held posts at Clark University and Northeastern University before he began teaching at Rutgers University in 1969, where he remained for the rest of his life. He was the founding director of DIMACS in 1989, and remained as its director until his death. Gorenstein was awarded many honors for his work on finite simple groups. He was recognised, in addition to his own research contributions such as work on signalizer functors, as a leader in directing the classification proof, the largest collaborative piece of pure mathematics ever attempted. In 1972 he was a Guggenheim Fellow and a Fulbright Scholar; in 1978 he gained membership in the National Academy of Sciences and the American Academy of Arts and Sciences, and in 1989 won the Steele Prize for mathematical exposition." from https://en.wikipedia.org/wiki/Daniel_Gorenstein.
Helmut Hofer is "a GermanAmerican mathematician, one of the founders of the area of symplectic topology. He is a member of the National Academy of Sciences, and the recipient of the 1999 Ostrowski Prize and the 2013 Heinz Hopf Prize. Since 2009, he is a faculty member at the Institute for Advanced Study in Princeton. He currently works on symplectic geometry, dynamical systems, and partial differential equations. His contributions to the field include Hofer geometry." From https://en.wikipedia.org/wiki/Helmut_Hofer
Jane Scanlon "received her doctorate from the University of Michigan in 1949 under the direction of Erich H. Rothe. After two postdoctoral fellowships, from the Office of Naval Research and the University of Michigan, she worked as a mathematician in the Air Force and for the American Optical Company, and as an instructor at Wheaton College and Stonehill College. In 1957, she moved to the Polytechnic Institute of Brooklyn, and in 1965 took a position as professor at Rutgers University. She became professor emeritus in 1991. She was awarded a Visiting Professorship for Women from the National Science Foundation to spend the 19841985 year at the Courant Institute of Mathematical Sciences. At the Joint Mathematics Meetings in Boulder in August 1989, she presented the Pi Mu Epsilon J. Sutherland Frame Lecture. Scanlon's research has focused on mathematical biology, singular perturbation theory, and nonlinear analysis. She has published more than fifty papers, two research monographs (Fixed Points and Topological Degree in Nonlinear Analysis and Mathematical Aspects of HodgkinHuxley Neural Theory), as well as a textbook (Differential Equations: Introduction and Qualitative Theory)." From http://www.awmmath.org/noetherbrochure/Scanlon85.html
Thomas Spencer is Professor in the School of Mathematics at the Institute for Advanced Study in Princeton. He "has made major contributions to the theory of phase transitions and the study of singularities at the transition temperature. In special cases, he and his collaborators have proved universality at the transition temperature. Spencer has also worked on partial differential equations with stochastic coefficients, especially localization theory. He is presently developing a mathematical theory of supersymmetric path integrals to study the quantum dynamics of a particle in random media. His other interests include random matrices, chaotic behavior of dynamical systems, and nonequilibrium theories of turbulence." https://www.ias.edu/scholars/spencer.
01:640:152  TEST PAGE FALL 2017
Math 151–152 is the introductory year course in the calculus sequence in New Brunswick for majors in the mathematical sciences, the physical sciences, and engineering.
 The first semester, Math 151 or 153, presents the differential calculus of the elementary functions of a single real variable: the rational, trigonometric and exponential functions and their inverses; various applications via the Mean Value Theorem; and an introduction to the integral calculus.
 The second semester, Math 152, continues the study of the integral calculus, with applications, and covers the theory of infinite series and power series, touching on differential equations and a few other topics as well.
Transitioning from Math 135 to Math 152:
Students who intend to go directly from Math 135 to Math 152 will need to fill in some gaps through selfstudy.
The details are in the document:
Transferring From 135 to 152
Textbook:
Jon Rogawski & Colin Adams, Calculus, Early Transcendentals, 3rd edition, plus WebAssign
Purchase options:
 Hardcover custom 3rd edition and WebAssign premium access code (for the duration of the 3rd edition).
ISBN 9781319048532
NJ Books: \(125.00.  Ebook custom 3rd edition and WebAssign premium access code (for the duration of the 3rd edition)
ISBN 9781319049119
NJ Books: \)107.50
The 3rd edition is purchased with a WebAssign access code which will be used throughout the sequence 151152251. The publisher is unable to replace this code if it is lost, so be careful to retain it.(The third edition was introduced beginning in Fall 2015.)
Course Materials
 152: Syllabus and Homework
 152: Announcements and Review Sheets
 General Course Information for Math 151152 (Spring 2017)
 Going from math 135 to math 152
{rucourse course = "01:640:152" semester = "92017"}
01:640:152  TEST PAGE FALL 2016
Math 151–152 is the introductory year course in the calculus sequence in New Brunswick for majors in the mathematical sciences, the physical sciences, and engineering.
 The first semester, Math 151 or 153, presents the differential calculus of the elementary functions of a single real variable: the rational, trigonometric and exponential functions and their inverses; various applications via the Mean Value Theorem; and an introduction to the integral calculus.
 The second semester, Math 152, continues the study of the integral calculus, with applications, and covers the theory of infinite series and power series, touching on differential equations and a few other topics as well.
Transitioning from Math 135 to Math 152:
Students who intend to go directly from Math 135 to Math 152 will need to fill in some gaps through selfstudy.
The details are in the document:
Transferring From 135 to 152
Textbook:
Jon Rogawski & Colin Adams, Calculus, Early Transcendentals, 3rd edition, plus WebAssign
Purchase options:
 Hardcover custom 3rd edition and WebAssign premium access code (for the duration of the 3rd edition).
ISBN 9781319048532
NJ Books: \(125.00.  Ebook custom 3rd edition and WebAssign premium access code (for the duration of the 3rd edition)
ISBN 9781319049119
NJ Books: \)107.50
The 3rd edition is purchased with a WebAssign access code which will be used throughout the sequence 151152251. The publisher is unable to replace this code if it is lost, so be careful to retain it.(The third edition was introduced beginning in Fall 2015.)
Course Materials
 152: Syllabus and Homework
 152: Announcements and Review Sheets
 General Course Information for Math 151152 (Spring 2017)
 Going from math 135 to math 152
{rucourse course = "01:640:152" semester = "92016"}
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Advising
During the first year of graduate studies, students are mainly focused on taking classes, preparing for the written qualifying exam and adjusting to graduate student life at Rutgers.
During the second year students are focused on identifying potential research areas and advisors, and preparing for the oral qualifying exam.
The graduate program mentoring committee consists of faculty members who are each assigned a group of entering students. The assignment of mentors to students is not necessarily based on research interests. Rather the mentor is available to the student to discuss concerns that arise during the first years, and to help the student make contacts with potential research advisors. The graduate program director also serves a general advising role for all students.
The assignment of mentors to students should not bound students to limit their interaction with other faculty members in any way; we courage students to establish their own informal mentoring relationships with additional faculty. You may find useful information in the handbook How to get the mentoring you want, published by the graduate school of the University of Michigan.
Directions to the Department
The Department of Mathematics at RutgersNew Brunswick is located in the Hill Center* on the Busch Campus of Rutgers University in Piscataway, NJ. (Piscataway is just across the Raritan River from New Brunswick.)
The University page for Hill Center has a map and driving directions. Please click on the map to zoom out.
Also, you can find more specific directions to the Hill Center by going to Google Maps and entering your starting location. Make sure to click "The Hill Center" link on the left hand side and then click "Get directions" and also select "to here" or "from here", depending on what you need. (The reason for doing this is that Google Maps, and other maps sites, does not have the correct location for the Hill Center. Hill Center is across Frelinghuysen Road from the northeast corner of the Rutgers Golf Course. )
*The rigorous definition is as follows: Longitude 74.47168 W, Latitude 40.52180 N.
Our own travel directions are as follows:
BY CAR:
Because of road construction on and near the Busch campus, the driving instructions given below may change. Some information about the current state of construction and detours can be found on the Route 18 Construction Information web page. The University also provides updated directions at University directions.
NOTE: Rutgers University has five campuses in New Brunswick. The Department of Mathematics is located on the Busch Campus. Road signs marked "Rutgers University" may lead to the wrong campus. If you follow signs, those directing you to "Rutgers Stadium" will bring you to Busch Campus, the location of the Mathematics Department.
From the NJ Turnpike: Take Exit 9 and proceed north (west) on New Jersey Route 18. It is recommended that you use either of the two leftmost lanes of Route 18. Follow Route 18 through New Brunswick and across the John A. Lynch Memorial Bridge. (Ignore the "George Street Rutgers University" exit.) Exit Route 18 at Campus Road (the sign also says Rutgers Stadium and Busch Campus). At the traffic circle, turn right onto Bartholmew Road. At the stop sign, turn left onto Brett Road. Follow Brett road until it vanishes in a maze of parking lots. Park in lot 64, 60A, 60B (or at lot 67 near Brett and Bartholomew Roads) and put your parking permit in the front window. If you do not have a permit, please to go the Department Office(Hill 346 or 311) and get a oneday guest permit. Hang the permit on your rearview mirror to avoid ticketing. The Hill Center is the seven story dark brick building, located just behind the CORE building.
From Interstate Highway 287: Take the exit marked "River Road, Bound Brook, Highland Park" (exit 9), following River Road east toward Highland Park. Continue on River Road past Colgate and past the traffic light at Hoes Lane. At the next left turn lane (not the next possible next left turn), turn left onto Sutphen Rd. At the 4 way stop just beyond the stadium, turn left and follow Frelinghuysen Road. At the traffic circle, continue straight onto Bartholomew Road (i.e., ignore the first right turn and do not continue around the circle). At the stop sign, turn left onto Brett Road. Follow Brett road until it vanishes in a maze of parking lots. Park as indicated above.
Note: If you miss the left turn onto Sutphen Rd., you will soon pass under the overpass for Route 18. Make the next left onto Route 18 North. Exit Route 18 at Campus Road (the sign also says Rutgers Stadium and Busch Campus). At the traffic circle, turn right onto Bartholmew Road. At the stop sign, turn left onto Brett Road. Follow Brett road until it vanishes in a maze of parking lots. Park as indicated above.
From Long Island or New York City Airports: Take the Verrazzano Bridge to the Goethals Bridge to the New Jersey Turnpike and proceed as above.
BY BUS:
The Suburban Transit (18002220492) runs convenient express buses from New York City to New Brunswick. There a few places that they pick up and drop off from. Please check the website to see what is available.
BY TRAIN:
Train service to New Brunswick is provided by Amtrak and NJ Transit. This may require changing trains in Trenton or NY/Penn Station. Amtrak info: 1800USARAIL; NJ Transit: 18007722222 from NJ; from out of state: 19737625100.
Once you reach downtown New Brunswick you can get to the Hill Center by taxi in 10 minutes for approximately \(10.00, or by campus bus FREE, in about 1020 minutes. Buses leave at 10 minute intervals. To reach a campus bus stop from the New Jersey Transit bus station on Albany Street, walk west on Albany St., then take the first right onto George Street and walk two blocks to the first traffic light. Turn left onto Hamilton Street, walk one block and you will see the campus bus shelter on your right across College Avenue. To reach the bus stop from the train station at Albany and Easton, walk uphill on Easton Ave. and turn right onto Hamilton Street at the second traffic light. Walk one block and you will see the campus bus shelter on your left. Take an "A", or "H" bus marked to Busch Campus and get off at the Hill Center.
How to walk from the New Brunswick Train Station to the Hill Center on the Busch Campus of Rutgers University
BY PLANE:
The nearest airport is Newark Liberty International Airport. If you fly there, you can either
 Rent a car.
 Take the
 Airporter (call 18003854000 for reservations) to the Hilton Hotel on Route 18, East Brunswick (cost is \)20.00 per person). Schedule of Departure and Arrival times to/from Newark Airport. Then you should take a taxi (about 15 minutes) to the Hill Center, Frelinghuysen Road, Busch Campus, Piscataway, N.J.
 State Shuttle to the Hyatt Hotel in New Brunswick. Call 18004273207 for reservations.
 Take the Airtrain Newark directly from the arrivals terminal to the new Rail Link station and then connect with NJ Transit trains to New Brunswick. (cost is \(8.95 to \)10.80).
 Take a bus to the Port Authority Bus Terminal in New York City (every 15 minutes).
 Take a taxi (the cost is approximately \(45 plus tolls plus tip).
From Kennedy airport, you can take the Airporter (call 18003854000 for reservations) to the Hilton Hotel in East Brunswick (it makes an intermediate stop at Newark Airport). The cost is \)38. The cost of a taxi could be as high as $120 plus tolls plus tip.
You should never have to fly via LaGuardia. But if you do, from LaGuardia airport, you can either rent a car or take public transportation to New York City and then on to New Brunswick.
How To Walk from The New Brunswick Train Station To The Hill Center in the Busch Campus of Rutgers University
Last Update: March 28, 2006 [to enter the name of Busch Campus Drive]
Previous Update: June 14, 2005. [To implement the new BuschCollege Ave walkway]
First Version: Jan. 14, 2002.
Written By Doron Zeilberger.
Note Added Aug. 2, , 2004: The construction seems to be over, at least for now, and the route below is again passable. [added June 20, 2005: the "route below" refers to the old route, so the above statement is true but unnecessary]
There is a safe way to walk, especially now with the new walkway. The whole way takes me appx. 32 minutes [using the new walkway] or 42 minutes [using the old route via Johnson Drive and the Stadium]. The instructions below also apply to biking, and the times then should be divided by 3.
 Go to the end of the platform (away from the station, in the direction of the train if you came from the West (Trenton) and in the opposite direction if you came from the East (NY) ), walk downstairs, make a left onto [ If you came from Trenton/Princeton: George and then immediately another left on] Somerset. Walk a block and make a right on College Ave. On the lefthand side, walk to the end of College Avenue and enter Buccleuch park (about 12 min. walks).
 Walk another minute on a path parallel to George St., and a little before the Buccleuch Mansion, make a right that leads to stairs. Walk down the stairs, and carefully cross George St. to the bike path/pedestrian walk on the Lynch bridge.
 After about two to three minutes you have a choice: turn left down to Johnson Drive and go the Old Way (see below, that takes 10 minutes longer) OR:
New Way (June 2005):
 DONT's turn left (downhill), but go straight and continue on the bridge and follow the path all the way to the end [ 7 additional minutes]. This ends at Busch Campus Drive. Take a left and Walk a few steps to the corner of Busch Campus Drive and Sutphen Road. [the street sign just says "Campus Drive"].
 Cross [Busch] Campus Drive at the crosswalk (carefully! the stupid cars go very fast and do not even slow down for you, even though they are supposed to give you the right of way) and make a left. Continte (after a few minutes past a traffic circle) onto Frelinghuysen Rd., and arive at Hill Center (6 minutes).
[OLD WAY: (be careful when you cross River Rd)
 Follow that path. It ends at Johnson Drive. (about 5 minutes) Make a right on Johnson Drive.
 Keep walking until you hit Landing Lane (3 minutes) after crossing Landing Lane (carefully!) make a right, staying on Landing Lane.
 Walk on the shoulder until you hit the light at River Rd. (2 minutes). Push the button for crossing. When the light turns GREEN, Cross carefully (watching the cars that are turning left, it is your right of way, but you still have to be careful, the light is very short and the cars are impatient.)
 Now you are at the beginning of a steep uphill path that leads to the Stadium. You hit the Stadium at the Hale Center. (3 minutes)
 After you hit the stadium at Hale Center, walk on the sidewalk along the stadium. At the North Entrance, cross Sutphen Road on the crosswalk (carefully!), and make a left (1.5 minutes)
 After less than a minute you hit FITCH Rd., make a right on Fitch. On your left you will have a Golf course, and on your right you have first Dfield and behind it the Busch Bubble, and later Yurack Field. At Yurack Field, Fitch Rd. continues to the right. Instead of turning right, keep going straight, still with the Golf course to your left, and Yurack Field on the right. You can see Hill Center at the top of the Hill. Walk to the end of that path (it ends at Parking Lot 53A), until you hit Frelinghuysen. Turn left, and after a few seconds cross Frelinghuysen at the crosswalk. (8 minutes)]