# Uncategorised

$$2^2$$

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

$\frac{x^2}{a^2}+\frac$

$$\frac{x^2}{a^2}+\frac$$

Mathematics Teachers' Circles consist of groups of mathematicians and K-12 teachers who meet regularly to discuss interesting mathematical problems.

The Rutgers Math Teachers’ Circle (RUMTC) was founded in 2014 and is a member of the national-level Math Teachers’ Circle Network (http://www.mathteacherscircle.org/), as well as of the National Association of Math Circles (https://www.mathcircles.org/). Our circle is mainly for middle school teachers, but we welcome high school and upper elementary teachers as well.

Mathematics Teachers' Circles consist of groups of mathematicians and K-12 teachers who meet regularly to discuss interesting mathematical problems.

The Rutgers Math Teachers’ Circle (RUMTC) was founded in 2014 and is a member of the national-level Math Teachers’ Circle Network (http://www.mathteacherscircle.org/), as well as of the National Association of Math Circles (https://www.mathcircles.org/). Our circle is mainly for middle school teachers, but we welcome high school and upper elementary teachers as well.

Each semester, the Mathematics Department hires undergraduate and graduate students in good standing to grade homework assignemtns, Maple labs, and Matlabs for several undergraduate and a few graduate courses.

Graders are typically given a few days to grade an assignment, so the working hours of graders are flexible. The pay for all courses, except Math 244 and Math 251, is \$11-13 per hour per course (depending on the level); the work load is a total of 3-4 hours per week, on average. The time commitment for each Math 244 or Math 251 is 3 hours per week, on average.

Before applying, please ask yourself if you will realistically have time to take on this commitment. It is extremely important that all deadlines the professors set for completing the grading are met. If you are interested in being considered for this position, please complete the entire form below. Please note there is often considerable interest in these grading positions, so not every applicant could be hired. To be considered for a course, an applicant needs to have successfully completed the course (with an A grade) at Rutgers, and have a GPA of at least 3.4.

This Fall, we will be hiring graders for the following courses only:
103, 104, 106, 152H(only), 192
244, 250, 251, 252, 285, 291
300, 311, 321, 336, 350, 351, 354, 356, 361, 373
411, 421, 423, 428, 432, 435, 437, 441, 451, 454, 477, 478, 481, 485, 486
503, 527, 550

We will NOT hire graders for any other courses. Please do not request them.

The Fall 2019 application

To apply for a Grader position for any course in Fall 2019, please complete the Fall 2019 Grader application.

=============

** If you have any questions, please email Professor Mavrea at grader_coordinator@math.rutgers.edu.

*** Due to the large number of applications, only applicants who are selected will be contacted (via email).

## 01:640:350:H Linear Algebra Section

 H1 12832 Woodward, Christopher Lecture MW4 0140P-0300 HLL-009 BUS

## This course is a proof-based 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 0-13-008451-4.   For this section, any recent edition of the textbook should be sufficient.

• Class  MW4 0140P-0300 HLL-009 BUS
• Office Hours:  Tues 2-3 pm, Hill 726
• Contact Information:  e-mail 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 proof-writing 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 almost-weekly 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 self-reported 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.

Make-ups for exams are generally not given; if a student has an extremely good reason (e.g. documented medical emergency) I may re-arrange the grading scheme to accomodate.

Problem sets are due on most Tuesdays. There are no problems due on the two midterm-exam Tuesdays.

Note that we will cover significant material from all the chapters in the book, Chapters 1-7.

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

WeekLecture 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. 1-2  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.3,4,5,6  Review and Exam 2 (4/22)
14 4/24, 4/29 Chapter 7  Orthogonal diagonalization
15 5/1, 5/6 Chapter 7  Jordan canonical form
17 5/14 (Tues) 12-3pm Final Exam HILL 009

Main 350 course page

#### 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 re-scheduled.

### Special Accommodations

Students with disabilities requesting accommodations must follow the procedures outlined at https://ods.rutgers.edu/students/applying-for-services

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 hand-written in reasonably clear writing, with an explanation of any assistance given.   Type-written 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

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 pre-college students with a strong interest in mathematics.

## 01:640:350:04 Linear Algebra Section

 04 11407 Woodward, Christopher Lecture TF2 1020 A - 1140 BE-250 LIV

## This course is a proof-based 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 0-13-008451-4.   For this section 04, any recent edition of the textbook should be sufficient.

• Class  TF2 1020 A - 1140 BE-250 LIV
• Office Hours:  Monday 2:15-3:15pm, Hill 726
• Contact Information:  e-mail 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 proof-writing 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 almost-weekly 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 self-reported 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.

Make-ups for exams are generally not given; if a student has an extremely good reason (e.g. documented medical emergency) I may re-arrange the grading scheme to accomodate.

Problem sets are due on most Tuesdays. There are no problems due on the two midterm-exam Tuesdays.

Note that we will cover significant material from all the chapters in the book, Chapters 1-7.

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

WeekLecture 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. 1-2  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) 8-11am Final Exam Location TBA

Main 350 course page

#### 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 re-scheduled.

### Special Accommodations

Students with disabilities requesting accommodations must follow the procedures outlined at https://ods.rutgers.edu/students/applying-for-services

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 hand-written in reasonably clear writing, with an explanation of any assistance given.   Type-written 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

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

## 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 151-152-251, 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 4-credit format of the course, a a 5-credit format has been used for some of the sections, but only the 4-credit format is now being offered.

# 01:640:135 Schedule of Sections

This option will not work correctly. Unfortunately, your browser does not support inline frames.

Abstract:  The Bianchi-Egnell 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 Bianchi-Egnell 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 one-parameter family of sharp Gagliardo-Nirenberg (GN) inequalities and how this link can be used to derive a new stability estimate on the one-parameter 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.

# Joomla/HTML Tips & Tricks Page

This page is contains instructions to help faculty members with updating the Mathematics site.

+CourseCrCourse TitleCross Listing
+listingcreditstitlecrossSectionsPrint
+CourseCrCourse TitleCross Listing
+listingcreditstitlecrossSectionsPrint

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:

• Full-Credit proficiency. A student earning full-credit 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.)
Course X will not appear on the student's transcript and will not earn credits toward graduation.

#### Full-credit proficiency exams

Full-credit 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.

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:

• Full-Credit proficiency. A student earning full-credit 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.)
Course X will not appear on the student's transcript and will not earn credits toward graduation.

#### Full-credit proficiency exams

Full-credit 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.

### Prof. Weibel (640:350:H1) — Fall 2017

This course is a proof-based 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 0-13-008451-4.

• Lectures MW6 (5:00-6:20PM) in ARC 333
• Weibel's Office hours: Monday 1:30-2:45 PM; Wednesday 10:30AM-12 noon

#### Tentative Course Syllabus

WeekLecture 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. 1-2  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  Cayley-Hamilton
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) 4-7 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 F2, 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 T2=T3
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

### Schedule of Sections:

This page describes programs sponsored by the Department of Mathematics for pre-college 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 four-week 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.

### Mathematical Outreach for K-12 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.

Information about past Rutgers MSc. recipients can be found here.

Pre-history: 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 1870-1906. 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 1873-74; MSc 1874) and Albert S. Cook (BSc 1872; Tutor 1872-73; 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 1940-1959.

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 1961-1975) the graduate program in mathematics gradually built up to a steady graduation rate of 13 doctorates per year in the mid-1970'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 mid-1990'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 1951-Present

2015-2019: 31 Ph.D.'s TOP
Michael Breeling May 2019 Avy Soffer University of Toronto, Ontario, Canada
Matthew Charnley May 2019 Michael Vogelius Rutgers University, NJ
Joel Clingempeel May 2019 Gregory Moore  Google, Inc., Pittsburgh, PA
William Cole Franks May 2019 Michael Saks Massachusetts Institute of Technology, MA
Alejandro Ginory May 2019 Siddhartha Sahi University of Ottawa, Ontario, Canada
Abigail Raz May 2019 Jeffry Kahn University of Nebraska, Lincoln, NE
Daniel Scheinerman May 2019 Swastik Kopparty Center for Communications Research, Princeton, NJ
Matthew Welsh May 2019 Henryk Iwaniec  University of Bristol, England
Rebecca Coulson Jan 2019 Gregory Cherlin United States Military Academy, West Point, NY
Johannes Flake Oct 2018 Siddhartha Sahi Lehrstulh B fur Mathematik, Germany
Katie McKeon Oct 2018 Alex Kontorovich Center for Communications Research, Princeton, NJ
Sijian Tang Oct 2018 Michael Saks Facebook, Inc., Seattle, WA
Zhuohui Zhang Oct 2018 Stephen Miller Weizmann Institute of Science, Rehovot, Israel
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 Yi-Zhi 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 Technion-Israeli 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
Siao-Hao 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 Bar-Ilan 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 Yi-Zhi 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
Rutgers University, NJ
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 Urbana-Champaign
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

2010-2014: 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

2005-2009: 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. Wisconsin-Eau 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. Tahvildar-Zadeh 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 Urbana-Champaign
Michael Weingart May 2007 F. Knop Rutgers-New 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.

2000-2004: 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 Urbana-Champaign
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. Minas-Gervais/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 State-Northridge
Silvia Fernandez May 2001 J. Beck California State-Northridge
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)

### 1995-1999: 72 Ph.D.'s

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 Rutgers-IEEE project
Wanglai Li Oct. 1997 J. Lepowsky / R. Wilson Telecommunications industry
Richard Ng Oct. 1997 E. Taft Univ. of California-Santa 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 California-Santa 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)
J-Y 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 Alvarez-Paiva   1995 T. Petrie
Wen-Yun 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

1990-1994: 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 Sanje-Mpacko 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. Cronin-Scanlon
Gábor Francsics May 1992 F. Treves
Nigel Pitt May 1992 H. Iwaniec
Denise Sakai May 1992 F. Roberts (RUTCOR)
Xueqing Tang May 1992 A. Ben-Israel (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
Da-mu Cai Oct. 1991 R. Falk
Gustavo Comezana Oct. 1991 J. Shaneson
Brenda Latka Oct. 1991 G. Cherlin
Richard Rosengarten Oct. 1991 G. Cherlin
To Tze-ming Oct. 1991 N. Wallach
Barr Von Oehsen Oct. 1991 P. Landweber
Xianwen Xie Oct. 1991 R. Nussbaum
Chua Seng-Kee 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
Yi-Zhi 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

1980-1989: 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
Suh-Ryung 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
Yuh-Dong 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 Barry-Cozzens 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
Cheng-Shung Ko Jan. 1980 P. Hell
Ira L. Robbin Jan. 1980 E. Speer
Bernadette Tutinas Jan. 1980 D. Gorenstein

1970-1979: 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. Cronin-Scanlon

Max Ashkenazi Oct. 1978 J. Cronin-Scanlon
Nancy H. Baxter Oct. 1978 R. Nussbaum
Nan-hung Chen Oct. 1978 B. Osofsky
Karl Heinz Dovermann Oct. 1978 T. Petrie
Stephen Hoyle Oct. 1978 J. Cronin-Scanlon
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
Leh-Sheng Tang Oct. 1977 H. Sussmann
Adalberto Bergamasco June 1977 J. Barros-Neto
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 W-C Wong June 1977 B. Mitchell
Edward Conjura Jan. 1977 W. Petryshyn
Anna Silverstein Jan. 1977 J.C.E. Dekker

Edgar Becerra-Bertram Oct. 1976 J. Shaneson
Oscar Campoli Oct. 1976 N. Wallach
Janey Daccach Oct. 1976 P. Landweber
Linda Anne Grieco Oct. 1976 C. Sims
Shyn-Ling 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 Frota-Mattos Oct. 1975 R. Goodman
Leslie Jones   1975 P. Landweber
Gerard Kiernan Oct. 1975 D. Gorenstein
Hsiao-wei 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

Jui-Chi Chang Oct. 1974 D. Gorenstein
Ching-an 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. Barros-Neto
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
Philip Zipse Jun 1970 S. Leader
Douglas McCarthy Jan. 1970 J. Cronin-Scanlon

1961-1969: 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. Cronin-Scanlon
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
Chung-Lie 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

### 1951-1960: 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

Data before 1984 compiled by M. Jablonski. Data 1984-2005 compiled by C. Weibel.

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

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. 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.

• 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.
• Non-matriculated 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.

## Fall 2019 Special Permission Rounds

### Rounds of Special Permission

#### Round 1:

Begins: 12:01am, Friday, August 23
Ends: 4:00pm, Wednesday, August 28
Decision Date: 3:00pm, Friday, August 30

#### Round 2:

Begins: 4:00pm, Friday, August 30
Ends: 4:00pm, Thursday, September 5
Decision Date: 3:00pm, Saturday, September 7

#### Round 3:

Begins: 4:00pm, Saturday, September 7
Ends: 4:00pm, Monday, September 9
Decision Date: 3:00pm, Tuesday, September 10

NOTE:

Please be aware of the following:

Last day to DROP courses without a "W" is Tuesday, September 10, 2019

Last day to ADD courses is Wednesday, September 11, 2019

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 SystemEnter Here

Special Note: If you are unable to load the page when following the 'Enter Here' link, please clear your browser's cache and cookies, close the broswer, then re-open and try again.

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 web-based system.
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 e-mail 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.

### Re-taking Precalculus, Calculus I or Calculus II previously failed twice

Starting in Fall semester 2019, students who have failed Precalculus (111, 112, or 115), Calculus I (either 135 or 151) or Calculus II (either 135 or 151) twice can no longer take the course again at Rutgers New Brunswick.

Students who have failed any of these courses twice because of extenuating circumstances can request an exception by submitting an appeal.

The only appeal requests taken into consideration will be from students whose education has been affected by very special circumstances and can provide supporting documentation. At a minimum, the extenuating circumstances, medical or otherwise, must be shown to have affected the student's performance in all courses taken when the Precalculus or Calculus course was failed, and to account for that failure.

Students belonging to SOE or RBS should see their Dean to submit an appeal. Students from all other schools can submit an appeal by filling out this form and attaching any supporting documentation: https://www.math.rutgers.edu/index.php?option=com_chronoforms5&chronoform=Multiple_Fails_Special

With the approval of the department, undergraduates may take graduate courses, under three conditions.

1. There are no undergraduate courses in mathematics which are more appropriate for the student's program.
2. Prior achievement in undergraduate or graduate mathematics courses provides a clear indication of the student's ability to do well in graduate level work.
3. 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.

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 odd-numbered 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 even-numbered 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.

SECTIONPROBLEMS
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.

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 odd-numbered 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 even-numbered 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.

SECTIONPROBLEMS
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 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 publicly-available 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 CRM-Fields-PIMS 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/07-08/071206.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 (1784-1834) 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/inessa-epstein-ph-d-b0a92914 .

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 co-leads 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://econwikis-mborg.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 hands-on 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/our-staff/

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/

Jean-Michelet Jean-Michel "was born in Petit-Goave, 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 auto-parallel, multi-host, open source Python project, Pyfora. He has a PhD in mathematics from Columbia University, where he specialized in low-dimensional topology, using Heegaard Floer homology to compute invariants of manifolds, and has a BA in mathematics from Rutgers University." http://mlconf.com/mlconf-2016-atlanta/

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/press-release/

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/our-people/stephen-h-rosen.

Timothy Rudderow "co-founded 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 co-founder 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 Vice-Chair 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/who-we-are/larry-sher

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 PSU-Brandywine. 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/michael-yatauro

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 president-elect 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 UC-SD in 2016 and now enjoys an NSF Postdoc at the University of Pennsylvania. She graduated from SAS-Rutgers in 2009.

#### Selected Alumni/Alumnae of the Graduate Program

Roy Goldman is former Chief Actuary at Humana Inc.  http://press.humana.com/press-release/current-releases/humana-names-roy-goldman-vice-president-and-chief-actuary.

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 sought-after 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 Business-Higher 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/william-e-kirwan .

Zoltan Szabo is a Professor of mathematics at Princeton University. With Peter Ozsvath he created Heegaard Floer homology, a homology theory for 3-manifolds. 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‚Â­-15. 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/new-college-of-science-and-engineering-faculty-for-2015-16/.

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 Max-Planck-Institute in Bonn a number of times and a Bye-Fellow 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 Calabi-Yau 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 co-authored 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 German-American 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 1984-1985 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 Hodgkin-Huxley Neural Theory), as well as a textbook (Differential Equations: Introduction and Qualitative Theory)." From http://www.awm-math.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.

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 self-study.
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 978-1-319-04853-2
NJ Books: $$125.00. • E-book custom 3rd edition and WebAssign premium access code (for the duration of the 3rd edition) ISBN 978-1-319-04911-9 NJ Books:$$107.50

The 3rd edition is purchased with a WebAssign access code which will be used throughout the sequence 151-152-251. 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

{rucourse course = "01:640:152" semester = "92017"}

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 self-study.
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 978-1-319-04853-2
NJ Books: $$125.00. • E-book custom 3rd edition and WebAssign premium access code (for the duration of the 3rd edition) ISBN 978-1-319-04911-9 NJ Books:$$107.50

The 3rd edition is purchased with a WebAssign access code which will be used throughout the sequence 151-152-251. 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

{rucourse course = "01:640:152" semester = "92016"}

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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.

The Department of Mathematics at Rutgers-New 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. 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 Bartholomew Road. At the stop sign, turn left onto Brett Road. Follow Brett road until it vanishes in a maze of parking lots.  Visitors with guest permits may park in lot 64, 60A, 60B (or at lot 67 near Brett and Bartholomew Roads).  The Hill Center is the seven story dark brick building, located just behind the CORE building.   A lot for visitors without permits is available near the visitor's center on Busch campus.

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 (1-800-222-0492) 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: 1-800-USA-RAIL; NJ Transit: 1-800-772-2222 from NJ; from out of state: 1-973-762-5100.

Once you reach downtown New Brunswick you can get to the Hill Center by taxi in 10 minutes for approximately $$10.00, or by campus bus FREE, in about 10-20 minutes. Buses leave at 10 minute intervals. To reach a campus bus stop from the New Jersey Transit bus station on Albany Street, walk west on Albany St., then take the first right onto George Street and walk two blocks to the first traffic light. Turn left onto Hamilton Street, walk one block and you will see the campus bus shelter on your right across College Avenue. To reach the bus stop from the train station at Albany and Easton, walk uphill on Easton Ave. and turn right onto Hamilton Street at the second traffic light. Walk one block and you will see the campus bus shelter on your left. Take an "A", or "H" bus marked to Busch Campus and get off at the Hill Center. How to walk from the New Brunswick Train Station to the Hill Center on the Busch Campus of Rutgers University ### BY PLANE: The nearest airport is Newark Liberty International Airport. If you fly there, you can either 1. Take the Airtrain Newark directly from the arrivals terminal to the new Rail Link station and then connect with NJ Transit trains to New Brunswick. (cost is approximately$$16.)
2. Take a taxi or hired car (the cost is approximately $$60 plus tolls plus tip). 3. Rent a car. 4. Take the State Shuttle to the Hyatt Hotel in New Brunswick. Call 1-800-427-3207 for reservations. From Kennedy airport, the cost of a taxi could be as high as$$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 Busch-College Ave walkway]
First Version: Jan. 14, 2002.

Written By Doron Zeilberger.

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. [Note by editor:  Doron walks quickly.]

1. 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 left-hand side, walk to the end of College Avenue and enter Buccleuch park (about 12 min. walks).

2. 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.

3. 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):

1. 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"].
2. 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. Continue (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)

1. Follow that path. It ends at Johnson Drive. (about 5 minutes) Make a right on Johnson Drive.
2. Keep walking until you hit Landing Lane (3 minutes) after crossing Landing Lane (carefully!) make a right, staying on Landing Lane.
3. 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.)
4. 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)
5. 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)
6. 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 D-field 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)]