#### Directions to the Department

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 $$10.00, or by campus bus FREE, in about 10-20 minutes. Buses leave at 10 minute intervals. To reach a campus bus stop from the New Jersey Transit bus station on Albany Street, walk west on Albany St., then take the first right onto George Street and walk two blocks to the first traffic light. Turn left onto Hamilton Street, walk one block and you will see the campus bus shelter on your right across College Avenue. To reach the bus stop from the train station at Albany and Easton, walk uphill on Easton Ave. and turn right onto Hamilton Street at the second traffic light. Walk one block and you will see the campus bus shelter on your left. Take an "A", or "H" bus marked to Busch Campus and get off at the Hill Center.How to walk from the New Brunswick Train Station to the Hill Center on the Busch Campus of Rutgers University BY PLANE: The nearest airport is Newark Liberty International Airport. If you fly there, you can either Take the Airtrain Newark directly from the arrivals terminal to the new Rail Link station and then connect with NJ Transit trains to New Brunswick. (cost is approximately$$16.) Take a taxi or hired car (the cost is approximately $$60 plus tolls plus tip). Rent a car. From Kennedy airport, the cost of a taxi could be as high as$$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.] 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). Walk another minute on a path parallel to George St., and a little before the Buccleuch Mansion, make a right that leads to stairs. Walk down the stairs, and carefully cross George St. to the bike path/pedestrian walk on the Lynch bridge. After about two to three minutes you have a choice: turn left down to Johnson Drive and go the Old Way (see below, that takes 10 minutes longer) OR: New Way (June 2005): DONT's turn left (downhill), but go straight and continue on the bridge and follow the path all the way to the end [ 7 additional minutes]. This ends at Busch Campus Drive. Take a left and Walk a few steps to the corner of Busch Campus Drive and Sutphen Road. [the street sign just says "Campus Drive"]. Cross [Busch] Campus Drive at the crosswalk (carefully! the stupid cars go very fast and do not even slow down for you, even though they are supposed to give you the right of way) and make a left. 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) Follow that path. It ends at Johnson Drive. (about 5 minutes) Make a right on Johnson Drive. Keep walking until you hit Landing Lane (3 minutes) after crossing Landing Lane (carefully!) make a right, staying on Landing Lane. Walk on the shoulder until you hit the light at River Rd. (2 minutes). Push the button for crossing. When the light turns GREEN, Cross carefully (watching the cars that are turning left, it is your right of way, but you still have to be careful, the light is very short and the cars are impatient.) Now you are at the beginning of a steep uphill path that leads to the Stadium. You hit the Stadium at the Hale Center. (3 minutes) After you hit the stadium at Hale Center, walk on the sidewalk along the stadium. At the North Entrance, cross Sutphen Road on the crosswalk (carefully!), and make a left (1.5 minutes) After less than a minute you hit FITCH Rd., make a right on Fitch. On your left you will have a Golf course, and on your right you have first 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)]

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

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 Return to Weibel's Home Page   Schedule of Sections:

#### Proficiency Exams

Undergraduate Proficiency Examinations The Mathematics Department offers proficiency examinations for selected courses. Depending on the course, and their performance on the exam, students may earn one of two types of proficiency pass: 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.

#### Proficiency Exams

Undergraduate Proficiency Examinations The Mathematics Department offers proficiency examinations for selected courses. Depending on the course, and their performance on the exam, students may earn one of two types of proficiency pass: 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 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 course 250. Internal proficiency exams are occasionally offered for other courses in unusual situations. 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. 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. Additionally, a student who has was previously enrolled in Math 123 cannot take a proficiency exam in either of the Calculus I courses Math 135 or Math 151. 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 Math Placement Exam Incoming freshmen can demonstrate proficiency in courses 025, 026, and 115 by taking the math placement exam. After completing at least 8 hours of provided review activities, students can also take the placement exam a second time. The higher of the two scores is used to determine placement. In the past, the math department offered proficiency exams in courses 025, 026, and 115. These proficiency exams are no longer available, as students can now take the placement exam twice. There is no third attempt or any other way to circumvent the results of the placement exam. The placement exam may also be appropriate for certain transfer students and continuing students who have not taken any of the courses 025, 026, 111, 112, or 115 at Rutgers yet. Please contact the Math Advisor for advice about this. For technical assistance with the placement exam, please contact the Office of Testing and Placement.

#### 01:640:152 - TEST PAGE FALL 2017

Math 151–152 is the introductory year course in the calculus sequence in New Brunswick for majors in the mathematical sciences, the physical sciences, and engineering. The first semester, Math 151 or 153, presents the differential calculus of the elementary functions of a single real variable: the rational, trigonometric and exponential functions and their inverses; various applications via the Mean Value Theorem; and an introduction to the integral calculus. The second semester, Math 152, continues the study of the integral calculus, with applications, and covers the theory of infinite series and power series, touching on differential equations and a few other topics as well. Transitioning from Math 135 to Math 152: Students who intend to go directly from Math 135 to Math 152 will need to fill in some gaps through 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 152: Syllabus and Homework 152: Announcements and Review Sheets General Course Information for Math 151-152 (Spring 2017) Going from math 135 to math 152

#### 01:640:152 - TEST PAGE FALL 2016

Math 151–152 is the introductory year course in the calculus sequence in New Brunswick for majors in the mathematical sciences, the physical sciences, and engineering. The first semester, Math 151 or 153, presents the differential calculus of the elementary functions of a single real variable: the rational, trigonometric and exponential functions and their inverses; various applications via the Mean Value Theorem; and an introduction to the integral calculus. The second semester, Math 152, continues the study of the integral calculus, with applications, and covers the theory of infinite series and power series, touching on differential equations and a few other topics as well. Transitioning from Math 135 to Math 152: Students who intend to go directly from Math 135 to Math 152 will need to fill in some gaps through 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 152: Syllabus and Homework 152: Announcements and Review Sheets General Course Information for Math 151-152 (Spring 2017) Going from math 135 to math 152

#### Joomla Tips

Joomla/HTML Tips & Tricks Page        This page is contains instructions to help faculty members with updating the Mathematics site. HOWTO-add-document.txt HOWTO-update-course-information-file-link-in-Joomla.txt Accessing Webassign through Sakai WebAssign - Guide for Instructors/Coordinators

#### Test Page iframe

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

#### JExtBOX test

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 $\dot^1$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 $\frac+\frac=1$test equation.

#### Homework - Fall 2018 - Draft

Here is the official list of homework problems from the 7th edition of the Kendall Hunt text. THE FINAL EXAM WILL ASSUME FAMILIARITY WITH THE MATERIAL COVERED BY THESE PROBLEMS.  THESE HOMEWORK PROBLEMS CONSTITUTE YOUR MAIN STUDY GUIDE FOR MATH 135. The exercises are listed by section of the book.  See the Lecture Topics page to determine which sections go with which lectures. The answers (not solutions) to the 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.

#### Courses - Calculus I - Fall 2018 - draft

Courses 01:640:135 - Calculus I Textbook:  For current textbook please refer to our Master Textbook List page Math 135 provides an introduction to calculus. It is taken primarily by students interested in the biological sciences, business, economics, and pharmacy. Math 135 may be followed by Math 136. There is another calculus sequence, Math 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. Course Materials Spring 2018 Previous Semesters Fall 2017 Spring 2017 Fall 2016 Spring 2016 Fall 2015 Spring 2015 Fall 2014 Spring 2014 Fall 2013 Spring 2013 Fall 2012 Spring 2012 Fall 2011 Spring 2011 Fall 2010 Spring 2010 Fall 2009     Instructors' web pages Summer 2009 Spring 2009 Schedule of Sections 01:640:135 Schedule of Sections This option will not work correctly. Unfortunately, your browser does not support inline frames.

#### Michael Weingart's homepage

Michael Weingart Associate Teaching Professor of Mathematics weingart [at] math [dot] rutgers [dot] edu      Fall 2018 Teaching: Math 104:01 Introduction to Probability Math 104:03 Introduction to Probability

#### Homework - Fall 2018 - Draft with correct frame

Here is the official list of homework problems from the 7th edition of the Kendall Hunt text. THE FINAL EXAM WILL ASSUME FAMILIARITY WITH THE MATERIAL COVERED BY THESE PROBLEMS.  THESE HOMEWORK PROBLEMS CONSTITUTE YOUR MAIN STUDY GUIDE FOR MATH 135. The exercises are listed by section of the book.  See the Lecture Topics page to determine which sections go with which lectures. The answers (not solutions) to the 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.

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#### Preparing for the First Semester Core Courses

The three core graduate mathematics courses normally taken in the first semester are: 640:501 Theory of Functions of a Real Variable I (Offered every fall) (Outline of topics) 640:551 Abstract Algebra I (Offered every fall) (Outline of topics) 640:503 Theory of Functions of a Complex Variable I (Offered every fall) (Outline of topics) Here are links to information about the preparation expected of students entering 640:501, 640:503 and 640:551. Students are encouraged to review this material in the months before the semester begins.

#### The Rutgers Math Ph.D. program ranked highly in the recent National Research Council Study

The National Research Council recently announced the results of its extensive Assessment of Research Doctorate Programs . The NRC study data were collected in 2006 and concerned with the period of several years prior to 2006. Concerning our Ph.D. program here at Rutgers: the NRC study recognizes the general excellence of our program. Among 127 mathematics PhD programs nationwide, our overall rankings based on two different methods are: Regression based, 12-36; Survey based, 14-41. The study also provided separate rankings for the following sub-categories: Research, 10-30; Student Outcomes, 36-96; Important: read more on student outcomes Diversity, 55-89.  As is evident this NRC study does not produce a single, linear ranking of program qualities. It uses a sophisticated, statistics based methodology. Here is a brief explanation of the NRC ranking methodology, andhere contains a detailed description by NRC of the NRC ranking methodology. The numbers provided in each rating reflects the range between the 5th and the 95th percentile of our rankings.  One way to extract linear orderings of all programs from the NRC data would be to compare their rankings at the 5th and 95th percentile. For the Regression-based Overall Ranking the data in the NRC Study shows that there are 17 programs ranked above Rutgers at the 5th percentile and 15 programs ranked above Rutgers at the 95th percentile. For the Survey-based Overall Ranking there are 24 programs ranked above at both percentiles. The NRC data give our program high marks for Percent Faculty with Grants; Citations per Publication; Publications per Allocated Faculty; Percent 1st yr Student w/ Full Support (100%); Percent Non-Asian Minority Faculty; Percent International Students. Our lower rankings on Student Outcomes are based on below average scores in the NRC study on Percent Completing within 6 Years and on Percent Students in Academic Positions . We are proud of our record in both of these areas, and believe the statistics reported in the NRC study do not provide an accurate picture of our program. Here is a link that discusses the graduation rate within our Ph.D. program Here is a link that discusses the success of our graduates in finding academic employment.

#### The PhD completion data of the Rutgers Math Ph.D. program since 1995

The PhD completion data of the Rutgers Math Ph.D. program since 1995 Mathematics Graduate Program   Entry YearSize of entering class# of PhDs completed# of PhDs completed by May of 6th year of entry# of PhDs completed by October of 6th year of entryPhD completion rate# of students who left with MS 1995 10 8 7 7 80% 2 1996 13 8 6 7 61.5% 3 1997 14 10 4 6 71.4% 2 1998 18 10 6 7 55.6% 2 1999 16 15 12 14 93.4% 1 2000 12 4 3 3 33.3% 1 2001 13 10 9 9 76.9% 1 2002 11 8 4 6 72.7% 1 2003 16 13 8 11 81.2% 1 2004 17 14 6 8 82.3% 1 2005 13 7 7 7 53.8% 1 2006 14 13 6 8 92.8% 1 2007 17 16 7 9 94.1% 1 2008 12 11 6 8 92.3% 1 2009 13 9 7 8 69.2% 2 2010 17 11 9 11 (2 still active) ≥ 64.7% 1 Total 218 167 107 129 ≥ 76.6% 22 The data in the table above lists students by their year of entrance. Another way to analyze completion data is to examine the completion time of recent PhD graduates. Of the 69 Ph.D.'s completed between Jan. 2005 and Oct. 2011, 30 completed in 5 years or less, 54 completed in 6 years or less. The average completion time is 5.73 years, 43.5% of them completed within 5 years, and over 78% completed within 6 years.

#### Syllabus of the SPP Algebra Program

To provide an in-depth  review and to fill in gaps in some background material in Abstract Linear Algebra, which is often presumed in standard first year graduate courses. The material to be covered is also part of the syllabus of the qualifying exams on Algebra. Below is a tentative list of topics to be covered; the actural coverage may vary depending on the instructor. Vector spaces, isomorphism, linear transformations: basis, dimension, quotient spaces, direct sums, rank and nullity. Coordinatization. Examples from various places: geometry, linear ODE, quantum mechanics, graph theory, etc. Similarity, eigenvalues, diagonalization, Jordan canonical form, application to ODE's and other areas, Rational canonical form. Role of the ground field (or extended ground field):  In particular applications involving linear operators on vector spaces over the complex field (E.g. Jordan canonical form) Bilinear forms, sesquilinear forms, nondegeneracy, Euclidean and Unitary inner products. Some detailed study of  Hermitian and unitary matrices, in particular, diagonalization involving  Hermitian and unitary matrices. Basic properties of orthogonal and unitary groups. Self-adjoint linear transformations. Duality, esp. finite-dimensional case. Additional topics, if time permits: tensor product defined by naming basis, symmetric and wedge square, higher powers, determinants, Kronecker product, $$V^*\otimes W$$, differential forms,  Schur duality.

#### Syllabus of the SPP Analysis Program

This program aims to provide an in-depth  review and to fill in gaps in some background material in Advanced Calculus expected in standard first year graduate courses. The material to be covered is also part of the syllabus of the qualifying exams on the subjects of  Real Variables and Elementary Point-Set Topology and Complex Variables and Advanced Calculus. Below is a tentative list of topics to be covered; the actual coverage varies depending on instructor. Basic properties of the reals: Limits (including upper and lower limits), Cauchy sequences, completeness, sequential compactness (Bolzano–Weierstrass theorem) and compactness (Heine-Borel Theorem). Basic tools: Cauchy-Schwarz inequality. Summation (integration) by parts. Sequences and series of numbers and functions, including absolute and uniform convergence, and equicontinuity. Applications involving power series, integration and differentiation. Basic topological notions such as connectivity, Hausdorff spaces, compactness, product spaces and quotient spaces. Emphasis on  examples in Euclidean and metric spaces. Compactness criteria in metric spaces. Arzelà–Ascoli Theorem and applications. Review of multiple, line and surface integrals, theorems of Green and Stokes and the divergence theorem. Jacobians, implicit and inverse function theorems, and applications. Change of variables formula. Role of exterior calculus.

#### Master's Degree Essays and Theses

Master's Theses  NameDate Advisor PDF  Dennis Hou  May 2021  James Lepowsky  PDF

#### Erdős Institute

The Erdős Institute is a multi-university collaboration focused on helping PhDs get jobs they love at every stage of their career. Founded in 2017, the Institute helps train and place a diverse pool of graduate students, postdocs, and graduate alumni. Rutgers School of Arts and Sciences is an academic member institution; all SAS graduate students, postdocs, and graduate alumni have free access to all of the programming and resources that the Institute provides. Examples include the "Invitation to Industry" seminar series, Data Science Bootcamps, Alumni-Led Mini-Courses, Interview Prep Workshops, and Career Coaching. Please visit https://www.erdosinstitute.org/ to enroll.

#### Research Centers

Centers with Contacts in the Mathematics Department

#### Gelfand Memorial

I. M. Gelfand 1913 – 2009 Memorial – December 6, 2009  Program Written versions of remarks presented at the Memorial  Tatiana V. Gelfand  Casimir Kulikowski  Dusa McDuff Other statements prepared for the Memorial  Yuri I. Arshavsky  Michael Atiyah  E. B. Dynkin  D. B. Fuchs  Roger Howe  Peter Lax  Leonid Margolis  Louis Nirenberg  Nikita Nekrasov  Peter Sarnak  Vera Serganova  Alexander Shen  Alik Wajnberg        Biographical sketch by Simon Gindikin (1991)  Essay on the Moscow Gelfand Seminar by Simon Gindikin (1993)  Remarks by I. M. Singer (1993) Photographs  Portrait from Family, Rutgers Photo (1993), At Blackboard, Portrait 1982 (from collected works) With Kister and Gabrielov, With Reutenauer Link to Israel Moiseevich Gelfand Website (maintained by Tatiana V. Gelfand and Tatiana I. Gelfand)   Though the content referenced heretofore is now hosted by the Mathematics Department, requests for additions to this page should be made to Dr. Robert Wilson.

#### Dean Jacqueline B. Lewis Memorial Lectures

The 2018 Jacqueline B. Lewis Memorial Lecturer is Camillo De Lellis Institute for Advanced Study, Princeton, NJ 26th Jacqueline B. Lewis Memorial Lectures Open to the Public – Use Lots 60A or 64 behind Hill Center For a Parking Permit, call 848-445-6991 Dates Wednesday, October 24   |   Thursday, October 25   |   Friday, October 26 Professor Jacqueline B. Lewis was a mathematician and former Dean of Rutgers' University College in New Brunswick who died in 1982 after a career spanning nearly 20 years at Rutgers. She served as an Associate Dean of University College from 1974 to 1978 and as Vice Dean of the school from 1978 to 1981, when she was appointed Dean. She also served as Acting Dean of the Faculty of Professional Studies from June 1981 to September 1982. The lectures were endowed in 1983 by a gift from Dean Lewis' aunt, Lillian Nassau. Previous Lewis Lectures LecturerDateTitle Nolan Wallach October 2015 Basic Geometric Invariant Theory I, IISome Applications of Geometric Invariant Theory Yum-Tong Siu December 2013 The Complex Neumann Problem and Multiplier Ideal Sheaves Methods of Partial Differential Equations in Complex Algebraic Geometry Analytic Methods of Constructing Bundle Sections and their Geometric Applications Jennifer Tour Chayes November 2010 The Mathematics of Dynamic Random Networks Andrei Zelevinsky April 2010* Introduction to Cluster Algebras Cluster Algebras of Finite Type and their Geometric Realizations Quivers with Potentials and Generalized Reflection Functors * – Postponed from 2009 Terence Tao March 2008 Szemerédi's Regularity Lemma Revisited Three Lectures on Discrete Random Matrices:   Singularity and Determinant of Discrete Random Matrices   The Least Singular Value of Discrete Random Matrices   Eigenvalue Distributions of Discrete Random Matrices Andrei Okounkov April 2007 Moduli of Curves and Combinatorics Shmuel Weinberger October 2004 Themes in Quantitative Topology:   Problems and naive examples   Computation, entropy, and variational problems   Embeddings, symmetry, and rigidity Jean-Michel Coron October 2003 Controllability and nonlinearity for some flow control systems Richard P. Stanley October 2002 Six Recent Developments in Algebraic Combinatorics:   The Laurent phenomenon; longest increasing subsequences   The Saturation Conjecture; the n! Conjecture   Gromov-Witten invariants; graphical degree sequences Graeme Segal April 2001 The Mathematical Structure of Quantum Field Theory; Quantum Field Theory and K-Theory; Quantum Field Theory and Representation Theory Yves Meyer March 2000 Wavelets and Image Processing: Theory and Application to Denoising   Hubble Space Telescope Images; Oscillations, Vibrations, Time-Frequency Analysis and the Virgo Program   (Detection of Gravitati onal Waves); The Role of Oscillations in Some Non-Linear Evolution Equations:   Application to Navier-Stokes Equations Don Zagier March 1997 Modular Forms and Differential Operators Alain Connes April 1996 Gravity Coupled with Matter and the Foundation of Noncommutative Geometry Karen Uhlenbeck September 1994 Moduli Spaces of Solutions to PDE V. I. Arnold November 1993 On Some Problems in Singularity Theory Ian Macdonald March 1993 Symmetric Functions and Orthogonal Polynomial L. Craig Evans March 1992 Compactness for Solutions of Nonlinear Partial Differential Equations Jurgen Moser March 1991 Stability in Dynamics and Minimal Solutions in the Calculus of Variations Yasha G. Sinai April 1990 Random Behavior of Eigenvalues of Laplacians Paul Rabinowitz April 1989 Periodic Solutions of Hamiltonian Systems H. Blaine Lawson April 1988 Algebraic Cycles David Kazhdan March 1987 Representations of Reductive P-Adic Groups Lipman Bers October 1985 Teichmüller Theory for Beginners G. D. Mostow March 1985 Braids, Hypergeometric Functions, and Lattices Stephen Smale March 1984 The Topology of Classical Algorithms

#### Memorial for Felix E. Browder

Memorial for Felix E. Browder Flyer

#### Nonlinear Analysis and PDE Seminar

Joint Princeton-Rutgers Seminar on Geometric PDE's Spring 2017 (Organizers on Rutgers side: Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song; Organizer on Princeton side: Alice Chang }   April 18, 2017, 1:40pm, Hill 705, Rutgers University Speaker: Philip Isett, MIT Title: A Proof of Onsager's Conjecture for the Incompressible Euler Equations Abstract: In an effort to explain how anomalous dissipation of energy occurs in hydrodynamic turbulence, Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations may fail to exhibit conservation of energy if their spatial regularity is below 1/3-Holder. I will discuss a proof of this conjecture that shows that there are nonzero, (1/3-\epsilon)-Holder Euler flows in 3D that have compact support in time. The construction is based on a method known as "convex integration," which has its origins in the work of Nash on isometric embeddings with low codimension and low regularity. A version of this method was first developed for the incompressible Euler equations by De Lellis and Szekelyhidi to build Holder-continuous Euler flows that fail to conserve energy, and was later improved by Isett and by Buckmaster-De Lellis-Szekelyhidi to obtain further partial results towards Onsager's conjecture. The proof of the full conjecture combines convex integration using the "Mikado flows" introduced by Daneri-Szekelyhidi with a new "gluing approximation" technique. The latter technique exploits a special structure in the linearization of the incompressible Euler equations.     April 18, 2017, 3:00pm, Hill 705, Rutgers University Speaker: Matthew J. Gursky, University of Notre Dame Title: Some existence and non-existence results for Poincare-Einstein metrics Abstract: I will begin with a brief overview of the existence question for conformally compact Einstein manifolds with prescribed conformal infinity. After stating the seminal result of Graham-Lee, I will discuss a non-existence result (joint with Qing Han) for certain conformal classes on the 7-dimensional sphere. I will also mention some ongoing work (with Gabor Szekelyhidi) on a version of "local existence" of Poincare-Einstein metrics.   Joint Princeton-Rutgers Seminar on Geometric PDE's ---- Fall 2016 (Organizers on Rutgers side: Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song; Organizer on Princeton side: Alice Chang }   October 21, 2016, 2:00pm, Princeton - Fine Hall 224 Speaker: Yanyan Li, Rutgers University Title: Blow up analysis of solutions of conformally invariant fully nonlinear elliptic equations Abstract: We establish blow-up profiles for any blowing-up sequence of solutions of genera l conformally invariant fully nonlinear elliptic equations on Euclidean domains. We prove that (i) the distance between blow-up points is bounded from below by a universal positive number, (ii) the solutions are very close to a single stand ard bubble in a universal positive distance around each blow-up point, and (iii) the heights of these bubbles are comparable by a universal factor. As an applic ation of this result, we establish a quantitative Liouville theorem. This is a joint work with Luc Nguyen.     October 21, 2016, 3:30pm, Princeton - Fine Hall 224 Speaker: Yi Wang, Johns Hopkins University Title: A fully nonlinear Sobolev trace inequality Abstract: The $k$$-Hessian operator$$sigma_k$$is the$$k$$-th elementary symmetric function of the eigenvalues of the Hessian. It is known that the$$k$$-Hessian equation$$sigma_k(D^2 u)=f$$with Dirichlet boundary condition$$u=0$$is variational; indeed, this problem can be studied by means of the$$k$$-Hessian energy$$int -u sigma_k(D^2 u)$$. We construct a natural boundary functional which, when added to the$$k$$-Hessian energy, yields as its critical points solutions of$$k$$-Hessian equations with general non-vanishing boundary data. As a consequence, we prove a sharp Sobolev trace inequality for$$k$$-admissible functions$$u$$which estimates the$$k$$-Hessian energy in terms of the boundary values of$$u$$. This is joint work with Jeffrey Case. Joint Princeton-Rutgers Seminar on Geometric PDE's ---- Spring 2016 (Organizers on Rutgers side: Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song; Organizer on Princeton side: Alice Chang } April 5, 2016, 4:00pm Hill 705 Speaker: Changfeng Gui, University of Connecticut Title: Moser-Trudinger type inequalities, mean field equations and Onsager vortices Abstract: In this talk, I will present a recent work confirming the best constant of a Moser-Trudinger type inequality conjectured by A. Chang and P. Yang. The proof is based on a new and powerful lower bound of total mass for mean field equations. Other applications of the lower bound include the classification of certain Onsager vortices on the sphere, the radially symmetry of solutions to Gaussian curvature equation on the plane, classification of solutions for mean field equations on tori and the sphere, etc. The resolution of several interesting problems in these areas will be presented. The work is jointly done with Amir Moradifam from UC Riverside. April 5, 2016, 5:15pm, Hill 705 Speaker: Jacob Bernstein, Johns Hopkins University Title: Hypersurfaces of low entropy Abstract: The entropy is a natural geometric quantity introduced by Colding and Minicozzi and may be thought of as a rough measure of the complexity of a hypersurface of Euclidean space. It is closely related to the mean curvature flow. On the one hand, the entropy controls what types of singularities the flow develops. On the other, the flow may be used to study the entropy. In this talk I will survey some recent results with Lu Wang that show that hypersurfaces of low entropy can't be too complicated. Joint Princeton-Rutgers Seminar on Geometric PDE's ---- Fall 2015 (Organizers on Rutgers side: Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song; Organizer on Princeton side: Alice Chang } Oct. 16, 2015, Friday, 3:00pm, Fine Hall 314, Princeton University Speaker: Andrea Malchiodi, Scuola Normale Superiore Title: Embedded Willmore tori in three-manifolds with small area constraint Abstract: While there are lots of contributions on Willmore surfaces in the three-dimensional Euclidean space, the literature on curved manifolds is still relatively limited. One of the main aspects of the Willmore problem is the loss of compactness under conformal transformations. We construct embedded Willmore tori in manifolds with a small area constraint by analyzing how the Willmore energy under the action of the Mobius group is affected by the curvature of the ambient manifold. The loss of compactness is then taken care of using minimization arguments or Morse theory. Oct. 16, 2015, Friday, 4:15pm, Fine Hall 314, Princeton University Speaker: Daniela De Silva, Columbia University Title: The two membranes problem Abstract: We will consider the two membranes obstacle problem for two different operators, possibly non-local. In the case when the two operators have different orders, we discuss how to obtain$$C^$$regularity of the solutions. In particular, for two fractional Laplacians of different orders, one obtains optimal regularity and a characterization of the boundary of the coincidence set. This is a joint work with L. Caffarellii and O. Savin. Joint Princeton-Rutgers Seminar on Geometric PDE's ---- Spring 2015 (Organizers on Rutgers side: Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song; Coordinator on Princeton side: Antonio Ache} May 5, 2015, Tuesday, 4:00pm, Hill 705, Rutgers University Speaker: Gregory Seregin, The University of Oxford Title: Ancient solutions to Navier-Stokes equations Abstract: In the talk, I shall try to explain the relationship between the so-called ancient (backwards) solutions to the Navier-Stokes equations in the space or in a half space and the global well-posedness of initial boundary value problems for these equations. Ancient solutions itself are an interesting part of the the theory of PDE's. Among important questions to ask are classification, smoothness, existence of non-trivial solutions, etc. The latter problem is in fact a Liouville type theory for non-stationary Navier-Stokes equations. The essential part of the talk will be addressed the so-called mild bounded ancient solutions. The Conjecture is that {\it any mild bounded ancient solution is a constant}, which should be identically zero in the case of the half space. The validity of the Conjecture would rule out Type I blowups that have the same kind of singularity as possible self-similar solutions. I am going to list known cases for which the Conjecture has been proven: the Stokes system, the 2D Navier-Stokes system, axially symmetric solutions in the whole space. Very little is known in the case of the half space. Other type of ancients solutions to the Navier-Stokes equations will be mentioned as well. May 5, 2015, Tuesday, 5:15pm, Hill 705, Rutgers University Speaker: Fernando Marques, Princeton University Title: Multiparameter sweepouts and the existence of minimal hypersurfaces Abstract: It follows from the work of Almgren in the 1960s that the space of unoriented closed hypersurfaces, in a compact Riemannian manifold M, endowed with the flat topology, is weakly homotopically equivalent to the infinite dimensional real projective space. Together with Andre Neves, we have used this nontrivial structure, and previous work of Gromov and Guth on the associated multiparameter sweepouts, to prove the existence of infinitely many smooth embedded closed minimal hypersurfaces in manifolds with positive Ricci curvature and dimension at most 7. This is motivated by a conjecture of Yau (1982). We will discuss this result, the higher dimensional case and current work in progress on the problem of the Morse index. March 27, 2015, Friday, 3:00pm, Room 314, Fine Hall, Princeton University Speaker: William Minicozzi, MIT Title: Uniqueness of blowups and Lojasiewicz inequalities Abstract: The mean curvature flow (MCF) of any closed hypersurface becomes singular in finite time. Once one knows that singularities occur, one naturally wonders what the singularities are like. For minimal varieties the first answer, by Federer-Fleming in 1959, is that they weakly resemble cones. For MCF, by the combined work of Huisken, Ilmanen, and White, singularities weakly resemble shrinkers. Unfortunately, the simple proofs leave open the possibility that a minimal variety or a MCF looked at under a microscope will resemble one blowup, but under higher magnification, it might (as far as anyone knows) resemble a completely different blowup. Whether this ever happens is perhaps the most fundamental question about singularities. We will discuss the proof of this long standing open question for MCF at all generic singularities and for mean convex MCF at all singularities. This is joint work with Toby Colding. March 27, 2015, Friday, 4:15pm, Room 314, Fine Hall, Princeton University Speaker: Luis Silvestre, University of Chicago Title:$$C^$$regularity for the parabolic homogeneous p-Laplacian equation Abstract: It is well known that p-harmonic functions are$$C^$$regular, for some$$\alpha>0$$. The classical proofs of this fact uses variational methods. In a recent work, Peres and Sheffield construct p-Harmonic functions from the value of a stochastic game. This construction also leads to a parabolic versions of the problem. However, the parabolic equation derived from the stochastic game is not the classical parabolic p-Laplace equation, but a homogeneous version. This equation is not in divergence form and variational methods are inapplicable. We prove that solutions to this equation are also$$C^$$regular in space. This is joint work with Tianling Jin. Joint Princeton-Rutgers Seminar on Geometric PDE's ---- Fall 2014 (Organizers on Rutgers side: Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song; Coordinator on Princeton side: Antonio Ache} Dec. 4, 2014, Thursday, 4:30pm, Fine 214, Princeton University Speaker: Sigurd Angenent, University of Wisconsin, Madison Title: Mean Curvature Flow of Cones Abstract: For smooth initial hypersurfaces one has short time existence and uniqueness of solutions to Mean Curvature Flow. For general initial data Brakke showed that varifold solutions exist, but that they need not be unique if the initial data are non smooth. In this talk I will discuss the multitude of solutions to MCF that exist if the initial hypersurface is a cone that is smooth except at the origin. Some of the examples go back to older work with Chopp, Ilmanen, and Velazquez, other examples are recent. Dec. 4, 2014, Thursday, 5:30pm, Fine 214, Princeton University Speaker: John Lott, University of California, Berkeley, Title: Geometry of the space of probability measures Abstract: The space of probability measures, on a compact Riemannian manifold, carries the Wasserstein metric coming from optimal transport. Otto found a remarkable formal Riemannian metric on this infinite-dimensional space. It is a challenge to make rigorous sense of the ensuing formal calculations, within the framework of metric geometry. I will describe what is known about geodesics, curvature, tangent spaces (cones) and parallel transport. Oct. 8, 2014, Weds., 4:45pm, Hill 705 Speaker: Panagiota Daskalopoulos, Columbia University Title: Ancient solutions to geometric flows Abstract: We will discuss ancient or eternal solutions to geometric parabolic partial differential equations. These are special solutions that appear as blow up limits near a singularity. They often represent models of singularities. We will address the classification of ancient solutions to geometric flows such as the Mean Curvature flow, the Ricci flow and the Yamabe flow, as well as methods of constructing new ancient solutions from the gluing of two or more solitons. We will also include future research directions. Oct. 8, 2014, Weds., 5:45pm, Hill 705 Speaker: Lan-Hsuan Huang, University of Connecticut Title: Geometry of asymptotically flat graphical hypersurfaces in Euclidean space Abstract: We consider a special class of asymptotically flat manifolds of nonnegative scalar curvature that can be isometrically embedded in Euclidean space as graphical hypersurfaces. In this setting, the scalar curvature equation becomes a fully nonlinear equation with a divergence structure, and we prove that the graph must be weakly mean convex. The arguments use some intriguing relation between the scalar curvature and mean curvature of the graph and the mean curvature of its level sets. Those observations enable one to give a direct proof of the positive mass theorem in this setting in all dimensions, as well as the stability statement that if the ADM masses of a sequence of such graphs approach zero, then the sequence converges to a flat plane in both Federer-Flemings flat topology and Sormani-Wenger's intrinsic flat topology. Joint Princeton-Rutgers Seminar on Geometric PDE's ---- Spring 2014 (Organizers on Rutgers side: Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song; Coordinator on Princeton side: Antonio Ache} April 30, 2014, Weds., 2:00pm, Jadwin A06, Princeton University Speaker: Fanghua Lin, Courant Institute Title: Large N asymptotics of Optimal partitions of Dirichlet eigenvalues Abstract: In this talk, we will discuss the following problem: Given a bounded domain . i n R^n, and a positive energy N, one divides . into N subdomains, .j,j=1,2,...,N. We consider the so-called optimal partitions that give the least possible value for the sum of the first Dirichelet eigenvalues on these sumdomains among all a dmissible partitions of$$\Omega$$. April 30, 2014, Weds., 3:15pm, Jadwin A06, Princeton University Speaker: Bruce Kleiner, Courant Institute Title: Ricci flow through singularities Abstract: It has been a long-standing problem in geometric analysis to find a good definition of generalized solutions to the Ricci flow equation that would formalize the heuristic idea of flowing through singularities. I will discuss a notion in the 3-d case that has good analytical properties, enabling one to prove existence and compactness of solutions, as well as a number of structural results. It may also be used to partly address a question of Perelman concerning the convergence of Ricci flow with surgery to a canonical flow through singularities. This is joint work with John Lott. March 11, 2014, Tuesday, 4:45pm, Hill 525, Rutgers University Speaker: Peter Constantin, Princeton University Title: Long time behavior of forced 2D SQG equations Abstract: We prove the absence of anomalous dissipation of energy for the forced critical surface quasi-geostrophic equation (SQG) in {\mathbb }^2 and the existence of a compact finite dimensional golbal attractor in {\mathbb T}^2. The absence of anomalous dissipation can be proved for rather rough forces, and employs methods that are suitable for situations when uniform bounds for the dissipation are not available. For the finite dimensionality of the attractor in the space-periodic case, the global regularity of the forced critical SQG equation needs to be revisited, with a new and final proof. We show that the system looses infinite dimensional information, by obtaining strong long time bounds that are independent of initial data. This is joint work with A. Tarfulea and V. Vicol. March 11, 2014, Tuesday, 5:45pm, Hill 525, Rutgers University Speaker: Mihalis Dafermos, Princeton University Title: The linear stability of the Schwarzschild solution under gravitational perturbations in general relativity Abstract: I will discuss joint work with G. Holzegel and I. Rodnianski showing the linear stability of the celebrated Schwarzschild black hole solution in general relativity. Joint Princeton-Rutgers Seminar on Geometric PDE's ---- Fall 2013 (Organizers on Rutgers side: Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song; Coordinator on Princeton side: Luc Nguyen) Tuesday, Dec. 3, 4:30pm, Hill 705, Rutgers University Speaker: Gaoyong Zhang, Polytechnic Institute of New York University Title: The logarithmic Minkowski problem Abstract: The logarithmic Minkowski problem asks for necessary and sufficient conditions in order that a nonnegative finite Borel measure in (n-1)-dimensional projective space be the cone-volume measure of the unit ball of an n-dimensional Banach spa ce. The solution to this problem is presented. Its relation to conjectured geometric inequalities that are stronger than the classical Brunn-Minkowski inequality will be explained. Tuesday, Dec. 3, 5:30pm, Hill 705, Rutgers University Speaker: Sergiu Klainerman, Princeton University Title: On the Reality of Black Holes Friday, Oct. 4, 4:15pm, Fine Hall 110, Princeton University Speaker: Natasa Sesum, Rutgers University Title: Yamabe flow, its singularity profiles and ancient solutions Abstract: We will discuss conformally flat complete Yamabe flow and show that in some case s we can give the precise description of singularity profiles close to the extin ction time of the solution. We will also talk about a construction of new compac t ancient solutions to the Yamabe flow. This is a joint work with Daskalopoulos, King and Manuel del Pino Friday, Oct. 4, 3:00pm, Fine Hall 110, Princeton University Speaker: Jeff Viaclovsky, University of Wisconsin-Madison Title: Critical metrics on connected sums of Einstein four-manifolds Abstract: I will discuss a gluing procedure designed to obtain canonical metrics on connected sums of Einstein four-manifolds. The main application is an existence result, using two well-known Einstein manifolds as building blocks: the Fubini-Study metric on CP^2, and the product metric on S^2 x S^2. Using these metrics in various gluing configurations, critical metrics are found on connected sums for a specific Riemannian functional, which depends on the global geometry of the factors. This is joint work with Matt Gursky. Joint Princeton-Rutgers Seminar on Geometric PDE's ---- Spring 2013 (Organizers on Rutgers side: Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song; Coordinator on Princeton side: Luc Nguyen) Tuesday, April 23, 5:30pm, Hill 425, Rutgers University Speaker: Camillo De Lellis, Zurich Title: Quantitative rigidity estimates Abstract: For many classical rigidity questions in differential geometry it is natural to ask to which extent they are stable. I will review several recent results in the literature. A typical example is the following: there is a constant$$C$$such th at, if$$Sigma$$is a$$2$$-dimensional embedded closed surface in$$R^3$$, then$$min_ lambda |A- lambda g|_ leq C |A - g/2|_$$, where$$A$$is the se cond fundamental form of the surface and$$g$$the Riemannian metric as a submanif old of$$R^3$$. Tuesday, April 23, 4:30pm, Hill 425, Rutgers University Speaker: Xiaochun Rong, Rutgers University Title: Degenerations of Ricci Flat Kahler Metrics under extremal transitions and flops Abstract: We will discuss degeneration of Ricci-flat Kahler metrics on Calabi-Yau manifold s under algebraic geometric surgeries: extremal transitions or flops. We will pr ove a version of Candelas and de la Ossa's conjecture: Ricci-flat Calabi-Yau man ifolds related via extremal transitions and flops can be connected by a path con sisting of continuous families of Ricci-flat Calabi-Yau manifolds and a compact metric space in the Gromov-Hausdorff topology. This is joint work with Yuguang Zhang Friday, March 1, 4:00pm, Fine Hall 110, Princeton University Speaker: Jian Song, Rutgers University Title: Analytic minimal model program with Ricci flow Abstract: I will introduce the analytic minimal model program proposed by Tian and myself to study formation of singularities of the Kahler-Ricci flow. We also construct geometric and analytic surgeries of codimension one and higher codimensions equ ivalent to birational transformations in algebraic geometry by Ricci flow. Friday, March 1, 3:00pm, Fine Hall 110, Princeton University Speaker: Antonio Ache, Princeton University Title: On the uniqueness of asymptotic limits of the Ricci flow Abstract: Given a compact Riemannian manifold we consider a solution of a normalization of the Ricci flow which exists for all time and such that both the full curvature tensor and the diameter of the manifold are uniformly bounded along the flow. It was proved by Natasa Sesum that any such solution of the normalized Ricci flow is sequentially convergent to a shrinking gradient Ricci soliton and moreover the limit is independent of the sequence if one assumes that one of the limiting solitons satisfies a certain integrability condition. We prove that this integrability condition can be removed using an idea of Sun and Wang for studying the stability of the Kaehler-Ricci flow near a Kaehler-Einstein metric. The method relies on the monotonicity of Perelman's W-functional along the Ricci flow and a Lojasiewicz-Simon inequality for the mu-functional. If time permits we will compare this result with recent Theorems on the stability of the Ricci flow. Joint Princeton-Rutgers Seminar on Geometric PDE's ---- Fall 2012 (Organizers on Rutgers side: Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song; Coordinator on Princeton side: Luc Nguyen) Thursday, September 13, 5:00pm, Hill 705, Rutgers University Speaker: Jie Qing, University of California, Santa Cruz Title: Hypersurfaces in hyperbolic space and conformal metrics on domains in sphere Abstract: In this talk I will introduce a global correspondence between properly immersed horospherically convex hyper surfaces in hyperbolic space and complete conforma l metrics on subdomains in the boundary at infinity of hyperbolic space. I will discuss when a horospherically convex hypersurface is proper, when its hyperboli c Gauss map is injective, and when it is embedded. These are expected to be usef ul to the understandings of both elliptic problems of Weingarten hypersurfaces i n hyperbolic space and elliptic problems of complete conformal metrics on subdom ains in sphere. Thursday, September 13, 4:00pm, Hill 705, Rutgers University Speaker: Alessio Figalli, University of Texas, Austin Title: Regularity Results For Optimal Transport Maps Abstract: Knowing whether optimal maps are smooth or not is an important step towards a qualitative understanding of them. In the 90's Caffarelli developed a regularity theory on R^n for the quadratic cost, which was then extended by Ma-Trudinger-Wang and Loeper to general cost functions which satisfy a suitable structural condition. Unfortunately, this condition is very restrictive, and when considered on Riemannian manifolds with the cost given by the squared distance, it is satisfied only in very particular cases. Hence the need to develop a partial regularity theory: is it true that optimal maps are always smooth outside a "small" singular set? The aim of this talk is to first review the "classical" regularity theory for optimal maps, and then describe some recent results about their partial regularity. Joint Princeton-Rutgers Seminar on Geometric PDE's ---- Spring 2012 (Organizers on Rutgers side: Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song; Coordinator on Princeton side: Luc Nguyen) Monday, April 30, 4:30-6:30pm, Fine Hall 110, Princeton University Speaker: Andre Neves, Imperial College Title: Min-max theory and the Willmore Conjecture Abstract: In 1965, T. J. Willmore conjectured that the integral of the square of the mean curvature of any torus immersed in Euclidean three-space is at least 2 pi^2. I w ill talk about my recent joint work with Fernando Marques in which we prove this conjecture using the min-max theory of minimal surfaces. Tuesday, March 6, 5:00pm, Hill 705, Rutgers University Speaker: Paul Yang, Princeton University Title: Compactness of conformally compact Einstein metrics Abstract: Tuesday, March 6, 4:00pm, Hill 705, Rutgers University Speaker: Ovidiu Savin, Columbia University Title: The thin one-phase problem Abstract: We discuss regularity properties of solutions and their free boundaries for minimizers of the thin Bernoulli problem. We show that Lipschitz free boundaries are classical and we obtain a bound on the Hausdorff dimension of the singular set of the free boundary of minimizers. This is a joint work with D. De Silva. Joint Princeton-Rutgers Seminar on Geometric PDE's ---- Fall 2011 (Organizers on Rutgers side: Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song; Coordinator on Princeton side: Luc Nguyen) Thursday, December 8, 5:00pm, Fine Hall 110, Princeton University Speaker: Haim Brezis, Rutgers University Title: Sobolev maps with values into the circle Abstract: Real-valued Sobolev functions are well-understood and play an immense role. By c ontrast, the theory of Sobolev maps with values into the unit circle is not yet sufficiently developed. Such maps occur in a number of physical problems. The re ason one is interested in Sobolev maps, rather than smooth maps is to allow maps with point singularities, such as x/|x| in 2-d, or line singularities in 3-d wh ich appear in physical problems. It turns out that these classes of maps have a rich structure. Geometrical and topological effects are already conspicuous, eve n in this very simple framework. On the other hand, the fact that the target spa ce is the circle (as opposed to higher-dimensional manifolds) offers the option to study their lifting and raises some tough questions in Analysis. Thursday, December 8, 4:00pm, Fine Hall 110, Princeton University Speaker: Gang Tian, Princeton University Title: Bounding scalar curvature along Kahler-Ricci flow Abstract: Thursday, Oct. 27, 5:00pm, Hill 552, Rutgers University Speaker: Nassif Ghoussoub , University of British Columbia Title: A self-dual polar decomposition for vector fields Abstract: I shall explain how any non-degenerate vector field on a bounded domain of$$R^n $$is monotone modulo a measure preserving involution$$S$$(i.e.,$$S2=Identity$). This is to be compared to Brenier's polar decomposition which yields that any su ch vector field is the gradient of a convex function (i.e., cyclically monotone) modulo a measure preserving transformation. Connections to mass transport --whi ch is at the heart of Brenier's decomposition-- is elucidated. This is joint wor k with A. Momeni.   Thursday, Oct. 27, 4:00pm, Hill 552, Rutgers University Speaker: Aaron Naber, MIT Title: Quantitative Stratification and regularity for Einstein manifolds, harmonic maps and minimal surfaces Abstract: In this talk we discuss new techniques for taking ineffective local, e.g. tangent cone, understanding and deriving from this effective estimates on regularity. Our primary applications are to Einstein manifolds, harmonic maps between Riemannian manifolds, and minimal surfaces. For Einstein manifolds the results include, for all p<2, 'apriori' L^p estimates on the curvature |Rm| and the much stronger curvature scale r_{|Rm|}(x)=max|Rm|leq r^{-2}}. If we assume additionally that the curvature lies in some L^q we are able to prove that r^{-1}_{|Rm|} lies in weak L^2q. For minimizing harmonic maps f we prove W^cap W^ estimates for p<3 for f and the stronger likewise defined regularity scale. These are the first gradient estimates for p>2 and the first L^p estimates on the hessian for any p. The estimates are sharp. For minimizing hypersurfaces we prove L^p estimates for p<7 for the second fundamental form and its regularity scale. The proofs include a new quantitative dimension reduction, that in the process stengthens hausdorff estimates on singular sets to minkowski estimates. This is joint work with Jeff Cheeger.

Conference

#### Joseph D'Atri Memorial Lectures 2019

2019 Joseph D'Atri was born in 1938, received an A.B. from Columbia College in 1959, and received a Ph.D. from Princeton University in 1964. He was a member of the Rutgers University Mathematics Department from 1963 until his death in 1993 and served as Chair of the Department from 1985 until 1990. Further information about Professor D'Atri and his work in geometry may be found in the book Topics in Geometry: in Memory of Joseph D'Atri edited by Simon Gindikin and published in 1996 by Birkhauser as volume 20 in the series Progress in Nonlinear Differential Equations and Their Applications. Previous D'Atri Memorial Lectures Lecturer Date Title(s) Luigi Ambrosio Nov 2017 New Estimates on the Matching Problem and Continuity of Nonlinear Eigenvalues with Respect to m-GH Convergence Fernando Coda Marques Feb 2016 Min-max Theory for the Area Functional - a Panorama Frank Merle Jan 2015 A Road Map for the Soliton Resolution Conjecture Universality Questions for Blow-up Behavior for the Mass Critical Korteweg-de-Vries Equations Nicola Fusco Jan 2014 Stability and Minimality of a Non-local Variational Problem The Quantitative Isoperimetric Inequality Vladimir Sverak Dec 2012 Mathematical Aspects of the Navier-Stokes and Euler's Equations Sun-Yung Alice Chang Feb 2012 Conformal Invariants: Perspectives From Geometric PDE Higher Order Isoperimetric Inequalities – An Approach via Method of Optimal Transport Gang Tian Dec 2010 Geometric Equations in Dimension 4 B-field Renormalization Flow on Complex Surfaces Carlos Kenig Feb 2010 Some Recent Applications of Unique Continuation to Mathematical Physics, PDE, and Fourier Analysis The Global Behavior of Solutions to Critical Non-Linear Dispersive and Wave Equations Yakov Eliashberg Oct 2008 Symplectic Topology of Stein ManifoldsOn the Border between Flexible and Rigid Mathematics Henri Berestycki Nov 2006 Reaction-Diffusion Equations in Nonhomogeneous Media Neil Trudinger Mar 2006 Nonlinear Elliptic PDE and Optimal TransportationNonlinear Elliptic PDE and Geometric Invariance Helmut Hofer Nov 2004 Somewhere Between Hamiltonian Dynamics and Symplectic Geometry Paul Rabinowitz 2004 An Aubry-Mather Theory for Partial Differential Equations Richard Hamilton 2003 On the Ricci Flow Luis A. Caffarelli 2002 Constraint Methods for Nonlinear Homogenization in Periodic and Random Media, I, II Brian White 2001 Total Curvature, Soap Films and the Unreasonable Effectiveness of Mathematics Stefan Hildebrandt 2000 On Two-dimensional Parametric Variational Problems Uniqueness Results for Minimal Surfaces with Free Boundaries Richard Schoen 1999 The Plateau Problem in Complex Geometry Nigel Hitchin 1998 Hyperkahler Geometry Misha Gromov 1997 Metric Geometry of Algebraic Manifolds Eugenio Calabi 1995 On Singular Sympletic Structures John Milnor 1994 Geometry and Dynamics Jacques Faraut 1993 Ordered Symmetric Spaces

poster

#### Mathematics Department Alumni Web Page - Archive

This purpose of this webpage is to provide contact information and news items about Rutgers Mathematics Department alumni. If you prefer that an item that you sent not be listed on this page or be modified, please send email to webmaster@math.rutgers.edu.

#### A History of Mathematics at Rutgers

For a history of Mathematics at Rutgers by Charles Weibel, please visit THIS PAGE . (originally written in 1995)

#### Facilities and Local Area

The Mathematics Department undertakes internationally-recognized research in all areas of pure and applied mathematics and mathematics education and provides quality instruction for an annual undergraduate enrollment of approximately twenty-four thousand, as well as five hundred majors in three different curriculum codes*.  Consistently ranked among the top twenty-five programs in the country, the Department counts over forty Fellows of the American Mathematical Society or Society for Industrial and Applied Mathematics, three members of the National Academy as well as a winners of national and university-wide teaching prizes. Approximately sixty tenure-track faculty hold lines entirely within the department or share appointments with computer science, physics, engineering, and education.  Together with thirty teaching-focused faculty the department educates students from all Schools at Rutgers as well as high-school students and teachers from around the State of New Jersey.     * Curriculum Codes: Mathematics 640, Biomathematics 122, and Statistics/Mathematics 961.

#### Garden State Math Competition Results

Rutgers undergraduates took the top two individual spots, and placed second and third in the team competition, in the Garden State Mathematics Competition.   Terence Coelho and Elliot Glazer placed first and second respectively, while in the team competition Rutgers took 2nd place (Maine Christos, Roberta Shapiro, and Patrick Chen), and 3rd place (Terence Coelho and Elliot Glazer)

#### New Math Biology Courses

Starting with the 2001 Academic Year, the math department expects to offer two new courses: 640:336, Differential Equations in Biology (F'01). 640:338, Discrete and Probabilistic Models in Biology (S'02). The new course Math 336 will have Ordinary Differential Equations (640:244 or 640:252) as a prerequisite. The course Math 338 will keep the old 338 prerequisites of linear algebra and probability. In the future, students will be able to get credit for both 336 and 338, and both courses will be required for Biomath majors. (But please note: if you take 338 before the 2001/2002 year, you will need to obtain special permission to have both courses count, because 338 in the Spring of 2001 is the same course as what will become 336.) For further information, please look at the web page for the Spring 01 338 course; this course covered the material which is expected to be covered in the new 336 course.

#### Rutgers shares top honors at International Association for Quantitative Finance (IAQF) competition

International Association for Quantitative Finance( IAQF) announced that Rutgers, UC Berkeley, and Baruch College NY share the honor of having the three winning student teams in the 2017 IAQF Academic Affiliate Membership Student Competition. MSMF's ACE team of six students -- Zongsheng Sun (team captain), Lingfeng Li, Haidong Gu, Xinrong Song, Lin Du, and Bowen Long were mentored by Sunita Jagtiani, our Director for Career Services Management, and Triet Pham, Teaching Assistant Professor of Mathematics.

#### The Daniel Gorenstein Memorial Award

Daniel Gorenstein (1923-1992)   The Daniel Gorenstein Memorial Award was established in 1993 by the family, friends, and colleagues of Danny Gorenstein to commemorate his outstanding mathematical research, his skillful and enthusiastic exposition of his field, and his wise and devoted service to Rutgers University. The Award is given for outstanding scholarly achievement to a Rutgers faculty member who has also performed exceptional service to the University community. The winners of the Gorenstein Memorial Award have been: 1994         Gerald N. Grob, History of Medicine1995        George L. Levine, English, Faculty of Arts and Sciences - New Brunswick1996        Hans Fisher, Nutritional Sciences, Cook College1997        G. Terence Wilson, Psychology, Faculty of Arts and Sciences - New Brunswick1998        Robert L. Wilson, Mathematics, Faculty of Arts and Sciences - New Brunswick1999        Lloyd C. Gardner, History, Faculty of Arts and Sciences - New Brunswick2000        Brent D. Ruben, Communication, SCILS2001        Noemie Koller, Physics and Astronomy, Faculty of Arts and Sciences - New Brunswick2002        Joanna Burger, Cell Biology and Neuroscience, Faculty of Arts and Sciences - New Brunswick2003        David Mechanic, University Professor2004        Glenn Shafer, Accounting and Information Systems, School of Business2005        Alan Conney, Cancer and Leukemia Research, Ernest Mario School of Pharmacy2006        Sandra Harris, Clinical Psychology, GSAPP2007        Richard S. Falk, Mathematics, School of Arts and Sciences - New Brunswick2008        Ziva Galili, History, School of Arts and Sciences - New Brunswick2009        Barbara A. Lee, Human Resource Management, School of Management and Labor Relations2010        Yogesh Jaluria, Mechanical and Aerospace Engineering, School of Engineering2011        Daniel Hart, Psychology and Childhood Students, Faculty of Arts and Sciences, Rutgers Camden2012        Joachim Kohn, Chemistry, School of Arts and Sciences2013        Allan Horwitz, Sociology, School of Arts and Sciences2014        Cheryl Wall, English, School of Arts and Sciences2015        James Turner Johnson, Department of Religion, School of Arts and Sciences2016        Dr. Jolie Cizewski, Distinguished Professor of Physics, Department of Physics and Astronomy, School of Arts and Sciences

#### Faculty honors: Joel Lebowitz awarded Dirac medal, Sontag receives Bellman award

Joel Lebowitz, the George William Hill Professor of Mathematics and Physics, has been awarded the 2022 Dirac Medal by the International Centre for Theoretical Physics in Trieste, one of the very top honors in mathematical physics. The award goes to Joel, Elliot Lieb, and David Ruelle, "for groundbreaking and mathematically rigorous contributions to the understanding of the statistical mechanics of classical and quantum physical systems".  David Ruelle was also a member of our department for many years . Rutgers is also the home of other winners of the Dirac Medal -- including Mathematics Graduate Faculty member Greg Moore.  More information can be found here: ICTP - 2022 ICTP Dirac Medal Winners Announced. Emeritus Professor Eduardo Sontag was awarded the 2022 Richard E. Bellman Control Heritage Award, which is the highest recognition in control theory and engineering in the US.  The citation reads “For pioneering contributions to stability analysis and nonlinear control, and for advancing the control theoretic foundations of systems biology.”

#### Contact Info

Department of Mathematics, Rutgers UniversityHill Center for the Mathematical Sciences 110 Frelinghuysen Rd.Piscataway, NJ 08854-8019  Directions to Hill Center Main Department Phone and Fax:  (Tel) 848-445-2390 - (Fax) 732-445-5530 Undergraduate Advisor:  advisor@math.rutgers.edu, Hill 308, 848-445-6989 Undergraduate Office:   ugoffice@math.rutgers.edu, Hill 303, 848-445-2390 Graduate Secretary:  grad-sec@math.rutgers.edu, Hill 306, 848-445-6994 Mathematical Finance Program:  finmath@math.rutgers.edu, Hill 348, 848-445-3920

#### Facilities

Undergraduate Common Room Hill Center 323 is a place for undergraduate math majors to meet, discuss mathematics, and use computers. The room is also used for meetings of the undergraduate honors seminar, and for special talks for undergraduates about mathematics or careers in the mathematical sciences. Computer Accounts All Rutgers students are entitled to an account on the university computer eden and every campus in Rutgers - New Brunswick/Piscataway has fully equipped computer labs for the use of students. The computer terminals in the undergraduate common room, Hill 323, are for math majors only. To use them it is necessary to open an account on the undergraduate server, gauss. This computer is for declared mathematics majors. Interested majors should inquire in Hill 322 (see Risa Hynes). Mathematical Software The department offers several courses which require the use of software packages capable of sophisticated scientific calculation, three-dimensional graphics, and symbolic manipulation. In some courses, including third-semester calculus, differental equations, and numerical analysis, Maple is used. Rutgers has a license that makes Maple available on many systems, including eden, the PC labs on every campus, and the mathematics department's servers. In other courses, for example the computer sections of linear algebra (Math 250, C sections), and Math 357, Matlab is used.  Matlab is available on gauss and at the Rutgers computer labs. For information on software and the servers where it is available, see the list of campus computing facilities. Full-scale versions of these software packages are costly. Student versions are available at a moderate price at the Rutgers University Bookstore and elsewhere. These student versions can handle only objects of moderate size (adequate for most uses) and do not include user support. Although formal courses dealing solely with the use of these packages do not constitute college-level work, it should be part of every mathematics student's out-of-class education to become thoroughly familiar with at least one such package.

#### Minors

School of Arts and Sciences Minor in Mathematics:   A minor in mathematics consists of: Three terms of calculus; ordinarily 01:640:151, 152, 251 Introduction to Linear Algebra (01:640:250) Four additional 3-credit courses chosen from 01:640:252, 244 and 300-400 level courses in the mathematics department (01:640:491, 492 do not satisfy this requirement). Grades of C or better are required in 01:640:250 and 251 at most one D is permitted in the four courses beyond 01:640:250. At least three out of the four elective courses must be taken at Rutgers - New Brunswick/Piscataway.

#### Majors

For the time being, all advising is being conducted via email or over the phone by appointment. For general inquiries, please contact the Head Advisor at <advisor@math.rutgers.edu>. For more specific contact information, see the chart below. Each math major should speak to an advisor in the math department at least once each semester, during the process of registering for the following semester.

#### Tutoring

Tutoring/Review in Mathematics on the New Brunswick Campuses   Mathematics Undergraduate Program Rutgers Learning Center Math and Science Learning Center Math Help Center   Televised Calculus Reviews, Schedules On Now Taped Sessions

#### Transfer Students

Transfer or Pre-Approval of Courses Taken Elsewhere Q. As a transfer student arriving at Rutgers, how do I get my courses taken elsewhere evaluated for credit at Rutgers? A. See the Head advisor. For courses taken outside the state of New Jersey bring in a syllabus if possible. References: Transfer Credit Chart:  View courses approved for transfer credit NJTransfer Q. As a continuing Rutgers student, when and how do I get approval of courses I wish to take elsewhere? A. Before registering for a summer course in mathematics taken elsewhere, see the Head Advisor to review your prerequisites and the acceptability of the course. No course given in a session of less than 5 weeks is accepted. Warning: Undergraduate students at Rutgers (New Brunswick/Piscataway) MUST have prior written approval from their college (or SAS) before taking a course elsewhere that they want to transfer onto their Rutgers transcript. If such approval is not obtained, no credit will be awarded. The Rutgers New Brunswick/Piscataway Math Department will not approve the transfer of any 3 or more credit course offered in any Session (Summer, Winter, or other) lasting less than 5 weeks. The Rutgers New Brunswick/Piscataway Department will not approve the transfer of courses taught at sites off the campus of the college offering them. Courses that are more than 10 years old are eligible to receive elective credit only and will not be given credit equivalent to a Rutgers New Brunswick course. Evaluation Forms Note: Make sure to also fill out the Transfer Credit Application for Mathematics Courses after reading When to Fill Out Math Transfer Credit Application.

#### Awards, Prizes Scholarships

Graduation with Honors Scholarships Awards and Prizes  Competitions

#### Learning Goals

The general liberal arts student will be able to employ algebra and discuss bringing abstract mathematics to bear on areas with no obvious mathematical content to the layman, such as political science, esthetics, or credit card security. Students whose majors require more advanced mathematics will be adequately prepared. Students aiming toward careers in elementary school education will be able to pass state-mandated examinations before certification, and to satisfy the University’s course requirements related to certification. Majors will be able to employ problem solving skills in a wide range of modern mathematics; analyze quantitative information and apply advance mathematic techniques and concepts where appropriate; communicate rigorous mathematical ideas and reasoning effectively; appropriately use supporting technology and work cooperatively as part of a team to solve mathematical problems; and top students will demonstrate experience in research students in combined math/education programs will be able to demonstrate a broad perspective on mathematics, including the history of the subject, and an understanding of the connections between college mathematics and the state's curriculum framework. Students in the B.S. program (Honors Track) will be able to engage in graduate level work toward the doctorate. Minors will be able to demonstrate an understanding of the special nature of mathematical thinking; create and communicate mathematical arguments; apply mathematical knowledge and techniques in advanced courses in their major discipline. Statistics/Mathematics joint major the joint major provides a stronger preparation for graduate study in statistics; the Statistics major is best for students who are interested in statistical applications in industry, government, or applied areas of graduate studeis.
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## Department Information

Department of Mathematics
Rutgers University
Hill Center - Busch Campus