course information book department of mathematics...

Course Information Book

Department of Mathematics

Tufts University

Fall 2017

This booklet contains the complete schedule of courses offered by the Math Department in the Fall

2017 semester, as well as descriptions of our upper-level courses and a few lower-level courses.

For descriptions of other lower-level courses, see the University catalog.

If you have any questions about the courses, please feel free to contact one of the instructors.

Course schedule p. 2

Math 61 p. 3

Math 63 p. 4

Math 70 p. 5

Math 72 p. 6

Math 87 p. 7

Math 135 p. 8

Math 145 p. 9

Math 150-01 p. 10

Math 150-02 p. 11

Math 151 p. 12

Math 155 p. 13

Math 161 p. 14

Math 211 p. 15

Math 215 p. 16

Math 217 p. 18

Math 250-01 p. 19

Math 250-02 p. 20

Math 250-03 p. 21

Mathematics Major Concentration Checklist p. 22

Applied Mathematics Major Concentration Checklist p. 24

Mathematics Minor Checklist p. 27

Jobs and Careers, Math Society, and SIAM p. 28

Block Schedule p. 29

Course Title Instructor Block Times Room

MATH 0019-01 Math Of Social Choice Michael Ben-Zvi C TWF - 9:30AM-10:20AM Bromfield-Pearson Room 007

MATH 0019-02 Math Of Social Choice Linda B Garant E+MW MW - 10:30AM-11:45AM Bromfield-Pearson Room 101

MATH 0021-01 Introductory Statistics Linda B Garant G+ MW - 1:30PM-2:45PM Bromfield-Pearson Room 101

MATH 0021-02 Introductory Statistics Patricia M. Garmirian G MWF - 1:30PM-2:20PM Bromfield-Pearson Room 007

MATH 0032-01 Calculus I Boris Hasselblatt B TRF - 8:30AM-9:20AM Anderson Wing SEC, Room 206

MATH 0032-02 Calculus I Mary E Glaser* D

M - 9:30AM-10:20AM, TR - 10:30AM-

11:20AM Bromfield-Pearson 002

MATH 0032-03 Calculus I Gail F Kaufmann F TRF - 12:00PM-12:50PM Anderson Wing SEC, Room 206

MATH 0032-04 Calculus I David Smyth H TR - 1:30PM-2:20PM, F - 2:30PM-3:20PM Lane Hall, Room 100

MATH 0032-05 Calculus I Fulton B Gonzalez E MWF - 10:30AM-11:20AM

Pearson Hall Room 106, Anderson Wing

SEC Room 112

Recitation A Robert Kropholler E MW - 10:30AM-11:20AM Bromfield-Pearson Room 002

Recitation B Robert Kropholler J T - 3:00PM-3:50PM Bromfield-Pearson Room 002

Recitation C Nariel Monteiro A W - 8:30AM-9:20AM Anderson Wing SEC, Room 210

Recitation D Nariel Monteiro G W - 1:30PM-2:20PM Bromfield-Pearson Room 002

Recitation E Robert Kropholler J R - 3:00PM-3:50PM Bromfield-Pearson Room 002

Recitation F Nariel Monteiro C F - 9:30AM-10:20AM Bromfield-Pearson Room 002

Recitation G Caleb Magruder E M - 10:30AM-11:20AM Bromfield-Pearson Room 005

Recitation H Caleb Magruder J T - 3:00PM-3:50PM Bromfield-pearson Room 003

Recitation I Caleb Magruder B R - 9:30AM-10:20AM Bromfield-Pearson Room 005

MATH 0034-01 Calculus II Zachary Faubion B TRF - 8:30AM-9:20AM Robinson Wing SEC, Room 253

MATH 0034-02 Calculus II Gail F Kaufmann* D

M - 9:30AM-10:20AM, TR - 10:30AM-

11:20AM Anderson Wing SEC Room 206

MATH 0034-03 Calculus II Mary E Glaser F TRF - 12:00PM-12:50PM Bromfield-Pearson Room 007

MATH 0034-04 Calculus II Zachary Faubion H TR 1:30PM-2:20PM, F 2:30PM-3:20PM Bromfield-Pearson Room 101

Recitation A Elizabeth Newman E M - 10:30AM-11:20AM Braker Hall Room 222

Recitation B Eunice Kim H T - 1:30PM-2:20PM Bromfield-Pearson Room 002

Recitation C Elizabeth Newman I W - 3:00-3:50PM Bromfield-Pearson Room 007

Recitation D Eunice Kim I W - 3:00-3:50PM Bromfield-Pearson Room 006

Recitation E Eunice Kim J R - 3:00PM-3:50PM Bromfield-Pearson Room 006

Recitation F Elizabeth Newman C F - 9:30AM-10:20AM Bromfield-Pearson Room 006

MATH 0042-01 Calculus III Montserrat Teixidor I Bigas* B TRF - 8:30AM-9:20AM Bromfield-Pearson Room 002

MATH 0042-02 Calculus III Jessica Dyer D

M - 9:30AM-10:20AM, TR - 10:30AM-

11:20AM Pearson Hall Room 106

MATH 0042-03 Calculus III Jessica Dyer E MWF - 10:30AM-11:20AM Anderson Wing SEC Room 206

Recitation A Hongyan Wang K M - 4:30PM-5:20PM Bromfield-Pearson Room 003

Recitation B Michael Chou H T - 1:30PM-2:20PM Eaton Hall Room 333

Recitation C Michael Chou A W - 8:30AM-9:20AM Bromfield-Pearson Room 006

Recitation D Hongyan Wang I W - 3:00-3:50PM Bromfield-Pearson Room 003

Recitation E Michael Chou J R - 3:00PM-3:50PM Bromfield-Pearson Room 003

Recitation F Hongyan Wang C F - 9:30AM-10:20AM Bromfield-Pearson Room 003

MATH 0051-01 Differential Equations Eunice Kim D

M - 9:30AM-10:20AM, TR - 10:30AM-

11:20AM Bromfield-Pearson Room 003

MATH 0051-02 Differential Equations Zbigniew H Nitecki* F TRF - 12:00PM-12:50PM Bromfield-Pearson Room 002

Recitation A Caleb Magruder E M - 10:30AM-11:20AM Bromfield-Pearson Room 005

Recitation B Caleb Magruder J T - 3:00PM-3:50PM Bromfield-Pearson Room 003

Recitation C Caleb Magruder A R - 9:30AM-10:20AM Bromfield-Pearson Room 005

MATH 0061-01 Discrete Mathematics Zachary Faubion F TRF - 12:00PM-12:50PM Bromfield-Pearson Room 005

MATH 0061-03 Discrete Mathematics Elena Strange I+ MW - 3:00PM-4:15PM Robinson Wing SEC, Room 253

MATH 0063-01 Number Theory Michael Chou C TWF - 9:30AM-10:20AM Bromfield-Pearson Room 005

MATH 0070-01 Linear Algebra Genevieve Walsh C TWF - 9:30AM-10:20AM Bromfield-Pearson Room 101

MATH 0070-02 Linear Algebra Kim Ruane D

M - 9:30AM-10:20AM, TR - 10:30AM-

11:20AM Bromfield-Pearson Room 101

MATH 0070-03 Linear Algebra Jessica Dyer H TR - 1:30PM-2:20PM, F - 2:30PM-3:20PM Bromfield-Pearson Room 007

MATH 0072-01 Abstract Linear Algebra Zbigniew H Nitecki H+ TR - 1:30PM-02:45PM Bromfield-Pearson Room 001

MATH 0087-01 Mathematical Modeling Caleb Magruder H+ TR - 1:30PM-02:45PM Bromfield-Pearson, Room 005

MATH 0102-01 Math-Ed: Change and Invariance Montserrat Teixidor I Bigas ARR Online N/A

MATH 0135-01 Real Analysis I Eric Todd Quinto F+TR TR - 12:00PM-01:15PM Bromfield-Pearson Room 101

MATH 0135-02 Real Analysis I Eric Todd Quinto J+ TR - 3:00PM-4:15PM Bromfield-Pearson Room 101

MATH 0145-01 Abstract Algebra I David Smyth B TRF - 8:30AM-9:20AM Bromfield-Pearson Room 005

MATH 0145-02 Abstract Algebra I Montserrat Teixidor I Bigas D+ TR - 10:30AM-11:45AM Bromfield-Pearson Room 006

MATH 0145-01 Recitation A David Smyth W - 7:00PM-8:00PM Bromfield-Pearson, Room 003

MATH 0150-01 Point-Set Topology Genevieve Walsh G MWF - 1:30PM-2:45PM Bromfield-Pearson Room 003

MATH 0150-02 Numerical Optimization Xiaozhe Hu H+ TR - 1:30PM-2:45PM Bromfield-Pearson Room 003

MATH 0150-03 Neural Network Algorithms Christoph Borgers TBD F - 1:30PM-3:00PM Bromfield-Pearson Room 005

MATH 0151-01 Partial Differential Equations I Bruce M Boghosian D+ TR - 10:30AM-11:45AM Bromfield-Pearson Room 005

MATH 0155-01 Nonlinear Dynamics and Chaos Christoph Borgers G+ MW - 1:30PM-2:45PM Lane Hall, Room 100A

MATH 0161-01 Probability Patricia M. Garmirian E+ MWF - 10:30AM-11:45AM Bromfield-Pearson Room 007

MATH 0211-01 Analysis Alex Hening F TRF - 12:00PM-12:50PM Bromfield-Pearson Room 006

MATH 0215-01 Algebra Robert Kropholler D+ TR - 10:30AM-11:45AM Bromfield-Pearson Room 003

MATH 0217-01 Geometry & Topology Loring W Tu J+ TR - 3:00PM-4:15PM Bromfield-Pearson Room 005

MATH 0226-01 Numerical Analysis Misha E Kilmer E+MW MW - 10:30AM-11:45AM Bromfield-Pearson Room 006

MATH 0250-01 The Distribution of Prime Numbers Robert J Lemke-Oliver H+ TR - 1:30PM-2:45PM Bromfield-Pearson Room 006

MATH 0250-02 Functional Analysis Fulton B Gonzalez G+ M - 4:15PM-5:30PM, W 6:00PM-7:15PM

SEC Research West Room 223, Bromfield-

Pearson Room 117

MATH 0250-03 Dynamical Systems Boris Hasselblatt 10+ M - 6:00PM-9:00PM Bromfield-Pearson Room 007

FALL 2017 SCHEDULE

Discrete Math 0061, Course Description: In this course we will examine, think about, play with

and get to know some of the objects and concepts that are at the core of advanced mathematics and

computer science. Some specific examples of these concepts are sets, logic, proofs, relations and functions.

We will also see these ideas in action by looking at combinatorics, cardinality and graphs (to list a few.)

The course is taught in the F and H blocks.

1

Math 63 Number Theory Course Information

Fall 2017

BLOCK: C, TuWF 9:30-10:20 INSTRUCTOR: Michael Chou EMAIL: [email protected]

PREREQUISITES: Math 32 or consent.

TEXT: TBD

COURSE DESCRIPTION:

Broadly speaking, number theory is the study of the integers. Despite having its origins in ancient Greece, it remains an active area of research, bringing together ideas from many different areas of mathematics.

Some motivating questions might be, are there infinitely many prime numbers? Of those, how many end in the digits 123456789? Is there any structure to the integer solutions to the equation a2 + b2 = c2, or do they occur as sporadic accidents? If n > 2, are there any non-zero integer solutions to the equation an + bn = cn? Which integers can be written as the sum of two squares, or three squares, or four squares? How are prime numbers used in cryptography? In this course, we will develop the tools needed to answer (some of) these questions, making connections with some open problems along the way.

Proofs play a central role in number theory, though no prior experience will be as- sumed. Grades will be based on a combination of homework, exams, and possibly a final project.

mailto:[email protected]

Math 70 Linear Algebra

Course Information

Fall 2017

Block: C (TWF 9.30-10.20)

Instructor: Genevieve Walsh

Email: [email protected] Office: 574 Boston Ave (CLIC Building) 211 G

Office hours: (S 2017)

T 8:30-10:30, Th 1-2 Phone: 617-627-4032

Block: D (M9.30-10.20, TTh 10.30-11.20)

Instructor: Kim Ruane

Email: [email protected] Office: 574 Boston Avenue

Suite I, Room 211.

Office hours: (Spring 2017)

M 1:30-2:30, T 3-4, Th 11-12

Phone: 617-627-2006

Block: H (T Th 1:20-2:20, F 2:30-3:20)

Instructor: Jessica Dyer

Email: [email protected] Office: BP 202

Office hours: (Spring 2017)

T, Th, F 11:30-12:30

Phone:617-627-2363

Prerequisites: Math 34 or 39, or consent of instructor.

Text: Linear Algebra and Its Applications , 4th edition, by David Lay, Addison-Wesley (Pearson),

2011.

Course description: Linear algebra begins the study of systems of linear equations in several

unknowns. The study of linear equations quickly leads to the important concepts of vector spaces,

dimension, linear transformations, eigenvectors and eigenvalues. These abstract ideas enable effi-

cient study of linear equations, and more importantly, they fit together in a beautiful setting that

provides a deeper understanding of these ideas.

Linear algebra arises everywhere in mathematics. It plays an important role in almost every

upper level math course. It is also crucial in physics, chemistry, economics, biology, and a range of

other fields. Even when a problem involves nonlinear equations, as is often the case in applications,

linear systems still play a central role, since “linearizing” is a common approach to non-linear

problems.

This course introduces students to axiomatic mathematics and proofs as well as fundamental

mathematical ideas. Mathematics majors and minors are required to take linear algebra (Math 70

or Math 72) and are urged to take it as early as possible, as it is a prerequisite for many upper-

level mathematics courses. The course is also useful to majors in computer science, economics,

engineering, and the natural and social sciences.

The course will have two midterms and a final, as well as daily homework assignments.




Math 72 Abstract Linear Algebra Course Information

Fall 2017

BLOCK: H+TR (Tuesday and Thursday, 1:30–2:45) INSTRUCTOR: Zbigniew Nitecki EMAIL: [email protected] OFFICE: 214 Bromfield-Pearson Hall OFFICE HOURS: (Spring 2017) Th 9:30-10:30 & 1:30-2:30, Fri 9:30-10:30 or by appointment PHONE: (617) 627-3843 (please note that email is a better way to reach me)

PREREQUISITES: Math 34 (or 39) or instructor’s consent.

TEXT: Sheldon Axler, Linear Algebra Done Right, 3rd edition, Springer, 2015. (ISBN: 978- 3-319-11079-0). Also available as an ebook, via Springer Link! (Ebook ISBN: 978-3-319- 11080-6) http://link.springer.com/book/10.1007/978-3-319-11080-6 I believe Tufts library gets the appropriate Springer eBook package, so that you can get the eBook version of this book for free at SpringerLink (you may need to be signed in in the Tufts network before you can do this).

COURSE DESCRIPTION: Linear algebra is a foundational subject, not just in mathematics but also in physics, engineering, economics, and many other disciplines. The reason is that many natural phenomena are inherently linear or can be approximated by expres- sions which vary linearly. Linear models appear in many contexts, including linear differential equations, image processing, stress analysis, scheduling problems, the Google ranking algorithm, game theory, and signal processing.

The material in this course is essentially the same as in Math 70 but will be presented from a different viewpoint. We will stress the development of abstract concepts and the proofs of theorems, alongside computations. Topics include vector spaces and related ideas (subspaces, linear independence, bases, dimension), linear transformations and their matrix representations (rank, nullity, trace, determinants, diagonalization, invariant subspaces, eigenvectors and eigenvalues).

If you want to know the why behind linear algebra as well as the how, this is the course for you.

The course is intended for majors or minors in mathematics, computer science, quan- titative economics, science and engineering.


http://link.springer.com/book/10.1007/978-3-319-11080-6

Math 87 Mathematical Modeling and Computation

Course Information

Fall 2017

Block: TBA

Instructor: Caleb Magruder

Email: [email protected] Office: TBA

Office hours: TBA

Prerequisites: Math 34 or 39, Math 70 or 72, or consent.

Text: none

Course description:

This course is about using elementary mathematics and computing to solve practical prob-

lems. Single-variable calculus is a prerequisite, as well as some basic linear algebra skills;

other mathematical and computational tools, such as elementary probability, elementary

combinatorics, and computing in MATLAB, will be introduced as they come up.

Mathematical modeling is an important area of study, where we consider how mathe-

matics can be used to model and solve problems in the real world. This class will be driven

by studying real-world questions where mathematical models can be used as part of the

decision-making process. Along the way, we’ll discover that many of these questions are best

answered by combining mathematical intuition with some computational experiments.

Some problems that we will study in this class include:

1. The managed use of natural resources. Consider a population of fi that has a nat-

ural growth rate, which is decreased by a certain amount of harvesting. How much

harvesting should be allowed each year in order to maintain a sustainable population?

2. The optimal use of labor. Suppose you run a construction company that has fi

numbers of tradespeople, such as carpenters and plumbers. How should you decide

what to build to maximize your annual profi What should you be willing to pay to

increase your labor force?

3. Project scheduling. Think about scheduling a complex project, consisting of a large

number of tasks, some of which cannot be started until others have fi What

is the shortest total amount of time needed to fi the project? How do delays in

completion of some activities affect the total completion time?

Using basic mathematics and calculus, we will address some of these issues and others, such

as dealing with the MBTA T system and penguins (separately of course...). This course will

also serve as a good starting point for those interested in participating in the Mathematical

Contest in Modeling each Spring.


Math 135 Real Analysis I Course Information

Fall 2017

Instructor for both sections: Todd Quinto Email: [email protected] Office: Bromfield-Pearson 204

Office hours: (Spring 2017), I am on a research leave and would be happy to talk with you anytime–just e-mail. Phone: (617) 627-3402

Block: F+ (Tue Thu 12:00–1:15p.m.)

Joint Problem Session: 12:00-1:15 Mondays

Block: J+ (Tuesday, Thursday 3:00–4:15 p.m.)

Joint Problem Session: 12:00-1:15 Mondays

Prerequisites: Math 42 or 44, and 70 or 72, or consent. (In the old numbering scheme, Math 13 or 18, and 46 or 54, or consent.)

Text: Patrick Fitzpatrick, Advanced Calculus, 2nd edition, American Mathematical Society, 2009. (ISBN 978-0-8218-4791-6)

Course description:

Real analysis is the rigorous study of real functions, their derivatives and integrals. It provides the theoretical underpinning of calculus and lays the foundation for higher mathematics, both pure and applied. Unlike Calculus I, II, and III, where the emphasis is on intuition and computation, the emphasis in real analysis is on justification and proofs.

Is this rigor really necessary? This course will convince you that the answer is an unequivocal yes, because intuition not grounded in rigor often fails us or leads us astray. This is especially true when one deals with the infinitely large or the infinitesimally small. For example, it is not intuitively obvious that, although the set of rational numbers contains the set of integers as a proper subset, there is a one-to-one correspondence between them. These two sets, in this sense, are the same size! On the other hand, there is no such correspondence between the real numbers and the rational numbers, and the set of real numbers is bigger (it is uncountably infinite).

A metric space is any set on which there is a distance function. In this course, we will study the topology of the real line and metric spaces, compactness, connectedness, continuous mappings, and uniform convergence. The topics constitute essentially the first five chapters of the textbook. Along the way, we will encounter theorems of calculus, such as the intermediate-value theorem and the maximum-minimum theorem, but in a more general setting that enlarges their range of applicability. This is one of the exciting aspects of real analysis and of upper-level math in general; by studying fundamental ideas in a general setting, we understand them more deeply and gain a broader perspective on and appreciation of the ideas. We anticipate ending with the contraction mapping principle, a fundamental theorem using which one can prove the existence and uniqueness of solutions of differential equations.

In addition to introducing a core of basic concepts in analysis, a companion goal of the course is to hone your skills in distinguishing true from false and in reading and writing proofs.

Math 135 is required of all pure and applied math majors. A math minor must take Math 135 or 145.

I am planning on weekly homework, two tests, and a final (and perhaps a few quizzes). The material in this course is beautiful, and I look forward to sharing it with my students.


Math 145 Abstract Algebra

Course Information

Fall 2017

Block: B, TThF, 8.30 -9.20 AM Instructor: David Smyth Email: Office: Bromfield-Pearson TBD Office hours: (Spring 2017) by appointment

Phone: TBD

Block: D+ (Tu, Th 10:30-11:45)

Instructor: montserat teixidor Email: [email protected] Office: Bromfield-Pearson 115 Office hours: (Spring 2017) M10.30-11.45, T 9.30-10.20,Th 2-3.45 and by appointment Phone: (617) 627-2358

Prerequisites: Linear Algebra (Math 70 or 72).

Text: A first course in Abstract Algebra seventh edition by John B. Fraleigh , Addison

Wesley 2003.

Course description: Algebra, along with Analysis and Geometry is one of the main

pillars of mathematics. It has ancient roots, especially in Europe, India and China. Histori- cally, algebra was concerned with the manipulation of equations and, in particular, with the problem of fi the roots of polynomials. This is the algebra that you know from high school. There are clay tablets from 1700B.C. that show that the Babylonians knew how to solve quadratic equations. The solutions to cubic and fourth degree polynomial equations were solved in Italy during the Renaissance. About the time of Beethoven, a young French mathematician Evariste Galois made the dramatic discovery that for polynomials of degree greater than four, no similar solution exists. To do this, Galois introduced the branch of mathematics known as group theory. This was not, of course, the end of the story. Algebra has continued its development to the present day most notably with the classification of fi simple groups and with Andrew Wiles proof of Fermat’s Last Theorem.

The concept of a group is now one of the most important in mathematics. Roughly speaking, group theory is the study of symmetry. There are deep connections between group theory, geometry and number theory. Groups pop up in every area of mathematics: symmetry groups can be used to fi solutions to diff tial equations, associating groups (and rings) to topological spaces allows to distinguish among them. Groups also appear in the attempts of physicists to describe the basic laws of nature.

In Math 145, we introduce the concepts of group and ring. Their properties mimic the arithmetic properties of numbers and polynomials. In Math 146, we describe the connection Galois discovered between group theory and the roots of polynomials.


Math 150-01 Point-Set Topology Course Information

Fall 2016

BLOCK: G+ (Mo, We 1:30 - 2:45) INSTRUCTOR: Genevieve Walsh EMAIL: [email protected] OFFICE: 211G 574 Boston Ave OFFICE HOURS: (Spring 2017) Tu 8:30 - 10:30, Th 1-2

PREREQUISITES: Some course involving proofs. For example: 70, 72, 61,63.

TEXT: Notes provided by the instructor.

COURSE DESCRIPTION: The subject of point-set topology is extremely useful in many areas, particularly in analysis and topology. This class works both before 135 or after. We will start by covering cardinality and the axiom of choice and general topology, including creating our own topologies. We will describe what a basis of a topology is, the sub- space topology, and the product topology. Then we will discuss various separation and covering properties, and investigate maps between topological spaces. Finally, we will discuss notions of connectivity of a topological space. Throughout, specific examples will be emphasized. There are many pathological and interesting examples in the field.

This course is designed to get you to think mathematically for yourself. To that end, there will be a running list of definitions and theorems and the goal of the class is to jointly work through proving the theorems. Everyday, students from the class will present problems and the class will discuss them and decide if they are ready to proceed. As such, this course is a good preparation for business, economics, law and mathematics. This method of instruction is called Inquiry Based Learning, and it is a very fun and challenging way to deeply engage rigorously with the material.

There will be daily homework assignments, a midterm, and a final.


Math 150-02 Numerical Optimization Course Information

Fall 2017

BLOCK: H+ (Tu, Th 1:30pm –2:45pm) INSTRUCTOR: Xiaozhe Hu EMAIL: [email protected] OFFICE: 212 Bromfield-Pearson Hall OFFICE HOURS: (Spring 2017) by appointment PHONE: (617) 627-2356

PREREQUISITES: Math 126 and 128 or consent. Some programming ability in a language such as C, C++, Fortran, Matlab, etc.

TEXT: TBD

COURSE DESCRIPTION: Many problems in science, engineering, economics, and industry involve optimiza-

tion, in which we seek to optimize objective function subject to constraints. Due to the wide and growing use of optimization in different areas, such as model fitting, machine learning, optimal control, and image processing, it is important for practitioners to understand optimization algorithms and their impact on various applications.

This course is an introductory survey of optimization algorithms and gives a compre- hensive description of the state-of-the-art techniques for solving continuous optimization problems. The primary objective of the course is to develop an understanding of optimization algorithm and, more importantly, the capabilities and limitations of these algorithms. We will focus on both theoretical foundations (e.g., convergence analysis, error analysis) and practical implementations (e.g., computational complexity, computer stor- age). The emphasis will be the accuracy, numerical stability, efficiency, robustness, and scalability. The topics include: line search, trust region, and (inexact) Newton methods for unconstrained optimization; penalty, barrier, augmented Lagrangian, and interior- point methods for convex and nonconvex constrained optimization; sequential quadratic programming; stochastic algorithms; alternating direction optimization methods; semi- definite programing, and more. In-class examples, homework, and projects will fea- ture some of the practical applications of these algorithms to solve real-world problems. Homework problems will consist of written problems as well as computer programming assignments in Matlab (or your favorite programming language).

This course is suitable for upper level undergraduate and beginning graduate students from Mathematics, Engineering, Operations research, Computer science, Biology, Chemistry, and Physics.


Math 151 Partial Differential Equations I Course Information

Fall 2017

BLOCK: D+ (Tue, Thu 10:30–11:45) INSTRUCTOR: Bruce Boghosian EMAIL: [email protected] OFFICE: 211 Bromfield-Pearson Hall OFFICE HOURS: (Spring 2017) Tu 1:00–2:30, Th 1:00–2:30 PHONE: (617) 627-3054

PREREQUISITES: MA 42 or MA 44, MA 51 or MA 155, and MA 70 or MA 72. (Note: MA 151 and ME 150 cannot both be taken for credit.)

TEXT: To be determined

COURSE DESCRIPTION: Partial differential equations are the principal language of mathematical science, and this course will provide the student with a working knowledge of that language. We shall derive and analyze the important prototypical linear partial differential equations for potential theory, diffusion and wave motion. We will study their fundamental solutions, mean-value formulas, maximum principles and energy principles. The mathematical tools that we will use for this purpose include elements of vector calculus, linear algebra, ordinary differential equations, Sturm-Liouville problems, special functions, Fourier series, eigenfunction expansions, Fourier transforms and Green’s functions.

This course is suitable for upper level undergraduate and beginning graduate students from Mathematics, Engineering, Biology, Chemistry and Physics.


Math 155 Nonlinear Dynamics and Chaos Course Information

Fall 2017

BLOCK: G+ (MW 1:30–2:45) INSTRUCTOR: Christoph Bo rgers EMAIL: [email protected] OFFICE: 215 Bromfield-Pearson Hall OFFICE HOURS: (Spring 2017) MTWTh 12:30–1:25 PHONE: (617) 627-2366

PREREQUISITES: Math 42 or Math 44, and at least one of the following three: Math 51, Math 70, Math 72.

TEXT: Steven H. Strogatz, Nonlinear Dynamics and Chaos, Westview Press

COURSE DESCRIPTION: This is a course on ordinary differential equations, with emphasis on qualitative, geometric aspects of the subject. We will do far more work on understanding properties of solutions than on computing solutions by hand. Students will be given a large set of Matlab programs with which they can (but will not be required to) conduct their own computational experiments.

Mathematical ideas include phase space analysis (stability of fixed points, limit cycles), bifurcations (saddle-node collisions, pitchfork and transcritical bifurcations, Hopf bifurcations, saddle-cycle collisions), reduction to iterated maps (Poincare maps, Lorenz map, the strobe light map for studying synchronization phenomena), fractals.

Strong emphasis will be placed on applications, including population growth models, “tipping points” (for instance, sudden collapse of a population in a slowly deteriorat- ing environment), thresholds in infectious disease, tumor growth models, competition of species, predator-prey cycles, lasers, the pendulum, neurons and neuronal networks, human sleep and circadian rhythms, oscillating chemical reactions, Lorenz’s equations (a simplified model of chaotic dynamics of convection rolls in the atmosphere), coding via synchronized chaos.

The course is suitable for upper level undergraduate and beginning graduate students from Mathematics, Engineering, Biology, Chemistry, and Physics.

Applied Mathematics majors can use Math 155 in place of Math 51 to satisfy their Differential Equations requirement.


Math 161 Probability Course Information

Fall 2017

BLOCK: E+ (M, W, F 10:30am–11:45am) INSTRUCTOR: Patricia Garmirian EMAIL: [email protected] OFFICE: 201 Bromfield-Pearson Hall OFFICE HOURS: (Spring 2017) M 1:00–3:00pm, W 1:00–3:00pm PHONE: (617) 627-2682


TEXT: A First Course in Probability by Sheldon Ross ISBN-13: 978-0321794772

COURSE DESCRIPTION: Suppose that you play a game where you flip a fair coin 100 times in succession. Each time the coin lands heads, you win $1, and each time the coin lands tails, you lose $1. After 100 flips, how much money do you have? It is pretty clear that we do not know–we cannot predict the future. However, we can talk about your possible winnings and the probabilities which correspond to each of these winnings. Your winnings after 100 flips is called a random variable, a function whose values correspond to the outcomes of a random experiment, and thus each value corresponds to a probability. It turns out that after 100 flips, your total winnings has an approximate normal or bell curve distribution centered at $0. The fact that this random variable is approximately normally distributed is a result of an extremely important theorem in probability: The Central Limit Theorem.

In this course, we will discuss not only the normal distribution but several other important discrete and continuous probability distributions: Bernoulli, geometric, binomial, Poisson, uniform, exponential, and Gamma. The course will conclude with the discussion of two very important theorems, each of which has a wide range of applications: the Cen- tral Limit Theorem and the Law of Large Numbers.

The course will have weekly homework assignments, weekly problem sessions, two midterm exams, and a final exam.


Math 211 Analysis Course Information

Fall 2017

BLOCK: F (Tue, Thu, Fri 12:00–12:50) INSTRUCTOR: Alex Hening EMAIL: OFFICE: OFFICE HOURS: PHONE:

PREREQUISITES: Math 135 or equivalent, Math 136 is recommended.

TEXT: Gerald B. Folland, Real Analysis: Modern Techniques and Their Applications, Sec- ond Edition.

COURSE DESCRIPTION: The course will cover chapters 1-6 of the text. However, not every chapter will be covered entirely. We will aim to cover what is most relevant for the Qual- ifying Exam (see http://math.tufts.edu/graduate/qualifyingExams.htm):

Metric and topological spaces: Topologies, bases, ways of generating topologies, Haus- dorff, separable, first and second countable, completion of metric spaces, complete metric spaces (Baire category theorem), compactness in arbitrary topological spaces, in metric spaces, in (C(K); d∞) with K compact (Arzela-Ascoli theorem), in product spaces with the product topology (Tychonoff’s theorem).

Measure and integration: General measure spaces (including sigma-algebras, measures), Caratheodory Extension theorem, Borel sets, Lebesgue measurable sets, counting measure, Cantor set and Cantor function, Borel measures on the real line, measurable functions, non-Lebesgue measurable set, completion of a measure, Lebesgue integral, relation of Riemann integral to the Lebesgue integral, Limit theorems for integrals (monotone and dominated convergence theorems, Fatou’s Lemma), absolutely continuous and singular measures (Radon-Nikodym theorem), product measures on product-measurable spaces, Fubini-Tonelli theorem.

Banach spaces: Lp(X; S; ·), 1 ≤ p < ∞ and lp-Ho lder ’s and Minkowski’s inequalities, relationships beween Lp spaces for different p, Hilbert spaces (inner products, orthogonal decomposition, orthonormal bases), (C(K); d∞), Bounded linear operators (dual spaces including Riesz representation theorems for Hilbert spaces, Lp-spaces, 1 ≤ p < ∞).

http://math.tufts.edu/graduate/qualifyingExams.htm)

Math 215 Algebra Course Information

Fall 2017

BLOCK: D+ (Tu, Th 10:30–11:45) INSTRUCTOR: Robert Kropholler EMAIL: [email protected] OFFICE: 202 Bromfield-Pearson Hall OFFICE HOURS: (Spring 2017) Tu 2:30 – 3:30, Th 2:30 – 4:30 PHONE: (617) 627-2363

PREREQUISITES: Math 146 or equivalent.

TEXT: Abstract Algebra, 3rd edition by David S. Dummit and Richard M. Foote, Wiley & Sons, 2004, New York. (ISBN 0-471-43334-9)

COURSE DESCRIPTION: Algebra is the study of structures, it is the underpinning of many areas of mathematics. This course concentrates on four basic algebraic structures: groups, rings, modules, and fields. Since one of the purposes of the course is to prepare the students for the algebra qualifying exam, we will follow closely the syllabus for that exam which is below.

1. Generalities: Quotients and isomorphism theorems for groups, rings, modules.

2. Groups:

• The action of a group on a set; applications to conjugacy classes and the class equation.

• The Sylow Theorems; simple groups.

• Simplicity of the alternating group An for n ? 5.

3. Rings and Modules:

• Polynomial rings, Euclidean domains, principal ideal domains.

• Unique factorization; the Gauss lemma and Eisenstein’s criteria for irreducibility.

• Free modules; the tensor product.

• Structure of finitely generated modules over a PID; applications (finitely generated abelian groups, canonical forms for linear transformations).

4. Fields:

• Algebraic, transcendental, separable, and Galois extensions, splitting fields.

• Finite fields, algebraic closures.

• The Fundamental Theorem of Galois theory for a finite extension of a field of arbitrary characteristic.


Many of these topics are covered in Math 145 and 146, but we will study them in greater depth. Students planning to take the algebra qualifying exam may need to do some additional study on their own if we do not cover all of these topics in one semester. The course is suitable for undergraduates who have done very well in Math 145 and/or 146, especially those wishing to attend graduate school in Mathematics.

Math 217 Geometry and Topology Course Information

Fall 2017

Block: J+ (Tue, Thu, 3:00–4:15 p.m.) Instructor: Loring Tu Email: [email protected]

Office: Bromfield-Pearson 206

Office hours: (Spring 2016) on leave

Phone: (617) 627-3262

Prerequisites: Math 135, 136, and 145.

Text: Loring Tu, An Introduction to Manifolds, 2nd edition, Springer, 2011.

Course description:

Undergraduate calculus progresses from differentiation and integration of functions on the real line to functions on the plane and in 3-space. Then one encounters vector-valued functions and learns about integrals on curves and surfaces. Real analysis extends differential and integral calculus from R3 to Rn. This course is about the extension of calculus from curves and surfaces to higher dimensions.

The higher-dimensional analogues of smooth curves and surfaces are called manifolds. The constructions and theorems of vector calculus become simpler in the more general setting of manifolds; gradient, curl, and divergence are all special cases of the exterior derivative, and the fundamental theorem for line integrals, Green’s theorem, Stokes’ theorem, and the divergence theorem are different manifestations of a single general Stokes’ theorem for manifolds.

Higher-dimensional manifolds arise even if one is interested only in the three-dimensional

space which we inhabit. For example, if we call a rotation followed by a translation an affine motion, then the set of all affine motions in R3 is a six-dimensional manifold. As another example, the zero set of a system of equations is often, though not always, a manifold. We will study conditions under which a topological space becomes a manifold. Combining aspects of algebra, topology, and analysis, the theory of manifolds has found applications to many areas of mathematics and even classical mechanics, general relativity, and quantum field theory.

Topics to be covered included manifolds and submanifolds, smooth maps, tangent spaces, vector bundles, vector fields, Lie groups and their Lie algebras, differential forms, exterior differentiation, orientations, and integration.

There will be weekly problem sets, a midterm, and a final. Students who have not take Math 136 (Real Analysis II) may take it concurrently with this course. Undergraduates who have done well in the prerequisite courses should find this course within their competence.


n=1

Math 250 The Distribution of Prime Numbers Course Information

Fall 2017

BLOCK: H+ TTh (Tue, Thu 1:30–2:45) INSTRUCTOR: Robert Lemke Oliver EMAIL: [email protected] OFFICE: Bromfield-Pearson 116 OFFICE HOURS: (Spring 2017) Tue 2-3, Wed 10:30-11:30, Fri 1-2 PHONE: (617) 627-0436

PREREQUISITES: Math 135 (Real Analysis I) and Math 145 (Abstract Algebra I). Math 63 (Number Theory) and Math 158 (Complex Variables) will be useful, but are not required. In particular, a crash course in the necessary techniques from complex analysis will be given.

TEXT: None.

COURSE DESCRIPTION: The field of analytic number theory began with Euler’s observa- tion that the zeta function ζ(s) =

),∞ 1/ns “knows” something about the set of prime

numbers; in particular, the fact that the harmonic series diverges provides an alternative proof of the infinitude of the primes. These ideas took off when Riemann observed that a sufficient understanding of the complex analytic properties of ζ(s) would lead to a proof of the so-called prime number theorem, the statement that the number of primes up to some number x is about x/ log x. A proof of the prime number theorem along the lines that Riemann imagined was found by Hadamard and de la Vallee Poussin at the end of the 19th century, and our understanding of the primes has only grown since. A standard first course in analytic number theory would develop these ideas carefully and would dive into the technical analytic details with gusto.

This is not that course. Instead, the mantra will be, “How should we really think about prime numbers?”

Thus, our initial focus will be on the intuition and ideas leading to the proof of the prime number theorem, and we will blackbox the analytic machinery that often obfuscates the actual point of the proof. We will then prove Dirichlet’s theorem (how many primes up to x are congruent to a (mod q)?), and then see how knowledge of the primes in arithmetic progressions percolates into an understanding of even more subtle properties of primes. Some things we will talk about, related to recent developments in number theory, include:

• The ternary Goldbach problem, that every odd integer is a sum of three primes

• The 2013-14 work of Zhang, Maynard, and Tao on “bounded gaps between primes,” our most tangible progress toward the twin prime conjecture

• The Maier matrix method, a tool that can be used, e.g., to show that there are a million primes in a row ending in the digits 8675309

Grades will be based on homework, and a final presentation if enrollment permits.


Math 250-02 Functional Analysis Course Information

Fall 2017

BLOCK: G+ (Mondays and Wednesdays, 1:30–2:45 pm) INSTRUCTOR: Fulton Gonzalez EMAIL: [email protected] OFFICE: 203 Bromfield-Pearson Hall OFFICE HOURS: (Spring 2017) Tuesdays 2:30–4:30 pm, Fridays 2:30–3:30 pm PHONE: (617) 627-2368


TEXT: Functional Analysis, 2nd Edition, by Walter Rudin, McGraw-Hill (1991).

COURSE DESCRIPTION: The preface to Rudin’s book provides an apt description of functional analysis: it is “the study of certain topological-algebraic structures and of the methods by which knowledge of these structures can be applied to analytic problems.” This course will therefore introduce ideas and concepts essential for further study and research in areas such as partial differential equations, harmonic analysis, global analysis, several complex variables, and parts of applied mathematics.

We will start with some axiomatics on topological vector spaces (which generalize normed linear spaces). Topics include completeness, metrizability, local convexity, dual- ity theory, compact operators, the Krein-Milman theorem on extreme points.

Next,we will introduce the basic function and distribution spaces such as D, S and E/, and their topologies and mapping properties. They are the natural function spaces used in the study of partial differential equations. We will apply the machinery we develop to the study of Fourier transforms, which are topological isomorphisms from L2 to L2, S to S, and D to H (Paley-Wiener space).

Finally, we will study the spectral theory of bounded linear operators via the Gelfand- Naimark theory and the symbolic calculus of Banach algebras. The goal is to generalize the familiar notions in linear algebra such as spectrum, diagonalizability, positivity, polar decomposition, etc., in the infinite dimensional setting. The concepts we introduce will be especially useful in the study of harmonic analysis.

There will be six to eight problem sets in the course, and possible class presentations by the students.


Math 250 Dynamical Systems Course Information

Fall 2017

BLOCK: 10 (Monday 6:00–9:00pm) INSTRUCTOR: Boris Hasselblatt EMAIL: [email protected] OFFICE: 217 Bromfield-Pearson Hall OFFICE HOURS: (Spring 2017) Tuesday, Thursday, Friday 9:20–10:00am PHONE: (617) 627-3419


TEXT: A. B. Katok, B. Hasselblatt: “Introduction to the Modern Theory of Dynamical Systems,” Cambridge University Press 1995

COURSE DESCRIPTION: An introduction to the modern theory of dynamical systems with topics chosen to complement those taught in Mathematics 250 in Spring 2017, but without making that class a prerequisite.

The course will begin with the core theory of hyperbolic dynamical systems and then either develop this subject further or broaden the perspective by covering elliptic and possibly parabolic dynamics—participants will get to influence that choice.

Course participants will be given an opportunity to present a topic in dynamical systems at the end of the semester.


MATHEMATICS MAJOR CHECKLIST

STUDENTS: Submit with the Advisement Report and any other major or minor checklists to the Student

Services Desk by the due date. See attached for instructions and policies. If substitutions are made, it is the

student’s responsibility to make sure the substitutions are acceptable to the Math Department.

Student Name: I.D.:

Other Major(s): Minors:

TEN COURSES TO BE DISTRIBUTED AS FOLLOWS:

I. Five courses required of all majors:

Semester/Year Grade Credit

1. Math 42 Calculus III OR

Math 44 Honors Calculus

2. Math 70 Linear Algebra OR

Math 72 Abstract Linear Algebra

3. Math 135 Real Analysis I

4. Math 145 Abstract Algebra I

5. Math 136 Real Analysis II OR

Math 146 Abstract Algebra II

II. Two additional 100-level math courses.

Course Number Course Title Semester/Year Grade Credit

III. Three additional mathematics courses numbered 50 or higher (in the new numbering scheme); up to

two of these courses may be replaced by courses in related fields including: Chemistry 133, 134; Computer

Science 15, 126, 160, 170; Economics 107, 154, 201, 202, 207; Electrical Engineering 18, 107, 108, 125;

Engineering Science 151, 152; Mechanical Engineering 137, 138, 150, 165, 166; Philosophy 33, 103, 114, 170;

Physics 12, 13 any course numbered above 30; Psychology 107, 108, 140.


IV. If you have taken any other Mathematics courses that are not being used for the above requirements,

and you would like to have them considered for Latin Honors, please list them here:


V. List any of the above courses that you are also using towards another major.


Student’s Signature: Date:

I/We certify that completion of the above courses will satisfy all requirements for the Mathematics major.

Advisor’s Signature:

Date:

Department Chair’s Signature:

Date:

MATHEMATICS MAJOR INSTRUCTIONS AND POLICIES

• Ten courses required, beyond Calculus II.

• No major course may be taken Pass/Fail.

• If you have more than one major, please see Bulletin for rules on double-counting courses.

• If you have a minor, no more than two course credits used toward the minor may be used toward

foundation, distribution, major, or other minor requirements.

• Please see Departmental Website for complete major requirements and policies.

APPLIED MATHEMATICS MAJOR CHECKLIST

STUDENTS: Submit with the Advisement Report and any other major or minor checklists to the Student

Services Desk by the due date. See attached for instructions and policies. If substitutions are made, it is the

student’s responsibility to make sure the substitutions are acceptable to the Math Department.

Student Name: I.D.:

Other Major(s): Minors:

THIRTEEN COURSES TO BE DISTRIBUTED AS FOLLOWS:

I. Seven courses required of all majors:

1. Math 42 Calculus III

Math 44 Honors Calculus

2. Math 70 Linear Algebra

Math 72 Abstract Linear Algebra

3. Math 51 Differential Equations

Math 155 Nonlinear Dynamics & Chaos

4. Math 87 Mathematical Modeling

5. Math 158 Complex Variables

6. Math 135 Real Analysis I

7. Math 136 Real Analysis II


OR

OR

OR

II. One of the following:

Math 145 Abstract Algebra I

Math 61/Comp 61 Discrete Mathematics

Comp 15 Data Structures

Math/Comp 163 Computational Geometry


III. One of the following three sequences:

1. Math 126 Numerical Analysis/

Math 128 Numerical Algebra

2. Math 151 Applications of Advanced Calculus/


Math 152 Nonlinear Partial Differential Equations

3. Math 161 Probability /

Math 162 Statistics

IV. An additional course from the list below but not one of the courses chosen in section III:


Math 126 Numerical Analysis

Math 128 Numerical Algebra

Math 151 Applications of Advanced Calculus

Math 152 Nonlinear Partial Differential Equations

Math 161 Probability

Math 162 Statistics

IV. Two elective courses (Math courses numbered 61 or above are acceptable electives. With the approval of the

Mathematics Department, students may also choose as electives courses with strong mathematical content that are not

listed as Math courses.)


V. If you have taken any other Mathematics courses that are not being used for the above requirements, and you

would like to have them considered for Latin Honors, please list them here: Course Number Course Title Semester/Year Grade Credit

VI. List any of the above courses that you are also using towards another major.


Student’s Signature: Date:

I/We certify that completion of the above courses will satisfy all requirements for the Applied Mathematics major.

Advisor’s Signature:

Date:

Department Chair’s Signature:

Date:

APPLIED MATHEMATICS MAJOR INSTRUCTIONS AND POLICIES

• Thirteen courses required, beyond Calculus II.

• No major course may be taken Pass/Fail.

• If you have more than one major, please see Bulletin for rules on double-counting courses.

• If you have a minor, no more than two course credits used toward the minor may be used toward

foundation, distribution, major, or other minor requirements.

• Please see Departmental Website for complete major requirements and policies.

MATHEMATICS MINOR CONCENTRATION CHECKLIST

In addition to this form, students must complete the “Declaration of

Major(s)/Minor/Change of Advisor for Liberal Arts Students” form.

Name: I.D.#:

E-Mail Address: College and expected graduation semester/year:

Major(s):

Faculty Advisor for Minor (please print)

Please list courses by number. For transfer courses, list by title and add “T”. Indicate which courses are

incomplete, in progress, or to be taken.

Courses numbered under 100 will be renumbered starting in the Fall 2012 semester. Courses are listed

here by their new number, with the old number in parentheses.

Note: If substitutions are made for courses listed as “to be taken”, it is the student’s responsibility to make sure

that the substitutions are acceptable.

Six courses distributed as follows:

I. Two courses required of all minors. (Check appropriate boxes.)

If “in progress” or future semester, note semester.

Grade: Grade:

1. Math 42 (old: 13): Calculus III or 2. Math 70 (old: 46): Linear Algebra or

Math 44 (old: 18): Honors Calculus Math 72 (old: 54): Abstract Linear Algebra

II. Four additional math courses with course numbers Math 50 or higher (in the new

numbering scheme).

These four courses must include Math 135: Real Analysis I or 145: Abstract Algebra (or both).

Note that Math 135 and 145 are typically only offered in the fall.

Grade: Grade:

1. 3.

2. 4.

Note: It is the student’s responsibility to return completed, signed degree sheets

to the Office of Student Services, Dowling Hall.

(form revised September 2, 2015)

Student’s signature: Date:

Advisor’s signature: Date:

Jobs and Careers

The Math Department encourages you go to discuss your career plans with your professors. All of

us would be happy to try and answer any questions you might have. Professor Quinto has built up

a collection of information on careers, summer opportunities, internships, and graduate schools

and his web site (http://equinto.math.tufts.edu) is a good source.

Career Services in Dowling Hall has information about writing cover letters, resumes and job-

hunting in general. They also organize on-campus interviews and networking sessions with

alumni. There are job fairs from time to time at various locations. Each January, for example,

there is a fair organized by the Actuarial Society of Greater New York.

On occasion, the Math Department organizes career talks, usually by recent Tufts graduates. In

the past we had talks on the careers in insurance, teaching, and accounting. Please let us know if

you have any suggestions.

The Math Society

The Math Society is a student run organization that involves mathematics beyond the classroom.

The club seeks to present mathematics in a new and interesting light through discussions,

presentations, and videos. The club is a resource for forming study groups and looking into career

options. You do not need to be a math major to join! See any of us about the details. Check out

http://ase.tufts.edu/mathclub for more information.

The SIAM Student Chapter

Students in the Society for Industrial and Applied Mathematics (SIAM) student chapter organize

talks on applied mathematics by students, faculty and researchers in industry. It is a great way to

talk with other interested students about the range of applied math that’s going on at Tufts. You

do not need to be a math major to be involved, and undergraduates and graduate students from a

range of fields are members. Check out https://sites.google.com/site/tuftssiam/ for more

information.

http://equinto.math.tufts.edu/

http://ase.tufts.edu/mathclub

https://sites.google.com/site/tuftssiam/

BLOCK SCHEDULE

50 and 75 Minute Mon Mon Tue Tue Wed Wed Thu Thu Fri Fri 150/180 Minute Classes

Classes and Seminars

8:05-9:20 (A+,B+)

8:30-9:20 (A,B)

9:30-10:20 (A,C,D)

8:30-11:30 (0+,1+,2+,3+,4+)

9-11:30 (0,1,2,3,4)

10:30-11:20 (D,E)

10:30-11:45 (D+,E+)

12:00-12:50 (F)

12:00-1:15 (F+)

1:30-2:20 (G,H)

1:30-2:45 (G+,H+)

2:30-3:20 (H on Fri)

3:00-3:50 (I,J)

3:00-4:15 (J+,I+)

3:30-4:20 (I on Fri)

4:30-5:20 ( K,L)

4:30-5:20 ((J on Mon)

4:30-5:45 (K+,L+i)

1:30-4:00 (5,6,7,8,9)

1:20-4:20 (5+,6+,7+,8+,9+)

6:00-6:50 (M,N)

6:00-7:15 (M+,N+)

7:30-8:15 (P,Q)

7:30-8:45 (P+,Q+)

6:00-9:00 (10+,11+,12+,13+)

6:30-9:00 (10,11,12,13)

Notes

* A plain letter (such as B) indicates a 50 minute meeting time.

* A letter augmented with a + (such as B+) indicates a 75 minute meeting time.

* A number (such as 2) indicates a 150 minute class or seminar. A number with a + (such as 2+) indicates a 180 minute meeting time.

* Lab schedules for dedicated laboratories are determined by department/program.

* Monday from 12:00-1:20 is departmental meetings/exam block.

* Wednesday from 12:00-1:20 is the AS&E-wide meeting time.

* If all days in a block are to be used, no designation is used. Otherwise, days of the week (MTWRF) are designated (for example, E+MW).

* Roughly 55% of all courses may be offered in the shaded area.

* Labs taught in seminar block 5+-9+ may run to 4:30. Students taking these courses are advised to avoid courses offered in the K or L block.

E

E+

E

E+

E

E+

D

D+

D

D+

F

F+

F

F+

F

F+

G

G+

5

5+

H

H+

6

6+

G

G+

7

7+

H

H+

8

8+

G

H (2:30-3:20)

A+

A

B+

B

A+

A

B+

B

0+

0

1+

1

2+

2

3+

3

B+

B

4+

4 D C C A C

I

I+

J

J+

I

I+

J

J+

9

9+

J/K

K+

L

L+

K

K+

L

L+

I (3:30-4:20)

N/M

M+

10+

10

N

N+

11+

11

M

M+

12+

12

N

N+

13+

13

Q/P

P+

Q

Q+

P

P+

Q

Q+

Open

Open

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