Primarily for Undergraduates
Mathematics Ma (formerly Mathematics Xa). Introduction to Functions and Calculus I Catalog Number: 1981 Enrollment: Normally limited to 15 students per section. Juliana Belding, Janet Chen, Rachel Epstein, Robin Gottlieb, John Hall, and members of the Department Half course (fall term). Section meeting times: Section I: M., W., F., at 10; Section II: M., W., F., at 11; Section III: M. W. F., at 12 (with sufficient enrollment); and a twice weekly lab session to be arranged. The study of functions and their rates of change. Fundamental ideas of calculus are introduced early and used to provide a framework for the study of mathematical modeling involving algebraic, exponential, and logarithmic functions. Thorough understanding of differential calculus promoted by year long reinforcement. Applications to biology and economics emphasized according to the interests of our students. Note: Required first meeting: Wednesday, September 1, 8:30 am, Science Center D. Participation in a one and a half hour workshop is required each week. Participation in the weekly problem sessions is also encouraged. This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning. This course, when taken for a letter grade together with Mathematics Mb, meets the Core area requirement for Quantitative Reasoning.
Mathematics Mb (formerly Mathematics Xb). Introduction to Functions and Calculus II
Mathematics 1a. Introduction to Calculus
Mathematics 1b. Calculus, Series, and Differential Equations
Mathematics 19a. Modeling and Differential Equations for the Life Sciences
Mathematics 19b. Linear Algebra, Probability, and Statistics for the Life Sciences
Mathematics 20. Algebra and Multivariable Mathematics for Social Sciences
Mathematics 21a. Multivariable Calculus
Mathematics 21b. Linear Algebra and Differential Equations
Mathematics 23a. Linear Algebra and Real Analysis I
Mathematics 23b. Linear Algebra and Real Analysis II
Mathematics 25a. Honors Linear Algebra and Real Analysis I
Mathematics 25b. Honors Linear Algebra and Real Analysis II
*Mathematics 55a. Honors Abstract Algebra
Mathematics 55b. Honors Real and Complex Analysis
*Mathematics 60r. Reading Course for Senior Honors Candidates
*Mathematics 91r. Supervised Reading and Research
*Mathematics 99r. Tutorial

For Undergraduates and Graduates
See also Applied Mathematics and Statistics. Mathematics 101. Sets, Groups and Topology Catalog Number: 8066 Clifford Taubes Half course (spring term). M., W., F., at 1. EXAM GROUP: 6 An introduction to rigorous mathematics, axioms, and proofs, via topics such as set theory, symmetry groups, and lowdimensional topology. Note: Familiarity with algebra, geometry and/or calculus is desirable. Students who have already taken Mathematics 23a,b, 25a,b or 55a,b should not take this course for credit. This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning or the Core area requirement for Quantitative Reasoning. Prerequisite: An interest in mathematical reasoning.
Mathematics 110. Vector Space Methods for Differential Equations  (New Course)
Mathematics 112. Introductory Real Analysis
Mathematics 113. Analysis I: Complex Function Theory
Mathematics 114. Analysis II: Measure, Integration and Banach Spaces
Mathematics 115. Methods of Analysis
Mathematics 116. Convexity and Optimization with Applications
Mathematics 118r. Dynamical Systems
Mathematics 121. Linear Algebra and Applications
Mathematics 122. Algebra I: Theory of Groups and Vector Spaces
Mathematics 123. Algebra II: Theory of Rings and Fields
Mathematics 124. Number Theory
Mathematics 129. Number Fields
Mathematics 130 (formerly Mathematics 138). Classical Geometry
Mathematics 131. Topology I: Topological Spaces and the Fundamental Group
Mathematics 132. Topology II: Smooth Manifolds
Mathematics 136. Differential Geometry
Mathematics 137. Algebraic Geometry
Mathematics 141. Introduction to Mathematical Logic
Mathematics 144. Model Theory and Algebra
Mathematics 152. Discrete Mathematics
[Mathematics 153. Mathematical BiologyEvolutionary Dynamics]
Mathematics 154 (formerly Mathematics 191). Probability Theory
Mathematics 155r (formerly Mathematics 192r). Combinatorics
Mathematics 162. Introduction to Quantum Computing  (New Course)

Primarily for Graduates
Mathematics 212a (formerly Mathematics 212ar). Real Analysis Catalog Number: 5446 Shlomo Z. Sternberg Half course (fall term). Tu., Th., 11:30–1. EXAM GROUP: 13, 14 Banach spaces, Hilbert spaces and functional analysis. Distributions, spectral theory and the Fourier transform. Prerequisite: Mathematics 114 or equivalent.
Mathematics 212br. Advanced Real Analysis
Mathematics 213a. Complex Analysis
Mathematics 213br. Advanced Complex Analysis
Mathematics 221. Commutative Algebra
Mathematics 222. Lie Groups and Lie Algebras
Mathematics 223a (formerly Mathematics 251a). Algebraic Number Theory
Mathematics 223b (formerly Mathematics 251b). Algebraic Number Theory
[Mathematics 224. Representations of Reductive Lie Groups]
[Mathematics 229x. Introduction to Analytic Number Theory]
Mathematics 230a. Differential Geometry
Mathematics 230br. Advanced Differential Geometry
Mathematics 231a (formerly Mathematics 272a). Algebraic Topology
Mathematics 231br (formerly Mathematics 272b). Advanced Algebraic Topology
Mathematics 232a (formerly Mathematics 260a). Introduction to Algebraic Geometry I
Mathematics 232br (formerly Mathematics 260b). Introduction to Algebraic Geometry II
[Mathematics 233a (formerly Mathematics 261a). Theory of Schemes I]
[Mathematics 233br (formerly Mathematics 261b). Theory of Schemes II]
Mathematics 243 (formerly Mathematics 234). Evolutionary Dynamics
Mathematics 253. Introduction to Computability and Randomness  (New Course)
Mathematics 255. Topics in General Relativity  (New Course)
Mathematics 258x. Random Matrix  (New Course)
Mathematics 267x. Semiclassical Analysis  (New Course)
Mathematics 276x. General Relativity Seminar  (New Course)
Mathematics 277x. Mapping Class Groups and Teichmuller Theory  (New Course)
Mathematics 278x. Analytic Methods in Complex and Algebraic Geometry  (New Course)
Mathematics 281x. Degeneration Methods in Enumerative Geometry  (New Course)
Mathematics 282x. Algebraic Differential Equations  (New Course)
Mathematics 283x. Some Aspects of Trace Formulae  (New Course)
Mathematics 286x. Finite Linear Groups and Their Representations  (New Course)
Mathematics 287x. Algebraic LTheory and Surgery  (New Course)
Mathematics 294x. Complex Manifolds, Its Complex Structure and the Metrics Supported by Them  (New Course)
Mathematics 296. Complex Dynamics and Fractal Groups  (New Course)
Mathematics 297. Stochastic Analysis  (New Course)

Crosslisted Courses
Applied Mathematics 105a. Complex and Fourier Analysis Applied Mathematics 105b. Ordinary and Partial Differential Equations Applied Mathematics 107. Graph Theory and Combinatorics Empirical and Mathematical Reasoning 14. Fat Chance *Freshman Seminar 21u. Calculating Pi *Freshman Seminar 24i. Mathematical Problem Solving *Freshman Seminar 26s. Mathematical Structures and Gödel’s Completeness Theorem *Philosophy 142. Set Theory: The Higher Infinite: Proseminar *Philosophy 142q. Topics in Set Theory: Proseminar  (New Course) 
Reading and Research
*Mathematics 300. Teaching Undergraduate Mathematics Catalog Number: 3996 Robin Gottlieb and Jameel AlAidroos Half course (fall term). Tu., 1–2:30. EXAM GROUP: 15, 16 Become an effective instructor. This course focuses on observation, practice, feedback, and reflection providing insight into teaching and learning. Involves iterated videotaped microteaching sessions, accompanied by individual consultations. Required of all mathematicsgraduate students.
*Mathematics 304. Topics in Algebraic Topology
*Mathematics 306. Topics in Representation Theory
*Mathematics 308. Topics in Number Theory and Modular Forms
*Mathematics 313. Topics in Geometrical Representation Theory
*Mathematics 314. Topics in Differential Geometry and Mathematical Physics
*Mathematics 316. Topics in Algebraic Topology / Arithmetic Geometry
*Mathematics 317. Topics in Number Theory and Algebraic Geometry
*Mathematics 318. Topics in Number Theory
*Mathematics 320. Topics in Deformation Theory
*Mathematics 321. Topics in Mathematical Physics
*Mathematics 327. Topics in Several Complex Variables
*Mathematics 332. Topics in Algebraic Geometry  (New Course)
*Mathematics 333. Topics in Complex Analysis, Dynamics and Geometry
*Mathematics 335. Topics in Differential Geometry and Analysis
*Mathematics 336. Topics in Mathematical Logic  (New Course)
*Mathematics 338. Topics in Complex Dynamics
*Mathematics 345. Topics in Geometry and Topology
*Mathematics 346y. Topics in Analysis: Quantum Dynamics
*Mathematics 350. Topics in Mathematical Logic
*Mathematics 351. Topics in Algebraic Number Theory
*Mathematics 352. Topics in Algebraic Number Theory
*Mathematics 353. Topics in Teichmüller Theory  (New Course)
*Mathematics 356. Topics in Harmonic Analysis
*Mathematics 358. Topics in Arithmetic Geometry  (New Course)
*Mathematics 365. Topics in Differential Geometry
*Mathematics 366. Topics in Probability and Analytic Number Theory  (New Course)
*Mathematics 373. Topics in Algebraic Topology
*Mathematics 377. Topics in Number Theory  (New Course)
*Mathematics 381. Introduction to Geometric Representation Theory
*Mathematics 382. Topics in Algebraic Geometry
*Mathematics 388. Topics in Mathematics and Biology
*Mathematics 389. Topics in Number Theory
*Mathematics 394. Topics in ManyBody Quantum System
*Mathematics 395. Topics in Symplectic, Contact, and Low  Dimensional Topology
*Mathematics 397. Some Aspects of Trace Formula  (New Course)

General education course
Source
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