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. Robin Gottlieb, Meghan Anderson, Janet Chen, Mboyo Esole, 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. EXAM GROUP: 3 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, August 31, 8:30 am, Science Center D. Participation in two, one and a half hour workshops are required each week. 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 Rachel Louise Epstein Half course (fall 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
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 117. Probability and Random Processes with Economic Applications  (New Course)
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 143. Set Theory
[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 167. Introduction to Symplectic Geometry  (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 251x. Vanishing of Torsion in the Cohomology of Arithmetic Groups  (New Course)
Mathematics 254y. Geometry with Valuations  (New Course)
Mathematics 259x. Analytic Theory of Modular Forms  (New Course)
Mathematics 261y. von Neumann Algebras  (New Course)
Mathematics 262y. Perverse Sheaves in Representation Theory  (New Course)
Mathematics 265y. Topics in the Moduli Theory of Sheaves  (New Course)
Mathematics 266x. Categorical Homotopy Theory  (New Course)
Mathematics 268x. Graph Limits  (New Course)
Mathematics 270. Advanced Probability Theory  (New Course)
Mathematics 271y. Probability Theory and Stochastic Process  (New Course)
Mathematics 273y. Contact Geometry in 3 Dimensions  (New Course)
Mathematics 285x. Representations of Reductive Groups over Local NonArchimedian Fields  (New Course)
Mathematics 287y. Geometry of Algebraic Curves  (New Course)
Mathematics 288x. The KahlerEinstein Metrics  (New Course)
Mathematics 289x. Equivariant Stable Homotopy Theory  (New Course)
Mathematics 291x. Seminar on Geometric Representation Theory  (New Course)
Mathematics 298. Random Matrices  (New Course)
*Mathematics 299. Graduate Tutorial in Number Theory

Crosslisted Courses
Applied Mathematics 104 (formerly Applied Mathematics 105a). Complex and Fourier Analysis Applied Mathematics 105 (formerly Applied Mathematics 105b). Ordinary and Partial Differential Equations Applied Mathematics 107. Graph Theory and Combinatorics Economics 2051r. Mathematical Methods in Economic Theory  (New Course) Empirical and Mathematical Reasoning 14. Fat Chance *Freshman Seminar 26s. Mathematical Structures and Gödel’s Completeness Theorem 
Math and History
East Asian Studies 131East Asian Studies 131. (Math+History) in East Asia: Time Behind Circles: Seminar. Catalog Number: 69724 Tomoko Kitagawa Half course (fall term). M., 13:30. EXAM GROUP: 6, 7, 8 This course examines the ideas behind various =93circles=94 that reflect the history of East Asian civilizations. The themes emphasized are the importance of time and metaphysics behind the mathematical ideas, the revolutionary developments in the field of geometry in East Asia, and the cultural exchange and influence of mathematical reasoning. The aim of the course is to learn the history of mathematics; instead of solving math problems, we will read various writings on mathematics, including passages from math textbooks, scribble notes, and biographies. This class also introduces the techniques in digital humanities for individual projects. Note: No background knowledge in mathematics is required. Intended for upperlevel undergraduate and graduate students.
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 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
*Mathematics 333. Topics in Complex Analysis, Dynamics and Geometry
*Mathematics 335. Topics in Differential Geometry and Analysis
*Mathematics 336. Topics in Mathematical Logic
*Mathematics 338. Topics in Complex Dynamics
*Mathematics 341. Topics in Number Theory  (New Course)
*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
*Mathematics 355. Topics in Category Theory and Homotopy Theory  (New Course)
*Mathematics 356. Topics in Harmonic Analysis
*Mathematics 358. Topics in Arithmetic Geometry
*Mathematics 365. Topics in Differential Geometry
*Mathematics 366. Topics in Probability and Analytic Number Theory
*Mathematics 373. Topics in Algebraic Topology
*Mathematics 377. Topics in Number Theory
*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 395. Topics in Symplectic, Contact, and Low  Dimensional Topology

General education course
Source
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