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. Meghan Anderson, Juliana Belding, 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: Tuesday, September 4, 8:30 am, Science Center D. Participation in two, one 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 18 (formerly Mathematics 20). Topics from Single and Multivariable Calculus for Social Sciences
Mathematics 19a. Modeling and Differential Equations for the Life Sciences
Mathematics 19b. Linear Algebra, Probability, and Statistics for the Life 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 103. Much Ado About Everything: The Mathematics of Leonhard Euler  (New Course)
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
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 168. Computability Theory  (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). 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 252y. Einstein Metrics  (New Course)
Mathematics 256y. Spectra and Stable Homotopy Theory  (New Course)
Mathematics 263x. Computational Techniques in Number Theory and Algebraic Geometry  (New Course)
Mathematics 264x. Random Matrix and Analytic Number Theory  (New Course)
Mathematics 266y. Geometry of Families of Curves  (New Course)
Mathematics 272y. Dynamics and Moduli Spaces  (New Course)
Mathematics 274y. Graph Limits Theory  (New Course)
Mathematics 276y. SYZ Mirror Symmetry  (New Course)
Mathematics 279y. Probability and Stochastic Processes  (New Course)
Mathematics 283y. Topics in Partial Differential Equations  (New Course)
Mathematics 285y. Tropical Geometry  (New Course)
Mathematics 288y. Aspects of Elliptic Fibrations in FTheory  (New Course)
Mathematics 290. Functional Analysis and Free Probability  (New Course)
Mathematics 292y. The Kahler Ricci Flow  (New Course)

Crosslisted Courses
Applied Mathematics 104 (formerly Applied Mathematics 105a). Series Expansions and Complex Analysis Applied Mathematics 105 (formerly Applied Mathematics 105b). Ordinary and Partial Differential Equations Applied Mathematics 107. Graph Theory and Combinatorics [Empirical and Mathematical Reasoning 14. Fat Chance] *Freshman Seminar 26s. Mathematical Structures and Gödel’s Completeness Theorem 
Nature of Evidence
Professor Noah Feldman, FAS Professor Barry MazurFall 2012 Seminar
Meets: Th 1:00pm  3:00pm in WCC Room 3008
2 classroom credits
Cotaught with mathematician Barry Mazur, this interdisciplinary, crosslisted class will explore and compare the nature of evidence and proof in a number of different fields: law, mathematics, the sciences, social sciences, and humanities. It will ask: What is considered evidence? How does what counts as evidence illuminate what it means to say we want to know and understand the truth? How can we communicate it across disciplines and contexts? Permission of instructors required. Single paper. Background in allied fields helpful but not required.
Subject Areas: Procedure & Practice.
Reading and Research
*Mathematics 300. Teaching Undergraduate Mathematics Catalog Number: 3996 Robin Gottlieb and Jameel AlAidroos Half course (fall term). Tu., Th., 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 mathematics graduate students.
*Mathematics 304. Topics in Algebraic Topology
*Mathematics 308. Topics in Number Theory and Modular Forms
*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 339. Topics in Combinatorics  (New Course)
*Mathematics 341. Topics in Number Theory
*Mathematics 345. Topics in Geometry and Topology
*Mathematics 346y. Topics in Analysis: Quantum Dynamics
*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
*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

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