Primarily for Undergraduates
Mathematics Ma. Introduction to Functions and Calculus I Catalog Number: 1981 Enrollment: Normally limited to 15 students per section. Meghan Anderson, Melody Chan, Peter M. Garfield, Meredith Hegg, 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 3, 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. Introduction to Functions and Calculus II
Mathematics 1a. Introduction to Calculus
Mathematics 1b. Calculus, Series, and Differential Equations
Mathematics 18 (formerly Mathematics 20). 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 Adam Jacob Half course (fall term). M., W., F., at 11. EXAM GROUP: 4 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. Real Analysis, Convexity, and Optimization
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. 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
Mathematics 145. Set Theory II  (New Course)
[Mathematics 152. Discrete Mathematics]
Mathematics 153. Mathematical BiologyEvolutionary Dynamics
Mathematics 154. Probability Theory
Mathematics 155r. Combinatorics
[Mathematics 168. Computability Theory]

Primarily for Graduates
Mathematics 212a. Real Analysis Catalog Number: 5446 Yum Tong Siu 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. Algebraic Number Theory]
[Mathematics 223b. 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. Algebraic Topology
Mathematics 231br. Advanced Algebraic Topology
Mathematics 232a. Introduction to Algebraic Geometry I
Mathematics 232br. Algebraic Geometry II
Mathematics 233a. Theory of Schemes I
Mathematics 233br. Theory of Schemes II
Mathematics 241. Fine Structure Theory  (New Course)
Mathematics 243. Evolutionary Dynamics
Mathematics 253x. Analysis on Manifolds via the Laplace Operator  (New Course)
Mathematics 253y. Probability and Brownian Motion  (New Course)
Mathematics 255x. Topics in Diophantine Geometry  (New Course)
Mathematics 255y. Spin Geometry and SuperSymmetry  (New Course)
Mathematics 256x. The Theory of ErrorCorrecting Codes  (New Course)
Mathematics 265x. Reasoning via Models  (New Course)
Mathematics 268. Pure Motives and Rigid Local Systems  (New Course)
Mathematics 270x. Topics in Automorphic Forms  (New Course)
Mathematics 273x. Topics in Algebraic Geometry  (New Course)
Mathematics 280x. Topics in Mathematical Physics: Bridgeland Stability Conditions  (New Course)
Mathematics 280y. Topics in Symplectic Geometry  (New Course)
Mathematics 282y. Tamagawa Numbers of Algebraic Groups over Function Fields  (New Course)
Mathematics 284x. Relations between Clifford Algebras and Lie Algebras  (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 *Freshman Seminar 40p. Making the Grade? Middle and High School Math Education in the U.S.  (New Course) Philosophy 144. Logic and Philosophy 
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., 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 318. Topics in Number Theory
*Mathematics 321. Topics in Mathematical Physics
*Mathematics 327. Topics in Several Complex Variables
*Mathematics 333. Topics in Complex Analysis, Dynamics and Geometry
*Mathematics 335. Topics in Differential Geometry and Analysis
*Mathematics 339. Topics in Combinatorics
*Mathematics 341. Topics in Number Theory
*Mathematics 345. Topics in Geometry and Topology
*Mathematics 346y. Topics in Analysis: Quantum Dynamics
*Mathematics 352. Topics in Algebraic Number Theory
*Mathematics 355. Topics in Category Theory and Homotopy Theory
*Mathematics 356. Topics in Harmonic Analysis
*Mathematics 358. Topics in Arithmetic Geometry
*Mathematics 361. Topics in Differential Geometry and Analysis  (New Course)
*Mathematics 363. Topics in Elliptic Fibrations and String Theory  (New Course)
*Mathematics 365. Topics in Differential Geometry
*Mathematics 373. Topics in Algebraic Topology
*Mathematics 374. Topics in Number Theory  (New Course)
*Mathematics 381. Introduction to Geometric Representation Theory
*Mathematics 382. Topics in Algebraic Geometry
*Mathematics 385. Topics in Set Theory  (New Course)
*Mathematics 387. Topics in Mathematical Physics: Bridgeland Stability Conditions  (New Course)
*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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