Primarily for Undergraduates
Mathematics Ma. Introduction to Functions and Calculus I Catalog Number: 1981 Enrollment: Normally limited to 15 students per section. Robin Gottlieb, Sarah Chisholm, Peter M. Garfield, Brendan Kelly, Upendra Prasad, 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 2, 8:30 am, Science Center C. 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 together with Mathematics Mb, can be followed by Mathematics 1b.
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 Jonathan Mboyo Esole Half course (spring term). M., W., F., at 1. EXAM GROUP: 8 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. 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 144. Model Theory]
Mathematics 145a. Set Theory I  (New Course)
Mathematics 145b. Set Theory II  (New Course)
Mathematics 152. Discrete Mathematics
[Mathematics 153. Mathematical BiologyEvolutionary Dynamics]
Mathematics 154. Probability Theory
Mathematics 155r. Combinatorics
Mathematics 156. Mathematical Foundations of Statistical Software  (New Course)
Mathematics 157. Mathematics in the World  (New Course)
Mathematics 161. Category Theory in Context  (New Course)

Primarily for Graduates
Mathematics 212a. Real Analysis Catalog Number: 5446 Shlomo Z. Sternberg Half course (fall term). Tu., Th., 11:30–1. EXAM GROUP: 15 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. 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 243. Evolutionary Dynamics
Mathematics 250. Algebraic Invariants of Knots  (New Course)
Mathematics 258x. Random Matrix
Mathematics 259. Diophantine Definability  (New Course)
Mathematics 261. Topics in Symplectic Geometry: Langrangian Intersection Theory and SYZ  (New Course)
Mathematics 262. The Geometry of the Complex MongeAmpere Equation  (New Course)
Mathematics 262x. Topics in Geometric Analysis  (New Course)
Mathematics 263y. Topics in Geometry and Physics: KTheory  (New Course)
[Mathematics 265. Reductive Groups Over Local and Global Fields]  (New Course)
Mathematics 266. Intersection Theory in Algebraic Geometry  (New Course)
Mathematics 269. Topics in Kinetic Theory  (New Course)
Mathematics 271. Topics in Arithmetic Statistics  (New Course)
Mathematics 275. Topics in Geometry and Dynamics  (New Course)
Mathematics 281. Algebraic Ktheory and Manifold Topology  (New Course)

Crosslisted Courses
Applied Mathematics 104. Series Expansions and Complex Analysis Applied Mathematics 105. 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. *History of Science 206r. "It’s Only a Hypothesis" [Philosophy 144. Logic and Philosophy] 
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: 11 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 303. Topics in Diophantine Problems  (New Course)
*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 343. Topics in Complex Geometry  (New Course)
*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
*Mathematics 362. Topics in Number Theory  (New Course)
*Mathematics 363. Topics in Elliptic Fibrations and String Theory
*Mathematics 365. Topics in Differential Geometry
*Mathematics 373. Topics in Algebraic Topology
*Mathematics 374. Topics in Number Theory
*Mathematics 381. Introduction to Geometric Representation Theory
*Mathematics 382. Topics in Algebraic Geometry
*Mathematics 385. Topics in Set Theory
*Mathematics 387. Topics in Mathematical Physics: Bridgeland Stability Conditions
*Mathematics 388. Topics in Mathematics and Biology
*Mathematics 389. Topics in Number Theory

Source
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