MATHEMATICS

110.105 (Q)

INTRODUCTION TO CALCULUS (4) Macdonald   Limit 30 per section   This course starts from scratch and provides students with all the background necessary for the study of calculus. It includes a review of algebra, trigonometry, exponential and logarithmic functions, coordinates and graphs. Each of these tools will be introduced in its cultural and historical context. The concept of the rate of change of a function will be introduced. Not open to students who have studied calculus in high school.

Lec.
 Sec. 01
02

MTW 10
F  9
Th 10:30

110.106 (Q)

CALCULUS I (For Biological and Social Science) (4)
Lec. I - Ha
Lec. II - Consani                    
Limit 25 per section 
Differential and integral calculus. Includes analytic geometry, functions, limits, integrals and derivatives, introduction to differential equations, functions of several variables, linear systems, applications for systems of linear differential equations, probability distributions. Many applications to the biological and social sciences will be discussed.

Lec.I
Sec. 01
02
03
04
05
Lec. II
 06
07
08
09

MTW 10
Th  9
Th 10:30
F  9
F 12
Th 9
MTW 10
Th 10:30
F  9
F 12
F 12

110.107 (Q)   

CALCULUS II  (For Biological and Social Science)  (4) Morava    Limit 30 per section   Prereq: C- or better in Calculus I Differential and integral calculus. Includes analytic geometry, functions, limits, integrals and derivatives, introduction to differential equations, functions of several variables, linear systems, and applications for systems of linear differential equations, probability distributions.

Lec.
Sec.01
02
03
04

MTW 10
Th  9
Th  9
Th 10:30
 Th 12

110.108 (Q)

CALCULUS I (For Physical Sciences and Engineering)  (4) Spinu   Limit 28 per section  Differential and integral calculus. Includes analytic geometry, functions, limits, integrals and derivatives, polar coordinates, parametric equations, Taylor's theorem and applications, infinite sequences and series. 

Lec. I
Sec. 01
02
Lec. II
03
04

MTW 10
Th 9
F 9
 MTW 11
Th 12
F 12

110.109 (Q)

CALCULUS II (For Physical Sciences and Engineering)  (4) Brown
Limit 28 per section  Prereq: C- or better in Calculus I  Differential and integral calculus. Includes analytic geometry, functions, limits, integrals and derivatives, polar coordinates, parametric equations, Taylor's theorem and applications, infinite sequences and series.  Some applications to the physical sciences and engineering will be discussed, and the courses are designed to meet the needs of students in these disciplines.

Lec. I
Sec. 01
02
03
04
Lec. II
Sec. 05
06
07
08

MTW 10
F   9
F 12
F 12
 F   9
MTW 11
Th 10:30
F   9
F 12
F   9

110.113 (Q)

HONORS ONE VARIABLE CALCULUS (4) Spruck   Limit 35   

Lec.

Sec. 01

MTW 10

F 12

110.201 (Q)

LINEAR ALGEBRA (4) Zucker Consani   Limit 25 per section   Prereq: Calculus Vector spaces, matrices, and linear transformations. Solutions of systems of linear equations. Eigenvalues, eigenvectors, and diagonalization of matrices. Applications to differential equations. Secs. 04, 05 & 06 added 04/16/07

Lec.
Sec. 01
02
03
04
05
06

MTW 3
Th 10:30
Th 12
F 12
Th 10:30
Th 12
F 12

110.202 (Q)

CALCULUS III (4) Wilson   Limit 28 per section. Prereq: 110.107, 110.109 or 110.112. Calculus of functions of more than one variable: partial derivatives, and applications; multiple integrals, line and surface integrals; Green's Theorem, Stokes' Theorem, and Gauss' Divergence Theorem.

Sec. 01 canceled 8/28/07

Lec. I
Sec. 01
02
03
04
Lec. II
05
06
07
08
09

MTW 11
Th 10:30
F  12
Th 10:30
Th 12
MTW 12
Th 12
F 9
F 9
F 12
F 9

110.211 (Q)

HONORS MULTIVARIABLE CALCULUS (4) Zhang
Limit 35 per section

Lec.

Sec. 01

02

MTW 12

F 10:30

F 12

110.212 (Q)

HONORS LINEAR ALGEBRA (4) Zucker    Limit 30  Prereq:  Calculus II or III or equivalent, preferably honors.  This course includes the material in Linear Algebra (201) with some additional applications and theory. Recommended for mathematically able students majoring in physical science, engineering, or mathematics. 211-212 used to be an integrated yearlong course, but now the two are independent courses and can be taken in either order.  This course satisfies a requirement for the math major that its non-honors sibling does not.

Sec. 01

MTW 12
F 12

110.302 (E,Q)

DIFFERENTIAL EQUATIONS WITH APPLICATIONS (4) ZelditchLimit 35 per section.  Prereq: Calculus II This is an applied course in ordinary differential equations, which is primarily for students in the biological, physical and social sciences, and engineering. The purpose of the course is to familiarize the student with the techniques of solving ordinary differential equations. The specific subjects to be covered include first order differential equations, second order linear differential equations, applications to electric circuits, oscillation of solutions, power series solutions, systems of linear differential equations, autonomous systems, Laplace transforms and linear differential equations, mathematical models (e.g., in the sciences or economics).

Lec. I

Sec. 01
02
03
04

Lec. II
Sec. 05
06
07

MTW 12

Th 10:30
F 12
Th 10:30
F 12

MTW 1
F 9
Th 10:30
F 12

110.304 (Q)

ELEMENTARY NUMBER  THEORY (4) Ono  Limit 25  

Lec.
Sec. 01

MTW 2
F 12

110.311 (Q)

METHODS OF COMPLEX ANALYSIS (4.5) Kong  Prereq: Calculus III    Limit 35  
This course is an introduction to the theory of functions of one complex variable. Its emphasis is on techniques and applications, and it serves as a basis for more advanced courses. Functions of a complex variable and their derivatives; power series and Laurent expansions; Cauchy integral theorem and formula; calculus of residues and contour integrals; harmonic functions.

Sec. 01

MTW 1

110.401 (Q)

ADVANCED ALGEBRA I (4.5) Ching   Limit 40   Prereq: Linear Algebra An introduction to the basic notions of modern algebra. Elements of group theory: groups, subgroups, normal subgroups, quotients, homomorphisms. Generators and relations, free groups, products, commutative (Abelian) groups, finite groups. Groups acting on sets, the Sylow theorems. Definition and examples of rings and ideals. Introduction to field theory. Linear algebra over a field. Field extensions, constructible polygons, non-trisectability.

Lec.

Sec. 01

MTW 11

F 10:30

110.405 (Q)

ANALYSIS I (4.5) Wilkin Goldberg  Limit 55 Prereq: Calculus III and Linear Algebra This course is designed to give a firm grounding in the basic tools of analysis. It is recommended as preparation (but may not be a prerequisite) for other advanced analysis courses. Real and complex number systems, topology of metric spaces, limits, continuity, infinite sequences and series, differentiation, Riemann-Stieltjes integration.

Lec.

Sec. 01

MTW 1

F 12

110.415 (Q)

HONORS ANALYSIS I (4.5) Sogge Goldberg Limit 25   Prereq: B+ or higher in Calculus III and Linear Algebra.     This highly theoretical sequence in analysis is reserved for the most able students. The sequence covers the real number system, metric spaces, basic functional analysis, the Lebesgue integral, and other topics.

Lec.

Sec. 01

MTW 1

F 9

110.427 (Q)

INTRODUCTION TO THE CALCULUS OF VARIATIONS (4) Khosravi   Limit  25   Prereq: Calculus I, II and III    The calculus of variations is concerned with finding optimal solutions (shapes, functions, etc.) where optimality is measured by minimizing a functional (usually an integral involving the unknown functions) possibly with constraints. This introductory (self-contained) course will cover one dimensional problems (often geometric):  brachistochrone, geodesics, minimum surface area of revolution, isoperimetric problem, curvature flows. Additional material as required (some differential geometry of curves and surfaces) holding prerequisites to a minimum.

Sec. 01

MTW 3

110.439 (Q)

INTRODUCTION TO DIFFERENTIAL GEOMETRY (4.5) Wilkin    Limit 35  
Prereq: Calculus III, Linear Algebra Theory of curves and surfaces in Euclidean space: Frenet equations, fundamental forms, curvatures of a surface, theorems of Gauss and Mainardi-Codazzi, curves on a surface; introduction to tensor analysis and Riemannian geometry; theorema egregium; elementary global theorems.

Sec. 01

MTW 2

110.443 (E,Q)

FOURIER ANALYSIS (4.5) Zhang   Limit 25   Prereq: Calculus III, Linear Algebra. Recommend: 110.405. An introduction to the Fourier transform and the construction of fundamental solutions of linear partial differential equations. Homogeneous distributions on the real line: the Dirac delta function, the Heaviside step function. Operations with distributions: convolution, differentiation, Fourier transforms. Construction of fundamental solutions of the wave, heat, Laplace and Schrödinger equations. Singularities of fundamental solutions and their physical interpretations (e.g., wave fronts). Fourier analysis of singularities, oscillatory integrals, method of stationary phase.

Sec. 01

MTW 11

110.462 (Q)

PRIME NUMBERS AND RIEMANN’S ZETA FUNCTION (4) Ha Limit 25  Course canceled 01/22/08

Sec. 01

MTW 12

110.601

ALGEBRA Shokurov   Limit 25   

Sec. 01

MTW 3 10 1 12

110.605

REAL VARIABLES Sogge Limit 25    Prereq: 110.405, 110.413 or equivalent.

Sec. 01

MTW 2

110.611

COMPLEX GEOMETRY Shiffman   Limit 25   

Sec. 01

MTW 11 10

110.615

ALGEBRAIC TOPOLOGY   Boardman    Limit 25  Prereq: 110.401, 110.413

Sec. 01

ThF 2-3:15

110.617

NUMBER THEORY
Consani   Limit 25   

Sec. 01

MTW 12

110.619

LIE, GROUPS & LIE ALGEBRAS
Shalika   Limit 25   

Sec. 01

MTW 1

110.631

PARTIAL DIFFERENTIAL EQUATIONS Spruck Limit 25    Prereq: 110.605-606

Sec. 01

MW 2-3:30 MTW 11

110.645

RIEMANNIAN GEOMETRY Minicozzi   Limit 25

Sec. 01

MW 9:30-11 MTW 12

110.665

REPRESENTATION THEORY Boardman   Limit 25

Sec. 01

MTW 2

110.723

TOPICS IN AUTOMORPHIC FUNCTIONS (MODULAR FORMS) Faber   Limit 25 Course canceled 8/24/07

Sec. 01

TBA

110.726

TOPICS IN SEVERAL COMPLEX VARIABLES Staff   Limit 25

Sec. 01

TBA

110.733

TOPICS IN ALGEBRAIC NUMBER THEORY Ono
Limit 25   

Sec. 01

MW 3:30-5

110.737

TOPICS IN ALGEBRAIC GEOMETRY (LOG ADJUNCTION) Shokurov    Limit 25

Sec. 01

TBA

110.739

TOPICS IN ANALYTICAL NUMBER THEORY Ha Limit 25 Course added 8/28/07

Sec. 01

TBA

110.799

THESIS RESEARCH

Sec. 01

TBA

110.800

INDEPENDENT STUDY -GRADUATES

Sec. 01

TBA