110.105 (Q)

INTRODUCTION TO CALCULUS (4) Breiner Mese  Limit 25 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) Ching/Budur Song     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

Lec. II

05

 06

07

08

 MTW 10

Th 9

Th 10:30

F 9

F12

MTW 10

Th 9

Th 10:30

F 9

F12

110.107 (Q)          

CALCULUS II  (FOR BIOLOGICAL AND SOCIAL SCIENCE)  (4) Zhang  Limit 27 25 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, applications for systems of linear differential equations, probability distributions. Many applications to the biological and social sciences will be discussed.  

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) Budur Song   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.  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

Lec. II

04

05

 MTW 10

Th 9

F 9

F 9

 MTW 11

Th  12

F 12

110.109 (Q)

CALCULUS II (FOR PHYSICAL SCIENCES AND ENGINEERING)  (4) Zucker  Limit 28 25 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

Th 10:30

F 9

F 12

110.113 (Q)

HONORS CALCULUS II (4) Goldberg Howald Limit 35   Prereq: A strong background in Calculus I, such as a 5 on the AP Calculus BC exam, or an “A” in 110.106 or 110.108     This is an honors alternative to 107 or 109 and meets general requirement for Calc. II. It is a more theoretical treatment of one variable integral calculus and is based on our modern understanding of the real number system as explained by Cantor, Dedekind, and Weierstrass. Rewarding to those who want to know the “why’s and how’s” of Calculus. Must already understand differential calculus (derivatives, differentiation, chain rule, optimization, related rates, etc.). Will learn about the theory of integration, the fundamental theorem(s) of Calculus, applications of integration, and Taylor series.

Lec.    Sec. 01

 MTW 3

Th 3

110.201 (Q)

LINEAR ALGEBRA (4) Faber   Limit 25 per section   Prereq: Calculus I
Vector spaces, matrices, and linear transformations. Solutions of systems of linear equations. Eigenvalues, eigenvectors, and diagonalization of matrices. Applications to differential equations.

Sec. 05 canceled 09/21/05

Lec.

Sec. 01

02

03

04

05

MTW 3

Th 10:30

Th12

F 9

F 12

F 12

110.202 (Q)

CALCULUS III (4) Brown  Limit 28 (secs 1-3) Limit 30 (sec. 4-9) Prerequisite: 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. 09 added 09/23/05

Lec. I

Sec. 01

02

03

04

Lec. II

05

06

07

08

09

 MTW 11

Th 10:30

Th 10:30

 Th 12 10:30

Th 12

MTW 12

 Th 12

F 9

F 9

F 12

F 11

110.204 (Q)

ELEMENTARY NUMBER THEORY (4) Shalika Prereq: Calculus I     The student is provided with many historical examples of topics each of which serves as an illustration of and provides a background for many years of current research in number theory. This course also provides the student with concrete examples of general abstract concepts studied in 110.401-402.  Primes and prime factorization, congruences, Euler's function, quadratic reciprocity, primitive roots, solutions to polynomial congruences (Chevalley's theorem), Diophantine equations including the Pythagorean and Pell equations, Gaussian integers, Dirichlet's theorem on primes.

Lec.

Sec. 01

MTW 12

F 12

110.209 (Q)

NUMBERS & GEOMETRY (3) Ono Limit 25  Prereq: Calculus I
In this course Algebra, Analysis & Geometry meet. The course will cover the main ideas of Euclid geometry, arithmetic, & the theory of real numbers.

Course canceled 09/21/05

Sec. 01

MTW 1

110.211 (Q)

HONORS CALCULUS III (4) Consani  Limit 35 Prereq: B+ or better in Calculus II, or 5 on the Calculus BC AP Exam
This course includes the material in Calculus III (202) with some additional applications and theory. Recommended for mathematically able students majoring in physical science, engineering, or especially mathematics.  211-212 used to be an integrated year-long course, but now the two are independent courses and can be taken in either order.

Lec.

Sec. 01

02

MTW 12

F 12

F 11

110.212 (Q)

HONORS LINEAR ALGEBRA (4) Porod Wilson  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 year-long 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

110.225 (Q)

PUTNAM PROBLEM SOLVING (3) Staff Problem solving course to prepare students for the Putnam exam

Sec. 01

TTh 6-7:15pm

110.228 (Q)

NON-EUCLIDEAN GEOMETRY (3) Wilson Mese Wilson  Prereq: high school geometry.    For 2,000 years, Euclidean geometry was the geometry.  In the 19th century, new, equally consistent but very different geometries were discovered.  This course will delve into these geometries on an elementary but mathematically rigorous level. 

Sec. 01

MTW 10 11

110.302 (E,Q)

DIFFERENTIAL EQUATIONS WITH APPLICATIONS (4) Zelditch Limit 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.

Sec. 01

02

03

04

MTW 1

Th10:30

F 12

Th 10:30

F 12

110.305 (Q)

INTRODUCTION TO LOGIC (4.5) Zhang  Prereq: None, but certain experience with mathematical thinking is assumed.    This is a course in formal mathematical logic. Techniques and strategies of proof, and study symbolic mathematical logic and formal logical reasoning will be learned. The process of building mathematics on a set theoretical foundation is explored and the Zermelo-Fraenkel set theory learned. The relationship between semantic truth and syntactic truth will be studied and theoretical limits to proof, including Godel's incompleteness theorem, will be discussed. Course canceled 03/24/05

Sec. 01

MTW 1

110.311 (Q)

METHODS OF COMPLEX ANALYSIS (4.5) Zhang Prereq: Calculus III    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

110.345 (Q)

BASIC NOTATIONS OF MATH (1) Howald  Prereq:  Calc III & Linear Algebra    This seminar course is intended to introduce majors and those interested in mathematics to a large collection of topics that they may not have seen before.  It meets weekly with a different speaker each week.  Course canceled 03/24/05

Sec. 01

W 4

110.369 (Q, N)

INTRODUCTION TO MATHEMATICAL BIOLOGY (4) Morava    Limit 25   Prereq: 110.107, 110.302
We will consider in some detail successful cases of mathematical modeling taken from the biological literature, such as segmentation in fruit flies, the clock and wave model for the development of the spinal column of vertebrates, computer simulation of the shoot apical meristem in botany, and algebraic models for DNA sequence and its possible application to immunology. The goal is to find common mathematical themes applicable across a wide spectrum of living systems.                                

Cross-listed with Physics

Sec. 01

MTW 11

110.401 (Q)

ADVANCED ALGEBRA I (4.5) Faber   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.

Sec. 01

MTW 11

110.405 (Q)

ANALYSIS I (4.5) Spinu 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 9

110.415 (Q)

HONORS ANALYSIS I (4.5) Minicozzi 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) Spruck  Prereq: Calculus I, II and III  Limit 25
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 (often geometric) problems:  brachistochrone, geodesics, minimum surface area of revolution, isoperimetric problem, curvature flows.  The course in a seminar style with active participation required. Additional material as required (some differential geometry of curves and surfaces) to hold prerequisites to a minimum.

Sec. 01

MTW 2

110.439 (Q)

INTRODUCTION TO DIFFERENTIAL GEOMETRY (4.5) Mese   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 9 11

110.443 (Q)

FOURIER ANALYSIS & GENERALIZED FUNCTIONS (4.5) Spinu  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 transform. 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 12

110.601

ALGEBRA Kong

Sec. 01

MTW 12 11

110.605

REAL VARIABLES Minicozzi Prereq: 110.405, 110.413 or equivalent.

Sec. 01

MTW 10

110.611

COMPLEX GEOMETRY    Shiffman    

Sec. 01

MT 1-2:15

110.615

ALGEBRAIC TOPOLOGY   Boardman    Prereq:110.401, 110.413

Sec. 01

ThF 2-3:15

110.619

LIE GROUPS & LIE ALGEBRAS Shalika  Prereq: 110.402

Sec. 01

MTW 11

110.631

PARTIAL DIFFERENTIAL EQUATIONS Spruck Prereq: 110.605-606

Sec. 01

MT 10-11:30

110.643

ALGEBRAIC GEOMETRY Shokurov Prereq: 110.601-602

Sec. 01

MW 4, T 3 MTW 2

110.669

INTRODUCTION TO MATHEMATICAL BIOLOGY Morava

Sec. 01

MTW 11

110.730

TOPICS IN COMPLEX GEOMETRY Wentworth

Sec. 01

MW 11-12:15

110.733

TOPICS IN ALGEBRAIC NUMBER THEORY Ono

Sec. 01

M 2:15-3:30, W 12-1:30
MTW 12

110.737

TOPICS IN ALGEBRAIC GEOMETRY  Consani

Sec. 01

MW 2:30-3:45

110.777

JAMI SEMINAR  Shokurov

Sec. 01

MW 1-2:15

110.799

THESIS RESEARCH

Sec. 01

TBA

110.800

INDEPENDENT STUDY -GRADUATES

Sec. 01

TBA