MATHEMATICS

110.105 (Q)

INTRODUCTION TO CALCULUS (4) Wright  Limit 30 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) Zhang/Wilson 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.  

Sec. 09 added 8/01/06

Lec.I

Sec. 01

02

03

04

Lec. II

05

 06

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09

 MTW 10

Th 9

Th 10:30

F 9

F12

MTW 10

Th 9

Th 10:30

F 9

F 12

F 12

110.107 (Q)          

CALCULUS II  (FOR BIOLOGICAL AND SOCIAL SCIENCE)  (4) Blair / Ching  Limit 30 27 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. 

Sec. 03 canceled 8/01/06

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) Popovici Paupert / Song  
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.

Sec. 06 canceled 7/27/06

Sec. 09 added 8/7/06

Lec. I

Sec. 01

02

03

04

Lec. II

Sec. 05

06

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09

 MTW 10

F 9

F 12

F 12

 F 9

MTW 11

Th 10:30

Th 10:30

F 9

F 12

F 9

110.113 (Q)

HONORS SINGLE ONE VARIABLE CALCULUS (4) Brown   Limit 35   

Lec.

Sec. 01

 MTW 3

F 12

110.201 (Q)

LINEAR ALGEBRA (4) Zucker   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.

Sec. 05 canceled 8/01/06

Sec. 03 canceled 8/28/06

Lec.

Sec. 01

02

03

04

05

MTW 3

Th 10:30

Th 12

F 9

F 12

F 10:30 12

110.202 (Q)

CALCULUS III (4) Wilkin Wilson/Ha 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. 09 added 8/01/06

Lec. I

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Lec. II

05

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 MTW 11

Th 10:30

Th F 12 10:30

 Th 10:30

Th 12

MTW 12

 Th 12

F 9

F 9

F 12

F 9 10:30

110.204 (Q)

ELEMENTARY NUMBER THEORY (4) Shalika Prereq: Calculus I     Limit 35 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

110.211 (Q)

HONORS MULTIVARIABLE CALCULUS (4) Wilkin    Limit 35 per section

Lec.

Sec. 01

02

MTW 12

F 10:30 11

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

110.225 (Q)

PUTNAM PROBLEM SOLVING (3) Staff
Limit 10 Minimum of 10 students  Problem solving course to prepare students for the Putnam exam Course canceled 9/11/06

Sec. 01

TTh 6-7:15pm

110.302 (E,Q)

DIFFERENTIAL EQUATIONS WITH APPLICATIONS (4) Shiffman   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).

Sec.07 added 6/29/06

Lec. I

Sec. 01

02

03

Lec. II

Sec. 04

05

06

07

MTW 12

Th 10:30

F 12

Th 10:30

MTW 1

F 9

F 12

Th 10:30-11:20

F 12

110.311 (Q)

METHODS OF COMPLEX ANALYSIS (4.5) Spruck 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

110.369 (Q, N)

INTRODUCTION TO MATHEMATICAL BIOLOGY (4) Morava    Limit 40 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) Consani   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) Mese  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.

Sec. 01

MTW 1

F 12

110.415 (Q)

HONORS ANALYSIS I (4.5) Sogge 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 12

110.427 (Q)

INTRODUCTION TO THE CALCULUS OF VARIATIONS (4) DeSilva   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.  The course in a seminar style with active participation required. Additional material as required (some differential geometry of curves and surfaces) holding prerequisites to a minimum.

Sec. 01

MTW 3

110.431 (Q)

INTRODUCTION TO KNOT THEORY (4) Ching  Limit 25 Prereq: Calculus III and Math 401 recommended    The theory of knots and links is a royal road to modern topology.  Course begins with braids and works up to knots and links. The fundamental group of a knot or a link complement will be the central algebraic focus, and spanning surfaces will be the main geometric tool. Together these lead very intuitively to homology groups (in low dimensions).

Sec. 01

MTW 1

110.439 (Q)

INTRODUCTION TO DIFFERENTIAL GEOMETRY (4.5) Spruck     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 (Q)

FOURIER ANALYSIS (4.5) Goldberg   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

110.480 (Q)

ELLIPTIC CURVES AND CRYPTOGRAPHY (4) Zhang    Limit 25   Prereq: Advanced Algebra.I  The topic of elliptic curves plays a central role in modern number theory.  It has found a significant application in the most recent development of cryptography.  This course covers the elementary theory of elliptical curves and its application to cryptography. Recommended for math majors who are interested in this area of number theory, as well non-math majors who want to have a mathematical understanding of elliptical curve cryptosystems.

Sec. 01

MTW 12

110.601

ALGEBRA Ono   Limit 25   

Sec. 01

MTW 12

110.605

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

Sec. 01

MTW 10

110.608

REIMANN SURFACES Kong    Limit 25   

Sec. 01

MTW 1

110.615

ALGEBRAIC TOPOLOGY Boardman 
Limit 25   Prereq: 110.401, 110.413

Sec. 01

ThF 2-3:15

110.619

LIE GROUPS & LIE ALGEBRAS Shalika  
Limit 25    Prereq: 110.402

Sec. 01

MTW 11

110.631

PARTIAL DIFFERENTIAL EQUATIONS Minicozzi Limit 25    Prereq: 110.605-606

Sec. 01

MTW 2 11

110.635

MICROLOCAL ANALYSIS Zelditch   Limit 25    Prereq: 110.605

Sec. 01

MTW 2 12

110.643

ALGEBRAIC GEOMETRY Consani  Limit 25 Prereq:  110.601-602

Sec. 01

MTW 12

110.645

RIEMANNIAN GEOMETRY Mese Limit 25

Sec. 01

MTW 12 2

110.711

TOPICS IN MATHEMATICAL PHYSICS Wentworth   Limit 10 Course added 6/29/06

Sec. 01

MTW 3

110.726

TOPICS IN SEVERAL COMPLEX VARIABLES Song   Course added 7/18/06

Sec. 01

Th 1-3

110.730

TOPICS IN COMPLEX GEOMETRY Wentworth   Limit 25 Course canceled 6/29/06

Sec. 01

TBA

110.733

TOPICS IN ALGEBRAIC NUMBER THEORY Ono Limit 25   

Sec. 01

TBA

110.737

TOPICS IN ALGEBRAIC GEOMETRY  Shokurov    Limit 25

Sec. 01

MW 3-4:30

110.799

THESIS RESEARCH

Sec. 01

TBA

110.800

INDEPENDENT STUDY -GRADUATES

Sec. 01

TBA