Courses for Mathematics

Unify Course Listings

MATH W 1003x or y College Algebra and Analytic Geometry

Columbia College students do not receive any credit for this course and must see their CSA advising dean. For students who wish to study calculus but do not know analytic geometry. Algebra review, graphs and functions, polynomial functions, rational functions, conic sections, systems of equations in two variables, exponential and logarithmic functions, trigonometric functions and trigonometric identities, applications of trigonometry, sequences, series, and limits.
Prerequisites: score of 550 on the mathematics portion of the SAT completed within the last year or the appropriate grade on the General Studies Mathematics Placement Examination.
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH W1003
MATH
1003
62436
001
MW 6:10p - 8:00p
407 MATHEMATICS BUILDING
S. Venkatesh 24 / 30 [ More Info ]
MATH
1003
71513
002
TuTh 12:10p - 2:00p
420 PUPIN LABORATORIES
L. Hayward 25 / 30 [ More Info ]
Autumn 2016 :: MATH W1003
MATH
1003
10762
001
MW 6:10p - 8:00p
TBA
V. Petkov 4 / 30 [ More Info ]
MATH
1003
13818
002
TuTh 12:10p - 2:00p
TBA
A. Osinenko 9 / 30 [ More Info ]

MATH V 1101x or y Calculus I

The Help Room in 333 Milbank Hall (Barnard College) is open during the day, Monday through Friday, to students seeking individual help from the teaching assistants. (SC)
Prerequisites: see Courses for First-Year Students. Functions, limits, derivatives, introduction to integrals. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH V1101
MATH
1101
22901
001
MW 8:40a - 9:55a
407 MATHEMATICS BUILDING
A. Deopurkar 26 / 30 [ More Info ]
MATH
1101
74461
002
MW 10:10a - 11:25a
203 MATHEMATICS BUILDING
P. Gallagher 69 / 100 [ More Info ]
MATH
1101
67557
003
MW 6:10p - 7:25p
203 MATHEMATICS BUILDING
C. Li 77 / 100 [ More Info ]
MATH
1101
23626
004
TuTh 11:40a - 12:55p
417 MATHEMATICS BUILDING
S. Krishnamoorthy 33 / 40 [ More Info ]
MATH
1101
16069
005
TuTh 2:40p - 3:55p
407 MATHEMATICS BUILDING
C. Wong 20 / 30 [ More Info ]
MATH
1101
87204
006
TuTh 10:10a - 11:25a
407 MATHEMATICS BUILDING
I. Filip 13 / 30 [ More Info ]
Autumn 2016 :: MATH V1101
MATH
1101
07384
001
MW 8:40a - 9:55a
TBA
D. McDuff 31 / 100 [ More Info ]
MATH
1101
67933
002
MW 10:10a - 11:25a
TBA
L. Diogo 11 / 100 [ More Info ]
MATH
1101
21107
003
MW 11:40a - 12:55p
TBA
L. Diogo 13 / 100 [ More Info ]
MATH
1101
27447
004
MW 2:40p - 3:55p
TBA
S. Picard 5 / 30 [ More Info ]
MATH
1101
11897
005
MW 4:10p - 5:25p
TBA
P. Pushkar 13 / 30 [ More Info ]
MATH
1101
26477
006
MW 6:10p - 7:25p
TBA
C. Li 29 / 100 [ More Info ]
MATH
1101
26739
007
TuTh 10:10a - 11:25a
TBA
P. Hung 2 / 30 [ More Info ]
MATH
1101
17570
008
TuTh 11:40a - 12:55p
TBA
Instructor To Be Announced 8 / 30 [ More Info ]
MATH
1101
29604
009
TuTh 1:10p - 2:25p
TBA
G. Di Cerbo 8 / 100 [ More Info ]
MATH
1101
73071
010
TuTh 2:40p - 3:55p
TBA
Instructor To Be Announced 4 / 30 [ More Info ]
MATH
1101
18565
011
TuTh 4:10p - 5:25p
TBA
Instructor To Be Announced 3 / 100 [ More Info ]
MATH
1101
73884
012
TuTh 6:10p - 7:25p
TBA
Instructor To Be Announced 3 / 100 [ More Info ]

MATH V 1102x or y Calculus II

Methods of integration, applications of the integral, Taylor's theorem, infinite series. (SC)
Prerequisites: MATH V1101 or the equivalent. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH V1102
MATH
1102
05648
001
MW 10:10a - 11:25a
324 MILBANK HALL
T. Petkova 29 / 100 [ More Info ]
MATH
1102
64994
002
MW 1:10p - 2:25p
323 MILBANK HALL
T. Petkova 34 / 100 [ More Info ]
MATH
1102
24866
003
MW 4:10p - 5:25p
417 MATHEMATICS BUILDING
H. Chang-Lara 33 / 64 [ More Info ]
MATH
1102
12743
004
MW 6:10p - 7:25p
312 MATHEMATICS BUILDING
H. Chang-Lara 25 / 110 [ More Info ]
MATH
1102
60559
006
TuTh 6:10p - 7:25p
516 HAMILTON HALL
E. Stein 27 / 100 [ More Info ]
Autumn 2016 :: MATH V1102
MATH
1102
26909
001
MW 10:10a - 11:25a
TBA
P. Gallagher 20 / 100 [ More Info ]
MATH
1102
64016
002
MW 11:40a - 12:55p
TBA
B. Guo 3 / 100 [ More Info ]
MATH
1102
21826
003
MW 1:10p - 2:25p
TBA
B. Guo 4 / 100 [ More Info ]
MATH
1102
67192
005
TuTh 10:10a - 11:25a
TBA
N. Arbesfeld 5 / 30 [ More Info ]
MATH
1102
70122
006
TuTh 2:40p - 3:55p
TBA
A. Zeitlin 18 / 100 [ More Info ]
MATH
1102
26180
007
TuTh 4:10p - 5:25p
TBA
A. Zeitlin 11 / 100 [ More Info ]
MATH
1102
22286
008
TuTh 6:10p - 7:25p
TBA
K. Choi 1 / 30 [ More Info ]

MATH V 1201x or y Calculus III

Vectors in dimensions 2 and 3, complex numbers and the complex exponential function with applications to differential equations, Cramer's rule, vector-valued functions of one variable, scalar-valued functions of several variables, partial derivatives, gradients, surfaces, optimization, the method of Lagrange multipliers. (SC)
Prerequisites: MATH V1101 or the equivalent. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH V1201
MATH
1201
05518
001
MW 10:10a - 11:25a
405 MILBANK HALL
D. De Silva 105 / 100 [ More Info ]
MATH
1201
63222
002
MW 1:10p - 2:25p
312 MATHEMATICS BUILDING
P. Chen 108 / 116 [ More Info ]
MATH
1201
60545
003
TuTh 4:10p - 5:25p
203 MATHEMATICS BUILDING
I. Krichever 94 / 110 [ More Info ]
MATH
1201
26016
004
TuTh 6:10p - 7:25p
203 MATHEMATICS BUILDING
I. Krichever 41 / 110 [ More Info ]
MATH
1201
11779
005
TuTh 1:10p - 2:25p
312 MATHEMATICS BUILDING
D. Halpern-Leistne 38 / 116 [ More Info ]
MATH
1201
73460
006
TuTh 2:40p - 3:55p
312 MATHEMATICS BUILDING
S. Altug 49 / 116 [ More Info ]
MATH
1201
65140
007
TuTh 10:10a - 11:25a
312 MATHEMATICS BUILDING
D. Halpern-Leistne 36 / 110 [ More Info ]
Autumn 2016 :: MATH V1201
MATH
1201
29410
001
MW 8:40a - 9:55a
TBA
C. Liu 17 / 100 [ More Info ]
MATH
1201
27988
002
MW 10:10a - 11:25a
TBA
A. Alishahi 29 / 100 [ More Info ]
MATH
1201
15820
003
MW 1:10p - 2:25p
TBA
G. Dobrovolska 19 / 100 [ More Info ]
MATH
1201
62151
004
MW 2:40p - 3:55p
TBA
G. Dobrovolska 27 / 100 [ More Info ]
MATH
1201
68024
005
MW 4:10p - 5:25p
TBA
J. Kuan 15 / 100 [ More Info ]
MATH
1201
63259
006
MW 11:40a - 12:55p
TBA
A. Alishahi 17 / 100 [ More Info ]
MATH
1201
27974
007
TuTh 8:40a - 9:55a
TBA
G. Barraquand 7 / 100 [ More Info ]
MATH
1201
24333
008
TuTh 10:10a - 11:25a
TBA
D. Litt 49 / 100 [ More Info ]
MATH
1201
11993
009
TuTh 11:40a - 12:55p
TBA
G. Barraquand 27 / 100 [ More Info ]
MATH
1201
26797
010
TuTh 2:40p - 3:55p
TBA
J. Nelson 36 / 100 [ More Info ]
MATH
1201
27023
011
TuTh 4:10p - 5:25p
TBA
Instructor To Be Announced 9 / 100 [ More Info ]
MATH
1201
25355
012
TuTh 6:10p - 7:25p
TBA
Instructor To Be Announced 7 / 100 [ More Info ]

MATH V 1202x or y Calculus IV

Multiple integrals, Taylor's formula in several variables, line and surface integrals, calculus of vector fields, Fourier series. (SC)
Prerequisites: MATH V1102, MATH V1201, or the equivalent. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH V1202
MATH
1202
60823
001
MW 11:40a - 12:55p
413 KENT HALL
X. Wan 45 / 100 [ More Info ]
MATH
1202
28598
002
MW 2:40p - 3:55p
420 PUPIN LABORATORIES
H. Shen 46 / 110 [ More Info ]
MATH
1202
63915
003
TuTh 8:40a - 9:55a
203 MATHEMATICS BUILDING
O. Savin 53 / 110 [ More Info ]
MATH
1202
68408
004
TuTh 10:10a - 11:25a
203 MATHEMATICS BUILDING
O. Savin 51 / 110 [ More Info ]
Autumn 2016 :: MATH V1202
MATH
1202
18445
001
MW 2:40p - 3:55p
TBA
H. Shen 48 / 100 [ More Info ]
MATH
1202
23233
002
MW 4:10p - 5:25p
TBA
H. Shen 30 / 100 [ More Info ]
MATH
1202
12064
003
MW 6:10p - 7:25p
TBA
M. Smirnov 50 / 110 [ More Info ]

MATH V 1208y Honors Mathematics B

The second term of this course may not be taken without the first. Multivariable calculus and linear algebra from a rigorous point of view. Recommended for mathematics majors. Fulfills the linear algebra requirement for the major. (SC)
Prerequisites: (see Courses for First-Year Students). Recitation Section Required. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
4 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH V1208
MATH
1208
68289
001
MW 4:10p - 5:25p
312 MATHEMATICS BUILDING
M. Thaddeus 54 / 100 [ More Info ]

MATH BC 2006y Combinatorics

Honors-level introductory course in enumerative combinatorics. Pigeonhole principle, binomial coefficients, permutations and combinations. Polya enumeration, inclusion-exclusion principle, generating functions and recurrence relations.
Corequisites: MATH V2010 is helpful as a corequisite, but not required.
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH BC2006
MATH
2006
02641
001
TuTh 10:10a - 11:25a
237 MILBANK HALL
D. Bayer 20 [ More Info ]

MATH V 2010x or y Linear Algebra

Matrices, vector spaces, linear transformations, eigenvalues and eigenvectors, canonical forms, applications. (SC)
Prerequisites: MATH V1201, or the equivalent. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH V2010
MATH
2010
14946
001
MW 11:40a - 12:55p
312 MATHEMATICS BUILDING
A. Alishahi 80 / 100 [ More Info ]
MATH
2010
75006
002
TuTh 11:40a - 12:55p
428 PUPIN LABORATORIES
G. Di Cerbo 109 / 110 [ More Info ]
MATH
2010
11085
003
TuTh 1:10p - 2:25p
203 MATHEMATICS BUILDING
G. Di Cerbo 101 / 110 [ More Info ]
Autumn 2016 :: MATH V2010
MATH
2010
15106
001
MW 1:10p - 2:25p
TBA
M. Khovanov 41 / 100 [ More Info ]
MATH
2010
02940
002
TuTh 10:10a - 11:25a
TBA
D. Bayer 90 / 100 [ More Info ]
MATH
2010
74190
003
TuTh 6:10p - 7:25p
TBA
E. Stein 100 / 100 [ More Info ]
MATH
2010
03818
004
TuTh 8:40a - 9:55a
TBA
D. Bayer 43 / 100 [ More Info ]

MATH V 2020x Honors Linear Algebra

A more extensive treatment of the material in Math V2010, with increased emphasis on proof. Not to be taken in addition to Math V2010 or Math V1207-Math V1208.
Prerequisites: MATH V1201. Not offered in 2016-2017.
3 points

MATH V 2500x or y Analysis and Optimization

Mathematical methods for economics. Quadratic forms, Hessian, implicit functions. Convex sets, convex functions. Optimization, constrained optimization, Kuhn-Tucker conditions. Elements of the calculus of variations and optimal control. (SC)
Prerequisites: MATH V1102-MATH V1201 or the equivalent and MATH V2010. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH V2500
MATH
2500
29408
001
MW 8:40a - 9:55a
312 MATHEMATICS BUILDING
A. Deopurkar 45 / 116 [ More Info ]
MATH
2500
70726
002
MW 10:10a - 11:25a
312 MATHEMATICS BUILDING
A. Deopurkar 105 / 116 [ More Info ]
Autumn 2016 :: MATH V2500
MATH
2500
18323
001
MW 8:40a - 9:55a
TBA
B. Jeon 23 / 100 [ More Info ]
MATH
2500
60822
002
MW 10:10a - 11:25a
TBA
B. Jeon 73 / 100 [ More Info ]

MATH V 3007y Complex Variables

Fundamental properties of the complex numbers, differentiability, Cauchy-Riemann equations. Cauchy integral theorem. Taylor and Laurent series, poles, and essential singularities. Residue theorem and conformal mapping.(SC)
Prerequisites: MATH V1202. An elementary course in functions of a complex variable. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH V3007
MATH
3007
68963
001
TuTh 10:10a - 11:25a
417 MATHEMATICS BUILDING
B. Jeon 63 / 64 [ More Info ]

MATH V 3020y Number Theory and Cryptography

Congruences. Primitive roots. Quadratic residues. Contemporary applications.
Prerequisites: one year of calculus. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH V3020
MATH
3020
64865
001
MW 10:10a - 11:25a
417 MATHEMATICS BUILDING
D. Hansen 47 / 64 [ More Info ]

MATH V 3025x Making, Breaking Codes

A concrete introduction to abstract algebra. Topics in abstract algebra used in cryptography and coding theory.
Prerequisites: MATH V1101, MATH V1102, MATH V1201 and MATH V2010.
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2016 :: MATH V3025
MATH
3025
74453
001
TuTh 2:40p - 3:55p
TBA
S. Shah 69 / 100 [ More Info ]

MATH V 3027x Ordinary Differential Equations

Equations of order one; systems of linear equations. Second-order equations. Series solutions at regular and singular points. Boundary value problems. Selected applications.
Prerequisites: MATH V1102-MATH V1201 or the equivalent. Corequisites: MATH V2010. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2016 :: MATH V3027
MATH
3027
62851
001
TuTh 1:10p - 2:25p
TBA
P. Daskalopoulos 78 / 100 [ More Info ]

MATH V 3028y Partial Differential Equations

Introduction to partial differential equations. First-order equations. Linear second-order equations; separation of variables, solution by series expansions. Boundary value problems.
Prerequisites: MATH V3027 and MATH V2010 or the equivalent BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH V3028
MATH
3028
12394
001
MW 1:10p - 2:25p
203 MATHEMATICS BUILDING
S. Brendle 36 / 110 [ More Info ]

MATH V 3050y Discrete Time Models in Finance

Elementary discrete time methods for pricing financial instruments, such as options. Notions of arbitrage, risk-neutral valuation, hedging, term-structure of interest rates.
Prerequisites: MATH V1102, MATH V1201(or MATH V1101, MATH V1102, MATH V1201), MATH V2010. Recommended: MATH V3027(or MATH V2030) and SIEO W3600.
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH V3050
MATH
3050
23237
001
MW 6:10p - 7:25p
417 MATHEMATICS BUILDING
M. Smirnov 41 / 64 [ More Info ]

MATH V 3386x Differential Geometry

Local and global differential geometry of submanifolds of Euclidiean 3-space. Frenet formulas for curves. Various types of curvatures for curves and surfaces and their relations. The Gauss-Bonnet theorem.
Prerequisites: MATH V1202 or the equivalent.
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2016 :: MATH V3386
MATH
3386
73447
001
TuTh 11:40a - 12:55p
TBA
R. Hamilton 35 / 49 [ More Info ]

MATH V 3901x Supervised Readings in Mathematics I

Guided reading and study in mathematics. A student who wishes to undertake individual study under this program must present a specific project to a member of the staff and secure his or her willingness to act as sponsor. Written reports and periodic conferences with the instructor.
Prerequisites: the written permission of the staff member who agrees to act as sponsor (sponsorship limited to full-time instructors on the staff list), as well as the director of undergraduate studies' permission. The written permission must be deposited with the director of undergraduate studies before registration is completed. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
2-3 points.

MATH V 3902y Supervised Readings in Mathematics II

Guided reading and study in mathematics. A student who wishes to undertake individual study under this program must present a specific project to a member of the staff and secure his or her willingness to act as sponsor. Written reports and periodic conferences with the instructor.
Prerequisites: the written permission of the staff member who agrees to act as sponsor (sponsorship limited to full-time instructors on the staff list), as well as the director of undergraduate studies' permission. The written permission must be deposited with the director of undergraduate studies before registration is completed. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
2-3 points.

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH V3902
MATH
3902
83449
001
TBA D. Hansen 3 [ More Info ]
MATH
3902
05662
002
TBA D. De Silva 1 [ More Info ]
MATH
3902
02292
003
TBA D. Bayer 0 [ More Info ]
MATH
3902
78548
004
TBA J. Dubedat 0 [ More Info ]
MATH
3902
68202
005
TBA D. Goldfeld 1 [ More Info ]
MATH
3902
67227
006
TBA P. Daskalopoulos 0 / 1 [ More Info ]
MATH
3902
63035
007
TBA A. Alishahi 1 / 1 [ More Info ]

MATH V 3951x Undergraduate Seminars in Mathematics I

The subject matter is announced at the start of registration and is different in each section. Each student prepares talks to be given to the seminar, under the supervision of a faculty member or senior teaching fellow.
Prerequisites: two years of calculus, at least one year of additional mathematics courses, and the director of undergraduate studies' permission. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2016 :: MATH V3951
MATH
3951
02944
001
TBA D. De Silva 44 [ More Info ]

MATH V 3952y Undergraduate Seminars in Mathematics II

The subject matter is announced at the start of registration and is different in each section. Each student prepares talks to be given to the seminar, under the supervision of a faculty member or senior teaching fellow.
Prerequisites: two years of calculus, at least one year of additional mathematics courses, and the director of undergraduate studies' permission. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH V3952
MATH
3952
00853
001
TBA D. Bayer 42 [ More Info ]

MATH V 3997x Supervised Individual Research

For specially selected mathematics majors, the opportunity to write a senior thesis on a problem in contemporary mathematics under the supervision of a faculty member.
Prerequisites: the written permission of the faculty member who agrees to act as a supervisor, and the director of undergraduate studies' permission.
3 points

MATH V 3998y Supervised Individual Research

For specially selected mathematics majors, the opportunity to write a senior thesis on a problem in contemporary mathematics under the supervision of a faculty member.
Prerequisites: the written permission of the faculty member who agrees to act as a supervisor, and the director of undergraduate studies' permission.
3 points

MATH W 4007y Analytic Number Theory

A one semeser course covering the theory of modular forms, zeta functions, L -functions, and the Riemann hypothesis. Particular topics covered include the Riemann zeta function, the prime number theorem, Dirichlet characters, Dirichlet L-functions, Siegel zeros, prime number theorem for arithmetic progressions, SL (2, Z) and subgroups, quotients of the upper half-plane and cusps, modular forms, Fourier expansions of modular forms, Hecke operators, L-functions of modular forms.
Prerequisites: MATH V3007.
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH W4007
MATH
4007
75700
001
TuTh 11:40a - 12:55p
520 MATHEMATICS BUILDING
D. Goldfeld 9 / 49 [ More Info ]

MATH W 4032y Fourier Analysis

Fourier series and integrals, discrete analogues, inversion and Poisson summation formulae, convolution. Heisenberg uncertainty principle. Stress on the application of Fourier analysis to a wide range of disciplines.
Prerequisites: three terms of calculus and linear algebra or four terms of calculus. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH W4032
MATH
4032
75696
001
TuTh 1:10p - 2:25p
520 MATHEMATICS BUILDING
O. Savin 13 / 49 [ More Info ]

MATH W 4041x or y Introduction to Modern Algebra I

The second term of this course may not be taken without the first. Groups, homomorphisms, rings, ideals, fields, polynomials, field extensions, Galois theory.
Prerequisites: MATH V1102-MATH V1202 and MATH V2010, or the equivalent. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH W4041
MATH
4041
62359
001
MW 11:40a - 12:55p
520 MATHEMATICS BUILDING
R. Friedman 26 / 49 [ More Info ]
Autumn 2016 :: MATH W4041
MATH
4041
13821
001
TuTh 4:10p - 5:25p
TBA
M. Thaddeus 79 / 100 [ More Info ]

MATH W 4042 Introduction to Modern Algebra II

The second term of this course may not be taken without the first. Groups, homomorphisms, rings, ideals, fields, polynomials, field extensions, Galois theory.
Prerequisites: MATH V1102-MATH V1202 and MATH V2010, or the equivalent. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH W4042
MATH
4042
16041
001
TuTh 4:10p - 5:25p
312 MATHEMATICS BUILDING
P. Gallagher 38 / 116 [ More Info ]
Autumn 2016 :: MATH W4042
MATH
4042
75532
001
MW 2:40p - 3:55p
TBA
R. Friedman 17 / 64 [ More Info ]

MATH W 4043x Advanced Topics in Algebra: Algebraic Number Theory

Algebraic number fields, unique factorization of ideals in the ring of algebraic integers in the field into prime ideals. Dirichlet unit theorem, finiteness of the class number, ramification. If time permits, p-adic numbers and Dedekind zeta function.
Prerequisites: MATH W4041-MATH W4042 or the equivalent. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2016 :: MATH W4043
MATH
4043
61264
001
MW 10:10a - 11:25a
TBA
C. Li 14 / 64 [ More Info ]

MATH W 4044y Representations of Finite Groups

Finite groups acting on finite sets and finite dimensional vector spaces. Group characters. Relations with subgroups and factor groups. Arithmetic properties of character values. Applications to the theory of finite groups: Frobenius groups, Hall subgroups and solvable groups. Characters of the symmetric groups. Spherical functions on finite groups.
Prerequisites: MATH V2010 and MATH W4041 or the equivalent.
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH W4044
MATH
4044
29298
001
MW 2:40p - 3:55p
417 MATHEMATICS BUILDING
M. Khovanov 14 / 64 [ More Info ]

MATH W 4045x Algebraic Curves

Plane curves, affine and projective varieties, singularities, normalization, Riemann surfaces, divisors, linear systems, Riemann-Roch theorem.
Prerequisites: MATH W4041, MATH W4042 and MATH V3007.
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2016 :: MATH W4045
MATH
4045
67148
001
TuTh 1:10p - 2:25p
TBA
M. Harris 7 / 64 [ More Info ]

MATH W 4046x Introduction to Category Theory

Categories, functors, natural transformations, adjoint functors, limits and colimits, introduction to higher categories and diagrammatic methods in algebra.
Prerequisites: MATH W4041. Not offered in 2016-2017.
3 points

MATH W 4051x Topology

Metric spaces, continuity, compactness, quotient spaces. The fundamental group of topological space. Examples from knot theory and surfaces. Covering spaces.
Prerequisites: MATH V1202, MATH V2010, and rudiments of group theory (e.g., MATH W4041). MATH V1208 or MATH W4061 is recommended, but not required. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2016 :: MATH W4051
MATH
4051
03710
001
MW 1:10p - 2:25p
TBA
W. Neumann 29 / 110 [ More Info ]

MATH W 4052y Introduction to Knot Theory

The study of algebraic and geometric properties of knots in R^3, including but not limited to knot projections and Reidemeister's theorm, Seifert surfaces, braids, tangles, knot polynomials, fundamental group of knot complements. Depending on time and student interest, we will discuss more advanced topics like knot concordance, relationship to 3-manifold topology, other algebraic knot invariants.
Prerequisites: MATH W4051 Topology and / or MATH W4061 Introduction To Modern Analysis I (or equivalents)
Recommended (can be taken concurrently): MATH V2010 linear algebra, or equivalent

3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH W4052
MATH
4052
11852
001
MW 4:10p - 5:25p
407 MATHEMATICS BUILDING
A. Keating 5 / 35 [ More Info ]

MATH W 4053y Introduction to Algebraic Topology

The study of topological spaces from algebraic properties, including the essentials of homology and the fundamental group. The Brouwer fixed point theorem. The homology of surfaces. Covering spaces.
Prerequisites: MATH V2010, MATH W4041, MATH W4051.
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH W4053
MATH
4053
72657
001
TuTh 5:40p - 6:55p
520 MATHEMATICS BUILDING
A. Zeitlin 7 / 49 [ More Info ]

MATH W 4061x or y Introduction To Modern Analysis I

Real numbers, metric spaces, elements of general topology. Continuous and differential functions. Implicit functions. Integration; change of variables. Function spaces.
Prerequisites: MATH V1202 or the equivalent, and MATH V2010. The second term of this course may not be taken without the first. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH W4061
MATH
4061
07691
001
MW 11:40a - 12:55p
405 MILBANK HALL
D. De Silva 69 / 100 [ More Info ]
Autumn 2016 :: MATH W4061
MATH
4061
70047
001
MW 8:40a - 9:55a
TBA
H. Chang-Lara 50 / 100 [ More Info ]

MATH W 4062 Introduction To Modern Analysis II

Real numbers, metric spaces, elements of general topology. Continuous and differential functions. Implicit functions. Integration; change of variables. Function spaces.
Prerequisites: MATH V1202 or the equivalent, and MATH V2010. The second term of this course may not be taken without the first. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH W4062
MATH
4062
29500
001
MW 2:40p - 3:55p
312 MATHEMATICS BUILDING
B. Guo 12 / 116 [ More Info ]
Autumn 2016 :: MATH W4062
MATH
4062
08001
001
TuTh 2:40p - 3:55p
TBA
D. De Silva 33 / 110 [ More Info ]

MATH W 4065x Honors Complex Variables

A theoretical introduction to analytic functions. Holomorphic functions, harmonic functions, power series, Cauchy-Riemann equations, Cauchy's integral formula, poles, Laurent series, residue theorem. Other topics as time permits: elliptic functions, the gamma and zeta function, the Riemann mapping theorem, Riemann surfaces, Nevanlinna theory.
Prerequisites: MATH V1207 and MATH V1208 or MATH W4061.
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2016 :: MATH W4065
MATH
4065
23107
001
TuTh 1:10p - 2:25p
TBA
E. Urban 19 / 30 [ More Info ]

MATH W 4071x and y Introduction to the Mathematics of Finance

The mathematics of finance, principally the problem of pricing of derivative securities, developed using only calculus and basic probability. Topics include mathematical models for financial instruments, Brownian motion, normal and lognormal distributions, the Black├╗Scholes formula, and binomial models.
Prerequisites: MATH V1202, MATH V3027, STAT W4150, SEIO W4150, or their equivalents. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH W4071
MATH
4071
21787
001
MW 7:40p - 8:55p
207 MATHEMATICS BUILDING
M. Smirnov 113 / 130 [ More Info ]

MATH W 4081y Introduction to Differentiable Manifolds

Concept of a differentiable manifold. Tangent spaces and vector fields. The inverse function theorem. Transversality and Sard's theorem. Intersection theory. Orientations. Poincare-Hopf theorem. Differential forms and Stoke's theorem. - O. Savin
Prerequisites: MATH W4051 or MATH W4061 and MATH V2010.
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH W4081
MATH
4081
71179
001
MW 10:10a - 11:25a
520 MATHEMATICS BUILDING
L. Diogo 16 / 49 [ More Info ]

MATH W 4391x Intro to Quantum Mechanics: An Introduction for Mathematicians and Physicists I

This course will focus on quantum mechanics, paying attention to both the underlying mathematical structures as well as their physical motivations and consequences. It is meant for undergraduates with no previous formal training in quantum theory. The measurement problem and issues of non-locality will be stressed.
Prerequisites: MATH V1202 or the equivalent and MATH V2010. Not offered in 2016-2017.
3 points

MATH W 5010x and y Introduction to the Mathematics of Finance

The mathematics of finance, principally the problem of pricing of derivative securities, developed using only calculus and basic probability. Topics include mathematical models for financial instruments, Brownian motion, normal and lognormal distributions, the Black├╗Scholes formula, and binomial models.
Prerequisites: MATH V1202, MATH V3027, STAT W5203, SIEO W3001, or their equivalents. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2016 :: MATH W5010
MATH
5010
18463
001
MW 7:40p - 8:55p
TBA
M. Smirnov 5 / 130 [ More Info ]

Engineering Courses

MATH V 1207x Honors Mathematics A

The second term of this course may not be taken without the first. Multivariable calculus and linear algebra from a rigorous point of view. Recommended for mathematics majors. Fulfills the linear algebra requirement for the major. (SC)
Prerequisites: (see Courses for First-Year Students). Recitation Section Required.
4 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2016 :: MATH V1207
MATH
1207
73444
001
MW 1:10p - 2:25p
TBA
D. Hansen 4 / 100 [ More Info ]

MATH V 1208y Honors Mathematics B

The second term of this course may not be taken without the first. Multivariable calculus and linear algebra from a rigorous point of view. Recommended for mathematics majors. Fulfills the linear algebra requirement for the major. (SC)
Prerequisites: (see Courses for First-Year Students). Recitation Section Required.
4 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH V1208
MATH
1208
68289
001
MW 4:10p - 5:25p
312 MATHEMATICS BUILDING
M. Thaddeus 54 / 100 [ More Info ]

MATH V 2000x or y An Introduction to Higher Mathematics

Introduction to understanding and writing mathematical proofs. Emphasis on precise thinking and the presentation of mathematical results, both in oral and in written form. Intended for students who are considering majoring in mathematics but wish additional training. CC/GS: Partial Fulfillment of Science Requirement. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH V2000
MATH
2000
07922
001
TuTh 10:10a - 11:25a
409 BARNARD HALL
D. McDuff 37 / 64 [ More Info ]
Autumn 2016 :: MATH V2000
MATH
2000
26047
001
TuTh 2:40p - 3:55p
TBA
M. Harris 19 / 64 [ More Info ]

MATH BC 2001x Perspectives in Mathematics

Intended as an enrichment to the mathemathics curriculum of the first years, this course introduces a variety of mathematical topics (such as three dimensional geometry, probability, number theory) that are often not discussed until later, and explains some current applications of mathematics in the sciences, technology and economics.
Prerequisites: some calculus or the instructor's permission.
1 point

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2016 :: MATH BC2001
MATH
2001
06129
001
W 6:10p - 7:25p
TBA
D. McDuff 11 / 64 [ More Info ]

MATH V 2002y The Magic of Numbers

In this class, we will cover many interesting aspects of math that can be used in everyday life. The goal will be to cover fun, exciting topics that don't require any prerequisites, but still capture some of the mystery of mathematics. We will emphasize discovering concepts in combinatorics (the mathematics of counting), geometry (the mathematics of shapes), number theory (the mathematics of whole numbers) and more. This class will be interactive and include demonstrations when possible.
BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH V2002
MATH
2002
96946
001
TuTh 10:10a - 11:25a
520 MATHEMATICS BUILDING
V. Pal 39 / 40 [ More Info ]

MATH V 2030x or y Ordinary Differential Equations

Special differential equations of order one. Linear differential equations with constant and variable coefficients. Systems of such equations. Transform and series solution techniques. Emphasis on applications.
Prerequisites: MATH V1102-MATH V1201 or the equivalent.
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: MATH V2030
MATH
2030
19239
001
TuTh 11:40a - 12:55p
312 MATHEMATICS BUILDING
M. Wang 98 / 116 [ More Info ]
MATH
2030
23047
002
TuTh 2:40p - 3:55p
203 MATHEMATICS BUILDING
M. Wang 58 / 110 [ More Info ]
Autumn 2016 :: MATH V2030
MATH
2030
77535
001
MW 6:10p - 7:25p
TBA
H. Chang-Lara 35 / 100 [ More Info ]
MATH
2030
23554
002
TuTh 11:40a - 12:55p
TBA
P. Daskalopoulos 79 / 100 [ More Info ]

APMA E 4101x Introduction to Dynamical Systems

An introduction to the analytic and geometric theory of dynamical systems; basic existence, uniqueness and parameter dependence of solutions to ordinary differential equations; constant coefficient and parametrically forced systems; Fundamental solutions; resonance; limit points, limit cycles and clasificiation of flows in the plane (poincare-Bendixson Therem); conservative and dissipative systems; linear and nonlinear stability analysis of equilibria and periodic solutions; stble and unstable manifoleds; bifurcations, e.g. Andronov-Hopf; sensitive depeneence and chaotic dynamics; slected applications. - M. Weinstein
Prerequisites: APMA E2101 (or MATH E1210) and APMA E3101.
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2016 :: APMA E4101
APMA
4101
29298
001
TuTh 8:40a - 9:55a
TBA
M. Spiegelman 42 / 70 [ More Info ]

APMA E 4101y Introduction to Dynamical Systems

An introduction to the analytic and geometric theory of dynamical systems; basic existence, uniqueness and parameter dependence of solutions to ordinary differential equations; constant coefficient and parametrically forced systems; Fundamental solutions; resonance; limit points, limit cycles and classification of flows in the plane (Poincare-Bendixson Therem); conservative and dissipative systems; linear and nonlinear stability analysis of equilibria and periodic solutions; stable and unstable manifolds; bifurcations, e.g. Andronov-Hopf; sensitive dependence and chaotic dynamics; selected applications. - M. Weinstein
Prerequisites: APMA E2101 (or MATH E1210) and APMA E3101.
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2016 :: APMA E4101
APMA
4101
29298
001
TuTh 8:40a - 9:55a
TBA
M. Spiegelman 42 / 70 [ More Info ]

APMA E 4150x Applied Function Analysis

Introduction to modern tools in functional analysis that are used in the analysis of deterministic and stochastic partial differential equations and in the analysis of numerical methods: metric and normed spaces. Banach space of continuous functions, measurable spaces, the contraction mapping theorem, Banach and Hilbert spaces bounded linear operators on Hilbert spaces and their spectral decomposition, and time permitting distributions and Fourier transforms.
Prerequisites: advanced calculus and a course in basic analysis, or the instructor's permission.
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2016 :: APMA E4150
APMA
4150
12391
001
M 10:10a - 12:40p
TBA
G. Bal 11 / 35 [ More Info ]

APMA E 4200x Partial Differential Equations

Techniques of solution of partial differential equations. Separtion of the variables. Orthogonality and characteristic functions, nonhomogeneous boundary value problems. Solutions in orthogonal curvilinear coordinate systems. Applications of Fourier integrals, Fourier and Laplace transforms. Problems from the fields of vibrations, heat conduction, electricity, fluid dynamics, and wave propagation are considered.
Prerequisites: a course in ordinary differential equations.
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2016 :: APMA E4200
APMA
4200
72657
001
M 4:10p - 6:40p
TBA
V. Quenneville-Belair 8 / 120 [ More Info ]

MATH W 4392y Quantum Mechanics: An Introduction for Mathematicians and Physicists II

This course will focus on quantum mechanics, paying attention to both the underlying mathematical structures as well as their physical motivations and consequences. It is meant for undergraduates with no previous formal training in quantum theory. The measurement problem and issues of non-locality will be stressed.
Prerequisites: MATH V1202 or the equivalent, MATH V2010, and MATH W4391. Not offered in 2016-2017.
3 points

APMA E 4400y Introduction to Biophysical Modeling

Introduction to physical and mathematical models of cellular and molecular biologoy. Physics at the cellular schale (viscosity, heat, diffusion, statistical mechanics). RNA transcription and regulation of genetic expression. Genetic and biochemical networks. Bioinformatics as applied to reverse-engineering of naturally-occurring networks and to forward-engineering of synthetic biological networks. Mathematical and physical aspects of functional genomics.
Prerequisites: advanced calculus or the instructor's permission.
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Spring 2016 :: APMA E4400
APMA
4400
12410
001
MW 10:10a - 11:25a
503 HAMILTON HALL
C. Wiggins 13 / 70 [ More Info ]

Cross-Listed Courses

Computer Science

W3203 Discrete Mathematics: Introduction to Combinatorics and Graph Theory

W3251 Computational Linear Algebra

W4203 Graph Theory

Industrial Engineering and Operations Research

E4010 Graph Theory: A Combinatorial View