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 gade on the General Studies Mathematics Placement Examination.
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2014 :: MATH W1003
MATH
1003
26008
001
MW 6:10p - 8:05p
520 MATHEMATICS BUILDING
P. Lewis 36 / 50 [ More Info ]
MATH
1003
68604
002
TuTh 12:30p - 2:25p
417 MATHEMATICS BUILDING
J. Keller 42 / 50 [ More Info ]

MATH V 1101x or y Calculus I

The Help Room on the 3rd floor of Milbank Hall (Barnard College) is open during the day, Monday through Friday, to students seeking individual help from the instructors and 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
Autumn 2014 :: MATH V1101
MATH
1101
07384
001
MW 8:40a - 9:55a
405 MILBANK HALL
D. McDuff 91 / 100 [ More Info ]
MATH
1101
60133
002
MW 1:10p - 2:25p
207 MATHEMATICS BUILDING
E. Gorskiy 84 / 100 [ More Info ]
MATH
1101
70363
003
MW 11:40a - 12:55p
203 MATHEMATICS BUILDING
E. Gorskiy 55 / 100 [ More Info ]
MATH
1101
70760
004
MW 10:10a - 11:25a
203 MATHEMATICS BUILDING
P. Siegel 83 / 100 [ More Info ]
MATH
1101
17221
005
MW 2:40p - 3:55p
312 MATHEMATICS BUILDING
D. Hansen 83 / 100 [ More Info ]
MATH
1101
10153
006
MW 4:10p - 5:25p
207 MATHEMATICS BUILDING
D. Hansen 52 / 100 [ More Info ]
MATH
1101
10486
007
MW 6:10p - 7:25p
417 MATHEMATICS BUILDING
J. Guerreiro 21 / 30 [ More Info ]
MATH
1101
87746
008
TuTh 8:40a - 9:55a
407 MATHEMATICS BUILDING
J. Zhao 24 / 30 [ More Info ]
MATH
1101
72497
009
TuTh 10:10a - 11:25a
312 MATHEMATICS BUILDING
L. Diogo 88 / 100 [ More Info ]
MATH
1101
26323
010
TuTh 11:40a - 12:55p
312 MATHEMATICS BUILDING
L. Diogo 93 / 100 [ More Info ]
MATH
1101
62024
011
TuTh 1:10p - 2:25p
717 HAMILTON HALL
H. Chang 26 / 100 [ More Info ]
MATH
1101
13196
012
TuTh 2:40p - 3:55p
203 MATHEMATICS BUILDING
H. Chang 28 / 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
Autumn 2014 :: MATH V1102
MATH
1102
06161
001
MW 10:10a - 11:25a
323 MILBANK HALL
W. Neumann 51 / 70 [ More Info ]
MATH
1102
28626
002
MW 11:40a - 12:55p
417 MATHEMATICS BUILDING
X. Wan 18 / 100 [ More Info ]
MATH
1102
23654
003
MW 1:10p - 2:25p
520 MATHEMATICS BUILDING
X. Wan 17 / 100 [ More Info ]
MATH
1102
76116
004
MW 2:40p - 3:55p
417 MATHEMATICS BUILDING
J. Dubedat 4 / 100 [ More Info ]
MATH
1102
62880
005
MW 6:10p - 7:25p
407 MATHEMATICS BUILDING
D. Gulotta 14 / 30 [ More Info ]
MATH
1102
65334
006
TuTh 10:10a - 11:25a
203 MATHEMATICS BUILDING
S. Altug 40 / 100 [ More Info ]
MATH
1102
23456
007
TuTh 11:40a - 12:55p
203 MATHEMATICS BUILDING
S. Altug 90 / 100 [ More Info ]
MATH
1102
64039
008
TuTh 6:10p - 7:25p
407 MATHEMATICS BUILDING
C. Wong 8 / 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
Autumn 2014 :: MATH V1201
MATH
1201
63798
001
MW 8:40a - 9:55a
203 MATHEMATICS BUILDING
A. Drewitz 41 / 100 [ More Info ]
MATH
1201
25903
002
MW 10:10a - 11:25a
417 MATHEMATICS BUILDING
A. Drewitz 43 / 64 [ More Info ]
MATH
1201
70498
003
MW 11:40a - 12:55p
227 SEELEY W. MUDD BUILDING
Q. Chen 31 / 100 [ More Info ]
MATH
1201
69419
004
MW 1:10p - 2:25p
717 HAMILTON HALL
C. Liu 20 / 100 [ More Info ]
MATH
1201
15512
005
MW 2:40p - 3:55p
207 MATHEMATICS BUILDING
O. Savin 95 / 100 [ More Info ]
MATH
1201
60692
006
MW 4:10p - 5:25p
312 MATHEMATICS BUILDING
S. Gautam 81 / 100 [ More Info ]
MATH
1201
24446
007
TuTh 8:40a - 9:55a
520 MATHEMATICS BUILDING
M. Abouzaid 15 / 100 [ More Info ]
MATH
1201
74995
008
TuTh 10:10a - 11:25a
207 MATHEMATICS BUILDING
M. Abouzaid 24 / 100 [ More Info ]
MATH
1201
76325
009
TuTh 11:40a - 12:55p
207 MATHEMATICS BUILDING
J. Hom 88 / 100 [ More Info ]
MATH
1201
70306
010
TuTh 1:10p - 2:25p
207 MATHEMATICS BUILDING
J. Hom 89 / 100 [ More Info ]
MATH
1201
11282
011
TuTh 2:40p - 3:55p
207 MATHEMATICS BUILDING
A. Zeitlin 107 / 152 [ More Info ]
MATH
1201
29666
012
TuTh 4:10p - 5:25p
312 MATHEMATICS BUILDING
A. Zeitlin 74 / 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, 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
Autumn 2014 :: MATH V1202
MATH
1202
28964
001
MW 8:40a - 9:55a
312 MATHEMATICS BUILDING
B. Jeon 32 / 100 [ More Info ]
MATH
1202
24465
002
MW 10:10a - 11:25a
312 MATHEMATICS BUILDING
B. Jeon 34 / 100 [ More Info ]
MATH
1202
19975
003
MW 6:10p - 7:25p
203 MATHEMATICS BUILDING
M. Smirnov 69 / 100 [ More Info ]

MATH V 1207x-V1208y Honors Mathematics A-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
Autumn 2014 :: MATH V1207
MATH
1207
72428
001
TuTh 4:10p - 5:25p
203 MATHEMATICS BUILDING
P. Gallagher 56 / 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.
BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2014 :: MATH V2000
MATH
2000
26704
001
TuTh 10:10a - 11:25a
520 MATHEMATICS BUILDING
M. Woodbury 22 / 64 [ More Info ]

MATH BC 2001x Perspectives in Mathematics

Intended as an enrichment to the mathematics curriculum of the first two 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 permission of the instructor.
1 point

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2014 :: MATH BC2001
MATH
2001
06129
001
W 6:10p - 7:25p
202 MILBANK HALL
D. McDuff 14 [ 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 corequisite, not required.
3 points

MATH V 2010x or y Linear Algebra

Matrices, vector spaces, linear transformations, eigenvalues and eigenvectors, canonical forms, applications. (SC)
Prerequisites: 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
Autumn 2014 :: MATH V2010
MATH
2010
07460
001
TuTh 8:40a - 9:55a
405 MILBANK HALL
D. Bayer 39 / 100 [ More Info ]
MATH
2010
23694
002
TuTh 11:40a - 12:55p
405 MILBANK HALL
D. Bayer 90 / 100 [ More Info ]
MATH
2010
15045
003
TuTh 6:10p - 7:25p
203 MATHEMATICS BUILDING
E. Stein 81 / 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-V1208.
Prerequisites: Math V1201
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2014 :: MATH V2020
MATH
2020
15976
001
TuTh 2:40p - 3:55p
407 MATHEMATICS BUILDING
A. de Jong 8 / 35 [ More Info ]

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
Autumn 2014 :: MATH V2500
MATH
2500
76293
001
MW 11:40a - 12:55p
413 KENT HALL
J. Dubedat 19 / 100 [ More Info ]
MATH
2500
10040
002
TuTh 10:10a - 11:25a
417 MATHEMATICS BUILDING
H. Pinkham 8 / 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

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

MATH V 3025x Making, Breaking Codes

A concrete introduction to abstract algebra. Topics in abstract algebra used in cryptography and coding theory.
Prerequisites: Calculus I, II, III and Linear Algebra.
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2014 :: MATH V3025
MATH
3025
77116
001
TuTh 2:40p - 3:55p
312 MATHEMATICS BUILDING
D. Goldfeld 70 / 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 2014 :: MATH V3027
MATH
3027
63222
001
TuTh 1:10p - 2:25p
203 MATHEMATICS BUILDING
P. Daskalopoulos 71 / 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

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, V1201(or V1101, V1102, V1201), V2010. Recommended: MATH V3027(or MATH E1210) and SIEO W3600.
3 points

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 2014 :: MATH V3386
MATH
3386
60545
001
TuTh 11:40a - 12:55p
520 MATHEMATICS BUILDING
R. Hamilton 18 / 70 [ More Info ]

MATH V 3901x-V3902y Supervised Readings in Mathematics

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 permission of the director of undergraduate studies. 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 3951x-V3952y Undergraduate Seminars in Mathematics

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 permission of the director of undergraduate studies. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)..
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2014 :: MATH V3951
MATH
3951
06516
001
TBA D. De Silva 22 [ More Info ]

MATH V 3997x-V3998y 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 permission of the director of the undergraduate studies.
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

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

MATH W 4041x or y-W4042 Introduction to Modern Algebra

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

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2014 :: MATH W4041
MATH
4041
11852
001
MW 2:40p - 3:55p
203 MATHEMATICS BUILDING
M. Khovanov 71 / 100 [ More Info ]
Autumn 2014 :: MATH W4042
MATH
4042
02354
001
MW 8:40a - 9:55a
LL103 Diana Center
W. Neumann 17 / 70 [ 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-W4042 or the equivalent. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).. Not offered in 2014-2015.
3 points

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

MATH W 4045y Algebraic Curves

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

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 2014-2015.
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 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 2014 :: MATH W4051
MATH
4051
18327
001
MW 1:10p - 2:25p
417 MATHEMATICS BUILDING
P. Siegel 21 / 100 [ 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 V2010 or equivalent, Math W4041 and Math W4051. Not offered in 2014-2015.
3 points

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

MATH W 4061x or y-W4062 Introduction To Modern Analysis

Real numbers, metric spaces, elements of general topology. Continuous and differential functions. Implicit functions. Integration; change of variables. Function spaces.
Prerequisites: The second term of this course may not be taken without the first. Prerequisites: MATH V1202 or the equivalent and 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 2014 :: MATH W4061
MATH
4061
68502
001
TuTh 8:40a - 9:55a
312 MATHEMATICS BUILDING
X. Zhang 75 / 100 [ More Info ]
Autumn 2014 :: MATH W4062
MATH
4062
60664
001
MW 4:10p - 5:25p
417 MATHEMATICS BUILDING
P. Gallagher 27 / 70 [ 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 2014 :: MATH W4065
MATH
4065
69015
001
TuTh 1:10p - 2:25p
407 MATHEMATICS BUILDING
E. Urban 7 / 18 [ More Info ]

MATH W 4071x 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, 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
Autumn 2014 :: MATH W4071
MATH
4071
67093
001
MW 7:40p - 8:55p
207 MATHEMATICS BUILDING
M. Smirnov 128 / 130 [ More Info ]

MATH W 4081y Introduction to Differentiable Manifolds

The implicit function theorem. Concept of a differentiable manifold. Tangent space and tangent bundle, vector fields, differentiable forms. Stoke's theorem, tensors. Introduction to Lie groups. - O. Savin
Prerequisites: MATH W4051 or W4061 and V2010.
3 points

MATH W 4391x-W4392y Quantum Mechanics: An Introduction for Mathematicans and Physicists

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.
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2014 :: MATH W4391
MATH
4391
72903
001
TuTh 4:10p - 5:25p
307 MATHEMATICS BUILDING
P. Woit 11 / 64 [ More Info ]

Engineering Courses

MATH E 1210x 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
Autumn 2014 :: MATH E1210
MATH
1210
17236
001
MW 10:10a - 11:25a
207 MATHEMATICS BUILDING
P. Chen 65 / 100 [ More Info ]
MATH
1210
61226
002
MW 1:10p - 2:25p
203 MATHEMATICS BUILDING
P. Chen 81 / 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. - <.>
Prerequisites: APMA E2101 (or MATH E1210)and APMA E3101
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2014 :: APMA E4101
APMA
4101
15272
001
MW 8:40a - 9:55a
1024 SEELEY W. MUDD BUILDING
M. Weinstein 49 / 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. - <.>
Prerequisites: APMA E2101 (or MATH E1210) and APMA E3101
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2014 :: APMA E4101
APMA
4101
15272
001
MW 8:40a - 9:55a
1024 SEELEY W. MUDD BUILDING
M. Weinstein 49 / 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 instructor's approval.
3 points

Course
Number
Call Number/
Section
Days & Times/
Location
Instructor Enrollment
Autumn 2014 :: APMA E4150
APMA
4150
64516
001
M 1:10p - 3:40p
214 SEELEY W. MUDD BUILDING
M. Weinstein 14 / 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 2014 :: APMA E4200
APMA
4200
27471
001
M 4:10p - 6:40p
329 PUPIN LABORATORIES
M. Spiegelman 108 / 120 [ More Info ]

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 approval.
3 points


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