printer friendly pageMATH 52: Integral Calculus of Several Variables
Iterated integrals, line and surface integrals, vector analysis with applications to vector potentials and conservative vector fields, physical interpretations. Divergence theorem and the theorems of Green, Gauss, and Stokes. Prerequisite: 51 and 42 or equivalents.
Terms: Aut, Win, Spr
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Dembo, A. (PI)
;
Edelen, N. (PI)
;
Jafarov, J. (PI)
;
Li, J. (PI)
;
Wieczorek, W. (PI)
;
Zhang, S. (PI)
;
Madnick, J. (TA)
;
Wang, G. (TA)
;
Zamorzaev, A. (TA)
MATH 53: Ordinary Differential Equations with Linear Algebra
Ordinary differential equations and initial value problems, systems of linear differential equations with constant coefficients, applications of second-order equations to oscillations, matrix exponentials, Laplace transforms, stability of non-linear systems and phase plane analysis, numerical methods. Prerequisite: 51 and 42 or equivalents.
Terms: Aut, Win, Spr
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Cheng, D. (PI)
;
Dozier, B. (PI)
;
Mantoulidis, C. (PI)
...
more instructors for MATH 53 »
Instructors:
Cheng, D. (PI)
;
Dozier, B. (PI)
;
Mantoulidis, C. (PI)
;
Poulson, J. (PI)
;
Savvas, M. (PI)
;
Wieczorek, W. (PI)
;
Ying, L. (PI)
;
Greer, F. (TA)
;
Pan, D. (TA)
MATH 110: Applied Number Theory and Field Theory
Number theory and its applications to modern cryptography. Topics: congruences, finite fields, primality testing and factorization, public key cryptography, error correcting codes, and elliptic curves, emphasizing algorithms. WIM.
Terms: Aut
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Entin, A. (PI)
;
Lim, B. (TA)
MATH 113: Linear Algebra and Matrix Theory
Algebraic properties of matrices and their interpretation in geometric terms. The relationship between the algebraic and geometric points of view and matters fundamental to the study and solution of linear equations. Topics: linear equations, vector spaces, linear dependence, bases and coordinate systems; linear transformations and matrices; similarity; eigenvectors and eigenvalues; diagonalization. (
Math 104 offers a more application-oriented treatment.)
Terms: Aut, Win, Spr
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Chatterjee, S. (PI)
;
Church, T. (PI)
;
Kerckhoff, S. (PI)
...
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Instructors:
Chatterjee, S. (PI)
;
Church, T. (PI)
;
Kerckhoff, S. (PI)
;
Helfer, J. (TA)
;
Sun, Q. (TA)
;
Wang, G. (TA)
MATH 115: Functions of a Real Variable
The development of real analysis in Euclidean space: sequences and series, limits, continuous functions, derivatives, integrals. Basic point set topology. Honors math majors and students who intend to do graduate work in mathematics should take 171. Prerequisite: 51.
Terms: Aut, Spr
| Units: 3
| UG Reqs: GER:DB-Math
MATH 120: Groups and Rings
Recommended for Mathematics majors and required of honors Mathematics majors. Similar to 109 but altered content and more theoretical orientation. Groups acting on sets, examples of finite groups, Sylow theorems, solvable and simple groups. Fields, rings, and ideals; polynomial rings over a field; PID and non-PID. Unique factorization domains. WIM.
Terms: Aut, Spr
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR
MATH 131P: Partial Differential Equations I
An introduction to PDE; particularly suitable for non-Math majors. Topics include physical examples of PDE's, method of characteristics, D'Alembert's formula, maximum principles, heat kernel, Duhamel's principle, separation of variables, Fourier series, Harmonic functions, Bessel functions, spherical harmonics. Students who have taken
MATH 171 should consider taking
MATH 173 rather than 131p. Prerequisite: 53.
Terms: Aut, Win
| Units: 3
| UG Reqs: GER:DB-Math
MATH 136: Stochastic Processes (STATS 219)
Introduction to measure theory, Lp spaces and Hilbert spaces. Random variables, expectation, conditional expectation, conditional distribution. Uniform integrability, almost sure and Lp convergence. Stochastic processes: definition, stationarity, sample path continuity. Examples: random walk, Markov chains, Gaussian processes, Poisson processes, Martingales. Construction and basic properties of Brownian motion. Prerequisite:
STATS 116 or
MATH 151 or equivalent. Recommended:
MATH 115 or equivalent.
Terms: Aut
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Zheng, T. (PI)
;
Jafarov, J. (TA)
MATH 159: Discrete Probabilistic Methods
Modern discrete probabilistic methods suitable for analyzing discrete structures of the type arising in number theory, graph theory, combinatorics, computer science, information theory and molecular sequence analysis. Prerequisite:
STATS 116/
MATH 151 or equivalent.
Terms: Aut
| Units: 3
Instructors:
Basu, R. (PI)
MATH 161: Set Theory
Informal and axiomatic set theory: sets, relations, functions, and set-theoretical operations. The Zermelo-Fraenkel axiom system and the special role of the axiom of choice and its various equivalents. Well-orderings and ordinal numbers; transfinite induction and transfinite recursion. Equinumerosity and cardinal numbers; Cantor's Alephs and cardinal arithmetic. Open problems in set theory. Prerequisite: students should be comfortable doing proofs.
Terms: Aut
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Sommer, R. (PI)
;
Wolf, A. (TA)
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