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 52H: Honors Multivariable Mathematics
Continuation of 51H. Prerequisite: 51H.
Terms: Win
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
De Groote, C. (PI)
;
Eliashberg, Y. (PI)
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)
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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 53H: Honors Multivariable Mathematics
Continuation of 52H. Prerequisite: 52H.
Terms: Spr
| Units: 5
| UG Reqs: WAY-FR, GER:DB-Math
Instructors:
Eliashberg, Y. (PI)
;
Lazarev, O. (TA)
MATH 78: Mathematics for Machine Learning
To make smart decisions efficiently without human intervention, a body of mathematical techniques originally developed within statistics has grown into the subject now called machine learning. This course explores some of these mathematical ideas, illustrating how they work in the context of real-world problems, leading to important notions such as binary classifiers and ultimately providing insight into a wide array of applications involving optimization, pattern recognition, and so on.
Terms: Spr
| Units: 3
| UG Reqs: GER:DB-Math
MATH 104: Applied Matrix Theory
Linear algebra for applications in science and engineering: orthogonality, projections, the four fundamental subspaces of a matrix, spectral theory for symmetric matrices, the singular value decomposition, the QR decomposition, least-squares, the condition number of a matrix, algorithms for solving linear systems. (
Math 113 offers a more theoretical treatment.) Prerequisites:
MATH 51 and
MATH 52 or 53.
Terms: Win, Spr
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Hicks, A. (PI)
;
Greverath, D. (TA)
;
Li, C. (TA)
;
Masullo, A. (TA)
;
Silliman, J. (TA)
MATH 106: Functions of a Complex Variable
Complex numbers, analytic functions, Cauchy-Riemann equations, complex integration, Cauchy integral formula, residues, elementary conformal mappings. (
Math 116 offers a more theoretical treatment.) Prerequisite: 52.
Terms: Win
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Gu, Y. (PI)
MATH 108: Introduction to Combinatorics and Its Applications
Topics: graphs, trees (Cayley's Theorem, application to phylogony), eigenvalues, basic enumeration (permutations, Stirling and Bell numbers), recurrences, generating functions, basic asymptotics. Prerequisites: 51 or equivalent.
Terms: Win
| Units: 3
| UG Reqs: GER:DB-Math
MATH 109: Applied Group Theory
Applications of the theory of groups. Topics: elements of group theory, groups of symmetries, matrix groups, group actions, and applications to combinatorics and computing. Applications: rotational symmetry groups, the study of the Platonic solids, crystallographic groups and their applications in chemistry and physics. Honors math majors and students who intend to do graduate work in mathematics should take 120. WIM.
Terms: Win
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Marberg, E. (PI)
;
Skryzalin, J. (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)
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