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 secondorder equations to oscillations, matrix exponentials, Laplace transforms, stability of nonlinear systems and phase plane analysis, numerical methods. Prerequisite: 51 or equivalents.
Terms: Aut, Win, Spr, Sum

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
De Groote, C. (PI)
;
Eliashberg, Y. (PI)
;
Fredrickson, L. (PI)
...
more instructors for MATH 53 »
Instructors:
De Groote, C. (PI)
;
Eliashberg, Y. (PI)
;
Fredrickson, L. (PI)
;
Hershkovits, O. (PI)
;
Love, J. (PI)
;
Mantoulidis, C. (PI)
;
Raju, C. (PI)
;
Tam, K. (PI)
;
Yang, T. (PI)
;
Madnick, J. (TA)
;
Silliman, J. (TA)
;
Ungemach, W. (TA)
MATH 61CM: Modern Mathematics: Continuous Methods
This is the first part of a theoretical (i.e., proofbased) sequence in multivariable calculus and linear algebra, providing a unified treatment of these topics. Covers general vector spaces, linear maps and duality, eigenvalues, inner product spaces, spectral theorem, metric spaces, differentiation in Euclidean space, submanifolds of Euclidean space, inverse and implicit function theorems, and many examples. Part of the linear algebra content is covered jointly with
Math 61DM. Students should know 1variable calculus and have an interest in a theoretical approach to the subject. Prerequisite: score of 5 on the BClevel Advanced Placement calculus exam, or consent of the instructor.
Terms: Aut

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter (ABCD/NP)
Instructors:
Vasy, A. (PI)
;
Zachos, E. (TA)
MATH 62CM: Modern Mathematics: Continuous Methods
A continuation of themes from
Math 61CM, centered around: manifolds, multivariable integration, and the general Stokes' theorem. This includes a treatment of multilinear algebra, further study of submanifolds of Euclidean space and an introduction to general manifolds (with many examples), differential forms and their geometric interpretations, integration of differential forms, Stokes' theorem, and some applications to topology. Prerequisite:
Math 61CM.
Terms: Win

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter (ABCD/NP)
Instructors:
Mazzeo, R. (PI)
;
Masullo, A. (TA)
MATH 63CM: Modern Mathematics: Continuous Methods
A proofbased course on ordinary differential equations, continuing themes from
Math 61CM and
Math 62CM. Topics include linear systems of differential equations and necessary tools from linear algebra, stability and asymptotic properties of solutions to linear systems, existence and uniqueness theorems for nonlinear differential equations with some applications to manifolds, behavior of solutions near an equilibrium point, and SturmLiouville theory. Prerequisites:
Math 61CM and
Math 62CM.
Terms: Spr

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter (ABCD/NP)
Instructors:
Luk, J. (PI)
;
Savvas, M. (TA)
MATH 104: Applied Matrix Theory
Linear algebra for applications in science and engineering: orthogonality, projections, spectral theory for symmetric matrices, the singular value decomposition, the QR decomposition, leastsquares, the condition number of a matrix, algorithms for solving linear systems. (
Math 113 offers a more theoretical treatment of linear algebra.) Prerequisites:
Math 51 and programming experience on par with CS106nnMath 104 and
EE103/CME103 cover complementary topics in applied linear algebra. The focus of
Math 104 is on algorithms and concepts; the focus of EE103 is on a few linear algebra concepts, and many applications.
Terms: Aut, Win

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Feldheim, O. (PI)
;
Ying, L. (PI)
;
Dore, D. (TA)
;
He, X. (TA)
;
McConnell, S. (TA)
;
Safaee, P. (TA)
;
Velcheva, K. (TA)
;
Wigderson, Y. (TA)
MATH 106: Functions of a Complex Variable
Complex numbers, analytic functions, CauchyRiemann equations, complex integration, Cauchy integral formula, residues, elementary conformal mappings. (
Math 116 offers a more theoretical treatment.) Prerequisite: 52.
Terms: Spr, Sum

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
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:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Vondrak, J. (PI)
;
Rosengarten, Z. (TA)
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: Spr

Units: 3

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Wieczorek, W. (PI)
;
Kraushar, N. (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:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Carlsson, G. (PI)
;
Guijarro Ordonez, J. (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 applicationoriented treatment.)
Terms: Aut, Win, Spr, Sum

Units: 3

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Chatterjee, S. (PI)
;
Li, J. (PI)
;
Manners, F. (PI)
...
more instructors for MATH 113 »
Instructors:
Chatterjee, S. (PI)
;
Li, J. (PI)
;
Manners, F. (PI)
;
Ohrt, C. (PI)
;
Dozier, B. (TA)
;
Pan, D. (TA)
;
Safaee, P. (TA)
;
Szucs, G. (TA)
;
Zhou, Y. (TA)
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