## 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, Sum
| Units: 3
| UG Reqs: GER:DB-Math

## MATH 107: Graph Theory

An introductory course in graph theory establishing fundamental concepts and results in variety of topics. Topics include: basic notions, connectivity, cycles, matchings, planar graphs, graph coloring, matrix-tree theorem, conditions for hamiltonicity, Kuratowski's theorem, Ramsey and Turan-type theorem. Prerequisites: 51 or equivalent and some familiarity with proofs is required.

Terms: Spr
| Units: 3

Instructors:
Manners, F. (PI)
;
Izzo, Z. (SI)

## 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

Instructors:
Manners, F. (PI)
;
He, J. (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:DB-Math, WAY-FR

Instructors:
Thorner, J. (PI)
;
Sprunger, C. (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: Spr
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Schaeffer, G. (PI)
;
Kraushar, N. (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, Sum
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Kazeev, V. (PI)
;
Kemeny, M. (PI)
;
Khoo, Y. (PI)
;
Manners, F. (PI)
;
Falcone, P. (TA)
;
Sherman, D. (TA)
;
Velcheva, K. (TA)
;
Wang, G. (TA)
;
Zhou, Y. (TA)

## MATH 114: Introduction to Scientific Computing (CME 108)

Introduction to Scientific Computing Numerical computation for mathematical, computational, physical sciences and engineering: error analysis, floating-point arithmetic, nonlinear equations, numerical solution of systems of algebraic equations, banded matrices, least squares, unconstrained optimization, polynomial interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations, truncation error, numerical stability for time dependent problems and stiffness. Implementation of numerical methods in MATLAB programming assignments. Prerequisites:
MATH 51, 52, 53; prior programming experience (MATLAB or other language at level of
CS 106A or higher).

Terms: Win, Sum
| Units: 3
| UG Reqs: GER:DB-EngrAppSci, WAY-AQR, WAY-FR

## 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: 21.

Terms: Aut, Spr, Sum
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR

## MATH 116: Complex Analysis

Analytic functions, Cauchy integral formula, power series and Laurent series, calculus of residues and applications, conformal mapping, analytic continuation, introduction to Riemann surfaces, Fourier series and integrals. (
Math 106 offers a less theoretical treatment.) Prerequisites: 52, and 115 or 171.

Terms: Aut
| Units: 3
| UG Reqs: GER:DB-Math

Instructors:
Tsai, C. (PI)
;
Masullo, A. (TA)

## MATH 118: Mathematics of Computation

Notions of analysis and algorithms central to modern scientific computing: continuous and discrete Fourier expansions, the fast Fourier transform, orthogonal polynomials, interpolation, quadrature, numerical differentiation, analysis and discretization of initial-value and boundary-value ODE, finite and spectral elements. Prerequisites:
MATH 51 and 53.

Terms: Win
| Units: 3
| UG Reqs: GER:DB-Math

Instructors:
Kazeev, V. (PI)

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