## 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:DB-Math, WAY-FR

Instructors:
Kerckhoff, S. (PI)

## MATH 62DM: Modern Mathematics: Discrete Methods

This is the second part of a proof-based sequence in discrete mathematics. This course covers topics in elementary number theory, group theory, and discrete Fourier analysis. For example, we'll discuss the basic examples of abelian groups arising from congruences in elementary number theory, as well as the non-abelian symmetric group of permutations. Prerequisites: 61DM or 61CM.

Terms: Win
| Units: 5
| UG Reqs: WAY-FR

Instructors:
Soundararajan, K. (PI)

## MATH 63CM: Modern Mathematics: Continuous Methods

A proof-based 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 Sturm-Liouville theory. Prerequisites:
Math 61CM and
Math 62CM.

Terms: Spr
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
White, B. (PI)
;
Dunlap, A. (TA)

## MATH 63DM: Modern Mathematics: Discrete Methods

Third part of a proof-based sequence in discrete mathematics. This course covers several topics in probability (random variables, independence and correlation, concentration bounds, the central limit theorem) and topology (metric spaces, point-set topology, continuous maps, compactness, Brouwer's fixed point and the Borsuk-Ulam theorem), with some applications in combinatorics. Prerequisites: 61DM or 61CM

Terms: Spr
| Units: 5
| UG Reqs: WAY-FR

Instructors:
Tokieda, T. (PI)
;
Bates, E. (TA)

## MATH 83N: Proofs and Modern Mathematics

How do mathematicians think? Why are the mathematical facts learned in school true? In this course students will explore higher-level mathematical thinking and will gain familiarity with a crucial aspect of mathematics: achieving certainty via mathematical proofs, a creative activity of figuring out what should be true and why. This course is ideal for students who would like to learn about the reasoning underlying mathematical results, but at a pace and level of abstraction not as intense as
Math 61CM/DM, as a consequence benefiting from additional opportunity to explore the reasoning. Familiarity with one-variable calculus is strongly recommended at least at the AB level of AP Calculus since a significant part of the seminar develops develops some of the main results in that material systematically from a small list of axioms. We also address linear algebra from the viewpoint of a mathematician, illuminating algebraic notions such as groups, rings, and fields. This seminar may be paired with
Math 51; though that course is not a pre- or co-requisite.

Terms: Aut
| Units: 3
| UG Reqs: WAY-FR

## MATH 87Q: Mathematics of Knots, Braids, Links, and Tangles

Preference to sophomores. Types of knots and how knots can be distinguished from one another by means of numerical or polynomial invariants. The geometry and algebra of braids, including their relationships to knots. Topology of surfaces. Brief summary of applications to biology, chemistry, and physics.

Terms: Win
| Units: 3
| UG Reqs: WAY-FR

Instructors:
Wieczorek, W. (PI)

## 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, least-squares, the condition number of a matrix, algorithms for solving linear systems.
MATH 113 offers a more theoretical treatment of linear algebra.
MATH 104 and
EE 103/
CME 103 cover complementary topics in applied linear algebra. The focus of
MATH 104 is on algorithms and concepts; the focus of
EE 103 is on a few linear algebra concepts, and many applications. Prerequisites:
MATH 51 and programming experience on par with
CS 106.

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

Instructors:
Kazeev, V. (PI)
;
Taylor, C. (PI)
;
Velcheva, K. (PI)
...
more instructors for MATH 104 »

Instructors:
Kazeev, V. (PI)
;
Taylor, C. (PI)
;
Velcheva, K. (PI)
;
Ying, L. (PI)
;
Guijarro Ordonez, J. (TA)
;
Liu, Y. (TA)
;
Luo, S. (TA)
;
Sloman, L. (TA)
;
Truong Vu, N. (TA)
;
Wang, G. (TA)
;
Wolf, A. (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: Spr, Sum
| Units: 3
| UG Reqs: GER:DB-Math

Instructors:
De Groote, C. (PI)
;
Zaman, A. (PI)
;
Cotner, S. (TA)
...
more instructors for MATH 106 »

Instructors:
De Groote, C. (PI)
;
Zaman, A. (PI)
;
Cotner, S. (TA)
;
Fauteux-Chapleau, F. (TA)
;
Nguyen, D. (TA)

## 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)
;
Chen, S. (TA)

## 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, WAY-FR

Instructors:
Manners, F. (PI)

Filter Results: