MATH 61DM: Modern Mathematics: Discrete Methods
This is the first part of a theoretical (i.e., proofbased) sequence in discrete mathematics and linear algebra. Covers general vector spaces, linear maps and duality, eigenvalues, inner product spaces, spectral theorem, counting techniques, and linear algebra methods in discrete mathematics including spectral graph theory and dimension arguments. The linear algebra content is covered jointly with
Math 61CM. Students should 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.nnThis sequence is not appropriate for students planning to major in natural sciences, economics, or engineering, but is suitable for majors in any other field (such as MCS ("data science"), computer science, and mathematics).
Terms: Aut

Units: 5

UG Reqs: WAYFR

Grading: Letter or Credit/No Credit
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)
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)
MATH 80Q: Capillary Surfaces: Explored and Unexplored Territory
Preference to sophomores. Capillary surfaces: the interfaces between fluids that are adjacent to each other and do not mix. Recently discovered phenomena, predicted mathematically and subsequently confirmed by experiments, some done in space shuttles. Interested students may participate in ongoing investigations with affinity between mathematics and physics.
Terms: Win

Units: 3

UG Reqs: WAYFR, WAYSMA

Grading: Letter (ABCD/NP)
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: Spr

Units: 3

UG Reqs: WAYFR

Grading: Letter (ABCD/NP)
Instructors:
Wieczorek, W. (PI)
MATH 101: Math Discovery Lab
MDL is a discoverybased project course in mathematics. Students work independently in small groups to explore openended mathematical problems and discover original mathematics. Students formulate conjectures and hypotheses; test predictions by computation, simulation, or pure thought; and present their results to classmates. No lecture component; inclass meetings reserved for student presentations, attendance mandatory. Admission is by application:
http://math101.stanford.edu. Motivated students with any level of mathematical background are encouraged to apply. WIM
Terms: Win

Units: 3

UG Reqs: WAYFR

Grading: Letter or Credit/No Credit
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:
Thorner, J. (PI)
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:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Schaeffer, G. (PI)
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

Units: 3

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 114: Introduction to Scientific Computing (CME 108)
Introduction to Scientific Computing Numerical computation for mathematical, computational, physical sciences and engineering: error analysis, floatingpoint 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:DBEngrAppSci, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
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