2019-2020 2020-2021 2021-2022 2022-2023 2023-2024
Browse
by subject...
    Schedule
view...
 

71 - 80 of 140 results for: all courses

MATH 62DM: Modern Mathematics: Discrete Methods

This is the second part of a theoretical (proof-based) sequence with a focus on discrete mathematics. The central objects discussed in this course are finite fields. These are beautiful structures in themselves, and very useful in large areas of modern mathematics, and beyond. Our goal will be to construct these, understand their structure, and along the way discuss unexpected applications in combinatorics and number theory. Highlights of the course include a complete proof of a polynomial time algorithm for primality testing, Sidon sets and finite projective planes, and an understanding of a lovely magic trick due to Persi Diaconis. Prerequisite: Math 61DM or 61CM.
Terms: Win | Units: 5 | UG Reqs: WAY-FR

MATH 63CM: Modern Mathematics: Continuous Methods

A proof-based course on ordinary differential equations. Topics include the inverse and implicit function theorems, implicitly-defined submanifolds of Euclidean space, 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, behavior of solutions near an equilibrium point, and Sturm-Liouville theory. Prerequisite: Math 61CM or Math 61DM.
Terms: Spr | Units: 5 | UG Reqs: WAY-FR, GER:DB-Math
Instructors: Ryzhik, L. (PI)

MATH 63DM: Modern Mathematics: Discrete Methods

Third part of a proof-based sequence in discrete mathematics, though independent of the second part (62DM). The first half of the quarter gives a brisk-paced coverage of probability and random processes with an intensive use of generating functions and a rich variety of applications. The second half treats entropy, Bayesian inference, Markov chains, game theory, probabilistic methods in solving non-probabilistic problems. We use continuous calculus, e.g. in handling the Gaussian, but anything needed will be reviewed in a self-contained manner. Prerequisite: Math 61DM or 61CM
Terms: Spr | Units: 5 | UG Reqs: WAY-FR
Instructors: Tokieda, T. (PI)

MATH 77Q: Probability and gambling

One of the earliest probabilistic discussions was in 1654 between two French mathematicians, Pascal and Fermat, on the following question: 'If a pair of six-sided dice is thrown 24 times, should you bet even money on the occurrence of at least one `double six'?' Shortly after the discussion, Huygens, a Dutch scientist, published De Ratiociniis in Ludo Aleae (The Value of all Chances in Games of Fortune) in 1657; this is considered to be the first treatise on probability. Due to the inherent appeal of games of chance, probability theory soon became popular, and the subject underwent rapid development in the 18th century with contributions from mathematical giants, such as Bernoulli, de Moivre, and Laplace. There are two fairly different lines of thought associated with applications of probability: the solution of betting/gambling and the analysis of statistical data related to quantitative subjects such as mortality tables and insurance rates. In this Introsem, we will discuss poker and more »
One of the earliest probabilistic discussions was in 1654 between two French mathematicians, Pascal and Fermat, on the following question: 'If a pair of six-sided dice is thrown 24 times, should you bet even money on the occurrence of at least one `double six'?' Shortly after the discussion, Huygens, a Dutch scientist, published De Ratiociniis in Ludo Aleae (The Value of all Chances in Games of Fortune) in 1657; this is considered to be the first treatise on probability. Due to the inherent appeal of games of chance, probability theory soon became popular, and the subject underwent rapid development in the 18th century with contributions from mathematical giants, such as Bernoulli, de Moivre, and Laplace. There are two fairly different lines of thought associated with applications of probability: the solution of betting/gambling and the analysis of statistical data related to quantitative subjects such as mortality tables and insurance rates. In this Introsem, we will discuss poker and other games of chance, such as daily fantasy sports, from the perspective of risk analysis. This Introsem does not require any programming knowledge, but some experience with Excel, MATLAB, R, and/or Python will enhance your experience in our discussion of daily fantasy sports. Students should be familiar with all material from Math 51. No prior knowledge of sports and games of chance is required. Students must apply through the IntroSem application process.
Terms: Win, Spr | Units: 3 | UG Reqs: WAY-FR
Instructors: Kim, G. (PI)

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: WAY-FR

MATH 101: Math Discovery Lab

MDL is a discovery-based project course in mathematics. Students work independently in small groups to explore open-ended 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. WIM. Admission is by application. Motivated students with a mathematical background of at least Math 51 or 61CM or 61DM (or equivalent) are encouraged to apply. Please visit https://mathematics.stanford.edu/math-101 for more information about the course and application.
Terms: Win | Units: 4 | UG Reqs: WAY-FR

MATH 104: Applied Matrix Theory

Linear algebra for applications in science and engineering. The course introduces the key mathematical ideas in matrix theory, which are used in modern methods of data analysis, scientific computing, optimization, and nearly all quantitative fields of science and engineering. While the choice of topics is motivated by their use in various disciplines, the course will emphasize the theoretical and conceptual underpinnings of this subject. Topics include orthogonality, projections, spectral theory for symmetric matrices, the singular value decomposition, the QR decomposition, least-squares methods, and algorithms for solving systems of linear equations; applications include clustering, principal component analysis and dimensionality reduction, regression. MATH 113 offers a more theoretical treatment of linear algebra. MATH 104 and ENGR 108 cover complementary topics in applied linear algebra. The focus of MATH 104 is on algorithms and concepts; the focus of ENGR 108 is on a few linear algebra concepts, and many applications. Prerequisites: MATH 51 and programming experience on par with CS 106A.
Terms: Aut, Win, Spr | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR

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: 4 | UG Reqs: GER:DB-Math, WAY-FR

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: Win | Units: 4 | UG Reqs: WAY-FR

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: Spr | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR
Instructors: Vondrak, J. (PI)
Filter Results:
term offered
updating results...
teaching presence
updating results...
number of units
updating results...
time offered
updating results...
days
updating results...
UG Requirements (GERs)
updating results...
component
updating results...
career
updating results...
© Stanford University | Terms of Use | Copyright Complaints