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11 - 20 of 48 results for: MATH

MATH 56: 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 course 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 notions such as fields and abstract vector spaces. This course may be paired with Math 51; though that course is not a pre- or co-requisite.
Terms: Aut, Win | Units: 4 | UG Reqs: WAY-FR

MATH 62CM: Modern Mathematics: Continuous Methods

A proof-based introduction to manifolds and the general Stokes' theorem. This includes a treatment of multilinear algebra, further study of submanifolds of Euclidean space (with many examples), differential forms and their geometric interpretations, integration of differential forms, Stokes' theorem, and some applications to topology. Prerequisites: Math 61CM.
Terms: Win | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR

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 75SI: Learn to Give a Math Talk

This class focuses on preparing and presenting math talks. The first few weeks introduce the main skills, learning from panels, guest lectures, and discussions. In the remaining weeks, participants practice presenting math topics to classmates that are selected through class votes, and feedback is provided for improving presentations. The material in the topics is new to the students, but not too advanced, so participants learn some math also. The course is aimed at students who have taken at least one proof-based math class, and preference is given to students who have less experience presenting math to others. Application to enroll is necessary: https://forms.gle/7GSA2Vh7xZhm5AUaA
Terms: Win | Units: 2
Instructors: Conrad, B. (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 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 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; dual space and dual basis; eigenvectors and eigenvalues; diagonalization. Includes an introduction to proof-writing. ( Math 104 offers a more application-oriented treatment.) Prerequisites: Math 51
Terms: Aut, Win, Spr | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR
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