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

1 - 9 of 9 results for: MATH

MATH 21: Calculus

This course addresses a variety of topics centered around the theme of "calculus with infinite processes", largely the content of BC-level AP Calculus that isn't in the AB-level syllabus. It is needed throughout probability and statistics at all levels, as well as to understand approximation procedures that arise in all quantitative fields (including economics and computer graphics). After an initial review of limit rules, the course goes on to discuss sequences of numbers and of functions, as well as limits "at infinity" for each (needed for any sensible discussion of long-term behavior of a numerical process, such as: iterative procedures and complexity in computer science, dynamic models throughout economics, and repeated trials with data in any field). Integration is discussed for rational functions (a loose end from Math 20) and especially (improper) integrals for unbounded functions and "to infinity": this shows up in contexts as diverse as escape velocity for a rocket, the pres more »
This course addresses a variety of topics centered around the theme of "calculus with infinite processes", largely the content of BC-level AP Calculus that isn't in the AB-level syllabus. It is needed throughout probability and statistics at all levels, as well as to understand approximation procedures that arise in all quantitative fields (including economics and computer graphics). After an initial review of limit rules, the course goes on to discuss sequences of numbers and of functions, as well as limits "at infinity" for each (needed for any sensible discussion of long-term behavior of a numerical process, such as: iterative procedures and complexity in computer science, dynamic models throughout economics, and repeated trials with data in any field). Integration is discussed for rational functions (a loose end from Math 20) and especially (improper) integrals for unbounded functions and "to infinity": this shows up in contexts as diverse as escape velocity for a rocket, the present value of a perpetual yield asset, and important calculations in probability (including the famous "bell curve" and to understand why many statistical tests work as they do). The course then turns to infinite series (how to "sum" an infinite collection of numbers), some useful convergence and divergence rests for these, and the associated killer app: power series and their properties, as well as Taylor approximations, all of which provide the framework that underlies virtually all mathematical models used in any quantitative field. Prerequisite: Math 20 or equivalent. If you have not previously taken a calculus course at Stanford then you must have taken the math placement diagnostic (offered through the Math Department website: https://mathematics.stanford.edu/academics/math-placement) in order to register for this course.
Terms: Aut, Win, Spr, Sum | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR

MATH 51: Linear Algebra, Multivariable Calculus, and Modern Applications

This course provides unified coverage of linear algebra and multivariable differential calculus, and the free course e-text connects the material to many fields. Linear algebra in large dimensions underlies the scientific, data-driven, and computational tasks of the 21st century. The linear algebra portion includes orthogonality, linear independence, matrix algebra, and eigenvalues with applications such as least squares, linear regression, and Markov chains (relevant to population dynamics, molecular chemistry, and PageRank); the singular value decomposition (essential in image compression, topic modeling, and data-intensive work in many fields) is introduced in the final chapter of the e-text. The multivariable calculus portion includes unconstrained optimization via gradients and Hessians (used for energy minimization), constrained optimization (via Lagrange multipliers, crucial in economics), gradient descent and the multivariable Chain Rule (which underlie many machine learning al more »
This course provides unified coverage of linear algebra and multivariable differential calculus, and the free course e-text connects the material to many fields. Linear algebra in large dimensions underlies the scientific, data-driven, and computational tasks of the 21st century. The linear algebra portion includes orthogonality, linear independence, matrix algebra, and eigenvalues with applications such as least squares, linear regression, and Markov chains (relevant to population dynamics, molecular chemistry, and PageRank); the singular value decomposition (essential in image compression, topic modeling, and data-intensive work in many fields) is introduced in the final chapter of the e-text. The multivariable calculus portion includes unconstrained optimization via gradients and Hessians (used for energy minimization), constrained optimization (via Lagrange multipliers, crucial in economics), gradient descent and the multivariable Chain Rule (which underlie many machine learning algorithms, such as backpropagation), and Newton's method (an ingredient in GPS and robotics). The course emphasizes computations alongside an intuitive understanding of key ideas. The widespread use of computers makes it important for users of math to understand concepts: novel users of quantitative tools in the future will be those who understand ideas and how they fit with examples and applications. This is the only course at Stanford whose syllabus includes nearly all the math background for CS 229, which is why CS 229 and CS 230 specifically recommend it (or other courses resting on it). For frequently asked questions about the differences between Math 51 and CME 100, see the FAQ on the placement page on the Math Department website. Prerequisite: Math 21 or equivalent (e.g. 5 on the AP Calculus BC test or suitable score on certain international exams: https://studentservices.stanford.edu/my-academics/earn-my-degree/undergraduate-degree-progress/test-transfer-credit/external-test-2). If you have not previously taken a calculus course at Stanford then you must have taken the math placement diagnostic (offered through the Math Department website: https://mathematics.stanford.edu/academics/math-placement) in order to register for this course.
Terms: Aut, Win, Spr, Sum | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR

MATH 197: Senior Honors Thesis

Honors math major working on senior honors thesis under an approved advisor carries out research and reading. Satisfactory written account of progress achieved during term must be submitted to advisor before term ends. May be repeated 3 times for a max of 9 units. Contact department student services specialist to enroll.
Terms: Aut, Win, Spr, Sum | Units: 1-6 | Repeatable 3 times (up to 9 units total)

MATH 199: Reading Topics

For Math majors only. Undergraduates pursue a reading program under the direction of a Math faculty member; topics limited to those not in regular department course offerings. Credit can fulfill the elective requirement for Math majors. Departmental approval required; please contact the Student Services Specialist for the enrollment proposal form at least 2 weeks before the final study list deadline. May be repeated for credit. Enrollment beyond a third section requires additional approval.
Terms: Aut, Win, Spr, Sum | Units: 3 | Repeatable for credit

MATH 298: Graduate Practical Training

Only for mathematics graduate students. Students obtain employment in a relevant industrial or research activity to enhance their professional experience. Students submit a concise report detailing work activities, problems worked on, and key results. May be repeated for credit up to 3 units. Prerequisite: qualified offer of employment and consent of department. Prior approval by Math Department is required; you must contact the Math Department's Student Services staff for instructions before being granted permission to enroll.
Terms: Aut, Win, Spr, Sum | Units: 1 | Repeatable for credit

MATH 360: Advanced Reading and Research

Terms: Aut, Win, Spr, Sum | Units: 1-10 | Repeatable for credit

MATH 382: Qualifying Examination Seminar

Terms: Win, Sum | Units: 1-3 | Repeatable for credit

MATH 802: TGR Dissertation

Terms: Aut, Win, Spr, Sum | Units: 0 | Repeatable for credit
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