2024 Spring Semester Dates
End Date: Friday, May 17, 2024
Online session times are set at the start of each term. There will be two sessions—late afternoon and early evening Pacific Time.
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Credits
Multivariable Calculus and Linear Algebra provides unified coverage of linear algebra and multivariable differential calculus, and is based on recently developed curriculum by the Stanford University Mathematics faculty for first-year Stanford University students. The course e-text, written by a group of Stanford University Mathematics faculty, connects the material to many fields. Linear algebra in large dimensions underlies the scientific, data-driven, and computational tasks of the 21st century. 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: innovative users of quantitative tools in the future will be those who understand ideas and how they fit with examples and applications. This course is different than many multivariable calculus and linear algebra courses offered in high schools and colleges in that it is more abstract and challenging without being proof-based.
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).
Prerequisites: Students should be well prepared in single variable calculus, and completed AP Calculus BC or equivalent.
Required text: Linear Algebra, Multivariable Calculus, and Modern Applications, Stanford University Mathematics Faculty.
Course Information
The course grade will be based on weekly homework and exam scores. The instructor will hold office hours.
Attendance Policy: Attendance is strongly encouraged and some classes may be required.
Format
Partially Synchronous: Students will listen to two or three recorded Stanford faculty lectures per week and also attend two synchronous online sessions where the instructor will expand on the material and facilitate group discussion and group work.
Tuition
Tuition: $4,900
Application Fee: $35
Financial Aid is available. Learn more about financial assistance on the Financial Aid page.
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Frequently Asked Questions
Does the course cover a full semester of Multivariable Calculus and Linear Algebra, given most institutions offer those as two separate classes?
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In particular, multivariable integration and vector calculus (line integrals, surface integrals, Green’s and Stokes’ theorems) are not covered in this course. Experience with Stanford undergraduates has shown that these topics are less relevant for students interested in many popular majors, including computer science, and engineering.
Similarly, while the coverage of linear algebra is extensive and sophisticated, it emphasizes certain aspects that are very important in applications like data science. For example, the focus on formulations and calculations in n-dimensional Euclidean space, introduction of singular values and matrix factorizations, but omits certain topics that are now regarded as less important (e.g., Gaussian reduction). It contains a good introduction to eigenvectors and eigenvalues, but does not cover these subjects in their entirety.