## 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
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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,
Math 42, or the math placement diagnostic (offered through the Math Department website) in order to register for this course.

Terms: Aut, Win, Spr, Sum
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Cant, D. (PI)
;
Chen, D. (PI)
;
Chetard, B. (PI)
;
Dore, D. (PI)
;
Helfer, J. (PI)
;
Izzo, Z. (PI)
;
Kim, G. (PI)
;
Kraushar, N. (PI)
;
Larson, H. (PI)
;
Lucianovic, M. (PI)
;
Perlman, M. (PI)
;
Sloman, L. (PI)
;
Taylor, C. (PI)
;
Trettel, S. (PI)
;
Wang, G. (PI)
;
White, B. (PI)
;
Wieczorek, W. (PI)
;
Ying, L. (PI)
;
Zavyalov, B. (PI)
;
Arana Herrera, F. (TA)
;
Cant, D. (TA)
;
Helfer, J. (TA)
;
Izzo, Z. (TA)
;
Libkind, S. (TA)
;
Sloman, L. (TA)

## SUST 230: Innovating Large Scale Sustainable Transformations/Collaborating for the Future (ENVRES 380)

The capacity to innovate system-level transformations is a crucial leadership modality in the face of complex systemic challenges. This class gives students the mindsets, theoretical framework, and hands-on experience in shaping innovative interventions that bring about scaled and profound transformations in the face of complex multi-factorial challenges. Students are immersed in the System Acupuncture Methodology, which combines systems thinking, strategy, design thinking, behavioral sciences, resilience theory, diffusion theory, decision theory, and a theoretical framework around scaled multi-stakeholder interventions. Tools and theories introduced in class will be used to structure large-scale transformations that simultaneously create sustainability and resilience on environmental, societal, and economic fronts. This project-based team-based class challenges students to find solutions for complex real-world challenges. Class meets in the spring quarter on Fridays 9:30am-4:20pm, weeks 1-9. Lunch will be provided. Final presentations on Friday of week 9, 3-7:30pm. Consent of instructor required. To be considered, please apply on the d.school website.

Terms: Spr
| Units: 3-4

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