EdusalsaDiscover Your Stanford

- Not Offered

5 units

Letter or Credit/No Credit

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

GER:DB-Math

WAY-FR

- BIOE 42
- BIOE 102
- BIOE 209
- CEE 101B
- CEE 101E
- CEE 154
- CEE 161I
- CEE 162A
- CEE 162I
- CEE 172
- CEE 254
- CEE 261I
- CEE 262I
- CEE 278A
- CME 106
- CME 108
- CME 200
- CME 209
- CME 251
- CS 21SI
- CS 109
- CS 129
- CS 148
- CS 205L
- CS 229
- CS 229M
- CS 233
- CS 248
- EE 178
- ENGR 62
- ENGR 62X
- ENGR 108
- ENGR 155C
- MS&E 111
- MS&E 111X
- MS&E 120
- MS&E 211
- MS&E 211X
- MS&E 226
- MS&E 230
- MS&E 232
- MS&E 232H
- ME 300A
- EARTHSYS 110
- EARTHSYS 146A
- EARTHSYS 146B
- ENERGY 191
- ENERGY 291
- ESS 246A
- ESS 246B
- ESS 247
- GEOPHYS 110
- GEOPHYS 128
- GEOPHYS 228
- GEOPHYS 281
- BIO 120
- BIO 220
- CHEM 171
- ECON 50
- ECON 135
- INTLPOL 204A
- MATH 52
- MATH 53
- MATH 104
- MATH 107
- MATH 108
- MATH 109
- MATH 110
- MATH 113
- MATH 114
- MATH 118
- MATH 120
- MATH 137
- PHYSICS 63
- PUBLPOL 51
- PUBLPOL 301A
- STATS 214
- STATS 229

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**Pranav Rajpurkar** is a PhD student in Computer Science at Stanford, working on Artificial Intelligence for Healthcare. He was previously a Stanford undergrad ('16).

**Brad Girardeau** got his B.S, M.S. degrees in computer science at Stanford ('16, '17). When not thinking about computer security, he can be found playing violin or running across the Golden Gate Bridge.

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