## BIO 165: Quantitative Cell Biology - from Molecules to Evolution

Modern research approaches of quantitative biology tightly integrate experimentation with data analysis and mathematical modeling to provide unprecedented insights into the organization and functioning of living systems. This course explores the quantitative basis of major cellular processes and their coordination to form a cohesive physiological entity which is capable of rapid growth and acclimation to changing environments. This is fundamental for the ecological and evolutionary dynamics of cellular populations across biological scenarios, from microbial community assembly to tumor growth. Weekly lectures will be accompanied by 'dry lab sessions' in which students analyze experimental data sets and employ modeling. As such, students will actively develop a fundamental skill set of quantitative biology which includes a knowledge of dynamical systems, numerical simulations, and modern statistical inference. Assumes basic (but not advanced) familiarity with math, e.g.
MATH51. Students with all ranges of coding experience are welcome.

Terms: Win
| Units: 3

Instructors:
Cremer, J. (PI)

## CEE 154: Data Analytics for Physical Systems (CEE 254)

This course introduces practical applications of data analytics and machine learning from understanding sensor data to extracting information and decision making in the context of sensed physical systems. Many civil engineering applications involve complex physical systems, such as buildings, transportation, and infrastructure systems, which are integral to urban systems and human activities. Emerging data science techniques and rapidly growing data about these systems have enabled us to better understand them and make informed decisions. In this course, students will work with real-world data to learn about challenges in analyzing data, applications of statistical analysis and machine learning techniques using MATLAB, and limitations of the outcomes in domain-specific contexts. Topics include data visualization, noise cleansing, frequency domain analysis, forward and inverse modeling, feature extraction, machine learning, and error analysis. Prerequisites:
CS106A,
CME 100/
Math51,
Stats110/101, or equivalent.

Terms: Aut
| Units: 3-4

## CEE 254: Data Analytics for Physical Systems (CEE 154)

This course introduces practical applications of data analytics and machine learning from understanding sensor data to extracting information and decision making in the context of sensed physical systems. Many civil engineering applications involve complex physical systems, such as buildings, transportation, and infrastructure systems, which are integral to urban systems and human activities. Emerging data science techniques and rapidly growing data about these systems have enabled us to better understand them and make informed decisions. In this course, students will work with real-world data to learn about challenges in analyzing data, applications of statistical analysis and machine learning techniques using MATLAB, and limitations of the outcomes in domain-specific contexts. Topics include data visualization, noise cleansing, frequency domain analysis, forward and inverse modeling, feature extraction, machine learning, and error analysis. Prerequisites:
CS106A,
CME 100/
Math51,
Stats110/101, or equivalent.

Terms: Aut
| Units: 3-4

## CME 200: Linear Algebra with Application to Engineering Computations (ME 300A)

Computer based solution of systems of algebraic equations obtained from engineering problems and eigen-system analysis, Gaussian elimination, effect of round-off error, operation counts, banded matrices arising from discretization of differential equations, ill-conditioned matrices, matrix theory, least square solution of unsolvable systems, solution of non-linear algebraic equations, eigenvalues and eigenvectors, similar matrices, unitary and Hermitian matrices, positive definiteness, Cayley-Hamilton theory and function of a matrix and iterative methods. Prerequisite: familiarity with computer programming, and
MATH51.

Terms: Aut
| Units: 3

Instructors:
Moin, P. (PI)
;
Aboumrad, G. (SI)
;
Gonzalez, C. (TA)
...
more instructors for CME 200 »

Instructors:
Moin, P. (PI)
;
Aboumrad, G. (SI)
;
Gonzalez, C. (TA)
;
Hollister, Q. (TA)
;
Karmarkar, I. (TA)
;
Wang, G. (TA)

## CME 251: Geometric and Topological Data Analysis (CS 233)

Mathematical and computational tools for the analysis of data with geometric content, such images, videos, 3D scans, GPS traces -- as well as for other data embedded into geometric spaces. Linear and non-linear dimensionality reduction techniques. Graph representations of data and spectral methods. The rudiments of computational topology and persistent homology on sampled spaces, with applications. Global and local geometry descriptors allowing for various kinds of invariances. Alignment, matching, and map/correspondence computation between geometric data sets. Annotation tools for geometric data. Geometric deep learning on graphs and sets. Function spaces and functional maps. Networks of data sets and joint learning for segmentation and labeling. Prerequisites: discrete algorithms at the level of
CS161; linear algebra at the level of Math51 or
CME103.

Last offered: Spring 2022

## CS 21SI: AI for Social Good

Students will learn about and apply cutting-edge artificial intelligence techniques to real-world social good spaces (such as healthcare, government, education, and environment). The class will focus on techniques from machine learning and deep learning, including regression, neural networks, convolutional neural networks (CNNs), and recurrent neural networks (RNNs). The course alternates between lectures on machine learning theory and discussions with invited speakers, who will challenge students to apply techniques in their social good domains. Students complete weekly coding assignments reinforcing machine learning concepts and applications. Prerequisites: programming experience at the level of
CS107, mathematical fluency at the level of
MATH51, comfort with probability at the level of
CS109 (or equivalent). Application required for enrollment.

Terms: Win, Spr
| Units: 2

## CS 229: Machine Learning (STATS 229)

Topics: statistical pattern recognition, linear and non-linear regression, non-parametric methods, exponential family, GLMs, support vector machines, kernel methods, deep learning, model/feature selection, learning theory, ML advice, clustering, density estimation, EM, dimensionality reduction, ICA, PCA, reinforcement learning and adaptive control, Markov decision processes, approximate dynamic programming, and policy search. Prerequisites: knowledge of basic computer science principles and skills at a level sufficient to write a reasonably non-trivial computer program in Python/NumPy to the equivalency of
CS106A,
CS106B, or
CS106X, familiarity with probability theory to the equivalency of
CS 109,
MATH151, or
STATS 116, and familiarity with multivariable calculus and linear algebra to the equivalency of MATH51 or
CS205.

Terms: Aut, Spr, Sum
| Units: 3-4

Instructors:
Avati, A. (PI)
;
Charikar, M. (PI)
;
Guestrin, C. (PI)
...
more instructors for CS 229 »

Instructors:
Avati, A. (PI)
;
Charikar, M. (PI)
;
Guestrin, C. (PI)
;
Ma, T. (PI)
;
Ng, A. (PI)
;
Re, C. (PI)
;
Balogun, E. (TA)
;
Bhaskhar, N. (TA)
;
Cao, Z. (TA)
;
Jung, S. (TA)
;
Khosla, S. (TA)
;
Kim, K. (TA)
;
Kohen Behar, B. (TA)
;
Lim, D. (TA)
;
Silberg, J. (TA)
;
Tran, H. (TA)
;
Young, G. (TA)
;
Yu, L. (TA)

## CS 233: Geometric and Topological Data Analysis (CME 251)

Mathematical and computational tools for the analysis of data with geometric content, such images, videos, 3D scans, GPS traces -- as well as for other data embedded into geometric spaces. Linear and non-linear dimensionality reduction techniques. Graph representations of data and spectral methods. The rudiments of computational topology and persistent homology on sampled spaces, with applications. Global and local geometry descriptors allowing for various kinds of invariances. Alignment, matching, and map/correspondence computation between geometric data sets. Annotation tools for geometric data. Geometric deep learning on graphs and sets. Function spaces and functional maps. Networks of data sets and joint learning for segmentation and labeling. Prerequisites: discrete algorithms at the level of
CS161; linear algebra at the level of Math51 or
CME103.

Last offered: Spring 2022

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

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

Instructors:
Hardt, A. (PI)
;
Lucianovic, M. (PI)
;
Swaminathan, M. (PI)
...
more instructors for MATH 51 »

Instructors:
Hardt, A. (PI)
;
Lucianovic, M. (PI)
;
Swaminathan, M. (PI)
;
Taylor, C. (PI)
;
Wickham, Z. (PI)
;
Ying, L. (PI)
;
Angelo, R. (TA)
;
Chaturvedi, S. (TA)
;
Frager, T. (TA)
;
Fushida-Hardy, S. (TA)
;
Kim, D. (TA)
;
Moreira, A. (TA)
;
Ongole, N. (TA)
;
Wu, Y. (TA)
;
Zhou, Y. (TA)

## MATH 51A: Linear Algebra, Multivariable Calculus, and Modern Applications, ACE

Students attend one of the regular
MATH 51 lectures with a longer discussion section of four hours per week instead of two. Active mode: students in small groups discuss and work on problems from a worksheet distributed 2 or 3 days in advance, with a TA providing guidance and answering questions. Application required:
https://forms.gle/ruykWBk6zJMgXRB49

Last offered: Spring 2022
| UG Reqs: GER:DB-Math, WAY-FR

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