## BIODS 206: Applied Multivariate Analysis (STATS 206)

Introduction to the statistical analysis of several quantitative measurements on each observational unit. Emphasis is on concepts, computer-intensive methods. Examples from economics, education, geology, psychology. Topics: multiple regression, multivariate analysis of variance, principal components, factor analysis, canonical correlations, multidimensional scaling, clustering. Prerequisites:
STATS 116/118,
STATS 191/203,
MATH104 (recommended). See
https://statistics.stanford.edu/course-equiv for equivalent courses in other departments that satisfy these prerequisites.

Last offered: Autumn 2023

## CS 205L: Continuous Mathematical Methods with an Emphasis on Machine Learning

A survey of numerical approaches to the continuous mathematics used throughout computer science with an emphasis on machine and deep learning. Although motivated from the standpoint of machine learning, the course will focus on the underlying mathematical methods including computational linear algebra and optimization, as well as special topics such as automatic differentiation via backward propagation, momentum methods from ordinary differential equations, CNNs, RNNs, etc. Written homework assignments and (straightforward) quizzes focus on various concepts; additionally, students can opt in to a series of programming assignments geared towards neural network creation, training, and inference. (Replaces
CS205A, and satisfies all similar requirements.) Prerequisites:
Math 51; Math104 or MATH113 or equivalent or comfort with the associated material.

Terms: Win
| Units: 3

Instructors:
Fedkiw, R. (PI)

## MATH 104: Applied Matrix Theory

Linear algebra for applications in science and engineering. The course introduces the key mathematical ideas in matrix theory, which are used in modern methods of data analysis, scientific computing, optimization, and nearly all quantitative fields of science and engineering. While the choice of topics is motivated by their use in various disciplines, the course will emphasize the theoretical and conceptual underpinnings of this subject. Topics include orthogonality, projections, spectral theory for symmetric matrices, the singular value decomposition, the QR decomposition, least-squares methods, and algorithms for solving systems of linear equations; applications include clustering, principal component analysis and dimensionality reduction, regression.
MATH 113 offers a more theoretical treatment of linear algebra.
MATH 104 and
ENGR 108 cover complementary topics in applied linear algebra. The focus of
MATH 104 is on algorithms and concepts; the focus of
ENGR 108 is on a few linear algebra concepts, and many applications. Prerequisites:
MATH 51 and programming experience on par with
CS 106A.

Terms: Aut, Win, Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR

## STATS 206: Applied Multivariate Analysis (BIODS 206)

Introduction to the statistical analysis of several quantitative measurements on each observational unit. Emphasis is on concepts, computer-intensive methods. Examples from economics, education, geology, psychology. Topics: multiple regression, multivariate analysis of variance, principal components, factor analysis, canonical correlations, multidimensional scaling, clustering. Prerequisites:
STATS 116/118,
STATS 191/203,
MATH104 (recommended). See
https://statistics.stanford.edu/course-equiv for equivalent courses in other departments that satisfy these prerequisites.

Terms: Spr
| Units: 3

Instructors:
Owen, A. (PI)

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