# 2023 Courses

Explore these Summer 2023 courses and when you're ready, apply to be a visiting Stanford student. Apply early for the best course choice when enrollment opens.

## Course List

• ### Vector Calculus for Engineers

Available
Catalog Number
CME 100
Course Cost
\$6410.00
Population
Summary

Computation and visualization using MATLAB. Differential vector calculus: vector-valued functions, analytic geometry in space, functions of several variables, partial derivatives, gradient, linearization, unconstrained maxima and minima, Lagrange multipliers and applications to trajectory simulation, least squares, and numerical optimization. Introduction to linear algebra: matrix operations, systems of algebraic equations with applications to coordinate transformations and equilibrium problems. Integral vector calculus: multiple integrals in Cartesian, cylindrical, and spherical coordinates, line integrals, scalar potential, surface integrals, Green's, divergence, and Stokes' theorems. Numerous examples and applications drawn from classical mechanics, fluid dynamics and electromagnetism. Placement Diagnostic (recommendation non-binding).

#### Details

Class Number
23490
Units
5
Interest Area
Math and Data Science
Course Format & Length
In-Person, 8 weeks
Instructors
Hung Le
Dates
-
Prerequisites

Knowledge of single-variable calculus equivalent to the content of MATH 19, MATH 20, MATH 21 (e.g., 5 on Calc BC, 4 on Calc BC with MATH 21, 5 on Calc AB with MATH 21)

Schedule
T/W/Th, 8:30A-10:20A
Cross Listings
ENGR 154
• ### Ordinary Differential Equations for Engineers

Available
Catalog Number
CME 102
Course Cost
\$6410.00
Population
Summary

applications: Solution of initial and boundary value problems, series solutions, Laplace transforms, and nonlinear equations; numerical methods for solving ordinary differential equations, accuracy of numerical methods, linear stability theory, finite differences. Introduction to MATLAB programming as a basic tool kit for computations. Problems from various engineering fields. Prerequisite: 10 units of AP credit (Calc BC with 5, or Calc AB with 5 or placing out of the single variable math placement test: Placement diagnostic), or MATH 19, MATH 20, MATH 21. Recommended: CME100.

#### Details

Class Number
6993
Units
5
Interest Area
Math and Data Science
Course Format & Length
In-Person, 8 weeks
Instructors
Hung Le
Dates
-
Prerequisites

10 units of AP credit (Calc BC with 5, or Calc AB with 5 or placing out of the single variable math placement test , or MATH 19, MATH 20 or MATH 21. Recommended: CME100.

Schedule
T/W/Th, 11:30A-1:20P
Cross Listings
ENGR 155A
• ### Introduction to Probability and Statistics for Engineers

Available
Catalog Number
CME 106
Course Cost
\$5128.00
Population
Summary

random variables, independence, and conditional probability; discrete and continuous distributions, moments, distributions of several random variables. Topics in mathematical statistics: random sampling, point estimation, confidence intervals, hypothesis testing, non-parametric tests, regression and correlation analyses; applications in engineering, industrial manufacturing, medicine, biology, and other fields.

#### Details

Class Number
4612
Units
4
Interest Area
Math and Data Science
Course Format & Length
In-Person, 8 weeks
Instructors
Dates
-
Prerequisites

CME 100, ENGR 154, MATH 51 or Math 52

Schedule
T/Th, 5:30P-8:00P
Cross Listings
ENGR 155C
• ### Introduction to Probability and Statistics for Epidemiology

Available
Catalog Number
EPI 259
Course Cost
\$3846.00
Population
Summary

Topics: random variables, expectation, variance, probability distributions, the central limit theorem, sampling theory, hypothesis testing, confidence intervals. Correlation, regression, analysis of variance, and nonparametric tests. Introduction to least squares and maximum likelihood estimation. Emphasis is on medical applications. EPI 259 in summer is offered for remote students.

#### Details

Class Number
22041
Units
3
Interest Area
Math and Data Science
Course Format & Length
Online, 8 weeks
Instructors
Kristin Sainani
Dates
-
Schedule
M/W, 9:30A-11:20A
Cross Listings
HUMBIO 89X
• ### Linear Algebra, Multivariable Calculus, and Modern Applications

Available
Catalog Number
MATH 51-02
Course Cost
\$6410.00
Population
Summary

This course provides unified coverage of linear algebra and multivariable differential calculus. It discusses applications connecting the material to many quantitative fields.  Linear algebra in large dimensions underlies the scientific, data-driven, and computational tasks of the 21st century. The linear algebra portion of the course includes orthogonality, linear independence, matrix algebra, and eigenvalues as well as ubiquitious applications: least squares, linear regression, Markov chains (relevant to population dynamics, molecular chemistry, and PageRank), singular value decomposition (essential in image compression, topic modeling, and data-intensive work in the natural sciences), and more. The multivariable calculus material includes unconstrained optimization via gradients and Hessians (used for energy minimization in physics and chemistry), 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 (a crucial part of how GPS works).  The course emphasizes computations alongside an intuitive understanding of key ideas,  making students well-prepared for further study of mathematics and its applications to other fields.  The widespread use of computers makes it more important, not less, for users of math to understand concepts: in all scientific fields, novel users of quantitative tools in the future will be those who understand ideas and how they fit with applications and examples.  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.

#### Details

Class Number
23549
Units
5
Interest Area
Math and Data Science
Course Format & Length
In-Person, 8 weeks
Instructors
Stavrianidi, A.
Dates
-
Prerequisites

MATH 21, MATH 42, or the math placement diagnostic (offered through the Math Department website) in order to register for this course

Schedule
MTWThF, 1:30P-2:50P
• ### Theory of Probability

Available
Catalog Number
STATS 116
Course Cost
\$6410.00
Population
Summary

Probability spaces as models for phenomena with statistical regularity. Discrete spaces (binomial, hypergeometric, Poisson). Continuous spaces (normal, exponential) and densities. Random variables, expectation, independence, conditional probability. Introduction to the laws of large numbers and central limit theorem. 5 units for Undergraduates with required discussion section. 4 units for Graduates, discussion section optional. The section 01 lecture is for UGs only. UGs are required to enroll in one of the sections.

#### Details

Class Number
7096
Units
5
Interest Area
Math and Data Science
Course Format & Length
In-Person, 8 weeks
Instructors
Li, H.
Dates
-
Prerequisites

MATH 52 and familiarity with infinite series, or equivalent.

Schedule
MTWTh, 10:30A-11:20A
• ### Data Mining and Analysis

Available
Catalog Number
STATS 202
Course Cost
\$3846.00
Population
Summary

Data mining is used to discover patterns and relationships in data. Emphasis is on large complex data sets such as those in very large databases or through web mining. Topics: decision trees, association rules, clustering, case based methods, and data visualization.

#### Details

Class Number
8606
Units
3
Interest Area
Math and Data Science
Course Format & Length
In-Person, 8 weeks
Instructors
Tran, Linh
Dates
-
Prerequisites

Introductory courses in statistics or probability (e.g., STATS 60), linear algebra (e.g., MATH 51), and computer programming (e.g., CS 105).

Schedule
M/W, 4:30P-5:50P
• ### Introduction to Regression Models and Analysis of Variance

Available
Catalog Number
STATS 203V
Course Cost
\$3846.00
Population
Summary

Modeling and interpretation of observational and experimental data using linear and nonlinear regression methods. Model building and selection methods. Multivariable analysis. Fixed and random effects models. Experimental design.

#### Details

Class Number
11831
Units
3
Interest Area
Math and Data Science
Course Format & Length
Online, 8 weeks
Instructors
Dey, A.
Dates
-
Prerequisites

Pre- or corequisite: STATS 200.

Schedule
online asynchronous
• ### Introduction to Statistical Learning

Available
Catalog Number
STATS 216V
Course Cost
\$3846.00
Population
Summary

Overview of supervised learning, with a focus on regression and classification methods. Syllabus includes: linear and polynomial regression, logistic regression and linear discriminant analysis; cross-validation and the bootstrap, model selection and regularization methods (ridge and lasso); nonlinear models, splines and generalized additive models; tree-based methods, random forests and boosting; support-vector machines; Some unsupervised learning: principal components and clustering (k-means and hierarchical). Computing is done in R, through tutorial sessions and homework assignments. This math-light course is offered remotely only via video segments (MOOC style). TAs will host remote weekly office hours using an online platform such as Google Hangout or BlueJeans. There are four homework assignments, a midterm, and a final exam, all of which are administered remotely.

#### Details

Class Number
11740
Units
3
Interest Area
Math and Data Science
Course Format & Length
Online, 8 weeks
Instructors
Sood, A.
Dates
-
Prerequisites

Introductory courses in statistics or probability (e.g., STATS 60), linear algebra (e.g., MATH 51), and computer programming (e.g., CS 105).

Schedule
T/Th, 10:30A-11:50A
• ### Introduction to Stochastic Processes I

Available
Catalog Number
STATS 217
Course Cost
\$3846.00
Population
Summary

Discrete and continuous time Markov chains, poisson processes, random walks, branching processes, first passage times, recurrence and transience, stationary distributions. Non-Statistics masters students may want to consider taking STATS 215 instead.

#### Details

Class Number
23427
Units
3
Interest Area
Math and Data Science
Course Format & Length
In-Person, 8 weeks
Instructors
Hartog, W.
Dates
-
Prerequisites

STATS 116 or consent of instructor

Schedule
T/Th, 10:30A-11:50A