Probability: random variables, independence, and conditional probability; discrete and continuous distributions, moments, distributions of several random variables. Numerical simulation using Monte Carlo techniques. Topics in mathematical statistics: random sampling, point estimation, confidence intervals, hypothesis testing, non-parametric tests, regression and correlation analyses. Numerous applications in engineering, manufacturing, reliability and quality assurance, medicine, biology, and other fields.

A hands-on introduction to the methods of data science. Strategies for analyzing and visualizing tabular data, including common patterns and pitfalls. Data acquisition through web scraping and REST APIs. Core principles of machine learning: supervised vs. unsupervised learning, training vs. test error, hyperparameter tuning, and ensemble methods. Introduction to data of different shapes and sizes, including text, image, and geospatial data. The focus is on intuition and implementation, rather than theory and math. Implementation is in Python and Jupyter notebooks, using libraries such as pandas and scikit-learn. Course culminates in a final project where students apply the methods to a data science problem of their choice. (Students with experience in another programming language should take CS 193Q to catch up on Python.)

This course has a required discussion section in addition to the main lecture section.

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.

Undergraduate students who do not need this course for WAYS requirement can enroll in EPI 259. EPI 259 is held remotely. Schedule: MW 9:30 AM - 10:30 AM.

This course addresses a variety of topics centered around the theme of "calculus with infinite processes", largely the content of BC-level AP Calculus that isn't in the AB-level syllabus. It is needed throughout probability and statistics at all levels, as well as to understand approximation procedures that arise in all quantitative fields (including economics and computer graphics). After an initial review of limit rules, the course goes on to discuss sequences of numbers and of functions, as well as limits "at infinity" for each (needed for any sensible discussion of long-term behavior of a numerical process, such as: iterative procedures and complexity in computer science, dynamic models throughout economics, and repeated trials with data in any field). Integration is discussed for rational functions (a loose end from Math 20) and especially (improper) integrals for unbounded functions and "to infinity": this shows up in contexts as diverse as escape velocity for a rocket, the present value of a perpetual yield asset, and important calculations in probability (including the famous "bell curve" and to understand why many statistical tests work as they do). The course then turns to infinite series (how to "sum" an infinite collection of numbers), some useful convergence and divergence rests for these, and the associated killer app: power series and their properties, as well as Taylor approximations, all of which provide the framework that underlies virtually all mathematical models used in any quantitative field. If you have not previously taken a calculus course at Stanford then you must have taken the math placement diagnostic (offered through the Math Department website) in order to register for this course.

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. 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. If you have not previously taken a calculus course at Stanford then you must have taken the math placement diagnostic (offered through the Math Department website) in order to register for this course.

All visiting students (i.e., non-Stanford) must fill out the Summer Prerequisite form.

Students develop the language and toolset to transform design concepts into tangible models/prototypes that cultivate the emergence of mechanical aptitude. Visual communication tools such as sketching, orthographic projection, and 2D/3D design software are introduced in the context of design and prototyping assignments. Due to COVID-19 restrictions during AY20-21, in-person use of the Product Realization Lab may be limited or not permitted. Lab kits will be sent to enrolled students to support exploration of prototyping and mechanical design techniques that will be practiced during synchronous lectures and coaching sessions. Project documentation, reflection, and presentations are opportunities for students to find their design voice and practice sharing it with others.

Introduction to probability theory, including probability axioms, conditional probability, independence, random variables, and expectation. Joint, marginal, and conditional distributions. Discrete models (binomial, hypergeometric, Poisson) and continuous models (normal, exponential).

Continuation of STATS 117, with a focus on probability topics useful for statistics. Sampling distributions of sums, means, variances, and order statistics of random variables. Convolutions, moment generating functions, and limit theorems. Probability distributions useful in statistics (gamma, beta, chi-square, t, multivariate normal).

Statistical tools for modern data analysis. Topics include regression and prediction, elements of the analysis of variance, bootstrap, and cross-validation. Emphasis is on conceptual rather than theoretical understanding. Applications to social/biological sciences. Student assignments/projects require use of the software package R.

Modern statistical concepts and procedures derived from a mathematical framework. Statistical inference, decision theory; point and interval estimation, tests of hypotheses; Neyman-Pearson theory. Bayesian analysis; maximum likelihood, large sample theory.

Note that students must enroll in one section in addition to the main lecture.