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Introduction to Probability and Statistics for Engineers
Available Catalog Number
 CME 10601
 Course Cost
 $6860.00
 Population
 High School, Undergraduate, Graduate
 Summary

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, nonparametric tests, regression and correlation analyses. Numerous applications in engineering, manufacturing, reliability and quality assurance, medicine, biology, and other fields.
Details
 Class Number
 2259
 Units
 5
 Interest Area
 Math and Data Science
 Course Format & Length
 InPerson, 8 weeks
 Instructors
 Vadim Khayms
 Dates
 
 Prerequisites

CME100/ENGR154, Math 51, or Math52.
 Schedule
 Tue, Thu 5:30 PM  7:20 PM
 Cross Listings
 ENGR 155C

Principles of Data Science
Available Catalog Number
 DATASCI 11201
 Course Cost
 $5488.00
 Population
 High School, Undergraduate, Graduate
 Summary

A handson 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 scikitlearn. 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.)
 Course Notes

This course has a required discussion section in addition to the main lecture section.
 Download syllabus (pdf)
Details
 Class Number
 22670
 Units
 4
 Interest Area
 Math and Data Science
 Course Format & Length
 InPerson, 8 weeks
 Instructors
 Alex Dekhtyar
 Dates
 
 Prerequisites

CS 106A or equivalent programming experience in Python
 Schedule
 Mon, Wed, Fri 10:30 AM  11:20 AM

Introduction to Probability and Statistics for Epidemiology
Available Catalog Number
 EPI 25901
 Course Cost
 $4116.00
 Population
 Undergraduate, Graduate
 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.
 Course Notes

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.
 Download syllabus (docx)
Details
 Class Number
 11897
 Units
 3
 Interest Area
 Math and Data Science
 Course Format & Length
 Online, 8 weeks
 Instructors
 Kristin Sainani
 Dates
 
 Schedule
 Mon, Wed 9:30 AM  10:30 AM.

Calculus
Full Catalog Number
 MATH 2101
 Course Cost
 $5488.00
 Population
 High School, Undergraduate, Graduate
 Summary

This course addresses a variety of topics centered around the theme of "calculus with infinite processes", largely the content of BClevel AP Calculus that isn't in the ABlevel 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 longterm 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.
 Download syllabus (pdf)
Details
 Class Number
 23054
 Units
 4
 Interest Area
 Math and Data Science
 Course Format & Length
 InPerson, 8 weeks
 Instructors
 Wickham, Z.
 Dates
 
 Prerequisites

MATH 20 or equivalent.
 Schedule
 Mon, Tue, Wed, Thu 10:30 AM  11:45 AM

Linear Algebra, Multivariable Calculus, and Modern Applications
Almost Full Catalog Number
 MATH 5101
 Course Cost
 $6860.00
 Population
 High School, Undergraduate, Graduate
 Summary

This course provides unified coverage of linear algebra and multivariable differential calculus, and the free course etext connects the material to many fields. Linear algebra in large dimensions underlies the scientific, datadriven, 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 dataintensive work in many fields) is introduced in the final chapter of the etext. 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.
 Course Notes

All visiting students (i.e., nonStanford) must fill out the Summer Prerequisite form.
 Download syllabus (pdf)
Details
 Class Number
 23055
 Units
 5
 Interest Area
 Math and Data Science
 Course Format & Length
 InPerson, 8 weeks
 Instructors
 Wickham, Z.
 Dates
 
 Prerequisites

Math 21 or equivalent (e.g. 5 on the AP Calculus BC test or suitable score on certain international exams: offered through the Math Department website.
 Schedule
 Mon, Tue, Wed, Thu, Fri 9:00 AM  10:15 AM

Foundations of Product Realization
Available Catalog Number
 ME 10201
 Course Cost
 $4116.00
 Population
 High School, Undergraduate, Graduate
 Summary

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 COVID19 restrictions during AY2021, inperson 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.
 Download syllabus (pdf)
Details
 Class Number
 23163
 Units
 3
 Interest Area
 Math and Data Science
 Course Format & Length
 InPerson, 8 weeks
 Instructors
 Jonathan Edelman
 Dates
 
 Prerequisites

ME 1 or ME 101 or consent of instructor.
 Schedule
 Tue, Thu 10:30 AM  12:20 PM

Theory of Probability I
Available Catalog Number
 STATS 11701
 Course Cost
 $4116.00
 Population
 High School, Undergraduate, Graduate
 Summary

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).
 Download syllabus (pdf)
Details
 Class Number
 22678
 Units
 3
 Interest Area
 Math and Data Science
 Course Format & Length
 InPerson, 8 weeks
 Instructors
 Gene Kim
 Dates
 
 Prerequisites

Singlevariable calculus including infinite series (e.g., MATH 21) and at least one MATH course at Stanford.
 Schedule
 Mon, Wed, Fri 11:30 AM  12:20 PM

Theory of Probability II
Available Catalog Number
 STATS 11801
 Course Cost
 $4116.00
 Population
 Undergraduate, Graduate
 Summary

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, chisquare, t, multivariate normal).
 Download syllabus (pdf)
Details
 Class Number
 22679
 Units
 3
 Interest Area
 Math and Data Science
 Course Format & Length
 InPerson, 8 weeks
 Instructors
 Jessica Hwang
 Dates
 
 Prerequisites

A calculusbased first course in probability (such as STATS 117, CS 109, or MS&E 120) and multivariable calculus, including multiple integrals ( MATH 52 or equivalent, can be taken concurrently).
 Schedule
 Mon, Wed, Fri 11:30 AM  12:20 PM

Introduction to Applied Statistics
Available Catalog Number
 STATS 19101
 Course Cost
 $4116.00
 Population
 High School, Undergraduate, Graduate
 Summary

Statistical tools for modern data analysis. Topics include regression and prediction, elements of the analysis of variance, bootstrap, and crossvalidation. Emphasis is on conceptual rather than theoretical understanding. Applications to social/biological sciences. Student assignments/projects require use of the software package R.
 Download syllabus (pdf)
Details
 Class Number
 22878
 Units
 3
 Interest Area
 Math and Data Science
 Course Format & Length
 InPerson, 8 weeks
 Instructors
 Cyrus DiCiccio
 Dates
 
 Prerequisites

Introductory statistical methods course. Recommended: STATS 60, STATS 110, or STATS 141.
 Schedule
 Mon, Tue, Wed, Thu 3:00 PM  3:50 PM

Introduction to Statistical Inference
Available Catalog Number
 STATS 20001
 Course Cost
 $5488.00
 Population
 Undergraduate, Graduate
 Summary

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

Note that students must enroll in one section in addition to the main lecture.
 Download syllabus (pdf)
Details
 Class Number
 22838
 Units
 4
 Interest Area
 Math and Data Science
 Course Format & Length
 InPerson, 8 weeks
 Instructors
 Jessica Hwang
 Dates
 
 Prerequisites

STATS 116
 Schedule
 Mon, Wed, Fri 1:30 PM  2:50 PM