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Vector Calculus for Engineers
Available Catalog Number
 CME 100
 Course Cost
 $6410.00
 Population
 High School, Undergraduate, Graduate
 Summary

Computation and visualization using MATLAB. Differential vector calculus: vectorvalued 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 nonbinding).
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Details
 Class Number
 23490
 Units
 5
 Interest Area
 Math and Data Science
 Course Format & Length
 InPerson, 8 weeks
 Instructors
 Hung Le
 Dates
 
 Prerequisites

Knowledge of singlevariable 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, 8:30A10:20A
 Cross Listings
 ENGR 154

Ordinary Differential Equations for Engineers
Available Catalog Number
 CME 102
 Course Cost
 $6410.00
 Population
 High School, Undergraduate, Graduate
 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.
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Details
 Class Number
 6993
 Units
 5
 Interest Area
 Math and Data Science
 Course Format & Length
 InPerson, 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, 11:30A1:20P
 Cross Listings
 ENGR 155A

Introduction to Probability and Statistics for Engineers
Available Catalog Number
 CME 106
 Course Cost
 $5128.00
 Population
 High School, Undergraduate, Graduate
 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, nonparametric tests, regression and correlation analyses; applications in engineering, industrial manufacturing, medicine, biology, and other fields.
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Details
 Class Number
 4612
 Units
 4
 Interest Area
 Math and Data Science
 Course Format & Length
 InPerson, 8 weeks
 Instructors
 Vadim Khayms
 Dates
 
 Prerequisites

CME 100, ENGR 154, MATH 51 or Math 52
 Schedule
 T/Th, 5:30P8:00P
 Cross Listings
 ENGR 155C

Introduction to Probability and Statistics for Epidemiology
Available Catalog Number
 EPI 259
 Course Cost
 $3846.00
 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. 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, 9:30A11:20A
 Cross Listings
 HUMBIO 89X

Linear Algebra, Multivariable Calculus, and Modern Applications
Available Catalog Number
 MATH 5102
 Course Cost
 $6410.00
 Population
 High School, Undergraduate, Graduate
 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, datadriven, 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 dataintensive 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 wellprepared 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
 InPerson, 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, 1:30P2:50P

Theory of Probability
Available Catalog Number
 STATS 116
 Course Cost
 $6410.00
 Population
 High School, Undergraduate, Graduate
 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.
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Details
 Class Number
 7096
 Units
 5
 Interest Area
 Math and Data Science
 Course Format & Length
 InPerson, 8 weeks
 Instructors
 Li, H.
 Dates
 
 Prerequisites

MATH 52 and familiarity with infinite series, or equivalent.
 Schedule
 MTWTh, 10:30A11:20A

Data Mining and Analysis
Available Catalog Number
 STATS 202
 Course Cost
 $3846.00
 Population
 High School, Undergraduate, Graduate
 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.
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Details
 Class Number
 8606
 Units
 3
 Interest Area
 Math and Data Science
 Course Format & Length
 InPerson, 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, 4:30P5:50P

Introduction to Regression Models and Analysis of Variance
Available Catalog Number
 STATS 203V
 Course Cost
 $3846.00
 Population
 Undergraduate, Graduate
 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
 Undergraduate, Graduate
 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; crossvalidation and the bootstrap, model selection and regularization methods (ridge and lasso); nonlinear models, splines and generalized additive models; treebased methods, random forests and boosting; supportvector machines; Some unsupervised learning: principal components and clustering (kmeans and hierarchical). Computing is done in R, through tutorial sessions and homework assignments. This mathlight 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.
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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, 10:30A11:50A

Introduction to Stochastic Processes I
Available Catalog Number
 STATS 217
 Course Cost
 $3846.00
 Population
 Undergraduate, Graduate
 Summary

Discrete and continuous time Markov chains, poisson processes, random walks, branching processes, first passage times, recurrence and transience, stationary distributions. NonStatistics masters students may want to consider taking STATS 215 instead.
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Details
 Class Number
 23427
 Units
 3
 Interest Area
 Math and Data Science
 Course Format & Length
 InPerson, 8 weeks
 Instructors
 Hartog, W.
 Dates
 
 Prerequisites

STATS 116 or consent of instructor
 Schedule
 T/Th, 10:30A11:50A