Stanford Degrees in Statistics

CourseDescriptionTextMATH 51. Linear Algebra and Differential Calculus of Several Variables. 5 Units.Geometry and algebra of vectors, matrices and linear transformations, eigenvalues of symmetric matrices, vector-valued functions and functions of several variables, partial derivatives and gradients, derivative as a matrix, chain rule in several variables, critical points and Hessian, least-squares, , constrained and unconstrained optimization in several variables, Lagrange multipliers. Prerequisite: 21, 42, or the math placement diagnostic (offered through the Math Department website) in order to register for this course.Levandosky's Linear Algebra, Colley's Vector CalculusMATH 52. Integral Calculus of Several Variables. 5 Units.Iterated integrals, line and surface integrals, vector analysis with applications to vector potentials and conservative vector fields, physical interpretations. Divergence theorem and the theorems of Green, Gauss, and Stokes. Prerequisite: 51 or equivalents.Calculus Early Transcendentals, by C. Henry Edwards and David E. Penney (Ch. 13,14, and 11)MATH 53. Ordinary Differential Equations with Linear Algebra. 5 Units.Ordinary differential equations and initial value problems, systems of linear differential equations with constant coefficients, applications of second-order equations to oscillations, matrix exponentials, Laplace transforms, stability of non-linear systems and phase plane analysis, numerical methods. Prerequisite: 51 or equivalents.Differential Equations: An Introduction to Modern Methods and Applications - Second Edition, by Brannan and BoyceCS 106A. Programming Methodology. 3-5 Units.Introduction to the engineering of computer applications emphasizing modern software engineering principles: object-oriented design, decomposition, encapsulation, abstraction, and testing. Uses the Java programming language. Emphasis is on good programming style and the built-in facilities of the Java language. No prior programming experience required. Summer quarter enrollment is limited.CS 106B. Programming Abstractions. 3-5 Units.Abstraction and its relation to programming. Software engineering principles of data abstraction and modularity. Object-oriented programming, fundamental data structures (such as stacks, queues, sets) and data-directed design. Recursion and recursive data structures (linked lists, trees, graphs). Introduction to time and space complexity analysis. Uses the programming language C++ covering its basic facilities. Prerequisite: 106A or equivalent. Summer quarter enrollment is limited.STATS 116. Theory of Probability. 3-5 Units.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. Prerequisites: MATH 52 and familiarity with infinite series, or equivalent.Introduction to Probability, Grinstead and Snell, AMS, second editionMATH 104. Applied Matrix Theory. 3 Units.Linear algebra for applications in science and engineering: orthogonality, projections, spectral theory for symmetric matrices, the singular value decomposition, the QR decomposition, least-squares, the condition number of a matrix, algorithms for solving linear systems. (Math 113 offers a more theoretical treatment of linear algebra.) Prerequisites: Math 51 and programming experience on par with CS106nnMath 104 and EE103/CME103 cover complementary topics in applied linear algebra. The focus of Math 104 is on algorithms and concepts; the focus of EE103 is on a few linear algebra concepts, and many applications.Numerical Linear Algebra by LLoyd N. Trefethen and David Bau, III, SIAM (required) Introduction to Linear Algebra by Gilbert Strang, Wellesley-Cambridge Press, 4th edition (optional)MATH 113. Linear Algebra and Matrix Theory. 3 Units.Algebraic properties of matrices and their interpretation in geometric terms. The relationship between the algebraic and geometric points of view and matters fundamental to the study and solution of linear equations. Topics: linear equations, vector spaces, linear dependence, bases and coordinate systems; linear transformations and matrices; similarity; eigenvectors and eigenvalues; diagonalization. (Math 104 offers a more application-oriented treatment.).Sheldon Axler, Linear Algebra Done Right (2nd ed), required.CS 103. Mathematical Foundations of Computing. 3-5 Units.Mathematical foundations required for computer science, including propositional predicate logic, induction, sets, functions, and relations. Formal language theory, including regular expressions, grammars, finite automata, Turing machines, and NP-completeness. Mathematical rigor, proof techniques, and applications. Prerequisite: 106A or equivalent.CS 107. Computer Organization and Systems. 3-5 Units.Introduction to the fundamental concepts of computer systems. Explores how computer systems execute programs and manipulate data, working from the C programming language down to the microprocessor. Topics covered include: the C programming language, data representation, machine-level code, computer arithmetic, elements of code compilation, memory organization and management, and performance evaluation and optimization. Prerequisites: 106B or X, or consent of instructor.B&O is Computer Systems (Bryant and O'Hallaron), K&R is The C Programming Language (Kernighan and Ritchie), and EssentialCSTATS 200. Introduction to Statistical Inference. 3 Units.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. Prerequisite: 116.John A. Rice, Mathematical Statistics and Data Analysis, 3rd edition. (REQUIRED) (OPTIONAL)Morris H. DeGroot and Mark J. Schervish, Probability and Statistics, 4th edition.

Larry Wasserman, All of Statistics: A concise course in statistical inference.

STATS 203. Introduction to Regression Models and Analysis of Variance. 3 Units.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. Pre- or corequisite: 200.Introduction to Linear Regression Analysis. D. Montgomery, E. Peck. (optional) Modern Applied Statistics with S. D. Venables, B. Ripley. (optional)STATS 217. Introduction to Stochastic Processes I. 2-3 Units.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. Prerequisite: STATS 116 or consent of instructor.Taylor and Karlin's book entitled, An Introduction to Stochastic Modeling, 3rd edition.CS 246. Mining Massive Data Sets. 3-4 Units.The course will discuss data mining and machine learning algorithms for analyzing very large amounts of data. The emphasis will be on Map Reduce as a tool for creating parallel algorithms that can process very large amounts of data. Topics include: Frequent itemsets and Association rules, Near Neighbor Search in High Dimensional Data, Locality Sensitive Hashing (LSH), Dimensionality reduction, Recommender Systems, Clustering, Link Analysis, Large-scale machine learning, Data streams, Analysis of Social-network Graphs, and Web Advertising. Prerequisites: At lease one of CS107 or CS145; At least one of CS109 or STAT116, or equivalent.Mining of Massive Datasets Jure Leskovec, Anand Rajaraman, Jeff UllmanCS 246H - Compation Compnion course to CS 246 that covers Hadoop