CS 103: Mathematical Foundations of Computing
What are the theoretical limits of computing power? What problems can be solved with computers? Which ones cannot? And how can we reason about the answers to these questions with mathematical certainty? This course explores the answers to these questions and serves as an introduction to discrete mathematics, computability theory, and complexity theory. At the completion of the course, students will feel comfortable writing mathematical proofs, reasoning about discrete structures, reading and writing statements in firstorder logic, and working with mathematical models of computing devices. Throughout the course, students will gain exposure to some of the most exciting mathematical and philosophical ideas of the late nineteenth and twentieth centuries. Specific topics covered include formal mathematical proofwriting, propositional and firstorder logic, set theory, binary relations, functions (injections, surjections, and bijections), cardinality, basic graph theory, the pigeonhole prin
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What are the theoretical limits of computing power? What problems can be solved with computers? Which ones cannot? And how can we reason about the answers to these questions with mathematical certainty? This course explores the answers to these questions and serves as an introduction to discrete mathematics, computability theory, and complexity theory. At the completion of the course, students will feel comfortable writing mathematical proofs, reasoning about discrete structures, reading and writing statements in firstorder logic, and working with mathematical models of computing devices. Throughout the course, students will gain exposure to some of the most exciting mathematical and philosophical ideas of the late nineteenth and twentieth centuries. Specific topics covered include formal mathematical proofwriting, propositional and firstorder logic, set theory, binary relations, functions (injections, surjections, and bijections), cardinality, basic graph theory, the pigeonhole principle, mathematical induction, finite automata, regular expressions, the MyhillNerode theorem, contextfree grammars, Turing machines, decidable and recognizable languages, selfreference and undecidability, verifiers, and the P versus NP question. Students with significant proofwriting experience are encouraged to instead take
CS154. Students interested in extra practice and support with the course are encouraged to concurrently enroll in
CS103A. Prerequisite: CS106B or equivalent. CS106B may be taken concurrently with
CS103.
Terms: Aut, Win, Spr

Units: 35

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Lee, C. (PI)
;
Schwarz, K. (PI)
;
Alvarez, J. (TA)
;
Brickner, A. (TA)
;
Hoag, E. (TA)
;
Kravitz, J. (TA)
;
Le, T. (TA)
;
MayerHirshfeld, R. (TA)
;
Melloni, J. (TA)
;
Noyola, T. (TA)
;
Saini, D. (TA)
;
Saleh, M. (TA)
;
Smith, R. (TA)
;
Sriram, P. (TA)
;
Zhu, M. (TA)
ECON 50: Economic Analysis I
Individual consumer and firm behavior under perfect competition. The role of markets and prices in a decentralized economy. Monopoly in partial equilibrium. Economic tools developed from multivariable calculus using partial differentiation and techniques for constrained and unconstrained optimization. Prerequisites:
Econ 1 or 1V, and
Math 51 or
Math 51A or
CME 100 or
CME 100A.
Terms: Aut, Win, Spr, Sum

Units: 5

UG Reqs: GER:DBMath, WAYFR, WAYSI

Grading: Letter or Credit/No Credit
Instructors:
Bennett, D. (PI)
;
Makler, C. (PI)
;
Cao, S. (TA)
;
Fletcher, R. (TA)
;
Lim, S. (TA)
;
Loo, A. (TA)
;
Vohra, A. (TA)
ECON 102A: Introduction to Statistical Methods (Postcalculus) for Social Scientists
Probabilistic modeling and statistical techniques relevant for economics. Concepts include: probability trees, conditional probability, random variables, discrete and continuous distributions, correlation, central limit theorems, point estimation, hypothesis testing and confidence intervals for both one and two populations. Prerequisite:
MATH 20 or equivalent.
Terms: Aut, Win

Units: 5

UG Reqs: GER:DBMath, WAYAQR, WAYSI

Grading: Letter or Credit/No Credit
Instructors:
McKeon, S. (PI)
;
Goke, S. (TA)
;
Jeong, S. (TA)
;
Kim, J. (TA)
;
Laguna Muggenburg, E. (TA)
;
Zhang, J. (TA)
EE 103: Introduction to Matrix Methods (CME 103)
Introduction to applied linear algebra with emphasis on applications. Vectors, norm, and angle; linear independence and orthonormal sets; applications to document analysis. Clustering and the kmeans algorithm. Matrices, left and right inverses, QR factorization. Leastsquares and model fitting, regularization and crossvalidation. Constrained and nonlinear leastsquares. Applications include timeseries prediction, tomography, optimal control, and portfolio optimization. Undergraduate students should enroll for 5 units, and graduate students should enroll for 3 units. Prerequisites:
MATH 51 or
CME 100, and basic knowledge of computing (
CS 106A is more than enough, and can be taken concurrently).
EE103/CME103 and
Math 104 cover complementary topics in applied linear algebra. The focus of EE103 is on a few linear algebra concepts, and many applications; the focus of
Math 104 is on algorithms and concepts.
Terms: Aut

Units: 35

UG Reqs: GER:DBMath, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
ENGR 154: Vector Calculus for Engineers (CME 100)
Computation and visualization using MATLAB. Differential vector calculus: analytic geometry in space, functions of several variables, partial derivatives, gradient, unconstrained maxima and minima, Lagrange multipliers. Introduction to linear algebra: matrix operations, systems of algebraic equations, methods of solution and applications. Integral vector calculus: multiple integrals in Cartesian, cylindrical, and spherical coordinates, line integrals, scalar potential, surface integrals, Green's, divergence, and Stokes' theorems. Examples and applications drawn from various engineering fields. Prerequisites: knowledge of singlevariable calculus equivalent to the content of
Math 1921 (e.g., 5 on Calc BC, 4 on Calc BC with
Math 21, 5 on Calc AB with
Math21). Placement diagnostic (recommendation non binding) at:(
https://exploredegrees.stanford.edu/undergraduatedegreesandprograms/#aptext).
Terms: Aut, Spr

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Khayms, V. (PI)
;
Le, H. (PI)
;
BougdalLambert, I. (TA)
...
more instructors for ENGR 154 »
Instructors:
Khayms, V. (PI)
;
Le, H. (PI)
;
BougdalLambert, I. (TA)
;
Chen, E. (TA)
;
Chen, G. (TA)
;
Chiu, D. (TA)
;
Earley, E. (TA)
;
Fry, K. (TA)
;
Homma, Y. (TA)
;
Mantravadi, S. (TA)
ENGR 155A: Ordinary Differential Equations for Engineers (CME 102)
Analytical and numerical methods for solving ordinary differential equations arising in engineering 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.Prerequisites: knowledge of singlevariable calculus equivalent to the content of
Math 1921 (e.g., 5 on Calc BC, 4 on Calc BC with
Math 21, 5 on Calc AB with
Math21). Placement diagnostic (recommendation non binding) at:(
https://exploredegrees.stanford.edu/undergraduatedegreesandprograms/#aptext). Recommended:
CME100.
Terms: Aut, Win, Spr, Sum

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
ENGR 155B: Linear Algebra and Partial Differential Equations for Engineers (CME 104)
Linear algebra: matrix operations, systems of algebraic equations, Gaussian elimination, undetermined and overdetermined systems, coupled systems of ordinary differential equations, eigensystem analysis, normal modes. Fourier series with applications, partial differential equations arising in science and engineering, analytical solutions of partial differential equations. Numerical methods for solution of partial differential equations: iterative techniques, stability and convergence, time advancement, implicit methods, von Neumann stability analysis. Examples and applications from various engineering fields. Prerequisite:
CME 102/
ENGR 155A.
Terms: Spr

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Khayms, V. (PI)
ENGR 155C: Introduction to Probability and Statistics for Engineers (CME 106)
Probability: 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. Prerequisite:
CME 100/ENGR154 or
MATH 51 or 52.
Terms: Win, Sum

Units: 4

UG Reqs: GER:DBMath, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Khayms, V. (PI)
HUMBIO 88: Introduction to Statistics for the Health Sciences
Students will learn the statistical tools used to describe and analyze data in the fields of medicine and epidemiology. This very applied course will rely on current research questions and publicly available data. Students will gain proficiency with Stata to do basic analyses of healthrelated data, including linear and logistic regression, and will become sophisticated consumers of healthrelated statistical results.
Terms: Win

Units: 4

UG Reqs: GER:DBMath, WAYAQR

Grading: Letter (ABCD/NP)
Instructors:
Kurina, L. (PI)
HUMBIO 89: Introduction to Health Sciences Statistics
This course aims to provide a firm grounding in the foundations of probability and statistics, with a focus on analyzing data from the health sciences. Students will learn how to read, interpret, and critically evaluate the statistics in medical and biological studies. The course also prepares students to be able to analyze their own data, guiding them on how to choose the correct statistical test, avoid common statistical pitfalls, and perform basic functions in R deducer. Cardinal Course certified by the Haas Center.
Terms: Aut, Win

Units: 3

UG Reqs: GER:DBMath, WAYAQR

Grading: Letter or Credit/No Credit
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