BIO 141: Biostatistics (STATS 141)
Introductory statistical methods for biological data: describing data (numerical and graphical summaries); introduction to probability; and statistical inference (hypothesis tests and confidence intervals). Intermediate statistical methods: comparing groups (analysis of variance); analyzing associations (linear and logistic regression); and methods for categorical data (contingency tables and odds ratio). Course content integrated with statistical computing in R.
Terms: Win
| Units: 5
| UG Reqs: GER:DB-Math, WAY-AQR
Instructors:
Erdmann-Pham, D. (PI)
;
Gablenz, P. (TA)
;
Morrison, T. (TA)
...
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Instructors:
Erdmann-Pham, D. (PI)
;
Gablenz, P. (TA)
;
Morrison, T. (TA)
;
Vu, V. (TA)
;
Zhou, K. (TA)
CME 100: Vector Calculus for Engineers (ENGR 154)
Computation and visualization using MATLAB. Differential vector calculus: vector-valued 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. Prerequisites: knowledge of single-variable calculus equivalent to the content of
Math 19-21 (e.g., 5 on Calc BC, 4 on Calc BC with
Math 21, 5 on Calc AB with
Math 21). Placement diagnostic (recommendation non-binding) at:
https://exploredegrees.stanford.edu/undergraduatedegreesandprograms/#aptext.
Terms: Aut, Spr
| Units: 5
| UG Reqs: WAY-FR, GER:DB-Math
CME 102: Ordinary Differential Equations for Engineers (ENGR 155A)
Analytical and numerical methods for solving ordinary differential equations arising in engineering applications are presented. For analytical methods students learn to solve linear and non-linear first order ODEs; linear second order ODEs; and Laplace transforms. Numerical methods using MATLAB programming tool kit are also introduced to solve various types of ODEs including: first and second order ODEs, higher order ODEs, systems of ODEs, initial and boundary value problems, finite differences, and multi-step methods. This also includes accuracy and linear stability analyses of various numerical algorithms which are essential tools for the modern engineer. This class is foundational for professional careers in engineering and as a preparation for more advanced classes at the undergraduate and graduate levels. Prerequisites: knowledge of single-variable calculus equivalent to the content of
Math 19-21 (e.g., 5 on Calc BC, 4 on Calc BC with
Math 21, 5 on Calc AB with
Math 21). Placement diagnostic (recommendation non-binding) at:
https://exploredegrees.stanford.edu/undergraduatedegreesandprograms/#aptext.
Terms: Aut, Win
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Darve, E. (PI)
;
Le, H. (PI)
;
Ankeney, G. (TA)
;
Ayala Bellido, C. (TA)
;
Chen, C. (TA)
;
Diller, E. (TA)
;
Nzia Yotchoum, H. (TA)
CME 104: Linear Algebra and Partial Differential Equations for Engineers (ENGR 155B)
Linear algebra: systems of algebraic equations, Gaussian elimination, undetermined and overdetermined systems, coupled systems of ordinary differential equations, LU factorization, eigensystem analysis, normal modes. Linear independence, vector spaces, subspaces and basis. Numerical analysis applied to structural equilibrium problems, electrical networks, and dynamic systems. Fourier series with applications, partial differential equations arising in science and engineering, analytical solutions of partial differential equations. Applications in heat and mass transport, mechanical vibration and acoustic waves, transmission lines, and fluid mechanics. Numerical methods for solution of partial differential equations: iterative techniques, stability and convergence, time advancement, implicit methods, von Neumann stability analysis. Examples and applications drawn from a variety of engineering fields. Prerequisite:
CME102/
ENGR155A.
Terms: Spr
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR
CME 106: Introduction to Probability and Statistics for Engineers (ENGR 155C)
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. Prerequisite:
CME100/ENGR154 or
Math 51 or 52.
Terms: Win, Sum
| Units: 4
| UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR
Instructors:
Khayms, V. (PI)
;
Muneton Gallego, J. (PI)
;
Ramanantsoa, R. (PI)
...
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Instructors:
Khayms, V. (PI)
;
Muneton Gallego, J. (PI)
;
Ramanantsoa, R. (PI)
;
Xu, B. (PI)
;
Xu, B. (TA)
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 first-order 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 first-order 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 first-order 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 first-order logic, set theory, binary relations, functions (injections, surjections, and bijections), cardinality, basic graph theory, the pigeonhole principle, mathematical induction, finite automata, regular expressions, the Myhill-Nerode theorem, context-free grammars, Turing machines, decidable and recognizable languages, self-reference 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, Sum
| Units: 3-5
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Aiken, A. (PI)
;
Liu, A. (PI)
;
Schwarz, K. (PI)
;
Agashe, R. (TA)
;
Aiu, K. (TA)
;
Anvari, M. (TA)
;
Cao, S. (TA)
;
Carrell, T. (TA)
;
Chang, T. (TA)
;
Chung, J. (TA)
;
Han, R. (TA)
;
Jee, Y. (TA)
;
Kung, B. (TA)
;
Pandya, D. (TA)
;
Raman, V. (TA)
;
Rodriguez, J. (TA)
;
Roman, E. (TA)
;
Saue- Fletcher, L. (TA)
;
Sotoudeh, M. (TA)
;
Xia, W. (TA)
;
Zhai, W. (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, Spr
| Units: 5
| UG Reqs: WAY-SI, WAY-FR, GER:DB-Math
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:DB-Math, WAY-AQR, WAY-SI
Instructors:
McKeon, S. (PI)
;
Crystal, M. (TA)
;
Francisco Pugliese, J. (TA)
...
more instructors for ECON 102A »
Instructors:
McKeon, S. (PI)
;
Crystal, M. (TA)
;
Francisco Pugliese, J. (TA)
;
Haberman, A. (TA)
;
He, C. (TA)
;
Lennie, M. (TA)
;
Love, S. (TA)
;
Tyger, E. (TA)
;
Yan, N. (TA)
ENGR 108: Introduction to Matrix Methods
Formerly
EE 103/
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 k-means algorithm. Matrices, left and right inverses, QR factorization. Least-squares and model fitting, regularization and cross-validation. Constrained and nonlinear least-squares. Applications include time-series 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).
ENGR 108 and
Math 104 cover complementary topics in applied linear algebra. The focus of
ENGR 108 is on a few linear algebra concepts, and many applications; the focus of
Math 104 is on algorithms and concepts.
Terms: Aut, Sum
| Units: 3-5
| UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR
Instructors:
Duchi, J. (PI)
;
Costacurta, J. (TA)
;
Kim, J. (TA)
...
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ENGR 154: Vector Calculus for Engineers (CME 100)
Computation and visualization using MATLAB. Differential vector calculus: vector-valued 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. Prerequisites: knowledge of single-variable calculus equivalent to the content of
Math 19-21 (e.g., 5 on Calc BC, 4 on Calc BC with
Math 21, 5 on Calc AB with
Math 21). Placement diagnostic (recommendation non-binding) at:
https://exploredegrees.stanford.edu/undergraduatedegreesandprograms/#aptext.
Terms: Aut, Spr
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR
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