BIOE 80:
Introduction to Bioengineering (Engineering Living Matter) (ENGR 80)
Students completing BIOE.80 should have a working understanding for how to approach the systematic engineering of living systems to benefit all people and the planet. Our main goals are (1) to help students learn ways of thinking about engineering living matter and (2) to empower students to explore the broader ramifications of engineering life. Specific concepts and skills covered include but are not limited to: capacities of natural life on Earth; scope of the existing humandirected bioeconomy; deconstructing complicated problems; reaction & diffusion systems; microbial human anatomy; conceptualizing the engineering of biology; how atoms can be organized to make molecules; how to print DNA from scratch; programming genetic sensors, logic, & actuators; biology beyond molecules (photons, electrons, etc.); what constraints limit what life can do?; what will be the major health challenges in 2030?; how does what we want shape bioengineering?; who should choose and realize various competing bioengineering futures?
Terms: Spr

Units: 4

UG Reqs: GER:DBEngrAppSci, WAYFR

Grading: Letter (ABCD/NP)
BIOHOPK 174H:
Experimental Design and Probability (BIOHOPK 274H)
(Graduate students register for 274H.) Variability is an integral part of biology. Introduction to probability and its use in addressing biological problems. Focus is on experimental design and the use of linear models in testing hypotheses (e.g., regression, analysis of variance, and general linear models). Students will use R to explore and analyze biological data from Monterey Bay. No programming or statistical background is assumed. Prerequisite: consent of instructor.
Terms: Spr

Units: 3

UG Reqs: GER: DBNatSci, GER:DBMath, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
BIOHOPK 177H:
Dynamics and Management of Marine Populations (BIOHOPK 277H)
(Graduate students register for 277H.) Course examines the ecological factors and processes that control natural and harvested marine populations. Course emphasizes mathematical models as tools to assess the dynamics of populations and to derive projections of their demographic fate under different management scenarios. Course objectives will be met by a combination of theoretical lectures, assigned readings and class discussions, case study analysis and interactive computer sessions.
Terms: not given this year

Units: 4

UG Reqs: WAYAQR, WAYFR

Repeatable for credit

Grading: Letter or Credit/No Credit
CME 100:
Vector Calculus for Engineers (ENGR 154)
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);
Chen, E. (TA);
Chen, G. (TA);
Chiu, D. (TA);
Earley, E. (TA);
Fry, K. (TA);
Homma, Y. (TA);
Mantravadi, S. (TA)
CME 100A:
Vector Calculus for Engineers, ACE
Students attend CME100/ENGR154 lectures with additional recitation sessions; two to four hours per week, emphasizing engineering mathematical applications and collaboration methods. Enrollment by department permission only. Prerequisite: must be enrolled in the regular CME10001 or 02. Application at: https://engineering.stanford.edu/students/programs/engineeringdiversityprograms/additionalcalculusengineers
Terms: Aut, Spr

Units: 6

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
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)
CME 102:
Ordinary Differential Equations for Engineers (ENGR 155A)
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
CME 102A:
Ordinary Differential Equations for Engineers, ACE
Students attend CME102/ENGR155A lectures with additional recitation sessions; two to four hours per week, emphasizing engineering mathematical applications and collaboration methods. Prerequisite: students must be enrolled in the regular section (CME102) prior to submitting application at:nhttps://engineering.stanford.edu/students/programs/engineeringdiversityprograms/additionalcalculusengineers
Terms: Aut, Win, Spr

Units: 6

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
CME 103:
Introduction to Matrix Methods (EE 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
CME 104:
Linear Algebra and Partial Differential Equations for Engineers (ENGR 155B)
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
CME 104A:
Linear Algebra and Partial Differential Equations for Engineers, ACE
Students attend CME104/ENGR155B lectures with additional recitation sessions; two to four hours per week, emphasizing engineering mathematical applications and collaboration methods. Prerequisite: students must be enrolled in the regular section (CME104) prior to submitting application at: https://engineering.stanford.edu/students/programs/engineeringdiversityprograms/additionalcalculusengineers
Terms: Spr

Units: 6

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
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. 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
CME 108:
Introduction to Scientific Computing (MATH 114)
Introduction to Scientific Computing Numerical computation for mathematical, computational, physical sciences and engineering: error analysis, floatingpoint arithmetic, nonlinear equations, numerical solution of systems of algebraic equations, banded matrices, least squares, unconstrained optimization, polynomial interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations, truncation error, numerical stability for time dependent problems and stiffness. Implementation of numerical methods in MATLAB programming assignments. Prerequisites: MATH 51, 52, 53; prior programming experience (MATLAB or other language at level of CS 106A or higher).
Terms: Win, Sum

Units: 3

UG Reqs: GER:DBEngrAppSci, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
CS 101:
Introduction to Computing Principles
Introduces the essential ideas of computing: data representation, algorithms, programming "code", computer hardware, networking, security, and social issues. Students learn how computers work and what they can do through handson exercises. In particular, students will see the capabilities and weaknesses of computer systems so they are not mysterious or intimidating. Course features many small programming exercises, although no prior programming experience is assumed or required. CS101 is not a complete programming course such as CS106A. CS101 is effectively an alternative to CS105. A laptop computer is recommended for the inclass exercises.
Terms: Aut

Units: 35

UG Reqs: GER:DBEngrAppSci, WAYFR

Grading: Letter or Credit/No Credit
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 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)
CS 105:
Introduction to Computers
For nontechnical majors. What computers are and how they work. Practical experience in programming. Construction of computer programs and basic design techniques. A survey of Internet technology and the basics of computer hardware. Students in technical fields and students looking to acquire programming skills should take 106A or 106X. Students with prior computer science experience at the level of 106 or above require consent of instructor. Prerequisite: minimal math skills.
Terms: Spr

Units: 35

UG Reqs: GER:DBEngrAppSci, WAYFR

Grading: Letter or Credit/No Credit
CS 106A:
Programming Methodology (ENGR 70A)
Introduction to the engineering of computer applications emphasizing modern software engineering principles: objectoriented design, decomposition, encapsulation, abstraction, and testing. Emphasis is on good programming style and the builtin facilities of respective languages. No prior programming experience required. Summer quarter enrollment is limited. Alternative versions of CS106A may be available which cover most of the same material but in different programming languages.
Terms: Aut, Win, Spr, Sum

Units: 35

UG Reqs: GER:DBEngrAppSci, WAYFR

Grading: Letter or Credit/No Credit
CS 106B:
Programming Abstractions (ENGR 70B)
Abstraction and its relation to programming. Software engineering principles of data abstraction and modularity. Objectoriented programming, fundamental data structures (such as stacks, queues, sets) and datadirected 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.
Terms: Aut, Win, Spr, Sum

Units: 35

UG Reqs: GER:DBEngrAppSci, WAYFR

Grading: Letter or Credit/No Credit
CS 106X:
Programming Abstractions (Accelerated) (ENGR 70X)
Intensive version of 106B for students with a strong programming background interested in a rigorous treatment of the topics at an accelerated pace. Significant amount of additional advanced material and substantially more challenging projects. Some projects may relate to CS department research. Prerequisite: excellence in 106A or equivalent, or consent of instructor.
Terms: Aut, Win

Units: 35

UG Reqs: GER:DBEngrAppSci, WAYFR

Grading: Letter or Credit/No Credit
CS 107:
Computer Organization and Systems
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, machinelevel code, computer arithmetic, elements of code compilation, memory organization and management, and performance evaluation and optimization. Prerequisites: 106B or X, or consent of instructor.
Terms: Aut, Win, Spr

Units: 35

UG Reqs: GER:DBEngrAppSci, WAYFR

Grading: Letter or Credit/No Credit
Instructors: ;
Lee, C. (PI);
Troccoli, N. (PI);
Cherivirala, S. (TA);
Culberg, K. (TA);
Lam, M. (TA);
Ling, E. (TA);
Marx, E. (TA);
Penkov, P. (TA);
Plattner, C. (TA);
Rashid, R. (TA);
VazquezGuzman, R. (TA);
Wegrzynski, M. (TA)
CS 107E:
Computer Systems from the Ground Up
Introduction to the fundamental concepts of computer systems through bare metal programming on the Raspberry Pi. Explores how five concepts come together in computer systems: hardware, architecture, assembly code, the C language, and software development tools. Students do all programming with a Raspberry Pi kit and several addons (LEDs, buttons). Topics covered include: the C programming language, data representation, machinelevel code, computer arithmetic, compilation, memory organization and management, debugging, hardware, and I/O. Prerequisite: 106B or X, and consent of instructor. There is a $75 required course fee.
Terms: Aut, Win

Units: 35

UG Reqs: WAYFR

Grading: Letter or Credit/No Credit
CS 109:
Introduction to Probability for Computer Scientists
Topics include: counting and combinatorics, random variables, conditional probability, independence, distributions, expectation, point estimation, and limit theorems. Applications of probability in computer science including machine learning and the use of probability in the analysis of algorithms. Prerequisites: 103, 106B or X, multivariate calculus at the level of MATH 51 or CME 100 or equivalent.
Terms: Aut, Spr, Sum

Units: 35

UG Reqs: GER:DBEngrAppSci, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
Instructors: ;
Piech, C. (PI);
Arthurs, N. (TA);
Banerjee, O. (TA);
Bowman, N. (TA);
Daniel, J. (TA);
Dass, N. (TA);
Hu, A. (TA);
Istrate, A. (TA);
Liang, D. (TA);
Raterink, C. (TA);
Schwager, S. (TA);
Smith, C. (TA)
CS 161:
Design and Analysis of Algorithms
Worst and average case analysis. Recurrences and asymptotics. Efficient algorithms for sorting, searching, and selection. Data structures: binary search trees, heaps, hash tables. Algorithm design techniques: divideandconquer, dynamic programming, greedy algorithms, amortized analysis, randomization. Algorithms for fundamental graph problems: minimumcost spanning tree, connected components, topological sort, and shortest paths. Possible additional topics: network flow, string searching. Prerequisite: 103 or 103B; 109 or STATS 116.
Terms: Aut, Win, Sum

Units: 35

UG Reqs: GER:DBEngrAppSci, WAYFR

Grading: Letter or Credit/No Credit
Instructors: ;
Rubinstein, A. (PI);
Wootters, M. (PI);
Baby, S. (TA);
Deaton, J. (TA);
Fosli, I. (TA);
Gupta, A. (TA);
Li, H. (TA);
Mu, R. (TA);
Murphy, D. (TA);
Narayanan, D. (TA);
Navarro, J. (TA);
Redondo, E. (TA);
Shi, A. (TA);
Starosta, A. (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
ECON 51:
Economic Analysis II
Neoclassical analysis of general equilibrium, welfare economics, imperfect competition, externalities and public goods, risk and uncertainty, game theory, adverse selection, and moral hazard. Multivariate calculus is used. Prerequisite: ECON 50.
Terms: Win, Spr

Units: 5

UG Reqs: WAYFR, WAYSI

Grading: Letter or Credit/No Credit
ECON 136:
Market Design
Use of economic theory and analysis to design allocation mechanisms and market institutions. Course focuses on three areas: the design of matching algorithms to solve assignment problems, with applications to school choice, entrylevel labor markets, and kidney exchanges; the design of auctions to solve general resource allocation problems, with applications to the sale of natural resources, financial assets, radio spectrum, and advertising; and the design of platforms and exchanges, with applications to internet markets. Emphasis on connecting economic theory to practical applications. Students must write term paper.
Terms: Win

Units: 5

UG Reqs: WAYFR

Grading: Letter or Credit/No Credit
ECON 137:
Decision Modeling and Information
Effective decision models consider a decision maker's alternatives, information and preferences. The construction of such models in singleparty situations with emphasis on the role of information. The course then evolves to twoparty decision situations where one party has more information than the other. Models examined include: bidding exercises and the winner's curse, the Akerlof Model and adverse selection, the PrincipalAgent model and risk sharing, moral hazard and contract design. Prerequisite: ECON 102A or equivalent. Recommended: Econ 50, Optimization and simulation in Excel.
Terms: Aut

Units: 5

UG Reqs: WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
ECON 160:
Game Theory and Economic Applications
Introduction to game theory and its applications to economics. Topics: strategic and extensive form games, dominant strategies, Nash equilibrium, subgameperfect equilibrium, and Bayesian equilibrium. The theory is applied to repeated games, voting, auctions, and bargaining with examples from economics and political science. Prerequisites: Working knowledge of calculus and basic probability theory.
Terms: Win

Units: 5

UG Reqs: WAYFR, WAYSI

Grading: Letter or Credit/No Credit
ECON 180:
Honors Game Theory
Rigorous introduction to game theory and applications. Topics include solution concepts for static and dynamic games of complete and incomplete information, signaling games, repeated games, bargaining, and elements of cooperative game theory. Applications mainly from economics, but also political science, biology, and computer science. Prerequisites: Experience with abstract mathematics and willingness to work hard. No background in economics required.
Terms: Aut

Units: 5

UG Reqs: GER:DBSocSci, WAYFR, WAYSI

Grading: Letter or Credit/No Credit
ECON 182:
Honors Market Design
Rigorous introduction to the theory of matching and resource allocation, and its application to practical market design. Theory covers twosided matching, "house allocation" problems, random assignment, and their variants. Applied topics include school choice, labor market, house allocation, and organ allocation for transplantation. Final paper required. Forms a sequence with ECON 180 and ECON 181, but can be taken independently. Prerequisites: Experience with abstract mathematics and willingness tonwork hard. No prior knowledge of economics is required, although basic knowledge in game theory is useful.
Terms: Spr

Units: 5

UG Reqs: WAYFR

Grading: Letter or Credit/No Credit
EE 102A:
Signal Processing and Linear Systems I
Concepts and tools for continuous and discretetime signal and system analysis with applications in signal processing, communications, and control. Mathematical representation of signals and systems. Linearity and time invariance. System impulse and step responses. System frequency response. Frequencydomain representations: Fourier series and Fourier transforms. Filtering and signal distortion. Time/frequency sampling and interpolation. Continuousdiscretetime signal conversion and quantization. Discretetime signal processing. Prerequisite: MATH 53 or CME 102.
Terms: Win, Sum

Units: 4

UG Reqs: GER:DBEngrAppSci, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
EE 102B:
Signal Processing and Linear Systems II
Continuation of EE 102A. Concepts and tools for continuous and discretetime signal and system analysis with applications in communications, signal processing and control. Analog and digital modulation and demodulation. Sampling, reconstruction, decimation and interpolation. Finite impulse response filter design. Discrete Fourier transforms, applications in convolution and spectral analysis. Laplace transforms, applications in circuits and feedback control. Z transforms, applications in infinite impulse response filter design. Prerequisite: EE 102A.
Terms: Spr

Units: 4

UG Reqs: GER:DBEngrAppSci, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
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
EE 142:
Engineering Electromagnetics
Introduction to electromagnetism and Maxwell's equations in static and dynamic regimes. Electrostatics and magnetostatics: Gauss's, Coulomb's, Faraday's, Ampere's, BiotSavart's laws. Electric and magnetic potentials. Boundary conditions. Electric and magnetic field energy. Electrodynamics: Wave equation; Electromagnetic waves; Phasor form of Maxwell's equations.nSolution of the wave equation in 1D free space: Wavelength, wavevector, forward and backward propagating plane waves.Poynting's theorem. Propagation in lossy media, skin depth. Reflection and refraction at planar boundaries, total internal reflection. Solutions of wave equation for various 1D3D problems: Electromagnetic resonators, waveguides periodic media, transmission lines. Formerly EE 141. Prerequisites: Phys 43 or EE 42, CME 100, CME 102 (recommended)
Terms: Spr

Units: 3

UG Reqs: GER:DBEngrAppSci, WAYFR, WAYSMA

Grading: Letter (ABCD/NP)
ENERGY 120:
Fundamentals of Petroleum Engineering (ENGR 120)
Lectures, problems, field trip. Engineering topics in petroleum recovery; origin, discovery, and development of oil and gas. Chemical, physical, and thermodynamic properties of oil and natural gas. Material balance equations and reserve estimates using volumetric calculations. Gas laws. Single phase and multiphase flow through porous media.
Terms: Aut

Units: 3

UG Reqs: GER:DBEngrAppSci, WAYFR, WAYSMA

Grading: Letter or Credit/No Credit
ENGR 70A:
Programming Methodology (CS 106A)
Introduction to the engineering of computer applications emphasizing modern software engineering principles: objectoriented design, decomposition, encapsulation, abstraction, and testing. Emphasis is on good programming style and the builtin facilities of respective languages. No prior programming experience required. Summer quarter enrollment is limited. Alternative versions of CS106A may be available which cover most of the same material but in different programming languages.
Terms: Aut, Win, Spr, Sum

Units: 35

UG Reqs: GER:DBEngrAppSci, WAYFR

Grading: Letter or Credit/No Credit
ENGR 70B:
Programming Abstractions (CS 106B)
Abstraction and its relation to programming. Software engineering principles of data abstraction and modularity. Objectoriented programming, fundamental data structures (such as stacks, queues, sets) and datadirected 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.
Terms: Aut, Win, Spr, Sum

Units: 35

UG Reqs: GER:DBEngrAppSci, WAYFR

Grading: Letter or Credit/No Credit
ENGR 70X:
Programming Abstractions (Accelerated) (CS 106X)
Intensive version of 106B for students with a strong programming background interested in a rigorous treatment of the topics at an accelerated pace. Significant amount of additional advanced material and substantially more challenging projects. Some projects may relate to CS department research. Prerequisite: excellence in 106A or equivalent, or consent of instructor.
Terms: Aut, Win

Units: 35

UG Reqs: GER:DBEngrAppSci, WAYFR

Grading: Letter or Credit/No Credit
ENGR 80:
Introduction to Bioengineering (Engineering Living Matter) (BIOE 80)
Students completing BIOE.80 should have a working understanding for how to approach the systematic engineering of living systems to benefit all people and the planet. Our main goals are (1) to help students learn ways of thinking about engineering living matter and (2) to empower students to explore the broader ramifications of engineering life. Specific concepts and skills covered include but are not limited to: capacities of natural life on Earth; scope of the existing humandirected bioeconomy; deconstructing complicated problems; reaction & diffusion systems; microbial human anatomy; conceptualizing the engineering of biology; how atoms can be organized to make molecules; how to print DNA from scratch; programming genetic sensors, logic, & actuators; biology beyond molecules (photons, electrons, etc.); what constraints limit what life can do?; what will be the major health challenges in 2030?; how does what we want shape bioengineering?; who should choose and realize various competing bioengineering futures?
Terms: Spr

Units: 4

UG Reqs: GER:DBEngrAppSci, WAYFR

Grading: Letter (ABCD/NP)
ENGR 120:
Fundamentals of Petroleum Engineering (ENERGY 120)
Lectures, problems, field trip. Engineering topics in petroleum recovery; origin, discovery, and development of oil and gas. Chemical, physical, and thermodynamic properties of oil and natural gas. Material balance equations and reserve estimates using volumetric calculations. Gas laws. Single phase and multiphase flow through porous media.
Terms: Aut

Units: 3

UG Reqs: GER:DBEngrAppSci, WAYFR, WAYSMA

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);
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
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
GEOPHYS 120:
Ice, Water, Fire (GEOPHYS 220)
Introductory application of continuum mechanics to ice sheets and glaciers, water waves and tsunamis, and volcanoes. Emphasis on physical processes and mathematical description using balance of mass and momentum, combined with constitutive equations for fluids and solids. Designed for undergraduates with no prior geophysics background; also appropriate for beginning graduate students. Prerequisites: CME 100 or MATH 52 and PHYSICS 41 (or equivalent).
Terms: Win

Units: 35

UG Reqs: GER: DBNatSci, WAYFR, WAYSMA

Grading: Letter or Credit/No Credit
LINGUIST 35:
Minds and Machines (PHIL 99, PSYCH 35, SYMSYS 1)
(Formerly SYMSYS 100). An overview of the interdisciplinary study of cognition, information, communication, and language, with an emphasis on foundational issues: What are minds? What is computation? What are rationality and intelligence? Can we predict human behavior? Can computers be truly intelligent? How do people and technology interact, and how might they do so in the future? Lectures focus on how the methods of philosophy, mathematics, empirical research, and computational modeling are used to study minds and machines. Undergraduates considering a major in symbolic systems should take this course as early as possible in their program of study.
Terms: Win

Units: 4

UG Reqs: GER:DBSocSci, WAYFR

Grading: Letter or Credit/No Credit
LINGUIST 110:
Introduction to Phonology
Introduction to the sound systems of the world's languages, their similarities and differences. Theories that account for the tacit generalizations that govern the sound patterns of languages.
Terms: Aut

Units: 4

UG Reqs: GER:DBSocSci, WAYFR

Grading: Letter or Credit/No Credit
LINGUIST 120:
Introduction to Syntax
Grammatical constructions, primarily English, and their consequences for a general theory of language. Practical experience in forming and testing linguistic hypotheses, reading, and constructing rules.
Terms: not given this year

Units: 4

UG Reqs: GER:DBSocSci, WAYFR

Grading: Letter or Credit/No Credit
LINGUIST 121A:
The Syntax of English
A datadriven introduction to the study of generative syntax through an indepth investigation of the sentence structure of English. Emphasis is on central aspects of English syntax, but the principles of theory and analysis extend to the study of the syntax of other languages. The course focuses on building up syntactic argumentation skills via the collective development of a partial formal theory of sentence structure, which attempts to model native speaker knowledge. Satisfies the WIM requirement for Linguistics and the WAYFR requirement. Prerequisites: none (can be taken before or after Linguistics 121B). The discussion section is mandatory.
Terms: Spr

Units: 4

UG Reqs: WAYFR

Grading: Letter or Credit/No Credit
LINGUIST 121B:
Crosslinguistic Syntax
A datadriven introduction to the study of syntax through the investigation of a diverse array of the world's languages, including but not limited to English. Emphasis is on understanding how languages are systematically alike and different in their basic sentence structure. The course focuses on building up syntactic argumentation skills via the collective development of a partial formal theory of sentence structure, which attempts to model native speaker knowledge. Satisfies the WIM requirement for Linguistics and the WAYFR requirement. Prerequisites: none (can be taken before or after Linguistics 121A). The discussion section is mandatory.
Terms: not given this year

Units: 4

UG Reqs: WAYFR

Grading: Letter or Credit/No Credit
LINGUIST 130A:
Introduction to Semantics and Pragmatics (LINGUIST 230A)
Linguistic meaning and its role in communication. Topics include logical semantics, conversational implicature, presupposition, and speech acts. Applications to issues in politics, the law, philosophy, advertising, and natural language processing. Those who have not taken logic, such as PHIL 150 or 151, should attend section. Pre or corequisite: 120, 121, consent of instructor, or graduate standing in Linguistics.
Terms: Win

Units: 4

UG Reqs: GER:DBSocSci, WAYFR

Grading: Letter or Credit/No Credit
MATH 19:
Calculus
Introduction to differential calculus of functions of one variable. Review of elementary functions (including exponentials and logarithms), limits, rates of change, the derivative and its properties, applications of the derivative. Prerequisites: trigonometry, advanced algebra, and analysis of elementary functions (including exponentials and logarithms). You must have taken the math placement diagnostic (offered through the Math Department website) in order to register for this course.
Terms: Aut, Win

Units: 3

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 20:
Calculus
The definite integral, Riemann sums, antiderivatives, the Fundamental Theorem of Calculus, and the Mean Value Theorem for integrals. Integration by substitution and by parts. Area between curves, and volume by slices, washers, and shells. Initialvalue problems, exponential and logistic models, direction fields, and parametric curves. Prerequisite: Math 19 or equivalent. 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.
Terms: Aut, Win, Spr

Units: 3

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 21:
Calculus
Review of limit rules. Sequences, functions, limits at infinity, and comparison of growth of functions. Review of integration rules, integrating rational functions, and improper integrals. Infinite series, special examples, convergence and divergence tests (limit comparison and alternating series tests). Power series and interval of convergence, Taylor polynomials, Taylor series and applications. Prerequisite: Math 20 or equivalent. 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.
Terms: Aut, Win, Spr

Units: 4

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 51:
Linear Algebra, Multivariable Calculus, and Modern Applications
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. Prerequisite: 21, 42, or the math placement diagnostic (offered through the Math Department website) in order to register for this course.
Terms: Aut, Win, Spr

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 51A:
Linear Algebra, Multivariable Calculus, and Modern Applications, ACE
Students attend MATH 51 lectures with different recitation sessions: three hours per week instead of two, emphasizing engineering applications. Prerequisite: application; see https://web.stanford.edu/dept/soe/osa/ace.fb
Terms: Aut, Win, Spr

Units: 6

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 52:
Integral Calculus of Several Variables
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.
Terms: Aut, Win, Spr

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 53:
Ordinary Differential Equations with Linear Algebra
Ordinary differential equations and initial value problems, systems of linear differential equations with constant coefficients, applications of secondorder equations to oscillations, matrix exponentials, Laplace transforms, stability of nonlinear systems and phase plane analysis, numerical methods. Prerequisite: 51 or equivalents.
Terms: Aut, Win, Spr

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 61CM:
Modern Mathematics: Continuous Methods
This is the first part of a theoretical (i.e., proofbased) sequence in multivariable calculus and linear algebra, providing a unified treatment of these topics. Covers general vector spaces, linear maps and duality, eigenvalues, inner product spaces, spectral theorem, metric spaces, differentiation in Euclidean space, submanifolds of Euclidean space, inverse and implicit function theorems, and many examples. The linear algebra content is covered jointly with Math 61DM. Students should know 1variable calculus and have an interest in a theoretical approach to the subject. Prerequisite: score of 5 on the BClevel Advanced Placement calculus exam, or consent of the instructor.
Terms: Aut

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 61DM:
Modern Mathematics: Discrete Methods
This is the first part of a theoretical (i.e., proofbased) sequence in discrete mathematics and linear algebra. Covers general vector spaces, linear maps and duality, eigenvalues, inner product spaces, spectral theorem, counting techniques, and linear algebra methods in discrete mathematics including spectral graph theory and dimension arguments. The linear algebra content is covered jointly with Math 61CM. Students should have an interest in a theoretical approach to the subject. Prerequisite: score of 5 on the BClevel Advanced Placement calculus exam, or consent of the instructor.nnThis sequence is not appropriate for students planning to major in natural sciences, economics, or engineering, but is suitable for majors in any other field (such as MCS ("data science"), computer science, and mathematics).
Terms: Aut

Units: 5

UG Reqs: WAYFR

Grading: Letter or Credit/No Credit
MATH 62CM:
Modern Mathematics: Continuous Methods
A continuation of themes from Math 61CM, centered around: manifolds, multivariable integration, and the general Stokes' theorem. This includes a treatment of multilinear algebra, further study of submanifolds of Euclidean space and an introduction to general manifolds (with many examples), differential forms and their geometric interpretations, integration of differential forms, Stokes' theorem, and some applications to topology. Prerequisite: Math 61CM.
Terms: Win

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter (ABCD/NP)
MATH 63CM:
Modern Mathematics: Continuous Methods
A proofbased course on ordinary differential equations, continuing themes from Math 61CM and Math 62CM. Topics include linear systems of differential equations and necessary tools from linear algebra, stability and asymptotic properties of solutions to linear systems, existence and uniqueness theorems for nonlinear differential equations with some applications to manifolds, behavior of solutions near an equilibrium point, and SturmLiouville theory. Prerequisites: Math 61CM and Math 62CM.
Terms: Spr

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter (ABCD/NP)
MATH 80Q:
Capillary Surfaces: Explored and Unexplored Territory
Preference to sophomores. Capillary surfaces: the interfaces between fluids that are adjacent to each other and do not mix. Recently discovered phenomena, predicted mathematically and subsequently confirmed by experiments, some done in space shuttles. Interested students may participate in ongoing investigations with affinity between mathematics and physics.
Terms: not given this year

Units: 3

UG Reqs: WAYFR, WAYSMA

Grading: Letter (ABCD/NP)
MATH 83N:
Proofs and Modern Mathematics
How do mathematicians think? Why are the mathematical facts learned in school true? In this course students will explore higherlevel mathematical thinking and will gain familiarity with a crucial aspect of mathematics: achieving certainty via mathematical proofs, a creative activity of figuring out what should be true and why. This course is ideal for students who would like to learn about the reasoning underlying mathematical results, but at a pace and level of abstraction not as intense as Math 61CM/DM, as a consequence benefiting from additional opportunity to explore the reasoning. Familiarity with onevariable calculus is strongly recommended at least at the AB level of AP Calculus since a significant part of the seminar develops develops some of the main results in that material systematically from a small list of axioms. We also address linear algebra from the viewpoint of a mathematician, illuminating algebraic notions such as groups, rings, and fields. This seminar may be paired with Math 51; though that course is not a pre or corequisite.
Terms: Aut

Units: 3

UG Reqs: WAYFR

Grading: Letter or Credit/No Credit
MATH 87Q:
Mathematics of Knots, Braids, Links, and Tangles
Preference to sophomores. Types of knots and how knots can be distinguished from one another by means of numerical or polynomial invariants. The geometry and algebra of braids, including their relationships to knots. Topology of surfaces. Brief summary of applications to biology, chemistry, and physics.
Terms: Win

Units: 3

UG Reqs: WAYFR

Grading: Letter (ABCD/NP)
MATH 101:
Math Discovery Lab
MDL is a discoverybased project course in mathematics. Students work independently in small groups to explore openended mathematical problems and discover original mathematics. Students formulate conjectures and hypotheses; test predictions by computation, simulation, or pure thought; and present their results to classmates. No lecture component; inclass meetings reserved for student presentations, attendance mandatory. Admission is by application: http://math101.stanford.edu. Motivated students with any level of mathematical background are encouraged to apply. WIM
Terms: Spr

Units: 3

UG Reqs: WAYFR

Grading: Letter or Credit/No Credit
MATH 109:
Applied Group Theory
Applications of the theory of groups. Topics: elements of group theory, groups of symmetries, matrix groups, group actions, and applications to combinatorics and computing. Applications: rotational symmetry groups, the study of the Platonic solids, crystallographic groups and their applications in chemistry and physics. Honors math majors and students who intend to do graduate work in mathematics should take 120. WIM.
Terms: Aut

Units: 3

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 110:
Applied Number Theory and Field Theory
Number theory and its applications to modern cryptography. Topics: congruences, finite fields, primality testing and factorization, public key cryptography, error correcting codes, and elliptic curves, emphasizing algorithms. WIM.
Terms: Spr

Units: 3

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 113:
Linear Algebra and Matrix Theory
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 applicationoriented treatment.)
Terms: Aut, Win, Spr

Units: 3

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 114:
Introduction to Scientific Computing (CME 108)
Introduction to Scientific Computing Numerical computation for mathematical, computational, physical sciences and engineering: error analysis, floatingpoint arithmetic, nonlinear equations, numerical solution of systems of algebraic equations, banded matrices, least squares, unconstrained optimization, polynomial interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations, truncation error, numerical stability for time dependent problems and stiffness. Implementation of numerical methods in MATLAB programming assignments. Prerequisites: MATH 51, 52, 53; prior programming experience (MATLAB or other language at level of CS 106A or higher).
Terms: Win, Sum

Units: 3

UG Reqs: GER:DBEngrAppSci, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
MATH 120:
Groups and Rings
Recommended for Mathematics majors and required of honors Mathematics majors. Similar to 109 but altered content and more theoretical orientation. Groups acting on sets, examples of finite groups, Sylow theorems, solvable and simple groups. Fields, rings, and ideals; polynomial rings over a field; PID and nonPID. Unique factorization domains. WIM.
Terms: Aut, Spr

Units: 3

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 171:
Fundamental Concepts of Analysis
Recommended for Mathematics majors and required of honors Mathematics majors. Similar to 115 but altered content and more theoretical orientation. Properties of Riemann integrals, continuous functions and convergence in metric spaces; compact metric spaces, basic point set topology. Prerequisite: 61CM or 61DM or 115 or consent of the instructor. WIM
Terms: Aut, Spr

Units: 3

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MS&E 20:
Discrete Probability Concepts And Models
Fundamental concepts and tools for the analysis of problems under uncertainty, focusing on structuring, model building, and analysis. Examples from legal, social, medical, and physical problems. Topics include axioms of probability, probability trees, belief networks, random variables, conditioning, and expectation. The course is fastpaced, but it has no prerequisites.
Terms: Sum

Units: 4

UG Reqs: WAYFR

Grading: Letter (ABCD/NP)
MS&E 120:
Probabilistic Analysis
Concepts and tools for the analysis of problems under uncertainty, focusing on focusing on structuring, model building, and analysis. Examples from legal, social, medical, and physical problems. Topics include axioms of probability, probability trees, random variables, distributions, conditioning, expectation, change of variables, and limit theorems. Prerequisite: CME 100 or MATH 51.
Terms: Aut

Units: 5

UG Reqs: GER:DBEngrAppSci, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
MS&E 152:
Introduction to Decision Analysis
How to make good decisions in a complex, dynamic, and uncertain world. People often make decisions that on close examination they regard as wrong. Decision analysis uses a structured conversation based on actional thought to obtain clarity of action in a wide variety of domains. Topics: distinctions, possibilities and probabilities, relevance, value of information and experimentation, relevance and decision diagrams, risk attitude.
Terms: Spr

Units: 34

UG Reqs: GER:DBEngrAppSci, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
PHIL 49:
Survey of Formal Methods
Survey of important formal methods used in philosophy. The course covers the basics of propositional and elementary predicate logic, probability and decision theory, game theory, and statistics, highlighting philosophical issues and applications. Specific topics include the languages of propositional and predicate logic and their interpretations, rationality arguments for the probability axioms, Nash equilibrium and dominance reasoning, and the meaning of statistical significance tests. Assessment is through a combination of problems designed to solidify competence with the mathematical tools and shortanswer questions designed to test conceptual understanding.
Terms: Spr

Units: 4

UG Reqs: GER:DBMath, WAYFR

Grading: Letter (ABCD/NP)
PHIL 99:
Minds and Machines (LINGUIST 35, PSYCH 35, SYMSYS 1)
(Formerly SYMSYS 100). An overview of the interdisciplinary study of cognition, information, communication, and language, with an emphasis on foundational issues: What are minds? What is computation? What are rationality and intelligence? Can we predict human behavior? Can computers be truly intelligent? How do people and technology interact, and how might they do so in the future? Lectures focus on how the methods of philosophy, mathematics, empirical research, and computational modeling are used to study minds and machines. Undergraduates considering a major in symbolic systems should take this course as early as possible in their program of study.
Terms: Win

Units: 4

UG Reqs: GER:DBSocSci, WAYFR

Grading: Letter or Credit/No Credit
PHIL 150:
Mathematical Logic (PHIL 250)
An introduction to the concepts and techniques used in mathematical logic, focusing on propositional, modal, and predicate logic. Highlights connections with philosophy, mathematics, computer science, linguistics, and neighboring fields.
Terms: Aut

Units: 4

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
PHIL 150E:
Logic in Action: A New Introduction to Logic
A new introduction to logic, covering propositional, modal, and firstorder logic, with special attention to major applications in describing information and informationdriven action. Highlights connections with philosophy, mathematics, computer science, linguistics, and neighboring fields. Based on the open source course 'Logic in Action,' available online at http://www.logicinaction.org/.nFulfills the undergraduate philosophy logic requirement.
Terms: not given this year

Units: 4

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
PHIL 151:
Metalogic (PHIL 251)
(Formerly 160A.) The syntax and semantics of sentential and firstorder logic. Concepts of model theory. Gödel's completeness theorem and its consequences: the LöwenheimSkolem theorem and the compactness theorem. Prerequisite: 150 or consent of instructor.
Terms: Win

Units: 4

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
PHIL 151A:
Recursion Theory (PHIL 251A)
Computable functions, Turing degrees, generalized computability and definability. "What does it mean for a function from the natural numbers to themselves to be computable?" and "How can noncomputable functions be classified into a hierarchy based on their level of noncomputability?". Theory of relative computability, reducibility notions and degree structures. Prerequisite is PHIL 150, or PHIL 151 or CS 103.
Terms: not given this year

Units: 4

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
PHIL 154:
Modal Logic (PHIL 254)
(Graduate students register for 254.) Syntax and semantics of modal logic and its basic theory: including expressive power, axiomatic completeness, correspondence, and complexity. Applications to topics in philosophy, computer science, mathematics, linguistics, and game theory. Prerequisite: 150 or preferably 151.
Terms: Spr

Units: 4

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
PHIL 166:
Probability: Ten Great Ideas About Chance (PHIL 266, STATS 167, STATS 267)
Foundational approaches to thinking about chance in matters such as gambling, the law, and everyday affairs. Topics include: chance and decisions; the mathematics of chance; frequencies, symmetry, and chance; Bayes great idea; chance and psychology; misuses of chance; and harnessing chance. Emphasis is on the philosophical underpinnings and problems. Prerequisite: exposure to probability or a first course in statistics at the level of STATS 60 or 116.
Terms: not given this year

Units: 4

UG Reqs: GER:DBMath, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
PHYSICS 14N:
Quantum Information: Visions and Emerging Technologies
What sets quantum information apart from its classical counterpart is that it can be encoded nonlocally, woven into correlations among multiple qubits in a phenomenon known as entanglement. We will discuss paradigms for harnessing entanglement to solve hitherto intractable computational problems or to push the precision of sensors to their fundamental quantum mechanical limits. We will also examine challenges that physicists and engineers are tackling in the laboratory today to enable the quantum technologies of the future.
Terms: not given this year

Units: 3

UG Reqs: WAYFR, WAYSMA

Grading: Letter or Credit/No Credit
PHYSICS 61:
Mechanics and Special Relativity
(First in a threepart advanced freshman physics series: PHYSICS 61, PHYSICS 63, PHYSICS 65.) This course covers Einstein's special theory of relativity and Newtonian mechanics at a level appropriate for students with a strong high school mathematics and physics background, who are contemplating a major in Physics or Engineering Physics, or are interested in a rigorous treatment of physics. Postulates of special relativity, simultaneity, time dilation, length contraction, the Lorentz transformation, causality, and relativistic mechanics. Central forces, contact forces, linear restoring forces. Momentum transport, work, energy, collisions. Angular momentum, torque, moment of inertia in three dimensions. Damped and forced harmonic oscillators. Uses the language of vectors and multivariable calculus. Recommended prerequisites: Mastery of mechanics at the level of AP Physics C and AP Calculus BC or equivalent. Corequisite: MATH 51 or MATH 61CM or MATH 61DM.
Terms: Aut

Units: 4

UG Reqs: GER: DBNatSci, WAYFR, WAYSMA

Grading: Letter or Credit/No Credit
PHYSICS 63:
Electricity, Magnetism, and Waves
(Second in a threepart advanced freshman physics series: PHYSICS 61, PHYSICS 63, PHYSICS 65.) This course covers the foundations of electricity and magnetism for students with a strong high school mathematics and physics background, who are contemplating a major in Physics or Engineering Physics, or are interested in a rigorous treatment of physics. Electricity, magnetism, and waves with some description of optics. Electrostatics and Gauss' law. Electric potential, electric field, conductors, image charges. Electric currents, DC circuits. Moving charges, magnetic field, Ampere's law. Solenoids, transformers, induction, AC circuits, resonance. Relativistic point of view for moving charges. Displacement current, Maxwell's equations. Electromagnetic waves, dielectrics. Diffraction, interference, refraction, reflection, polarization. Prerequisite: PHYSICS 61 and MATH 51 or MATH 61CM or MATH 61DM. Pre or corequisite: MATH 52 or MATH 62CM or MATH 62DM.
Terms: Win

Units: 4

UG Reqs: GER: DBNatSci, WAYFR, WAYSMA

Grading: Letter or Credit/No Credit
PHYSICS 65:
Quantum and Thermal Physics
(Third in a threepart advanced freshman physics series: PHYSICS 61, PHYSICS 63, PHYSICS 65.) This course introduces the foundations of quantum and statistical mechanics for students with a strong high school mathematics and physics background, who are contemplating a major in Physics or Engineering Physics, or are interested in a rigorous treatment of physics. Quantum mechanics: atoms, electrons, nuclei. Quantization of light, Planck's constant. Photoelectric effect, Compton and Bragg scattering. Bohr model, atomic spectra. Matter waves, wave packets, interference. Fourier analysis and transforms, Heisenberg uncertainty relationships. Schrödinger equation, eigenfunctions and eigenvalues. Particleinabox, simple harmonic oscillator, barrier penetration, tunneling, WKB and approximate solutions. Timedependent and multidimensional solution concepts. Coulomb potential and hydrogen atom structure. Thermodynamics and statistical mechanics: ideal gas, equipartition, heat capacity. Probability, counting states, entropy, equilibrium, chemical potential. Laws of thermodynamics. Cycles, heat engines, free energy. Partition function, Boltzmann statistics, Maxwell speed distribution, ideal gas in a box, Einstein model. Quantum statistical mechanics: classical vs. quantum distribution functions, fermions vs. bosons. Prerequisites: PHYSICS 61 & PHYSICS 63. Pre or corequisite: MATH 53 or MATH 63CM or MATH 63DM.
Terms: Spr

Units: 4

UG Reqs: GER: DBNatSci, WAYFR, WAYSMA

Grading: Letter or Credit/No Credit
PHYSICS 110:
Advanced Mechanics (PHYSICS 210)
Lagrangian and Hamiltonian mechanics. Principle of least action, EulerLagrange equations. Small oscillations and beyond. Symmetries, canonical transformations, HamiltonJacobi theory, actionangle variables. Introduction to classical field theory. Selected other topics, including nonlinear dynamical systems, attractors, chaotic motion. Undergraduates register for Physics 110 (4 units). Graduates register for Physics 210 (3 units). Prerequisites: MATH 131P or PHYSICS 111, and PHYSICS 112 or MATH elective 104 or higher. Recommended prerequisite: PHYSICS 130.
Terms: Aut

Units: 34

UG Reqs: GER: DBNatSci, WAYFR, WAYSMA

Grading: Letter or Credit/No Credit
PHYSICS 112:
Mathematical Methods for Physics
This course will cover methods of mathematical physics that are pertinent to physics. Topics include: Complex analysis, group theory, calculus of variations. Emphasis will be on indepth coverage of selected topics. Prerequisites: MATH 50 or 60 series
Terms: Win

Units: 4

UG Reqs: GER: DBNatSci, WAYFR

Grading: Letter or Credit/No Credit
PHYSICS 113:
Computational Physics
Numerical methods for solving problems in mechanics, astrophysics, electromagnetism, quantum mechanics, and statistical mechanics. Methods include numerical integration; solutions of ordinary and partial differential equations; solutions of the diffusion equation, Laplace's equation and Poisson's equation with various methods; statistical methods including Monte Carlo techniques; matrix methods and eigenvalue problems. Short introduction to Python, which is used for class examples and active learning notebooks; independent class projects make up more than half of the grade and may be programmed in any language such as C, Python or Matlab. No Prerequisites but some previous programming experience is advisable.
Terms: Spr

Units: 4

UG Reqs: GER: DBNatSci, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
PHYSICS 120:
Intermediate Electricity and Magnetism I
Vector analysis. Electrostatic fields, including boundaryvalue problems and multipole expansion. Dielectrics, static and variable magnetic fields, magnetic materials. Maxwell's equations. Prerequisites: PHYSICS 43 or PHYS 63; MATH 52 and MATH 53. Pre or corequisite: PHYS 111, MATH 131P or MATH 173. Recommended corequisite: PHYS 112.
Terms: Win

Units: 4

UG Reqs: GER: DBNatSci, WAYFR, WAYSMA

Grading: Letter or Credit/No Credit
PHYSICS 130:
Quantum Mechanics I
The origins of quantum mechanics and wave mechanics. Schrödinger equation and solutions for onedimensional systems. Commutation relations. Generalized uncertainty principle. Timeenergy uncertainty principle. Separation of variables and solutions for threedimensional systems; application to hydrogen atom. Spherically symmetric potentials and angular momentum eigenstates. Spin angular momentum. Addition of angular momentum. Prerequisites: PHYSICS 65 or PHYSICS 70 and PHYSICS 111 or MATH 131P or MATH 173. MATH 173 can be taken concurrently. Pre or corequisites: PHYSICS 120.
Terms: Win

Units: 4

UG Reqs: GER: DBNatSci, WAYFR, WAYSMA

Grading: Letter or Credit/No Credit
POLISCI 152:
Introduction to Game Theoretic Methods in Political Science (POLISCI 352)
Concepts and tools of noncooperative game theory developed using political science questions and applications. Formal treatment of Hobbes' theory of the state and major criticisms of it; examples from international politics. Primarily for graduate students; undergraduates admitted with consent of instructor.
Terms: not given this year

Units: 35

UG Reqs: WAYFR, WAYSI

Grading: Letter or Credit/No Credit
POLISCI 153:
Thinking Strategically (POLISCI 354)
This course provides an introduction to strategic reasoning. We discuss ideas such as the commitment problem, credibility in signaling, cheap talk, moral hazard and adverse selection. Concepts are developed through games played in class, and applied to politics, business and everyday life.
Terms: not given this year

Units: 5

UG Reqs: WAYFR

Repeatable for credit

Grading: Letter (ABCD/NP)
POLISCI 153Z:
Thinking Strategically
This course provides an introduction to strategic reasoning. We discuss ideas such as the commitment problem, credibility in signaling, cheap talk, moral hazard and adverse selection. Concepts are developed through games played in class, and applied to politics, business and everyday life.
Terms: not given this year

Units: 4

UG Reqs: WAYFR

Grading: Letter (ABCD/NP)
PSYCH 10:
Introduction to Statistical Methods: Precalculus (STATS 60, STATS 160)
Techniques for organizing data, computing, and interpreting measures of central tendency, variability, and association. Estimation, confidence intervals, tests of hypotheses, ttests, correlation, and regression. Possible topics: analysis of variance and chisquare tests, computer statistical packages.
Terms: Aut, Win, Spr, Sum

Units: 5

UG Reqs: GER:DBMath, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
PSYCH 35:
Minds and Machines (LINGUIST 35, PHIL 99, SYMSYS 1)
(Formerly SYMSYS 100). An overview of the interdisciplinary study of cognition, information, communication, and language, with an emphasis on foundational issues: What are minds? What is computation? What are rationality and intelligence? Can we predict human behavior? Can computers be truly intelligent? How do people and technology interact, and how might they do so in the future? Lectures focus on how the methods of philosophy, mathematics, empirical research, and computational modeling are used to study minds and machines. Undergraduates considering a major in symbolic systems should take this course as early as possible in their program of study.
Terms: Win

Units: 4

UG Reqs: GER:DBSocSci, WAYFR

Grading: Letter or Credit/No Credit
STATS 48N:
Riding the Data Wave
Imagine collecting a bit of your saliva and sending it in to one of the personalized genomics company: for very little money you will get back information about hundreds of thousands of variable sites in your genome. Records of exposure to a variety of chemicals in the areas you have lived are only a few clicks away on the web; as are thousands of studies and informal reports on the effects of different diets, to which you can compare your own. What does this all mean for you? Never before in history humans have recorded so much information about themselves and the world that surrounds them. Nor has this data been so readily available to the lay person. Expression as "data deluge'' are used to describe such wealth as well as the loss of proper bearings that it often generates. How to summarize all this information in a useful way? How to boil down millions of numbers to just a meaningful few? How to convey the gist of the story in a picture without misleading oversimplifications? To answer these questions we need to consider the use of the data, appreciate the diversity that they represent, and understand how people instinctively interpret numbers and pictures. During each week, we will consider a different data set to be summarized with a different goal. We will review analysis of similar problems carried out in the past and explore if and how the same tools can be useful today. We will pay attention to contemporary media (newspapers, blogs, etc.) to identify settings similar to the ones we are examining and critique the displays and summaries there documented. Taking an experimental approach, we will evaluate the effectiveness of different data summaries in conveying the desired information by testing them on subsets of the enrolled students.
Terms: not given this year

Units: 3

UG Reqs: WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
STATS 60:
Introduction to Statistical Methods: Precalculus (PSYCH 10, STATS 160)
Techniques for organizing data, computing, and interpreting measures of central tendency, variability, and association. Estimation, confidence intervals, tests of hypotheses, ttests, correlation, and regression. Possible topics: analysis of variance and chisquare tests, computer statistical packages.
Terms: Aut, Win, Spr, Sum

Units: 5

UG Reqs: GER:DBMath, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
STATS 110:
Statistical Methods in Engineering and the Physical Sciences
Introduction to statistics for engineers and physical scientists. Topics: descriptive statistics, probability, interval estimation, tests of hypotheses, nonparametric methods, linear regression, analysis of variance, elementary experimental design. Prerequisite: one year of calculus.
Terms: Aut, Sum

Units: 45

UG Reqs: GER:DBMath, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
STATS 116:
Theory of Probability
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.
Terms: Aut, Spr, Sum

Units: 35

UG Reqs: GER:DBMath, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
STATS 167:
Probability: Ten Great Ideas About Chance (PHIL 166, PHIL 266, STATS 267)
Foundational approaches to thinking about chance in matters such as gambling, the law, and everyday affairs. Topics include: chance and decisions; the mathematics of chance; frequencies, symmetry, and chance; Bayes great idea; chance and psychology; misuses of chance; and harnessing chance. Emphasis is on the philosophical underpinnings and problems. Prerequisite: exposure to probability or a first course in statistics at the level of STATS 60 or 116.
Terms: not given this year

Units: 4

UG Reqs: GER:DBMath, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
SYMSYS 1:
Minds and Machines (LINGUIST 35, PHIL 99, PSYCH 35)
(Formerly SYMSYS 100). An overview of the interdisciplinary study of cognition, information, communication, and language, with an emphasis on foundational issues: What are minds? What is computation? What are rationality and intelligence? Can we predict human behavior? Can computers be truly intelligent? How do people and technology interact, and how might they do so in the future? Lectures focus on how the methods of philosophy, mathematics, empirical research, and computational modeling are used to study minds and machines. Undergraduates considering a major in symbolic systems should take this course as early as possible in their program of study.
Terms: Win

Units: 4

UG Reqs: GER:DBSocSci, WAYFR

Grading: Letter or Credit/No Credit
THINK 3:
Breaking Codes, Finding Patterns
Why are humans drawn to making and breaking codes? To what extent is finding patterns both an art and a science? Cryptography has been used for millennia for secure communications, and its counterpart, cryptanalysis, or code breaking, has been around for just slightly less time. In this course we will explore the history of cryptography and cryptanalysis including the Enigma code, Navajo windtalkers, early computer science and the invention of modern Bayesian inference. We will try our own hand at breaking codes using some basic statistical tools for which no prior experience is necessary. Finally, we will consider the topic of patterns more generally, raising such questions as why we impute meaning to patterns, such as Biblical codes, and why we assume a complexity within a pattern when it's not there, such as the coincidence of birthdays in a group.
Terms: Aut

Units: 4

UG Reqs: THINK, WAYAQR, WAYFR

Grading: Letter (ABCD/NP)