BIOE 80:
Introduction to Bioengineering (ENGR 80)
Broad but rigorous overview of the field of bioengineering, centered around the common theme of engineering analysis and design of biological systems. Topics include biomechanics, systems and synthetic biology, physical biology, biomolecular engineering, tissue engineering, and devices. Emphasis on critical thinking and problem solving approaches, and quantitative methods applied to biology. 4 units, Spr (Cochran)
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 designing experiments to address biological problems. Focus is on analysis of variance, when and how to use it, why it works, and how to interpret the results. Design of complex, but practical, asymmetrical experiments and environmental impact studies, and regression and analysis of covariance. Computerbased data analysis. Prerequisite: Biology core or 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: Win

Units: 4

UG Reqs: WAYAQR, WAYFR

Repeatable for credit

Grading: Letter or Credit/No Credit
CEE 195:
Fundamentals of Structural Geology (GES 111)
Techniques for mapping using GPS and differential geometry to characterize structures; dimensional analysis and scaling relations; kinematics of deformation and flow; measurement and analysis of stress; elastic deformation and properties of rock; brittle deformation including fracture and faulting; linear viscous flow including folding and magma dynamics; model development and methodology. Models of tectonic processes are constructed and solutions visualized using MATLAB. Prerequisites: GES 1, MATH 51
Terms: Win

Units: 3

UG Reqs: WAYFR, WAYSMA

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. 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: MATH 41 and 42, or 10 units AP credit.
Terms: Aut, Spr

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
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: application at:http://soe.stanford.edu/current_students/edp/programs/ace.html
Terms: Aut, Spr

Units: 6

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
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. Prerequisite: CME 100/ENGR 154 or MATH 51.
Terms: 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: application at:http://soe.stanford.edu/current_students/edp/programs/ace.html
Terms: Win, Spr

Units: 6

UG Reqs: GER:DBMath, 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: application at:http://soe.stanford.edu/current_students/edp/programs/ace.html
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.
Terms: Win, Sum

Units: 34

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.nImplementation of numerical methods in MATLAB programming assignments.nPrerequisites: MATH 51, 52, 53; prior programming experience (MATLAB or other language at level of CS 106A or higher).
Terms: Win, Sum

Units: 34

UG Reqs: GER:DBEngrAppSci, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
CS 103:
Mathematical Foundations of Computing
Mathematical foundations required for computer science, including propositional predicate logic, induction, sets, functions, and relations. Formal language theory, including regular expressions, grammars, finite automata, Turing machines, and NPcompleteness. Mathematical rigor, proof techniques, and applications. May not be taken by students who have completed 103A,B or 103X. Prerequisite: 106A or equivalent.
Terms: Aut, Win, Spr

Units: 35

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
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: Aut, Win

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. Uses the Java programming language. Emphasis is on good programming style and the builtin facilities of the Java language. No prior programming experience required. Summer quarter enrollment is limited and requires an application.
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; application required.
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. Additional advanced material and more challenging projects. 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, Sum

Units: 35

UG Reqs: GER:DBEngrAppSci, 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, MATH 51 or equivalent.
Terms: Win, Spr, Sum

Units: 35

UG Reqs: GER:DBEngrAppSci, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
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, Spr, Sum

Units: 35

UG Reqs: GER:DBEngrAppSci, WAYFR

Grading: Letter or Credit/No Credit
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, and Math 51 or CME 100. Must be taken for a Letter grade if majoring/minoring in Economics.
Terms: Aut, Win, 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, intertemporal choice and asset markets, risk and uncertainty, game theory, adverse selection, and moral hazard. Multivariate calculus is used. Prerequisite: ECON 50.
Terms: Win, Spr, Sum

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, 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. Prerequisites: recommended: ECON 51.
Terms: Spr

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 its applications. Topics include solution concepts for static and dynamic games of complete and incomplete information, repeated games, bargaining, and reputation formation. applications from economics, political science, biology, and computer science. Prerequisites: Experience with abstract mathematics and willingness to work hard. No prior knowledge of economics required.
Terms: Aut

Units: 5

UG Reqs: 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.nnForms a sequence with ECON 180 and ECON 181, but can be taken independently.nnPrerequisites: Experience with abstract mathematics and willingness tonnwork 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 41:
Physics of Electrical Engineering (ENGR 40P)
How everything from electrostatics to quantum mechanics is used in common hightechnology products. Electrostatics are critical in micromechanical systems used in many sensors and displays, and Electromagnetic waves are essential in all highspeed communication systems. How to propagate energy on transmission lines, optical fibers,and in free space. Which aspects of modern physics are needed to generate light for the operation of a DVD player or TV. Introduction to semiconductors, solidstate light bulbs, and laser pointers. Handson labs to connect physics to everyday experience. Prerequisites: Physics 43
Terms: Win

Units: 5

UG Reqs: GER:DBEngrAppSci, WAYFR, WAYSMA

Grading: Letter (ABCD/NP)
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 ENGR 155A.
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 141:
Engineering Electromagnetics
Lumped versus distributed circuits. Transient response of transmission lines with resistive and reactive loads. Reflection, transmission, attenuation and dispersion. Steadystate waves on transmission lines. Standing wave ratio, impedance matching, and power flow. Coulomb's law, electrostatic field, potential and gradient, electric flux and Gauss's Law and divergence. Metallic conductors, Poisson's and Laplace's equations, capacitance, dielectric materials. Electrostatic energy and forces. Steady electric currents, Ohm's Law, Kirchoff's Laws, charge conservation and the continuity equation, Joule's Law. BiotSavart's law and the static magnetic field. Ampere's Law and curl. Vector magnetic potential and magnetic dipole. Magnetic materials, forces and torques. Faraday's Law, magnetic energy, displacement current and Maxwell's equations. Uniform plane waves. Prerequisites: 102A, MATH 52.
Terms: Win

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 40C:
Engineering Wireless Networks
A hands on introduction to the design and implementation of modern wireless networks. Via a quarter long project on programmable radios, students will learn the fundamentals of wireless channels, encoding and decoding information, modeling of errors and error recovery algorithms, and the engineering of packetswitched networks. These concepts will be used to illustrate general themes in EE and CS: the role of abstraction and modularity in engineering design, building reliable systems using imperfect components, understanding the limits imposed by energy and noise, choosing effective representations for information, and engineering tradeoffs in complex systems. Formerly ENGR40N.
Terms: Spr

Units: 5

UG Reqs: WAYAQR, WAYFR

Grading: Letter (ABCD/NP)
ENGR 40P:
Physics of Electrical Engineering (EE 41)
How everything from electrostatics to quantum mechanics is used in common hightechnology products. Electrostatics are critical in micromechanical systems used in many sensors and displays, and Electromagnetic waves are essential in all highspeed communication systems. How to propagate energy on transmission lines, optical fibers,and in free space. Which aspects of modern physics are needed to generate light for the operation of a DVD player or TV. Introduction to semiconductors, solidstate light bulbs, and laser pointers. Handson labs to connect physics to everyday experience. Prerequisites: Physics 43
Terms: Win

Units: 5

UG Reqs: GER:DBEngrAppSci, WAYFR, WAYSMA

Grading: Letter (ABCD/NP)
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. Uses the Java programming language. Emphasis is on good programming style and the builtin facilities of the Java language. No prior programming experience required. Summer quarter enrollment is limited and requires an application.
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; application required.
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. Additional advanced material and more challenging projects. 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 (BIOE 80)
Broad but rigorous overview of the field of bioengineering, centered around the common theme of engineering analysis and design of biological systems. Topics include biomechanics, systems and synthetic biology, physical biology, biomolecular engineering, tissue engineering, and devices. Emphasis on critical thinking and problem solving approaches, and quantitative methods applied to biology. 4 units, Spr (Cochran)
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. 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: MATH 41 and 42, or 10 units AP credit.
Terms: Aut, Spr

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
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. Prerequisite: CME 100/ENGR 154 or MATH 51.
Terms: 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.
Terms: Win, Sum

Units: 34

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.nnPrerequisites: CME 100 or MATH 52 and PHYSICS 41 (or equivalent).nnOffered every year, winter quarter (except 20132014, when offered in spring).
Terms: Spr

Units: 35

UG Reqs: GER: DBNatSci, WAYFR, WAYSMA

Grading: Letter or Credit/No Credit
GES 1B:
Introduction to Geology: California Desert Geology
For nonmajors and prospective majors or minors in the Earth Sciences. The landscapes and rock formations of California's Death Valley and Owens Valley are used as natural laboratories for studying active geologic processes that shape Earth's surface (earthquakes, mountain building, volcanoes, glaciers) and for tracing a billion years of Earth history, climate change, and historic human impacts. Lectures on these topics and handson laboratory exercises involving rock identification and interpreting topographic and geologic maps and satellite imagery provide an introduction to physical geology and the background necessary to appreciate an optional 6day field trip to these desert areas during the Thanksgiving recess, which can be taken separately as GES183. Only one of GES 1A, 1B, or 1C may be taken for credit. Recommended: high school chemistry.
Terms: Aut

Units: 4

UG Reqs: GER: DBNatSci, WAYFR, WAYSMA

Grading: Letter or Credit/No Credit
GES 111:
Fundamentals of Structural Geology (CEE 195)
Techniques for mapping using GPS and differential geometry to characterize structures; dimensional analysis and scaling relations; kinematics of deformation and flow; measurement and analysis of stress; elastic deformation and properties of rock; brittle deformation including fracture and faulting; linear viscous flow including folding and magma dynamics; model development and methodology. Models of tectonic processes are constructed and solutions visualized using MATLAB. Prerequisites: GES 1, MATH 51
Terms: Win

Units: 3

UG Reqs: WAYFR, WAYSMA

Grading: Letter or Credit/No Credit
LINGUIST 110:
Introduction to Phonetics and Phonology
Differences in the sounds of the world's languages and how these sounds are made by the human vocal tract. Theories that account for crosslinguistic similarities in the face of differences.
Terms: Win

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: Aut

Units: 4

UG Reqs: GER:DBSocSci, WAYFR

Grading: Letter or Credit/No Credit
LINGUIST 121:
Crosslinguistic Syntax
A datadriven introduction to the methods of syntactic analysis, and their results. Emphasis is on understanding how languages are systematically alike and different in their basic sentence structure. 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. Draws on data from a diverse array of the world's languages, including but not limited to English. Satisfies the WIM requirement for Linguistics if taken for 4 units
Terms: Spr

Units: 34

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 ambiguity, vagueness, presupposition, intonational meaning, and Grice's theory of conversational implicature. 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 also enroll in 130C. 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
LINGUIST 144:
Introduction to Cognitive and Information Sciences (PHIL 190, PSYCH 35, SYMSYS 100)
The history, foundations, and accomplishments of the cognitive sciences, including presentations by leading Stanford researchers in artificial intelligence, linguistics, philosophy, and psychology. Overview of the issues addressed in the Symbolic Systems major.
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. Topics: review of elementary functions including exponentials and logarithms, limits, rates of change, the derivative, and applications. Math 19, 20, and 21 cover the same material as Math 41 and 42, but in three quarters rather than two. Prerequisites: precalculus, including trigonometry, advanced algebra, and analysis of elementary functions.
Terms: Aut, Win, Sum

Units: 3

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 20:
Calculus
Continuation of 19. Applications of differential calculus; introduction to integral calculus of functions of one variable, including: the definite integral, methods of symbolic and numerical integration, applications of the definite integral. Prerequisites: 19 or equivalent.
Terms: Win, Spr

Units: 3

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 21:
Calculus
Continuation of 20. Applications of integral calculus, introduction to differential equations, infinite series. Prerequisite: 20 or equivalent.
Terms: Spr

Units: 4

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 41:
Calculus (accelerated)
Introduction to differential and integral calculus of functions of one variable. Topics: limits, rates of change, the derivative and applications, introduction to the definite integral and integration. Math 41 and 42 cover the same material as Math 192021, but in two quarters rather than three. Prerequisites: trigonometry, advanced algebra, and analysis of elementary functions, including exponentials and logarithms.
Terms: Aut

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 41A:
Calculus ACE
Students attend MATH 41 lectures with different recitation sessions, four hours instead of two, emphasizing engineering applications. Prerequisite: application; see http://soe.stanford.edu/edp/programs/ace.html.
Terms: Aut

Units: 6

UG Reqs: GER:DBMath, WAYFR

Grading: Letter (ABCD/NP)
MATH 42:
Calculus (Accelerated)
Continuation of 41. Methods of symbolic and numerical integration, applications of the definite integral, introduction to differential equations, infinite series. Prerequisite: 41 or equivalent.
Terms: Aut, Win

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 42A:
Calculus ACE
Students attend MATH 42 lectures with different recitation sessions, four hours instead of two, emphasizing engineering applications. Prerequisite: application; see http://soe.stanford.edu/edp/programs/ace.html.
Terms: Aut, Win

Units: 6

UG Reqs: GER:DBMath, WAYFR

Grading: Letter (ABCD/NP)
MATH 51:
Linear Algebra and Differential Calculus of Several Variables
Geometry and algebra of vectors, systems of linear equations, matrices and linear transformations, diagonalization and eigenvectors, vector valued functions and functions of several variables, parametric curves, partial derivatives and gradients, the derivative as a matrix, chain rule in several variables, constrained and unconstrained optimization. Prerequisite: 21, or 42, or a score of 4 on the BC Advanced Placement exam or 5 on the AB Advanced Placement exam, or consent of instructor.
Terms: Aut, Win, Spr, Sum

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors: ;
Goodman, E. (PI);
Hasson, H. (PI);
Hicks, A. (PI);
Ionel, E. (PI);
Lucianovic, M. (PI);
Maximo, D. (PI);
Moore, K. (PI);
Wang, Y. (PI);
Wieczorek, W. (PI);
Yang, T. (PI);
Yun, Z. (PI);
Zheng, T. (PI);
Lucianovic, M. (GP)
MATH 51A:
Linear Algebra and Differential Calculus of Several Variables, ACE
Students attend MATH 51 lectures with different recitation sessions: four hours per week instead of two, emphasizing engineering applications. Prerequisite: application; see http://soe.stanford.edu/edp/programs/ace.html.
Terms: Aut, Win, Spr

Units: 6

UG Reqs: GER:DBMath, WAYFR

Grading: Letter (ABCD/NP)
MATH 51H:
Honors Multivariable Mathematics
For prospective Mathematics majors in the honors program and students from other areas of science or engineering who have a strong mathematics background. Three quarter sequence covers the material of 51, 52, 53, and additional advanced calculus and ordinary and partial differential equations. Unified treatment of multivariable calculus, linear algebra, and differential equations with a different order of topics and emphasis from standard courses. Students should know onevariable calculus and have an interest in a theoretical approach to the subject. Prerequisite: score of 5 on BC Advanced Placement exam, or consent of instructor.
Terms: Aut

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter (ABCD/NP)
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 and 42 or equivalents.
Terms: Aut, Win, Spr

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 52H:
Honors Multivariable Mathematics
Continuation of 51H. Prerequisite: 51H.
Terms: Win

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter (ABCD/NP)
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 and 42 or equivalents.
Terms: Aut, Win, Spr, Sum

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 53H:
Honors Multivariable Mathematics
Continuation of 52H. Prerequisite: 52H.
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: Spr

Units: 3

UG Reqs: WAYFR, WAYSMA

Grading: Letter (ABCD/NP)
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 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. WIM.
Terms: Win

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.
Terms: Aut, Win, Spr

Units: 3

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 120:
Groups and Rings
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: 51H 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
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.
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: 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 (MS&E 152W)
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. Students seeking to fulfill the Writing in the Major requirement should register for MS&E 152W.
Terms: Spr

Units: 34

UG Reqs: GER:DBEngrAppSci, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
MS&E 152W:
Introduction to Decision Analysis (MS&E 152)
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. Students seeking to fulfill the Writing in the Major requirement should register for MS&E 152W.
Terms: Spr

Units: 34

UG Reqs: GER:DBEngrAppSci, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
PHIL 50:
Introductory Logic
Propositional and predicate logic; emphasis is on translating English sentences into logical symbols and constructing derivations of valid arguments.
Terms: Aut, Spr

Units: 4

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
PHIL 150:
Basic Concepts in Mathematical Logic (PHIL 250)
The concepts and techniques used in mathematical logic, primarily through the study of the language of first order logic. Topics: formalization, proof, propositional logic, quantifiers, sets, mathematical induction, modal logics and the logic of diagrams.
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: Spr

Units: 4

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
PHIL 151:
FirstOrder Logic (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 technical topics like completeness and correspondence theory, including both classical and recent developments. Applications to topics in philosophy, computer science, and other fields. 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
PHIL 190:
Introduction to Cognitive and Information Sciences (LINGUIST 144, PSYCH 35, SYMSYS 100)
The history, foundations, and accomplishments of the cognitive sciences, including presentations by leading Stanford researchers in artificial intelligence, linguistics, philosophy, and psychology. Overview of the issues addressed in the Symbolic Systems major.
Terms: Win

Units: 4

UG Reqs: GER:DBSocSci, WAYFR

Grading: Letter or Credit/No Credit
PHYSICS 61:
Mechanics and Special Relativity
(First in a threepart series: PHYSICS 61, PHYSICS 63, PHYSICS 65.) Advanced freshman physics. For students with a strong high school mathematics and physics background contemplating a major in Physics or interested in a rigorous treatment of physics. Special theory of relativity and Newtonian mechanics with multi variable calculus. 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. Recommended prerequisites: Mastery of mechanics at the level of AP Physics C and AP Calculus B/C or equivalent. Corequisite: MATH 51.
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 series: PHYSICS 61, PHYSICS 63, PHYSICS 65.) Advanced freshman physics. For students with a strong high school mathematics and physics background contemplating a major in Physics or 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. Other theorems of vector calculus. 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; Pre or corequisite: MATH 52.
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 series: PHYSICS 61, PHYSICS 63, PHYSICS 65.) Advanced freshman physics. For students with a strong high school mathematics and physics background contemplating a major in Physics or interested in a rigorous treatment of physics. Introduction to quantum mechanics: matter waves, atomic structure, Schrödinger's equation. Thermodynamics and statistical mechanics: entropy and heat, Boltzmann statistics, quantum statistics. Prerequisites: PHYSICS 61 & PHYSICS 63. Pre or corequisite: MATH 53.
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). (Graduate student enrollees will be required to complete additional assignments in a format determined by the instructor.) Prerequisites: MATH 131P, and PHYS 112 or MATH elective 104 or higher. Recommended prerequisite: PHYS 130.
Terms: Aut

Units: 34

UG Reqs: GER: DBNatSci, WAYFR, WAYSMA

Grading: Letter or Credit/No Credit
PHYSICS 112:
Mathematical Methods of Physics
Theory of complex variables, complex functions, and complex analysis. Fourier series and Fourier transforms. Special functions such as Laguerre, Legendre, and Hermite polynomials, and Bessel functions. The uses of Green's functions. Covers material of MATH 106 and MATH 132 most pertinent to Physics majors. Prerequisites: MATH 50 or 50H series, and MATH 131P or MATH 173.
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, 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 relaxation methods; statistical methods including Monte Carlo techniques; matrix methods and eigenvalue problems. Short introduction to MatLab, used for class examples; class projects may be programmed in any language such as C. Prerequisites: MATH 53 and PHYS 120. Previous programming experience not required.
Terms: Aut

Units: 4

UG Reqs: GER: DBNatSci, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
PHYSICS 120:
Intermediate Electricity and Magnetism I
(First in a twopart series: PHYS 120, PHYS 121.) 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: 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
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. Pre or corequisites: PHYSICS 120 and MATH 131P or MATH 173.
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: Spr

Units: 35

UG Reqs: WAYFR, WAYSI

Grading: Letter or Credit/No Credit
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:
Introduction to Cognitive and Information Sciences (LINGUIST 144, PHIL 190, SYMSYS 100)
The history, foundations, and accomplishments of the cognitive sciences, including presentations by leading Stanford researchers in artificial intelligence, linguistics, philosophy, and psychology. Overview of the issues addressed in the Symbolic Systems major.
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: Aut

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 100:
Introduction to Cognitive and Information Sciences (LINGUIST 144, PHIL 190, PSYCH 35)
The history, foundations, and accomplishments of the cognitive sciences, including presentations by leading Stanford researchers in artificial intelligence, linguistics, philosophy, and psychology. Overview of the issues addressed in the Symbolic Systems major.
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? nnnCryptography 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)