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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 human-directed 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:DB-EngrAppSci, WAY-FR

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. Computer-based data analysis. Prerequisite: Biology core or consent of instructor.
Terms: Win, Spr | Units: 3 | UG Reqs: GER: DB-NatSci, GER:DB-Math, WAY-AQR, WAY-FR
Instructors: ; Watanabe, J. (PI)

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: WAY-AQR, WAY-FR | Repeatable 2 times (up to 8 units total)
Instructors: ; De Leo, G. (PI)

CEE 195: Fundamentals of Structural Geology (GS 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: GS 1, MATH 51
Terms: Win | Units: 3 | UG Reqs: WAY-FR, WAY-SMA

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: 10 units of AP credit (Calc BC with 4 or 5, or Calc AB with 5), or Math 41 and 42. Note: Students enrolled in section 100-02 and 100A-02 are required to attend the discussion section (section 03) on Thursdays 4:30-5:50pm.
Terms: Aut, Win | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR

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, Win | Units: 6 | UG Reqs: GER:DB-Math, WAY-FR

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: 10 units of AP credit (Calc BC with 4 or 5, or Calc AB with 5), or Math 41 and 42. Recommended: CME100.
Terms: Aut, Win, Spr, Sum | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR

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:http://soe.stanford.edu/current_students/edp/programs/ace.html
Terms: Aut, Win, Spr | Units: 6 | UG Reqs: GER:DB-Math, WAY-FR

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. Matrices, left and right inverses, QR factorization. Least- squares and model fitting, regularization and cross-validation, time-series prediction, and other examples. Constrained least-squares; applications to least-norm reconstruction, optimal control, and portfolio optimization. Newton methods and nonlinear least-squares. Prerequisites: MATH 51 or CME 100.
Terms: Aut | Units: 4-5 | UG Reqs: GER:DB-Math, WAY-FR
Instructors: ; Boyd, S. (PI); Hong, J. (GP)

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:DB-Math, WAY-FR

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 (CME102) prior to submittingapplication at:http://soe.stanford.edu/current_students/edp/programs/ace.html
Terms: Spr | Units: 6 | UG Reqs: GER:DB-Math, WAY-FR

CME 106: Introduction to Probability and Statistics for Engineers (ENGR 155C)

Probability: random variables, independence, and conditional probability; discrete and continuous distributions, moments, distributions of several random variables. Topics in mathematical statistics: random sampling, point estimation, confidence intervals, hypothesis testing, non-parametric 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:DB-Math, WAY-AQR, WAY-FR

CME 108: Introduction to Scientific Computing (MATH 114)

Introduction to Scientific Computing Numerical computation for mathematical, computational, physical sciences and engineering: error analysis, floating-point 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).nGraduate students should take it for 3 units and undergraduate students should take it for 4 units.
Terms: Win, Sum | Units: 3 | UG Reqs: GER:DB-EngrAppSci, WAY-AQR, WAY-FR

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 NP-completeness. Mathematical rigor, proof techniques, and applications. Prerequisite: 106A or equivalent.
Terms: Aut, Win, Sum | Units: 3-5 | UG Reqs: GER:DB-Math, WAY-FR

CS 105: Introduction to Computers

For non-technical 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 | Units: 3-5 | UG Reqs: GER:DB-EngrAppSci, WAY-FR

CS 106A: Programming Methodology (ENGR 70A)

Introduction to the engineering of computer applications emphasizing modern software engineering principles: object-oriented design, decomposition, encapsulation, abstraction, and testing. Uses the Java programming language. Emphasis is on good programming style and the built-in facilities of the Java language. No prior programming experience required. Summer quarter enrollment is limited.
Terms: Aut, Win, Spr, Sum | Units: 3-5 | UG Reqs: GER:DB-EngrAppSci, WAY-FR

CS 106B: Programming Abstractions (ENGR 70B)

Abstraction and its relation to programming. Software engineering principles of data abstraction and modularity. Object-oriented programming, fundamental data structures (such as stacks, queues, sets) and data-directed design. Recursion and recursive data structures (linked lists, trees, graphs). Introduction to time and space complexity analysis. Uses the programming language C++ covering its basic facilities. Prerequisite: 106A or equivalent. Summer quarter enrollment is limited.
Terms: Aut, Win, Spr, Sum | Units: 3-5 | UG Reqs: GER:DB-EngrAppSci, WAY-FR

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: 3-5 | UG Reqs: GER:DB-EngrAppSci, WAY-FR

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, machine-level code, computer arithmetic, elements of code compilation, memory organization and management, and performance evaluation and optimization. Prerequisites: 106B or X, or consent of instructor.
Terms: Aut, Win, Spr | Units: 3-5 | UG Reqs: GER:DB-EngrAppSci, WAY-FR

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, Win, Spr | Units: 3-5 | UG Reqs: GER:DB-EngrAppSci, WAY-AQR, WAY-FR

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: divide-and-conquer, dynamic programming, greedy algorithms, amortized analysis, randomization. Algorithms for fundamental graph problems: minimum-cost 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, Spr, Sum | Units: 3-5 | UG Reqs: GER:DB-EngrAppSci, WAY-FR

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 taken for letter grades: Econ 1 or 1A or 1V, and Math 51 or CME 100 or CME 100A. Must be taken for a Letter grade if majoring/minoring in Economics.
Terms: Aut, Win, Sum | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR, WAY-SI

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, Sum | Units: 5 | UG Reqs: WAY-FR, WAY-SI

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, entry-level 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: Win | Units: 5 | UG Reqs: WAY-FR
Instructors: ; Levin, J. (PI)

ECON 137: Decision Modeling and Information

Effective decision models consider a decision maker's alternatives, information and preferences. The construction of such models in single-party situations with emphasis on the role of information. The course then evolves to two-party 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 Principal-Agent 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: WAY-AQR, WAY-FR
Instructors: ; McKeon, S. (PI)

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, subgame-perfect 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: WAY-FR, WAY-SI
Instructors: ; Niederle, M. (PI)

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: Spr | Units: 5 | UG Reqs: GER:DB-SocSci, WAY-FR, WAY-SI
Instructors: ; Carroll, G. (PI)

ECON 182: Honors Market Design

Rigorous introduction to the theory of matching and resource allocation, and its application to practical market design. Theory covers two-sided 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.nForms a sequence with ECON 180 and ECON 181, but can be taken independently.nPrerequisites: Experience with abstract mathematics and willingness tonwork hard. No prior knowledge of economics is required, although basic knowledge in game theory is useful.
Terms: Aut | Units: 5 | UG Reqs: WAY-FR
Instructors: ; Kojima, F. (PI)

EE 41: Physics of Electrical Engineering (ENGR 40P)

How everything from electrostatics to quantum mechanics is used in common high-technology products. Electrostatics are critical in micro-mechanical systems used in many sensors and displays, and Electromagnetic waves are essential in all high-speed 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, solid-state light bulbs, and laser pointers. Hands-on labs to connect physics to everyday experience. Prerequisites: Physics 43
Last offered: Winter 2014 | Units: 5 | UG Reqs: GER:DB-EngrAppSci, WAY-FR, WAY-SMA

EE 102A: Signal Processing and Linear Systems I

Concepts and tools for continuous- and discrete-time 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. Frequency-domain representations: Fourier series and Fourier transforms. Filtering and signal distortion. Time/frequency sampling and interpolation. Continuous-discrete-time signal conversion and quantization. Discrete-time signal processing. Prerequisite: MATH 53 or CME 102.
Terms: Win, Sum | Units: 4 | UG Reqs: GER:DB-EngrAppSci, WAY-AQR, WAY-FR

EE 102B: Signal Processing and Linear Systems II

Continuation of EE 102A. Concepts and tools for continuous- and discrete-time 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:DB-EngrAppSci, WAY-AQR, WAY-FR

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. Matrices, left and right inverses, QR factorization. Least- squares and model fitting, regularization and cross-validation, time-series prediction, and other examples. Constrained least-squares; applications to least-norm reconstruction, optimal control, and portfolio optimization. Newton methods and nonlinear least-squares. Prerequisites: MATH 51 or CME 100.
Terms: Aut | Units: 4-5 | UG Reqs: GER:DB-Math, WAY-FR
Instructors: ; Boyd, S. (PI); Hong, J. (GP)

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, Biot-Savart'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, wave-vector, 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 1D-3D problems: Electromagnetic resonators, waveguides periodic media, transmission lines. Formerly EE 141. Pre-requisites: Phys 43 or EE 42, CME 100, CME 102 (recommended)
Terms: Aut | Units: 3 | UG Reqs: GER:DB-EngrAppSci, WAY-FR, WAY-SMA
Instructors: ; Fan, J. (PI)

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:DB-EngrAppSci, WAY-FR, WAY-SMA

ENGR 40P: Physics of Electrical Engineering (EE 41)

How everything from electrostatics to quantum mechanics is used in common high-technology products. Electrostatics are critical in micro-mechanical systems used in many sensors and displays, and Electromagnetic waves are essential in all high-speed 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, solid-state light bulbs, and laser pointers. Hands-on labs to connect physics to everyday experience. Prerequisites: Physics 43
Last offered: Winter 2014 | Units: 5 | UG Reqs: GER:DB-EngrAppSci, WAY-FR, WAY-SMA

ENGR 70A: Programming Methodology (CS 106A)

Introduction to the engineering of computer applications emphasizing modern software engineering principles: object-oriented design, decomposition, encapsulation, abstraction, and testing. Uses the Java programming language. Emphasis is on good programming style and the built-in facilities of the Java language. No prior programming experience required. Summer quarter enrollment is limited.
Terms: Aut, Win, Spr, Sum | Units: 3-5 | UG Reqs: GER:DB-EngrAppSci, WAY-FR

ENGR 70B: Programming Abstractions (CS 106B)

Abstraction and its relation to programming. Software engineering principles of data abstraction and modularity. Object-oriented programming, fundamental data structures (such as stacks, queues, sets) and data-directed design. Recursion and recursive data structures (linked lists, trees, graphs). Introduction to time and space complexity analysis. Uses the programming language C++ covering its basic facilities. Prerequisite: 106A or equivalent. Summer quarter enrollment is limited.
Terms: Aut, Win, Spr, Sum | Units: 3-5 | UG Reqs: GER:DB-EngrAppSci, WAY-FR

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: 3-5 | UG Reqs: GER:DB-EngrAppSci, WAY-FR

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 human-directed 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:DB-EngrAppSci, WAY-FR

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:DB-EngrAppSci, WAY-FR, WAY-SMA

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: 10 units of AP credit (Calc BC with 4 or 5, or Calc AB with 5), or Math 41 and 42. Note: Students enrolled in section 100-02 and 100A-02 are required to attend the discussion section (section 03) on Thursdays 4:30-5:50pm.
Terms: Aut, Win | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR

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: 10 units of AP credit (Calc BC with 4 or 5, or Calc AB with 5), or Math 41 and 42. Recommended: CME100.
Terms: Aut, Win, Spr, Sum | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR

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:DB-Math, WAY-FR

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, non-parametric 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:DB-Math, WAY-AQR, WAY-FR

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). Offered every year. Spring 2015-2016 and Winter 2016-2017.
Terms: Spr | Units: 3-5 | UG Reqs: GER: DB-NatSci, WAY-FR, WAY-SMA

GS 1B: Introduction to Geology

For non-majors and prospective majors or minors in the Earth Sciences. Introduction to physical geology. Lectures and lab exercises focus on understanding the dynamics of Earth¿s ongoing physical and chemical processes. Major themes include plate tectonics, the rock cycle, the hydrologic cycle, and mineral resources. We will employ local CA geology, current events, and the state-of-the-art to drive discussions on landscapes, hazards, and economics. Only one of GS 1A, 1B, or 1C may be taken for credit. Recommended: high school chemistry.
| Units: 4 | UG Reqs: GER: DB-NatSci, WAY-FR, WAY-SMA

GS 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: GS 1, MATH 51
Terms: Win | Units: 3 | UG Reqs: WAY-FR, WAY-SMA

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:DB-SocSci, WAY-FR

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:DB-SocSci, WAY-FR

LINGUIST 121A: The Syntax of English

Course description: A data-driven introduction to the study of generative syntax through an in-depth 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 WAY-FR requirement. Prerequisites: none (can be taken before or after Linguistics 121B). The discussion section is mandatory.
Terms: Win | Units: 4 | UG Reqs: WAY-FR

LINGUIST 121B: Crosslinguistic Syntax

Course description: A data-driven 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 WAY-FR requirement. Prerequisites: none (can be taken before or after Linguistics 121A). The discussion section is mandatory.
Terms: Spr | Units: 4 | UG Reqs: WAY-FR
Instructors: ; Harizanov, B. (PI)

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:DB-SocSci, WAY-FR

LINGUIST 144: Minds and Machines (PHIL 99, PSYCH 35, 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: Aut | Units: 4 | UG Reqs: GER:DB-SocSci, WAY-FR

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:DB-Math, WAY-FR

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: Aut, Win, Spr | Units: 3 | UG Reqs: GER:DB-Math, WAY-FR

MATH 21: Calculus

Continuation of 20. Applications of integral calculus, introduction to differential equations, infinite series. Prerequisite: 20 or equivalent.
Terms: Win, Spr | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR

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 19-20-21, 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:DB-Math, WAY-FR
Instructors: ; Yang, T. (PI)

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:DB-Math, WAY-FR
Instructors: ; Yang, T. (PI)

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:DB-Math, WAY-FR

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:DB-Math, WAY-FR

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:DB-Math, WAY-FR

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:DB-Math, WAY-FR

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 one-variable 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:DB-Math, WAY-FR
Instructors: ; Vasy, A. (PI)

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:DB-Math, WAY-FR

MATH 52H: Honors Multivariable Mathematics

Continuation of 51H. Prerequisite: 51H.
Terms: Win | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR
Instructors: ; Eliashberg, Y. (PI)

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 second-order equations to oscillations, matrix exponentials, Laplace transforms, stability of non-linear systems and phase plane analysis, numerical methods. Prerequisite: 51 and 42 or equivalents.
Terms: Aut, Win, Spr | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR

MATH 53H: Honors Multivariable Mathematics

Continuation of 52H. Prerequisite: 52H.
Terms: Spr | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR

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: Win | Units: 3 | UG Reqs: WAY-FR, WAY-SMA
Instructors: ; Finn, R. (PI)

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: WAY-FR
Instructors: ; Wieczorek, W. (PI)

MATH 101: Math Discovery Lab

MDL is a discovery-based project course in mathematics. Students work independently in small groups to explore open-ended 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; in-class 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: Win | Units: 3 | UG Reqs: WAY-FR

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: Win | Units: 3 | UG Reqs: GER:DB-Math, WAY-FR

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: Aut | Units: 3 | UG Reqs: GER:DB-Math, WAY-FR
Instructors: ; Entin, A. (PI); Lim, B. (TA)

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 application-oriented treatment.)
Terms: Aut, Win, Spr | Units: 3 | UG Reqs: GER:DB-Math, WAY-FR

MATH 114: Introduction to Scientific Computing (CME 108)

Introduction to Scientific Computing Numerical computation for mathematical, computational, physical sciences and engineering: error analysis, floating-point 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).nGraduate students should take it for 3 units and undergraduate students should take it for 4 units.
Terms: Win, Sum | Units: 3 | UG Reqs: GER:DB-EngrAppSci, WAY-AQR, WAY-FR

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 non-PID. Unique factorization domains. WIM.
Terms: Aut, Spr | Units: 3 | UG Reqs: GER:DB-Math, WAY-FR

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:DB-Math, WAY-FR

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: WAY-FR
Instructors: ; Shachter, R. (PI)

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:DB-EngrAppSci, WAY-AQR, WAY-FR

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: 3-4 | UG Reqs: GER:DB-EngrAppSci, WAY-AQR, WAY-FR

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: 3-4 | UG Reqs: GER:DB-EngrAppSci, WAY-AQR, WAY-FR

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 problem sets and short-answer questions designed to solidify competence with the mathematical tools and to test conceptual understanding. This course replaces PHIL 50.
Terms: Aut, Win | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR

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 | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR

PHIL 99: Minds and Machines (LINGUIST 144, PSYCH 35, 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: Aut | Units: 4 | UG Reqs: GER:DB-SocSci, WAY-FR

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:DB-Math, WAY-FR

PHIL 150E: Logic in Action: A New Introduction to Logic

A new introduction to logic, covering propositional, modal, and first-order logic, with special attention to major applications in describing information and information-driven 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.
Last offered: Spring 2014 | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR

PHIL 151: Metalogic (PHIL 251)

(Formerly 160A.) The syntax and semantics of sentential and first-order logic. Concepts of model theory. Gödel's completeness theorem and its consequences: the Löwenheim-Skolem theorem and the compactness theorem. Prerequisite: 150 or consent of instructor.
Terms: Win | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR
Instructors: ; Icard, T. (PI)

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.
Last offered: Winter 2013 | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR

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:DB-Math, WAY-FR

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: Spr | Units: 4 | UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR

PHYSICS 61: Mechanics and Special Relativity

(First in a three-part 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.
Terms: Aut | Units: 4 | UG Reqs: GER: DB-NatSci, WAY-FR, WAY-SMA
Instructors: ; Moler, K. (PI)

PHYSICS 63: Electricity, Magnetism, and Waves

(Second in a three-part 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. Pre- or corequisite: MATH 52.
Terms: Win | Units: 4 | UG Reqs: GER: DB-NatSci, WAY-FR, WAY-SMA
Instructors: ; Cabrera, B. (PI)

PHYSICS 65: Quantum and Thermal Physics

(Third in a three-part 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. Particle-in-a-box, simple harmonic oscillator, barrier penetration, tunneling, WKB and approximate solutions. Time-dependent and multi-dimensional 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.
Terms: Spr | Units: 4 | UG Reqs: GER: DB-NatSci, WAY-FR, WAY-SMA
Instructors: ; Manoharan, H. (PI)

PHYSICS 110: Advanced Mechanics (PHYSICS 210)

Lagrangian and Hamiltonian mechanics. Principle of least action, Euler-Lagrange equations. Small oscillations and beyond. Symmetries, canonical transformations, Hamilton-Jacobi theory, action-angle 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, and PHYSICS 112 or MATH elective 104 or higher. Recommended prerequisite: PHYSICS 130.
Terms: Aut | Units: 3-4 | UG Reqs: GER: DB-NatSci, WAY-FR, WAY-SMA
Instructors: ; Hartnoll, S. (PI)

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: DB-NatSci, WAY-FR
Instructors: ; Kachru, S. (PI)

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: DB-NatSci, WAY-AQR, WAY-FR
Instructors: ; Abel, T. (PI)

PHYSICS 120: Intermediate Electricity and Magnetism I

Vector analysis. Electrostatic fields, including boundary-value 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: DB-NatSci, WAY-FR, WAY-SMA
Instructors: ; Church, S. (PI)

PHYSICS 130: Quantum Mechanics I

The origins of quantum mechanics and wave mechanics. Schrödinger equation and solutions for one-dimensional systems. Commutation relations. Generalized uncertainty principle. Time-energy uncertainty principle. Separation of variables and solutions for three-dimensional 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 MATH 131P or MATH 173. MATH 173 can be taken concurrently. Pre- or corequisites: PHYSICS 120.
Terms: Win | Units: 4 | UG Reqs: GER: DB-NatSci, WAY-FR, WAY-SMA
Instructors: ; Burchat, P. (PI)

POLISCI 152: Introduction to Game Theoretic Methods in Political Science (POLISCI 352)

Concepts and tools of non-cooperative 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.
Last offered: Spring 2014 | Units: 3-5 | UG Reqs: WAY-FR, WAY-SI

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: Spr | Units: 5 | UG Reqs: WAY-FR | Repeatable 2 times (up to 10 units total)
Instructors: ; Acharya, A. (PI)

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, t-tests, correlation, and regression. Possible topics: analysis of variance and chi-square tests, computer statistical packages.
Terms: Aut, Win, Spr, Sum | Units: 5 | UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR

PSYCH 35: Minds and Machines (LINGUIST 144, PHIL 99, 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: Aut | Units: 4 | UG Reqs: GER:DB-SocSci, WAY-FR

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: WAY-AQR, WAY-FR
Instructors: ; Sabatti, C. (PI)

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, t-tests, correlation, and regression. Possible topics: analysis of variance and chi-square tests, computer statistical packages.
Terms: Aut, Win, Spr, Sum | Units: 5 | UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR

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: 4-5 | UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR

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: 3-5 | UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR

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: Spr | Units: 4 | UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR

SYMSYS 100: Minds and Machines (LINGUIST 144, PHIL 99, PSYCH 35)

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: Aut | Units: 4 | UG Reqs: GER:DB-SocSci, WAY-FR

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: Spr | Units: 4 | UG Reqs: College, THINK, WAY-AQR, WAY-FR
Instructors: ; Holmes, S. (PI)
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