# Course Descriptions

Highlighted course titles indicate that the course is an HMC mathematics Core course.

The department also offers some Integrative Experience courses, which are listed below.

Descriptions for retired courses are near the bottom of the page.

- Math 15: Application and Art of Calculus (0.5 credits)
- This course is a fun and casual problem solving experience in single variable calculus. We will help the students strengthen mathematical skills essential to excel in the HMC Core. Students work in groups and solve calculus problems with an emphasis on applications to the sciences.
- Corequisites: Registration in Math 30B or Math 30G
- Prerequisites: none
- Instructors: Karp, Omar, Williams
- Offered: Fall, first half
- Math 21: Mathematics of Games and Puzzles (1.5 credits)
- Students are introduced to important mathematical topics as motivated through games and puzzles including casino games, backgammon, poker, Suodku, and Rubik's cube. Topics include combinatorics, probability, dynamic programming, game theory, and group theory.
- Prerequisites: One year of calculus at the high-school level (open to first year HMC students)
- Instructors: Benjamin, Omar
- Offered: Fall (half course; offered both halves)
- Math 30G: Calculus (1.5 credits) [HMC Core]
- A comprehensive view of the theory and techniques of differential and integral calculus of a single variable; infinite series, including Taylor series and convergence tests. Focus on mathematical reasoning, rigor and proof, including continuity, limits, induction. Introduction to multivariable calculus, including partial derivatives, double and triple integrals.
- Prerequisites: One year of calculus at the high-school level
- Instructors: Benjamin, de Pillis, Karp, Levy, Omar, Orrison, Su
- Offered: Fall, first half
- Math 30B: Calculus (1.5 credits) [HMC Core]
- A comprehensive view of the theory and techniques of differential and integral calculus of a single variable; infinite series, including Taylor series and convergence tests. Focus on mathematical reasoning, rigor and proof, including continuity, limits, induction. Introduction to multivariable calculus, including partial derivatives, double and triple integrals. Placement into Math 30B is by exam and assumes a more thorough background than Math 30G; it allows for a deeper study of selected topics in calculus.
- Prerequisites: Mastery of single-variable calculus—entry by department placement only
- Instructors: Benjamin, de Pillis, Karp, Levy, Omar, Orrison, Su
- Offered: Fall, first half
- Math 35: Probability and Statistics (1.5 credits) [HMC Core]
- Sample spaces, events, axioms for probabilities; conditional probabilities and Bayes' theorem; random variables and their distributions, discrete and continuous; expected values, means and variances; covariance and correlation; law of large numbers and central limit theorem; point and interval estimation; hypothesis testing; simple linear regression; applications to analyzing real data sets.
- Prerequisites: Math 30B or Math 30G
- Instructors: Benjamin, Martonosi, Omar, Orrison, Su, Williams
- Offered: Fall, second half
- Math 40: Introduction to Linear Algebra (1.5 credits) [HMC Core]
- Theory and applications of linearity, including vectors, matrices, systems of linear equations, dot and cross products, determinants, linear transformations in Euclidean space, linear independence, bases, eigenvalues, eigenvectors, and diagonalization.
- Prerequisites: Math 30 or one year of calculus at the high-school level
- Instructors: Benjamin, de Pillis, Gu, Martonosi, Omar, Orrison, Pippenger, Su, Yong
- Offered: Spring, first half
- Math 45: Introduction to Differential Equations (1.5 credits) [HMC Core]
- Modeling physical systems, first-order ordinary differential equations, existence, uniqueness, and long-term behavior of solutions; bifurcations; approximate solutions; second-order ordinary differential equations and their properties, applications; first-order systems of ordinary differential equations.
- Prerequisites: Math 30B or Math 30G
- Instructors: Bernoff, Castro, de Pillis, Jacobsen, Levy, Su, Yong
- Offered: Spring, second half
- Math 55: Discrete Mathematics (3 credits)
- Topics include combinatorics (clever ways of counting things), number theory, and graph theory with an emphasis on creative problem solving and learning to read and write rigorous proofs. Possible applications include probability, analysis of algorithms, and cryptography.
- Corequisites: Math 40
- Prerequisites: Math 30; or permission of instructor
- Instructors: Benjamin, Bernoff, Orrison, Pippenger
- Offered: Fall and Spring
- Math 60: Multivariable Calculus (1.5 credits) [HMC Core]
- Linear approximations, the gradient, directional derivatives and the Jacobian; optimization and the second derivative test; higher-order derivatives and Taylor approximations; line integrals; vector fields, curl, and divergence; Green's theorem, divergence theorem and Stokes' theorem, outline of proof and applications.
- Prerequisites: (Math 30B or Math 30G) and Math 40
- Instructors: Bernoff, Castro, Gu, Karp, Levy, Omar, Orrison, Su, Yong
- Offered: Fall, first half, and Summer Math
- Math 65: Differential Equations and Linear Algebra II (1.5 credits) [HMC Core]
- General vector spaces and linear transformations; change of basis and similarity. Applications to linear systems of ordinary differential equations, matrix exponential; nonlinear systems of differential equations; equilibrium points and their stability.
- Prerequisites: Math 40 and Math 45; or permission of instructor
- Instructors: Bernoff, Castro, Jacobsen, Levy, Martonosi
- Offered: Fall, second half, and Summer Math
- Math 70: Intermediate Linear Algebra (1.5 credits)
- This half course is a continuation of Math 65 and is designed to increase the depth and breadth of students' knowledge of linear algebra. Topics include: Vector spaces, linear transformations, eigenvalues, eigenvectors, inner-product spaces, spectral theorems, Jordan Canonical Form, singular value decomposition, and others as time permits.
- Prerequisites: Math 65; or equivalent
- Instructors: de Pillis, Omar, Orrison
- Offered: Spring, first half
- Math 72: Applied Mathematics for Engineering (1.5 credits)
- Applications of differential equations, linear algebra, and probability to engineering problems in multiple disciplines. Mathematical modeling, dimensional analysis, scale, approximation, model validation, Laplace Transforms. (May not be included in a mathematics major program.) (Formerly Math 110.)
- Prerequisites: Math 35 and Math 65; or equivalent
- Instructors: Levy, Yong, Bassman (Engineering)
- Crosslisted As: Engr 72.
- Offered: Spring, first half
- Math 80: Intermediate Differential Equations (1.5 credits)
- This half course is a continuation of Math 65 and is designed to increase the depth and breadth of students' knowledge of differential equations. Topics include Existence and Uniqueness, Power Series and Frobenius Series Methods, Laplace Transform, and additional topics as time permits.
- Prerequisites: Math 65; or equivalent
- Instructors: Bernoff, Castro, de Pillis, Jacobsen, Levy
- Offered: Spring, second half
- Math 92: Mathematical Contest in Modeling/Interdisciplinary Contest in Modeling Seminar (1 credit)
- This seminar meets one evening per week during which students solve and present solutions to challenging mathematical problems in preparation for the Mathematical Contest in Modeling (MCM) and Interdisciplinary Contest in Modeling (ICM), an international undergraduate mathematics competition. (Formerly Math 190.)
- Prerequisites: none
- Instructors: Martonosi
- Offered: Fall
- Math 93: Putnam Seminar (1 credit)
- This seminar meets one evening per week during which students solve and present solutions to challenging mathematical problems in preparation for the William Lowell Putnam Mathematics Competition, a national undergraduate mathematics competition. (Formerly Math 191.)
- Prerequisites: none
- Instructors: Bernoff, Pippenger, Su
- Offered: Fall
- Math 94: Problem Solving Seminar (1 credit)
- This seminar meets one evening per week during which students solve and present solutions to problems posed in mathematics journals, such as the American Mathematical Monthly. Solutions are submitted to these journals for potential publication. (Formerly Math 192.)
- Prerequisites: none
- Instructors: Bernoff, Omar
- Offered: Spring
- Math 104: Graph Theory (3 credits)
- An introduction to graph theory with applications. Theory and applications of trees, matchings, graph coloring, planarity, graph algorithms, and other topics.
- Prerequisites: Math 40 and Math 55
- Instructors: Martonosi, Omar, Orrison, Pippenger
- Offered: Spring, alternate years
- Math 106: Combinatorics (3 credits)
- An introduction to the techniques and ideas of combinatorics, including counting methods, Stirling numbers, Catalan numbers, generating functions, Ramsey theory and partially ordered sets.
- Prerequisites: Math 55; or permission of instructor
- Instructors: Benjamin, Omar, Orrison, Pippenger
- Offered: Spring, alternate years
- Math 108: History of Mathematics (3 credits)
- A survey of the history of mathematics from antiquity to the present. Topics emphasized will include: the development of the idea of proof, the “analytic method” of algebra, the invention of the calculus, the psychology of mathematical discovery, and the interactions between mathematics and philosophy.
- Prerequisites: Math 30B or Math 30G
- Instructors: Grabiner (Pitzer)
- Offered: Alternate years
- Math 109: Introduction to the Mathematics of Finance (3 credits)
- This is a first course in Mathematical Finance sequence. This course introduces the concepts of arbitrage and risk-neutral pricing within the context of single- and multi-period financial models. Key elements of stochastic calculus such as Markov processes, martingales, filtration and stopping times will be developed within this context. Pricing by replication is studied in a multi-period binomial model. Within this model, the replicating strategies for European and American options are determined.
- Prerequisites: Math 65; or equivalent or permission of instructor
- Instructors: Aksoy (CMC)
- Offered: Alternate years
- Math 115: Fourier Series and Boundary Value Problems (3 credits)
- Complex variables and residue calculus; Laplace transforms; Fourier series and the Fourier transform; Partial Differential Equations including the heat equation, wave equation, and Laplace's equation; Separation of variables; Sturm-Liouville theory and orthogonal expansions; Bessel functions. (May not be included in a mathematics major program. Students may not receive credit for both Mathematics 115 and 180.)
- Prerequisites: Math 65; or equivalent
- Instructors: Bernoff, Levy, Yong
- Offered: Spring
- Math 119: Advanced Mathematical Biology (2 credits)
- Further study of mathematical models of biological processes, including discrete and continuous models. Examples are drawn from a variety of areas of biology, which may include physiology, systems biology, cancer biology, epidemiology, ecology, evolution, and spatiotemporal dynamics.
- Prerequisites: Bio 52, Math 118 or Bio 118; or permission of instructor
- Instructors: de Pillis, Jacobsen, Levy, Adolph (Biology)
- Crosslisted As: Bio 119.
- Offered: Fall, not offered in 2011
- Math 131: Mathematical Analysis I (3 credits)
- This course is a rigorous analysis of the real numbers, and an introduction to writing and communicating mathematics well. Topics include properties of the rational and the real number fields, the least upper bound property, induction, countable sets, metric spaces, limit points, compactness, connectedness, careful treatment of sequences and series, functions, differentiation and the mean value theorem, and an introduction to sequences of functions. Additional topics as time permits.
- Prerequisites: Math 55 or Math 101
- Instructors: Castro, Karp, Omar, Su
- Offered: Jointly; Fall semester at HMC and Pomona, Spring semester at HMC and CMC
- Math 132: Mathematical Analysis II (3 credits)
- A rigorous study of calculus in Euclidean spaces including multiple Riemann integrals, derivatives of transformations and the inverse function theorem.
- Prerequisites: Math 131
- Instructors: Castro, Omar, Su, Radunskaya (Pomona)
- Offered: Jointly; Fall semester at HMC, Spring semester at Pomona
- Math 136: Complex Variables and Integral Transforms (3 credits)
- Complex differentiation, Cauchy-Riemann equations, Cauchy integral formulas, residue theory, Taylor and Laurent expansions, conformal mapping, Fourier and Laplace transforms, inversion formulas, other integral transforms, applications to solutions of partial differential equations.
- Prerequisites: Math 65; or equivalent
- Instructors: Gu, Jacobsen, Karp, Yong
- Offered: Fall
- Math 137: Graduate Analysis I (3 credits)
- Abstract Measures, Lebesgue measure, and Lebesgue-Stieltjes measures on R; Lebesgue integral and limit theorems; product measures and the Fubini theorem; additional topics.
- Prerequisites: Math 132
- Instructors: Castro, Krieger, Grabiner (Pomona), O'Neill (CMC)
- Crosslisted As: Math 331.
- Offered: Fall
- Math 138: Graduate Analysis II (3 credits)
- Banach and Hilbert spaces; Lp spaces; complex measures and the Radon-Nikodym theorem.
- Prerequisites: Math 137 or Math 331
- Instructors: Castro, Krieger, Grabiner (Pomona), Omar, O'Neill (CMC)
- Crosslisted As: Math 332.
- Offered: Spring
- Math 142: Differential Geometry (3 credits)
- Curves and surfaces, Gauss curvature; isometries, tensor analysis, covariant differentiation with application to physics and geometry (intended for majors in physics or mathematics).
- Prerequisites: Math 65; or equivalent
- Instructors: Gu, Karp, Bachman (Pitzer)
- Offered: Fall, alternate years
- Math 143: Seminar in Differential Geometry (3 credits)
- Selected topics in Riemannian geometry, low dimensional manifold theory, elementary Lie groups and Lie algebra, and contemporary applications in mathematics and physics.
- Prerequisites: Math 131 and Math 142;
*recommended*Math 147; or permission of instructor - Instructors: Gu
- Offered: Spring, alternate years
- Math 147: Topology (3 credits)
- Topology is the study of properties of objects preserved by continuous deformations (much like geometry is the study of properties preserved by rigid motions). Hence, topology is sometimes called “rubber-sheet” geometry. This course is an introduction to point-set topology with additional topics chosen from geometric and algebraic topology. It will cover topological spaces, metric spaces, product spaces, quotient spaces, Hausdorff spaces, compactness, connectedness and path connectedness. Additional topics will be chosen from metrization theorems, fundamental groups, homotopy of maps, covering spaces, the Jordan curve theorem, classification of surfaces and simplicial homology.
- Prerequisites: Math 131; or permission of instructor
- Instructors: Karp, Pippenger, Su, Flapan (Pomona)
- Offered: jointly with Pomona; Spring semester
- Math 148: Knot Theory (3 credits)
- An introduction to theory of knots and links from combinatorial, algebraic, and geometric perspectives. Topics will include knot diagrams, p-colorings, Alexander, Jones, and HOMFLY polynomials, Seifert surfaces, genus, Seifert matrices, the fundamental group, representations of knot groups, covering spaces, surgery on knots, and important families of knots.
- Prerequisites: Math 40; or permission of instructor
- Instructors: Hoste (Pitzer)
- Offered: Alternate years
- Math 152: Statistical Theory (3 credits)
- An introduction to the general theory of statistical inference, including estimation of parameters, confidence intervals and tests of hypotheses.
- Prerequisites: Math 151 or Math 157; or permission of instructor
- Instructors: Martonosi, Williams, Hardin (Pomona), Huber (CMC)
- Offered: jointly; Spring semester at Pomona and CMC
- Math 153: Bayesian Statistics (3 credits)
- An introduction to principles of data analysis and advanced statistical modeling using Bayesian inference. Topics include a combination of Bayesian principles and advanced methods; general, conjugate and noninformative priors, posteriors, credible intervals, Markov Chain Monte Carlo methods, and hierarchical models. The emphasis throughout is on the application of Bayesian thinking to problems in data analysis. Statistical software will be used as a tool to implement many of the techniques.
- Prerequisites: Math 35; or permission of the instructor
- Instructors: Williams
- Offered: Spring, alternate years
- Math 155: Time Series (3 credits)
- An introduction to the theory of statistical time series. Topics include decomposition of time series, seasonal models, forecasting models including causal models, trend models, and smoothing models, autoregressive (AR), moving average (MA), and integrated (ARIMA) forecasting models. Time permitting we will also discuss state space models, which include Markov processes and hidden Markov processes, and derive the famous Kalman filter, which is a recursive algorithm to compute predictions. Statistical software will be used as a tool to aid calculations required for many of the techniques.
- Prerequisites: Math 35; or permission of the instructor
- Instructors: Williams
- Offered: Spring, alternate years
- Math 156: Stochastic Processes (3 credits)
- This course is particularly well-suited for those wanting to see how probability theory can be applied to the study of random phenomena in fields such as engineering, management science, the physical and social sciences, and operations research. Topics include conditional expectation, Markov chains, Poisson processes, and queuing theory. Additional applications chosen from such topics as reliability theory, Brownian motion, finance and asset pricing, inventory theory, dynamic programming, and simulation.
- Prerequisites: Math 40 and (Math 151 or Math 157); or permission of instructor
- Instructors: Benjamin, Martonosi, Huber (CMC)
- Offered: jointly; Alternate Fall semester at HMC
- Math 157: Intermediate Probability (2 credits)
- Continuous random variables, distribution functions, joint density functions, marginal and conditional distributions, functions of random variables, conditional expectation, covariance and correlation, moment generating functions, law of large numbers, Chebyshev' theorem and central-limit theorem. (Formerly Math 151.)
- Prerequisites: Math 35; or permission of instructor
- Instructors: Benjamin, Martonosi, Pippenger, Su, Williams
- Offered: Fall and Spring, first half
- Math 158: Statistical Linear Models (3 credits)
- An introduction to linear regression including simple linear regression, multiple regression, variable selection, stepwise regression and analysis of residual plots and analysis of variance including one-way and two-way fixed effects ANOVA. Emphasis will be on both methods and applications to data. Statistical software will be used to analyze data.
- Prerequisites: Math 35; or permission of instructor
- Instructors: Martonosi, Williams, Hardin (Pomona)
- Offered: Fall
- Math 161: Environmental and Spatial Statistics (3 credits)
- Extension of the classical linear model to observations correlated in space (and time) with applications to real-life data. The course covers fundamentals of spatial random processes, geostatistics and spatial interpolation (Kriging), introduction to spatio-temporal processes and hierarchical modeling. Statistical software will be used as a tool to implement many of the techniques. Instructors: Srebotjnak
- Prerequisites: Math 35; or permission of instructor
- Offered: Spring
- Math 164: Scientific Computing (3 credits)
- Computational techniques applied to problems in the sciences and engineering. Modeling of physical problems, computer implementation, analysis of results; use of mathematical software; numerical methods chosen from: solutions of linear and nonlinear algebraic equations, solutions of ordinary and partial differential equations, finite elements, linear programming, optimization algorithms and fast-Fourier transforms.
- Prerequisites: Math 65 and CS 60; or permission of instructor
- Instructors: Bernoff, de Pillis, Levy, Yong
- Crosslisted As: CS 144.
- Offered: Spring
- Math 165: Numerical Analysis (3 credits)
- An introduction to the analysis and computer implementation of basic numerical techniques. Solution of linear equations, eigenvalue problems, local and global methods for non-linear equations, interpolation, approximate integration (quadrature), and numerical solutions to ordinary differential equations.
- Prerequisites: Math 65; or equivalent or permission of instructor
- Instructors: Bernoff, Castro, de Pillis, Levy, Pippenger, Yong
- Offered: Fall
- Math 167: Complexity Theory (3 credits)
- Specific topics include finite automata, pushdown automata, Turing machines, and their corresponding languages and grammars; undecidability; complexity classes, reductions, and hierarchies.
- Prerequisites: CS 60 and Math 55
- Instructors: Pippenger, Libeskind-Hadas (Computer Science), Bull (Pomona)
- Crosslisted As: CS 142.
- Offered: in alternate years, Fall
- Math 168: Algorithms (3 credits)
- Algorithm design, computer implementation, and analysis of efficiency. Discrete structures, sorting and searching, time and space complexity, and topics selected from algorithms for arithmetic circuits, sorting networks, parallel algorithms, computational geometry, parsing, and pattern-matching.
- Prerequisites: Math 55 and CS 60 and Math 131
- Instructors: Pippenger, Sweedyk (Computer Science), Libeskind-Hadas (Computer Science)
- Crosslisted As: CS 140.
- Offered: Fall and Spring
- Math 171: Abstract Algebra I (3 credits)
- Groups, rings, fields and additional topics. Topics in group theory include groups, subgroups, quotient groups, Lagrange's theorem, symmetry groups, and the isomorphism theorems. Topics in Ring theory include Euclidean domains, PIDs, UFDs, fields, polynomial rings, ideal theory, and the isomorphism theorems. In recent years, additional topics have included the Sylow theorems, group actions, modules, representations, and introductory category theory.
- Prerequisites: Math 40 and Math 55; or permission of instructor
- Instructors: Benjamin, Karp, Omar, Orrison, Shahriari (Pomona), Sarkis (Pomona)
- Offered: jointly; Fall semester at HMC and CMC, Spring semester at HMC and Pomona
- Math 172: Abstract Algebra II: Galois Theory (3 credits)
- The topics covered will include polynomial rings, field extensions, classical constructions, splitting fields, algebraic closure, separability, Fundamental Theorem of Galois Theory, Galois groups of polynomials and solvability.
- Prerequisites: Math 171
- Instructors: Karp, Omar, Orrison, Su, Shahriari (Pomona), Sarkis (Pomona)
- Offered: jointly; Spring semester at HMC and Pomona
- Math 173: Advanced Linear Algebra (3 credits)
- Topics from among the following: Similarity of matrices and the Jordan form, the Cayley-Hamilton theorem, limits of sequences and series of matrices; the Perron-Frobenius theory of nonnegative matrices, estimating eigenvalues of matrices; stability of systems of linear differential equations and Lyapunov's Theorem; iterative solutions of large systems of linear algebraic equations.
- Prerequisites: Math 131; or permission of instructor
- Instructors: de Pillis, Gu, Orrison
- Offered: jointly; Fall in alternate years
- Math 174: Abstract Algebra II: Representation Theory (3 credits)
- The topics covered will include group rings, characters, orthogonality relations, induced representations, applications of representation theory, and other select topics from module theory.
- Prerequisites: Math 171
- Instructors: Karp, Omar, Orrison, Su
- Offered: jointly; Spring by HMC and Pomona
- Math 175: Number Theory (3 credits)
- Properties of integers, congruences, Diophantine problems, quadratic reciprocity, number theoretic functions, primes.
- Prerequisites: Math 55; or permission of instructor
- Instructors: Benjamin, Omar, Pippenger, Towse (Scripps)
- Offered: alternate years; jointly; Spring at HMC, Fall at Scripps
- Math 176: Algebraic Geometry (3 credits)
- Topics include affine and projective varieties, the Nullstellensatz, rational maps and morphisms, birational geometry, tangent spaces, nonsingularity and intersection theory. Additional topics may be included depending on the interest and pace of the class.
- Prerequisites: Math 171;
*recommended*previous courses in Analysis, Galois Theory, Differential Geometry and Topology are helpful but not required; or permission of the instructor - Instructors: Karp, Omar
- Offered: Fall, alternate years
- Math 180: Introduction to Partial Differential Equations (3 credits)
- Partial Differential Equations (PDEs) including the heat equation, wave equation, and Laplace's equation; existence and uniqueness of solutions to PDEs via the maximum principle and energy methods; method of characteristics; Fourier series; Fourier transforms and Green's functions; Separation of variables; Sturm-Liouville theory and orthogonal expansions; Bessel functions.
- Prerequisites: Math 80 and Math 131; or permission of instructor
- Instructors: Bernoff, Castro, de Pillis, Jacobsen, Levy
- Offered: Fall
- Math 181: Dynamical Systems (3 credits)
- Existence and uniqueness theorems for systems of differential equations, dependence on data, linear systems, fundamental matrices, asymptotic behavior of solutions, stability theory, and other selected topics, as time permits.
- Prerequisites: Math 115 or Math 180; or permission of instructor
- Instructors: Bernoff, de Pillis, Jacobsen, Levy, Radunskaya (Pomona)
- Offered: jointly; Fall semester at Pomona, Spring semester at HMC in alternate years
- Math 184: Graduate Partial Differential Equations (3 credits)
- Advanced topics in the study of linear and nonlinear partial differential equations. Topics may include the theory of distributions; Hilbert spaces; conservation laws, characteristics and entropy methods; fixed point theory; critical point theory; the calculus of variations and numerical methods. Applications to fluid mechanics, mathematical physics, mathematical biology and related fields. (Formerly Math 182.)
- Prerequisites: (Math 115 and Math 131) or Math 180;
*recommended*Math 132 - Instructors: Bernoff, Castro, Jacobsen, Levy
- Offered: Spring; offered in alternate years
- Math 185: Introduction to Wavelets and their Applications (2 credits)
- An introduction to the mathematical theory of wavelets, with applications to signal processing, data compression and other areas of science and engineering.
- Prerequisites: Math 115 or Math 180; or permission of instructor
- Instructors: Staff
- Math 187: Operations Research (3 credits)
- Linear, integer, non-linear and dynamic programming, classical optimization problems, and network theory.
- Prerequisites: Math 40; or equivalent
- Instructors: Benjamin, Martonosi, Huber (CMC), Shahriari (Pomona)
- Offered: Fall
- Math 188: Social Choice and Decision Making (3 credits)
- Basic concepts of game theory and social choice theory, representations of games, Nash equilibria, utility theory, non-cooperative games, cooperative games, voting games, paradoxes, Arrow's impossibility theorem, Shapley value, power indices, “fair division” problems, and applications.
- Prerequisites: Prior or concurrent enrollment in Math 30 or equivalent;
*recommended*Math 55; or permission of instructor - Instructors: Su
- Crosslisted As: IE 198.
- Offered: Spring, alternate years
- Math 189: Special Topics in Mathematics (1-3 credits)
- A course devoted to exploring topics of current interest to faculty or students. Recent topics have included: Algebraic Geometry, Algebraic Topology, Complex Dynamics, Fluid Dynamics, Games and Gambling, Mathematical Toys, and Riemann Zeta Functions.
- Prerequisites: Varies with topics chosen
- Instructors: Staff
- Offered: Fall and Spring
- Math 193: Mathematics Clinic (3 credits)
- The Clinic Program brings together teams of students to work on a research problem sponsored by business, industry or government. Teams work closely with a faculty advisor and a liaison provided by the sponsoring organization to solve complex real-world problems using mathematical and computational methods. Students are expected to present their work orally and to produce a final report conforming to the publication standards of a professional mathematician.
- Prerequisites: none
- Instructors: Bernoff, Castro, de Pillis, Gu, Levy, Martonosi, Williams
- Offered: Fall and Spring
- Math 196: Independent Study (1-5 credits)
- Readings in special topics.
- Prerequisites: Permission of department or instructor
- Instructors: Staff
- Offered: Fall and Spring
- Math 197: Senior Thesis (3 credits)
- Senior thesis offers the student, guided by the faculty advisor, a chance to experience a taste of the life of a professional research mathematician. The work is largely independent with guidance from the research advisor. The principal objective of the senior thesis program is to help you develop intellectually and improve your written and verbal communication skills. Students are expected to present their work orally and to produce a thesis conforming to the publication standards of a professional mathematician.
- Prerequisites: Permission of department
- Instructors: Staff
- Offered: Fall and Spring
- Math 198: Undergraduate Mathematics Forum (1 credit)
- The goal of this course is to improve students' ability to communicate mathematics, both to a general and technical audience. Students will present material on assigned topics and have their presentations evaluated by students and faculty. This format simultaneously exposes students to a broad range of topics from modern and classical mathematics.
- Prerequisites: none; none
- Instructors: Castro, Jacobsen, Levy, Orrison, Yong
- Offered: Fall and Spring
- Math 199: Math Colloquium (0.5 credits)
- Students will attend weekly Claremont Math Colloquium, offered through the cooperative efforts of the mathematics faculty at the Claremont Colleges. Most of the talks discuss current research in mathematical sciences, and are accessible to undergraduates.
- Prerequisites: none
- Instructors: Benjamin, Jacobsen, Su
- Offered: Fall and Spring

## Choice Labs

The following courses are often taught by mathematics faculty:

- CL 57: Traffic Measurement and Management (1 credit)
- Prerequisites: none
- Instructors: Martonosi, Little
- Offered: Spring

## Integrative Experience Courses

The following courses are often taught by mathematics faculty:

- IE 144: Mathematics, Music, Art: Cosmic Harmony (Integrative Experience) (3 credits)
- A seminar exploring some of the many intersections between mathematics and music within our own and non-Western cultures, including proportion in art, tuning systems, algorithmic composition, artificial intelligence and creativity, and music synthesis. The class will also examine the ethical, aesthetic, and cultural ramifications of compression technology, sampling, downloading, and the effects of technology on music and vice-versa.
- Prerequisites: none
- Instructors: Orrison, Alves (Humanities, Social Sciences, and the Arts)
- Offered: Fall or Spring
- IE 142: Seminar on Math and Science Education (Integrative Experience) (3 credits)
- Students will learn about and contribute to math and science education in our community. Over the course of the semester, students observe math and science classrooms and reach out to integrate with our readings and discussions, which will be centered around questions such as, “What is effective math and science teaching?”, “What is effective math and science education?”, and, “How does math and science education impact our society?”
- Prerequisites: none
- Instructors: Levy, Yong, Dodds (Computer Science)
- Offered: Fall or Spring

## Joint Computer Science/Mathematics Courses

- CSMT 183: Computer Science and Mathematics Clinic I (3 credits)
- Team project in joint computer science and mathematics, with corporate affiliation.
- Prerequisites: CS 121
- Instructors: Staff
- Offered: Fall
- CSMT 184: Computer Science and Mathematics Clinic II (3 credits)
- Team project in joint computer science and mathematics, with corporate affiliation.
- Prerequisites: CS 121
- Instructors: Staff
- Offered: Spring

## Mathematical and Computational Biology Courses

- MCBI 118B: Introduction to Computational Biology (1.5 credits)
- An introduction to the field of computational biology. Algorithms for phylogenetic inference and computational methods for solving problems in molecular evolution and population genetics.
- Prerequisites: CS 5 and Bio 52; or permission of instructor
- Instructors: Bush (Biology), Donaldson-Matasci (Biology), Libeskind-Hadas (Computer Science)
- Crosslisted As: Bio 118.
- Offered: Spring
- MCBI 118A: Introduction to Mathematical Biology (1.5 credits)
- An introduction to the field of mathematical biology. Continuous and discrete mathematical models of biological processes and their analytical and computational solutions. Examples may include models in epidemiology, ecology, cancer biology, systems biology, molecular evolution, and phylogenetics.
- Prerequisites: Math 65 and Bio 52; or permission of instructor
- Instructors: Adolph (Biology), de Pillis, Jacobsen, Levy
- Crosslisted As: Bio 118.
- Offered: Spring
- MCBI 199: Mathematics and Computational Biology Colloquium (0.5 credits)
- Students attend weekly colloquia. Most talks discuss current research and are accessible to undergraduates.
- Prerequisites: none
- Instructors: Staff
- Offered: Fall and Spring

## Retired Courses

- Math 11: Calculus (2 credits) [HMC Core]
- Limits, derivatives and differentiation rules; partial derivatives; gradients and directional derivatives; introduction to calculus of complex-valued functions; infinite series, Taylor series, convergence tests; fundamental theorem of calculus; techniques of integration; double and triple integrals.
- Prerequisites: One year of calculus at the high-school level
- Instructors: Benjamin, Jacobsen, Karp, Levy
- Offered: Fall, second half
*Course not offered after 2010*- Math 11M: Calculus (2 credits) [HMC Core]
- With an emphasis on multivariable calculus topics: partial derivatives, gradients and directional derivatives, double and triple integrals. Also, various topics from single variable calculus studied from a more theoretical perspective.
- Prerequisites: Strong background in calculus at the high-school level (at least one year)
- Instructors: Benjamin, Jacobsen, Karp, Levy
- Offered: Fall, first half
*Course not offered after 2010*- Math 12: Introduction to Linear Algebra (2 credits) [HMC Core]
- Complex numbers; proofs by contradiction and induction; matrix representation of systems of equations, matrices, operations, determinants, row and column spaces; vectors, dot and cross products; vector descriptions of lines and planes; linear independence and dependence, bases; eigenvalues and eigenvectors; examples of discrete dynamical systems.
- Prerequisites: One year of calculus at the high-school level
- Instructors: Benjamin, de Pillis, Gu, Martonosi, Orrison, Pippenger, Su, Yong
- Offered: Fall, both halves
*Course not offered after 2010*- Math 13: Differential Equations (1.5 credits) [HMC Core]
- Modeling physical systems, first-order ordinary differential equations, existence, uniqueness, and long-term behavior of solutions; bifurcations; approximate solutions; second-order ordinary differential equations and their properties, applications; first-order systems of ordinary differential equations.
- Prerequisites: Math 11 or Math 11M; or equivalent
- Instructors: Bernoff, Castro, de Pillis, Jacobsen, Levy, Su, Yong
- Offered: Spring, both halves
*Course not offered after 2010*- Math 14: Multivariable Calculus I (1.5 credits) [HMC Core]
- Review of basic multivariable calculus; optimization and the second derivative test; higher order derivatives and Taylor approximations; line integrals; vector fields, curl, and divergence; Green's theorem, divergence theorem and Stokes' theorem, outline of proof and applications.
- Prerequisites: Math 11 or Math 11M; or equivalent
- Instructors: Castro, Gu, Karp, Orrison, Su, Yong
- Offered: Spring, both halves
*Course not offered after 2010*- Math 25B: Calculus and Linear Algebra (3 credits) [HMC Core]
- Theory and techniques of differential and integral calculus of a single real or complex variable; infinite series, including Taylor series and convergence tests. Theory and applications of vectors and matrices, including systems of linear equations; linear transformations in Euclidean space; determinants, eigenvalues, eigenvectors, and diagonalization. An introduction to multivariable calculus, including partial derivatives, double and triple integrals. The topics covered in 25B are the same as those covered in 25G, but 25B digs deeper into the theory and applications of the materials.
- Prerequisites: Mastery of single-variable calculus—entry by department placement only
- Instructors: Benjamin, de Pillis, Karp, Levy, Orrison, Su, Yong
- Offered: Fall
*Course not offered after 2011*- Math 25G: Calculus and Linear Algebra (3 credits) [HMC Core]
- Theory and techniques of differential and integral calculus of a single real or complex variable; infinite series, including Taylor series and convergence tests. Theory and applications of vectors and matrices, including systems of linear equations; linear transformations in Euclidean space; determinants, eigenvalues, eigenvectors, and diagonalization. An introduction to multivariable calculus, including partial derivatives, double and triple integrals.
- Prerequisites: One year of calculus at the high-school level
- Instructors: Benjamin, de Pillis, Karp, Levy, Orrison, Su, Yong
- Offered: Fall
*Course not offered after 2011*- Math 61: Multivariable Calculus II (1.5 credits) [HMC Core]
- Constrained optimization using Lagrange multipliers; conservative and nonconservative vector fields; Green's theorem; parameterized surfaces and surface integrals; divergence theorem, outline of proof and applications; Stokes' theorem, outline of proof and applications, unification of major vector theorems.
- Prerequisites: Math 14
- Instructors: Bernoff, Gu, Karp, Su, Yong
- Offered: Fall, first half
*Course not offered after 2010*- Math 62: Introduction to Probability and Statistics (1.5 credits) [HMC Core]
- Sample spaces, events, axioms for probabilities; conditional probabilities and Bayes's theorem; random variables and their distributions, discrete and continuous; expected values, means and variances; covariance and correlation; law of large numbers and central limit theorem; point and interval estimation; hypothesis testing; simple linear regression; applications to analyzing real data sets.
- Prerequisites: Math 12
- Instructors: Benjamin, Martonosi, Orrison, Su, Williams
- Offered: Fall, second half
*Course not offered after 2011*- Math 63: Linear Algebra II (1.5 credits) [HMC Core]
- General vector spaces and linear transformations; rank-nullity theorem; orthogonal expansion and Fourier coefficients; change of basis and similarity; generalized eigenvalues and eigenvectors; diagonalization of symmetric matrices; applications of eigenvalues to systems of ordinary differential equations; LU, QR, and singular value decomposition theorems; Jordan canonical forms.
- Prerequisites: Math 12
- Instructors: Benjamin, de Pillis, Gu, Martonosi, Orrison
- Offered: Spring, first half
*Course not offered after 2010*- Math 64A: Differential Equations/Linear Algebra II (1.5 credits) [HMC Core]
- General vector spaces and linear transformations; change of basis and similarity; generalized eigenvectors; Jordan canonical forms. Applications to linear systems of ordinary differential equations, matrix exponential; Nonlinear systems of differential equations; equilibrium points and their stability.
- Prerequisites: Math 12 and Math 13; or permission of instructor
- Instructors: Bernoff, Castro, Jacobsen, Levy, Martonosi
- Offered: Fall, second half
*Course not offered after 2011*- Math 64: Differential Equations II (1.5 credits) [HMC Core]
- Linear systems of homogeneous ordinary differential equations, matrix exponential and non-homogeneous linear systems; non-linear systems; equilibrium points and their stability; phase portraits.
- Prerequisites: Math 12 and Math 13
- Instructors: Bernoff, Castro, de Pillis, Jacobsen, Levy, Martonosi, Yong
- Offered: Spring, second half
*Course not offered after 2010*- Math 110: Applied Mathematics for Engineering (1.5 credits)
- Renumbered as Mathematics 72.
- Prerequisites: Math 35 and Math 65; or equivalent
- Instructors: Levy, Yong, Bassman (Engineering)
- Crosslisted As: Engr 72.
- Offered: Spring, first half
*Course not offered after 2013*- Math 118: Introduction to Mathematical and Computational Biology (3 credits)
- Renumbered as Mathematical and Computational Biology 118.
- Prerequisites: Math 65 and Bio 52; or permission of instructor
- Instructors: de Pillis, Jacobsen, Levy, Adolph (Biology), Bush (Biology), Libeskind-Hadas (Computer Science)
- Crosslisted As: Bio 118.
- Offered: Spring
*Course not offered after 2013*- MCBI 118: Introduction to Mathematical and Computational Biology (3 credits)
- An introduction to the fields of mathematical and computational biology. Continuous and discrete mathematical models of biological processes and their analytical and computational solutions. Examples may include models in epidemiology, ecology, cancer biology, systems biology, molecular evolution, and phylogenetics.
- Prerequisites: Math 65 and Bio 52; or permission of instructor
- Instructors: de Pillis, Jacobsen, Levy, Adolph (Biology), Bush (Biology), Libeskind-Hadas (Computer Science)
- Crosslisted As: Bio 118.
- Offered: Spring
*Course not offered after 2015*- Math 159: Design and Analysis of Experiments (2 credits)
- Prior to conducting an experiment, a scientist or engineer must properly structure the trials in order to draw meaningful conclusions from the data s/he collects. This course addresses, from a statistical perspective, how experiments should be designed so that the effects of the factors being tested can be distinguished from one another and from the variability inherent in the system. We will consider several design types, from practical and mathematical standpoints, such as Randomized Blocks, Latin Squares, Two-Level Factorial and Fractional Factorial designs, Response Surface Methods, Random Factors, and Robust Design. Students will use statistical software to analyze real data and complete a term project.
- Prerequisites: (Math 12 or (Math 25B or Math 25G) or Math 40) and (Math 62 or Math 35); or permission of instructor
- Instructors: Martonosi, Williams
- Offered: in alternate years, second-half spring semester.
*Course not offered after 2011*- Math 182: Graduate Partial Differential Equations (3 credits)
- Renumbered as Mathematics 184.
- Prerequisites: (Math 115 and Math 131) or Math 180;
*recommended*Math 132 - Instructors: Bernoff, Castro, Jacobsen, Levy
- Offered: Spring; offered in alternate years
*Course not offered after 2013*- Math 190: Mathematical Contest in Modeling/Interdisciplinary Contest in Modeling Seminar (1 credit)
- Renumbered as Mathematics 92.
- Prerequisites: none
- Instructors: Martonosi
- Offered: Fall
*Course not offered after 2013*- Math 191: Putnam Seminar (1 credit)
- Renumbered as Mathematics 93.
- Prerequisites: none
- Instructors: Bernoff, Pippenger, Su
- Offered: Fall
*Course not offered after 2013*- Math 192: Problem Solving Seminar (1 credit)
- Renumbered as Mathematics 94.
- Prerequisites: none
- Instructors: Bernoff
- Offered: Spring
*Course not offered after 2013*