Course Descriptions

Math 11M: Calculus (2 credits): 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
Math 11: Calculus (2 credits): 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
Math 12: Introduction to Linear Algebra (2 credits): 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
Math 13: Differential Equations (1.5 credits): 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 the equivalent; Instructors: Bernoff, Castro, de Pillis, Jacobsen, Levy, Su, Yong; Offered: Spring, both halves
Math 14: Multivariable Calculus I (1.5 credits): 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 the equivalent; Instructors: Castro, Gu, Karp, Orrison, Su, Yong; Offered: Spring, both halves
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.; Prerequisites: Math 12; or permission of the instructor; Instructors: Benjamin, Bernoff, Orrison, Tucker; Offered: Fall and Spring
Math 61: Multivariable Calculus II (1.5 credits): 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: First half of Fall semester
Math 62: Introduction to Probability and Statistics (1.5 credits): 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 12; Instructors: Benjamin, Martonosi, Orrison, Su, Williams; Offered: Second half of Fall semester
Math 63: Linear Algebra II (1.5 credits): 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: First half of Spring semester
Math 64: Differential Equations II (1.5 credits): 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: Second half of Spring semester
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 12 and Math 55; Instructors: Benjamin, Orrison, Pippenger; Offered: alternate years
Math 106: Combinatorics (2 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, Orrison, Pippenger; Offered: alternate years
Math 107: Set Theory ( credits): Naive set theory, Zermelo-Fraenkel axioms and the axiom of choice; ordinal and cardinal arithmetic; construction of real numbers.; Prerequisites: Math 12; Instructors: Bull (Pomona); Offered: alternate years
Math 108: History of Mathematics ( credits): A survey of the history of mathematics from anitquity 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 11; Instructors: Grabiner (Pitzer); Offered: alternate years
Math 109: Introduction to the Mathematics of Finance ( credits): This course emphasizes the math used in the valuation of derivative securities. Topics will include partial differential equations (diffusion iequation), mathematical modeling of financial derivatives (calls and puts), and numerical methods for solving differential equations; Black-Scholes Model.; Prerequisites: Math 63; Instructors: Aksoy (CMC); Offered: alternate years
Math 115: Fourier Series and Boundary Value Problems (3 credits): Sturm-Liouville theory, orthogonal expansions, convergence properties of Fourier series, separation of variables for partial differential equations, regular singular point theory, Bessel functions and Legendre polynomials. (May not be included in a mathematics major program. Students may not receive credit for both Mathematics 115 and 180.); Prerequisites: Math 64; Instructors: Bernoff, Castro, Jacobsen, Levy, Yong; Offered: Fall
Math 118: Mathematical Biology I (2 credits): Mathematical models of biological processes emphasizing continuous models. May include models in epidemiology, population dynamics, cancer modeling, and disease treatment modeling.; Prerequisites: Math 64, Bio 52; or permission of instructor; Instructors: de Pillis, Jacobsen, Adolph (Biology), Nadim (CGU/KGI); Offered: first half of Spring semester
Math 119: Mathematical Biology II (2 credits): Mathematical models of biological processes emphasizing discrete and continuous models. May include one- and two-locus population genetics, metapopulations, and matrix population models as well as models in physiology and neurobiology.; Prerequisites: Math 64, Bio 52; or permission of instructor; Instructors: de Pillis, Jacobsen, Adolph (Biology), Nadim (CGU/KGI); Offered: second half of Spring semester
Math 120: Chirality (2 credits): A structure is chiral if it is different from its mirror image. This interdisciplinary course introduces students to topological and geometric symmetry and provides descriptions of chirality in molecular systems. Connections will be made between the chemical and mathematical theories of chirality. Molecules with interesting topological features will be introduced and their structural behavior discussed.; Prerequisites: Math 12; Instructors: Flapan (Pomona); Offered: alternate years in Spring semester
Math 123: Logic (3 credits): Propositional and first order predicate logic. The completeness, compactness and Lowenheim/Skolem theorems. Decidable theories. Applications to other areas of mathematics, e.g., nonstandard analysis.; Prerequisites: Math 12; Instructors: Bull (Pomona); Offered: jointly at Pomona in alternate years
Math 131: Mathematical Analysis I (3 credits): Countable sets, least upper bound, and metric space topology including compactness, completeness, connectivity, and uniform convergence. Related topics as time permits.; Prerequisites: Math 12 and Math 14; Instructors: Castro, Karp, Su, S. Grabiner (Pomona), Martelli (CMC); Offered: jointly; Fall semester at 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, Su, Radunskaya (Pomona); Offered: jointly; Fall semester at HMC, second 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 64; 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); Offered: Fall
Math 138: Graduate Analysis II (3 credits): Banach and Hilbert spaces; L^p spaces; complex measures and the Radon-Nikodym theorem.; Prerequisites: Math 137 or Math 331; Instructors: Castro, Krieger, Grabiner (Pomona), O'Neill (CMC); 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 64; Instructors: Gu; Offered: Fall
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: Yong, Dodds; Offered: Fall or Spring
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 or Math 132 or Math 142; recommended Math 147; or permission of instructor; Instructors: Gu; Offered: Spring
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: Alves, Orrison; Offered: Fall or Spring
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: 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 147 or Math 171; 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 157 or Math 151; or permission of instructor; Instructors: Williams, Hardin (Pomona), Myhre (CMC); Offered: jointly; Spring semester at Pomona and CMC
Math 156: Stochastic Processes (3 credits): Continuation of Math 157. This course is particularly well suited for those wanting to see how probability theory can be applied to the study of 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 63 and ( Math 151 or Math 157 ); or permission of the instructor; Instructors: Martonosi, Myhre (CMC); Offered: jointly; 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 62; or permission of instructor; Instructors: Benjamin, Martonosi, Pippenger, Su, Williams; Offered: First half of Spring semester
Math 158: Statistical Data Analysis (3 credits): An introduction to analysis of variance (including one-way and two-way fixed effects ANOVA) and linear regression (including simple linear regression, multiple regression, variable selection, stepwise regression and analysis of residual plots). Emphasis will be both on methods and on applications to data using statistical software.; Prerequisites: Math 62; or AP Statistics or permission of instructor; Instructors: Martonosi, Williams, Hardin (Pomona); Offered: Second half of Spring semester, alternate years
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 62; or equivalent; Instructors: Martonosi, Williams; Offered: in alternate years, second-half spring semester.
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 64 and Cs 60; or permission of instructor; Instructors: Bernoff, de Pillis, Levy, Yong; 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 and approximate integration.; Prerequisites: Math 64; or permission of instructor; Instructors: Bernoff, Castro, de Pillis, 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); Offered: 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); Offered: Fall and Spring
Math 171: Abstract Algebra I (3 credits): Groups and isomorphism theorems. Rings and other structures.; Prerequisites: Math 12 and Math 55; or permission of instructor; Instructors: Benjamin, Karp, Orrison, Shahriari (Pomona), Sarkis (Pomona); Offered: jointly; Fall semester at HMC and CMC, Spring semester at 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, 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 equivalent; Instructors: Gu, Orrison; Offered: jointly 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: none; Instructors: Karp, Orrison, Su; Offered: jointly; Spring by HMC and Pomona Colleges
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, Towse (Scripps); Offered: Spring; offered jointly Fall semester at Scripps
Math 180: Applied Analysis (3 credits): Selected topics from Fourier series, Fourier and Laplace transforms, ordinary and partial differential equations.; Prerequisites: Math 131; Instructors: Bernoff, Castro, 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; Instructors: Bernoff, Jacobsen, Levy, Radunskaya (Pomona); Offered: jointly; Fall semester at Pomona, Spring semster at HMC in alternate years
Math 182: Partial Differential Equations (3 credits): Theory and applications of quasi-linear and linear equations of first order, including systems. Theory of higher order linear equations, including classical methods of solutions for the wave, heat, and potential equations.; Prerequisites: Math 115 or Math 180; 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; (Fourier series) or permission of instructor; Instructors:; Offered:
Math 187: Operations Research (3 credits): Linear, integer, non-linear and dynamic programming, classical optimization problems, and network theory.; Prerequisites: Math 12; Instructors: Benjamin, Martonosi, Myhre (CMC), Shahriari (Pomona); Offered: jointly; Fall semester at HMC/CMC, alternate years
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: Math 63; recommended Math 55; or permission of instructor; Instructors: Su; Offered: alternate years in Spring semester
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 Rieman Zeta Functions.; Prerequisites: permission of instructor; Instructors: Staff; Offered:
Math 191: Putnam Seminar (1 credits): This seminar meets one evening per week during which students solve and present solutions to challenging mathematical problems in preparation for the Putnam Examination, a national undergraduate mathematics competition.; Prerequisites: none; Instructors: Bernoff, Pippenger, Su; Offered: Fall
Math 192: Problem Solving Seminar (1 credits): 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.; Prerequisites: none; Instructors: Bernoff; Offered: Spring
Math 193: Mathematics Clinic (3 credits): Participation in projects or problems with a substantial mathematical and/or computational content. Students typically work in teams of two to four, with appropriate faculty supervision. Problems vary considerably, depending upon student interest and program of study, but normally require computer implementation and documentation. All work required for completion of Mathematics Clinic must be completed in a form acceptable to the clinic advisor by noon on Monday of the week prior to graduation.; Prerequisites: none; Instructors: Gu and staff; Offered: Fall and Spring
Math 196: Independent Study (1-5 credits): Readings in special topics.; Prerequisites: permission of department; Instructors: Staff; Offered: Fall and Spring
Math 197: Senior Thesis (3 credits): A research or expository paper based on independent work done under the supervision of a faculty member. The paper must be submitted to the mathematics department in a form suitable for publication in a mathematics journal.; Prerequisites: permission of department; Instructors: Staff; Offered: Fall and Spring
Math 198: Undergraduate Mathematics Forum (1 credits): 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: Required for all majors; recommended for all joint CS-math majors and mathematical biology majors, typically in the junior year; Instructors: Castro, Jacobsen, Levy, Yong; Offered: Fall and Spring
Math 199: Math Colloquium (None 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: Jacobsen; Offered: Fall and Spring