Mathematics Course Descriptions

CSMT181 HM  Special Topics in Computer Science and Mathematics
Credits: 1.53
Instructor: Staff
Description: A course devoted to exploring topics of current interest. Topics announced prior to registration.

CSMT183 HM  Computer Science and Mathematics Clinic I
Credits: 3
Instructor: Staff
Offered: Fall
Description: Team project in joint computer science and mathematics, with corporate affiliation. CSMT183 HM and CSMT184 HM must be taken consecutively to count toward the major.

CSMT184 HM  Computer Science and Mathematics Clinic II
Credits: 3
Instructor: Staff.
Offered: Spring
Description: Team project in joint computer science and mathematics, with corporate affiliation. CSMT183 HM and CSMT184 HM must be taken consecutively to count toward the major.
Prerequisites: CSMT183 HM

MATH019 HM  Calculus
Credits: 3
Instructor: Staff
Offered: Fall
Description: A comprehensive view of the theory and techniques of differential and integral calculus of a single variable together with a robust introduction to multivariable calculus. Topics include limits, continuity, derivatives, definite integrals, infinite series, Taylor series in one and several variables, partial derivatives, double and triple integrals, linear approximations, the gradient, directional derivatives and the Jacobian, optimization and the second derivative test, higherorder derivatives and Taylor approximations, line integrals, vector fields, curl, divergence, Green's theorem, and an introduction to flux and surface integrals.

MATH021 HM  Mathematics of Games and Puzzles
Credits: 1.5
Instructor: Benjamin
Offered: Fall
Description: Using simple mathematical tools, many popular games and puzzles can be analyzed, leading to improved performance and a more enjoyable experience. In this class we will derive probabilities, expected values and optimal strategies for games like roulette, craps, blackjack, backgammon, and poker. The theory of zero sum games will be introduced, along with optimal wagering strategies. We will also explore solution methods for classic puzzles like Lights Out, Sudoku, and Rubik's Cube. Halfsemester course.
Prerequisites: Harvey Mudd College firstyear students only.

MATH030B HM  Calculus
Credits: 1.5
Instructors: Benjamin, de Pillis, Karp, Omar, Orrison, Su
Offered: Fall, first half
Description: 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 MATH030G HM; it allows for a deeper study of selected topics in calculus.
Prerequisites: Mastery of singlevariable calculus—entry by department placement only

MATH030G HM  Calculus
Credits: 1.5
Instructors: Benjamin, de Pillis, Karp, Orrison, Su
Offered: Fall, first half
Description: 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

MATH035 HM  Probability and Statistics
Credits: 1.5
Instructors: Benjamin, Martonosi, Omar, Orrison, Su, Williams
Offered: Fall, second half
Description: 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: MATH030B HM or MATH030G HM

MATH040 HM  Introduction to Linear Algebra
Credits: 1.5
Instructors: Benjamin, de Pillis, Gu, Martonosi, Omar, Orrison, Pippenger, Su, Yong
Offered: Spring, first half
Description: 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: One year of calculus at the high school level

MATH045 HM  Introduction to Differential Equations
Credits: 1.5
Instructors: Bernoff, Castro, de Pillis, Jacobsen, Su, Yong
Offered: Spring, second half
Description: Modeling physical systems, firstorder ordinary differential equations, existence, uniqueness, and longterm behavior of solutions; bifurcations; approximate solutions; secondorder ordinary differential equations and their properties, applications; firstorder systems of ordinary differential equations.
Prerequisites: MATH030B HM or MATH030G HM

MATH055 HM  Discrete Mathematics
Credits: 3
Instructors: Benjamin, Bernoff, Orrison, Pippenger
Offered: Fall and Spring
Description: 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: MATH040 HM or MATH073 HM

MATH055A HM  Topics in Discrete Mathematics
Credit: 1
Instructor: Benjamin
Description: 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: By permission only

MATH060 HM  Multivariable Calculus
Credits: 1.5
Instructors: Bernoff, Castro, Gu, Karp, Omar, Orrison, Su, Yong
Offered: Fall, first half, and Summer
Description: Linear approximations, the gradient, directional derivatives and the Jacobian; optimization and the second derivative test; higherorder 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: (MATH030B HM or MATH030G HM) and MATH040 HM

MATH065 HM  Differential Equations and Linear Algebra II
Credits: 1.5
Instructors: Bernoff, Castro, Jacobsen, Martonosi
Offered: Fall, second half, and summer
Description: 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: MATH040 HM and MATH045 HM

MATH070 HM  Intermediate Linear Algebra
Credits: 1.5
Instructors: de Pillis, Omar, Orrison
Offered: Spring, first half
Description: This half course is a continuation of MATH065 HM and is designed to increase the depth and breadth of students' knowledge of linear algebra. Topics include: Vector spaces, linear transformations, eigenvalues, eigenvectors, innerproduct spaces, spectral theorems, Jordan Canonical Form, singular value decomposition, and others as time permits.
Prerequisites: MATH065 HM

MATH073 HM  Linear Algebra
Credits: 3
Instructor: Staff
Offered: Spring
Description: 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. General vector spaces and linear transformations; change of basis and similarity. Additional Topics.
Prerequisites: MATH019 HM or equivalent

MATH080 HM  Intermediate Differential Equations
Credits: 1.5
Instructors: Bernoff, Castro, de Pillis, Jacobsen
Offered: Spring, second half
Description: This half course is a continuation of MATH065 HM 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: MATH065 HM

MATH082 HM  Differential Equations
Credits: 3
Instructor: Staff
Offered: Fall
Description: Modeling physical systems, firstorder ordinary differential equations, existence, uniqueness, and longterm behavior of solutions; bifurcations; approximate solutions; secondorder ordinary differential equations and their properties, applications; firstorder systems of ordinary differential equations. Applications to linear systems of ordinary differential equations, matrix exponential; nonlinear systems of differential equations; equilibrium points and their stability. Additional topics.
Prerequisites: (MATH019 HM and MATH073 HM) or equivalent

MATH092 HM  Mathematical Contest in Modeling/Interdisciplinary Contest in Modeling Seminar
Credit: 1
Instructor: Martonosi
Offered: Fall
Description: 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. This course is not eligible for major elective credit in the HMC mathematics major.

MATH093 HM  Putnam Seminar
Credit: 1
Instructors: Bernoff, Omar, Pippenger, Su
Offered: Fall
Description: 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 contest. This course is not eligible for major elective credit in the HMC mathematics major.

MATH094 HM  Problem Solving Seminar
Credit: 1
Instructors: Bernoff, Omar
Offered: Spring
Description: 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.

MATH104 HM  Graph Theory
Credits: 3
Instructors: Martonosi, Omar, Orrison, Pippenger
Offered: Alternate years
Description: An introduction to graph theory with applications. Theory and applications of trees, matchings, graph coloring, planarity, graph algorithms, and other topics.
Prerequisites: (MATH040 HM or MATH073 HM) and MATH055 HM

MATH106 HM  Combinatorics
Credits: 3
Instructors: Benjamin, Omar, Orrison, Pippenger
Offered: Alternate years
Description: 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: MATH055 HM

MATH108 PZ  History of Mathematics
Credits: 3
Instructor: Staff (Pitzer)
Offered: Alternate years
Description: 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: MATH019 HM, MATH030B HM, or MATH030G HM

MATH109 CM  Introduction to the Mathematics of Finance
Credits: 3
Instructor: Staff (CMC)
Offered: Alternate years
Description: This is a first course in Mathematical Finance sequence. This course introduces the concepts of arbitrage and riskneutral pricing within the context of single and multiperiod 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 multiperiod binomial model. Within this model, the replicating strategies for European and American options are determined.
Prerequisites: MATH065 HM or (MATH073 HM and MATH082 HM)

MATH115 HM  Fourier Series and Boundary Value Problems
Credits: 3
Instructors: Bernoff, Yong
Offered: Spring
Description: 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; SturmLiouville 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 MATH180 HM.
Prerequisites: MATH065 HM or (MATH073 HM and MATH082 HM)

MATH119 HM  Advanced Mathematical Biology
Credits: 3
Instructors: de Pillis, Jacobsen, Adolph (Biology)
Description: 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: MCBI118A HM and MCBI118B HM

MATH131 HM  Mathematical Analysis I
Credits: 3
Instructors: Castro, Karp, Omar, Su
Offered: Jointly; Fall semester at HMC and Pomona, Spring semester at HMC and CMC
Description: 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: MATH055 HM

MATH132 HM  Mathematical Analysis II
Credits: 3
Instructors: Castro, Omar, Su, Staff (Pomona)
Offered: Jointly; Fall semester at HMC, Spring semester at Pomona
Description: A rigorous study of calculus in Euclidean spaces including multiple Riemann integrals, derivatives of transformations, and the inverse function theorem.
Prerequisites: MATH131 HM

MATH136 HM  Complex Variables and Integral Transforms
Credits: 3
Instructors: Gu, Jacobsen, Karp, Yong
Offered: Fall
Description: Complex differentiation, CauchyRiemann 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: MATH065 HM or (MATH073 HM and MATH082 HM)

MATH137 HM  Graduate Analysis I
Credits: 3
Instructors: Castro, Staff (Pomona), Staff (CMC)
Offered: Fall
Description: Abstract Measures, Lebesgue measure, and LebesgueStieltjes measures on R; Lebesgue integral and limit theorems; product measures and the Fubini theorem; additional topics.
Prerequisites: MATH132 HM

MATH138 HM  Graduate Analysis II
Credits: 3
Instructors: Castro, Omar, Staff (Pomona), Staff (CMC)
Offered: Spring
Description: Banach and Hilbert spaces; Lp spaces; complex measures and the RadonNikodym theorem.
Prerequisites: MATH137 HM or MATH331 CG

MATH142 HM  Differential Geometry
Credits: 3
Instructors: Gu, Karp, Staff (Pitzer)
Offered: Fall
Description: Curves and surfaces, Gauss curvature; isometries, tensor analysis, covariant differentiation with application to physics and geometry (intended for majors in physics or mathematics).
Prerequisites: MATH065 HM or (MATH073 HM and MATH082 HM)

MATH143 HM  Seminar in Differential Geometry
Credits: 3
Instructor: Gu
Offered: Spring
Description: Selected topics in Riemannian geometry, low dimensional manifold theory, elementary Lie groups and Lie algebra, and contemporary applications in mathematics and physics.
Prerequisites: MATH131 HM and MATH142 HM; MATH147 HM recommended

MATH147 HM  Topology
Credits: 3
Instructors: Karp, Pippenger, Su, Staff (Pomona)
Offered: Jointly with Pomona; Spring semester
Description: 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 "rubbersheet" geometry. This course is an introduction to pointset 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: MATH131 HM

MATH148 PZ  Knot Theory
Credits: 3
Instructor: Staff (Pitzer)
Offered: Alternate years
Description: An introduction to theory of knots and links from combinatorial, algebraic, and geometric perspectives. Topics will include knot diagrams, pcolorings, 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: MATH040 HM or MATH073 HM

MATH152 HM  Statistical Theory
Credits: 3
Instructors: Martonosi, Williams, Staff (Pomona), Staff (CMC)
Offered: Jointly; Spring semester at Pomona and CMC
Description: An introduction to the general theory of statistical inference, including estimation of parameters, confidence intervals, and tests of hypotheses.
Prerequisites: MATH 157 HM

MATH153 HM  Bayesian Statistics
Credits: 3
Instructor: Williams
Offered: Spring, alternate years
Description: 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: MATH035 HM

MATH155 HM  Time Series
Credits: 3
Instructor: Williams
Offered: Spring, alternate years
Description: 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: MATH035 HM

MATH156 HM  Stochastic Processes
Credits: 3
Instructors: Benjamin, Martonosi, Staff (CMC)
Offered: Jointly; Fall, alternate years at HMC
Description: This course is particularly wellsuited 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: (MATH040 HM or MATH073 HM) and MATH157 HM

MATH157 HM  Intermediate Probability
Credits: 1.5
Instructors: Benjamin, Martonosi, Pippenger, Su, Williams
Offered: Fall and Spring
Description: 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's theorem, and centrallimit theorem.
Prerequisites: MATH019 HM or MATH060 HM

MATH158 HM  Statistical Linear Models
Credits: 3
Instructors: Martonosi, Williams, Staff (Pomona)
Offered: Fall, alternate years
Description: 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 oneway and twoway fixed effects ANOVA. Emphasis will be on both methods and applications to data. Statistical software will be used to analyze data.
Prerequisites: MATH035 HM

MATH161 HM  Introduction to Environmental and Spatial Statistics
Credits: 3
Instructor: Srebotnjak
Description: Extension of the classical linear model to observations correlated in space (and time) with applications to reallife data. The course covers fundamentals of spatial random processes, geostatistics and spatial interpolation (Kriging), introduction to spatiotemporal processes and hierarchical modeling. Statistical software will be used as a tool to implement many of the techniques.
Prerequisites: MATH035 HM

MATH164 HM  Scientific Computing
Credits: 3
Instructors: Bernoff, de Pillis, Yong
Offered: Spring
Description: 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 fastFourier transforms.
Prerequisites: (MATH065 HM or (MATH073 HM and MATH082 HM)) and CSCI060 HM

MATH165 HM  Numerical Analysis
Credits: 3
Instructors: Bernoff, Castro, de Pillis, Pippenger, Yong
Offered: Fall
Description: An introduction to the analysis and computer implementation of basic numerical techniques. Solution of linear equations, eigenvalue problems, local and global methods for nonlinear equations, interpolation, approximate integration (quadrature), and numerical solutions to ordinary differential equations.
Prerequisites: MATH065 HM or (MATH073 HM and MATH082 HM)

MATH167 HM  Complexity Theory
Credits: 3
Instructors: Pippenger, LibeskindHadas (Computer Science), Staff (Pomona)
Offered: Fall
Description: Brief review of computability theory, followed by a rigorous treatment of complexity theory. The complexity classes P, NP, and the CookLevin Theorem. Approximability of NPcomplete problems. The polynomial hierarchy, PSPACEcompleteness, L and NLcompleteness, #Pcompleteness. IP and Zeroknowledge proofs. Randomized and parallel complexity classes. The speedup, hierarchy, and gap theorems.
Prerequisites: (CSCI060 HM or CSCI042 HM) and MATH055 HM

MATH168 HM  Algorithms
Credits: 3
Instructors: Pippenger, Sweedyk (Computer Science), LibeskindHadas (Computer Science)
Offered: Fall and Spring
Description: 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 patternmatching.
Prerequisites: (CSCI070 HM and CSCI081 HM) or ((CSCI060 HM or CSCI042 HM) and MATH131 HM))

MATH171 HM  Abstract Algebra I
Credits: 3
Instructors: Benjamin, Karp, Omar, Orrison, Staff (CMC), Staff (Pomona)
Offered: Jointly; Fall semester at HMC and CMC, Spring semester at HMC and Pomona
Description: 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: (MATH040 HM or MATH073 HM) and MATH055 HM

MATH172 HM  Abstract Algebra II: Galois Theory
Credits: 3
Instructors: Karp, Omar, Orrison, Su, Staff (Pomona)
Offered: Jointly; Spring semester at HMC and Pomona
Description: 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: MATH171 HM

MATH173 HM  Advanced Linear Algebra
Credits: 3
Instructors: de Pillis, Gu, Orrison
Offered: Jointly in alternate years
Description: Topics from among the following: Similarity of matrices and the Jordan form, the CayleyHamilton theorem, limits of sequences and series of matrices; the PerronFrobenius 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: MATH131 HM

MATH174 HM  Abstract Algebra II: Representation Theory
Credits: 3
Instructors: Karp, Omar, Orrison, Su
Offered: Jointly; Spring semester at HMC and Pomona
Description: The topics covered will include group rings, characters, orthogonality relations, induced representations, applications of representation theory, and other select topics from module theory.
Prerequisites: MATH171 HM

MATH175 HM  Number Theory
Credits: 3
Instructors: Benjamin, Omar, Pippenger, Staff (Scripps)
Offered: Spring; offered jointly Fall semester at Scripps
Description: Properties of integers, congruences, Diophantine problems, quadratic reciprocity, number theoretic functions, primes.
Prerequisites: MATH055 HM

MATH176 HM  Algebraic Geometry
Credits: 3
Instructors: Karp, Omar
Offered: Fall, alternate years
Description: 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: MATH171 HM; Previous courses in Analysis, Galois Theory, Differential Geometry, and Topology are recommended

MATH178 HM  Nonlinear Data Analytics
Credits: 3
Instructor: Gu
Offered: Fall
Description: Analysis of nonlinear large dynamic data including but not limited from automobiles, cell phones, robots, and unmanned aerial vehicles (UAVs). Visualization of such data using geometric methods, followed by representation in certain configuration spaces to capture the intrinsic nonlinear relationship in the data. (For example, UAVs' data, including accelerometer and gyroscope data, obeys nonlinear kinematics and dynamics relationships, a curved 3D sphere S3 can capture their rotations when we use unit quaternion representations. A traditional statistical correlation matrix cannot capture those nonlinear relations since a correlation matrix only captures linear relationships in the data.) Advanced geometric data analysis techniques including nonlinear Riemannian (nonEuclidean) distances for modeling such big data problems (as used for building a cost function). We will also demonstrate how to perform optimization techniques on curved configuration spaces by extending optimization methods such as gradient descent and Newton's method to such curved spaces. Application of learned techniques to solve real world problems involving big nonlinear dynamic data.
Prerequisites: CSCI070 HM and (CSCI140 HM or MATH131 HM or MATH157 HM or MATH168 HM)

MATH180 HM  Introduction to Partial Differential Equations
Credits: 3
Instructors: Bernoff, Castro, de Pillis, Jacobsen
Offered: Fall
Description: 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; SturmLiouville theory and orthogonal expansions; Bessel functions.
Prerequisites: MATH080 HM and MATH131 HM

MATH181 HM  Dynamical Systems
Credits: 3
Instructors: Bernoff, de Pillis, Jacobsen, Staff (Pomona)
Offered: Jointly; Fall semester at Pomona, Spring semester at HMC in alternate years
Description: 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: MATH115 HM or MATH180 HM

MATH184 HM  Graduate Partial Differential Equations
Credits: 3
Instructors: Bernoff, Castro, Jacobsen
Offered: Spring, alternate years
Description: 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.
Prerequisites: (MATH115 HM and MATH131 HM) or MATH180 HM; recommended MATH132 HM

MATH185 HM  Introduction to Wavelets and Their Applications
Credits: 2
Instructor: Staff
Description: An introduction to the mathematical theory of wavelets, with applications to signal processing, data compression, and other areas of science and engineering.
Prerequisites: MATH115 HM or MATH180 HM

MATH187 HM  Operations Research
Credits: 3
Instructors: Benjamin, Martonosi, Staff (CMC), Staff (Pomona)
Offered: Fall
Description: Linear, integer, nonlinear and dynamic programming, classical optimization problems, and network theory.
Prerequisites: MATH040 HM or MATH073 HM

MATH188 HM  Social Choice and Decision Making
Credits: 3
Instructor: Su
Offered: Spring, alternate years
Description: Basic concepts of game theory and social choice theory, representations of games, Nash equilibria, utility theory, noncooperative games, cooperative games, voting games, paradoxes, Arrow's impossibility theorem, Shapley value, power indices, "fair division" problems and applications.
Corequisites: MATH030B HM or MATH030G HM; MATH055 HM recommended

MATH189 HM  Special Topics in Mathematics
Credit: 13
Instructor: Staff
Description: A course devoted to exploring topics of current interest to faculty or students. Recent topics have included: Algebraic Geometry, Algebraic Topology, Convexity, Games and Gambling, Logic, Numerical Linear Algebra, and Mathematics of Big Data.
Prerequisites: Dependent on topic

MATH193 HM  Mathematics Clinic
Credits: 3
Instructors: Bernoff, Castro, de Pillis, Gu, Martonosi, Williams
Offered: Fall and Spring
Description: 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, realworld 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. Students are expected to take the two semesters of Clinic within a single academic year.

MATH196 HM  Independent Study in Mathematics
Credit: 13
Instructor: Staff
Offered: Fall and Spring
Description: Readings in special topics.
Prerequisites: Permission of department or instructor

MATH197 HM  Senior Thesis in Mathematics
Credits: 3
Instructor: Staff
Offered: Fall and Spring
Description: 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

MATH198 HM  Undergraduate Mathematics Forum
Credit: 1
Instructors: Castro, Jacobsen, Orrison, Yong
Offered: Fall and Spring
Description: 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. Required for all majors; recommended for all joint CSmath majors and mathematical biology majors, typically in the junior year.

MATH199 HM  Mathematics Colloquium
Credit: 0.5
Instructors: Benjamin, Jacobsen, Su
Offered: Fall and Spring
Description: 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. No more than 2.0 credits can be earned for departmental seminars/colloquia.

MCBI117 HM  Game Theory and the Evolution of Cooperation
Credits: 3
Instructor: DonaldsonMatasci (Biology)
Offered: Fall, alternate years
Description: An introduction to game theory, a branch of mathematics that studies strategic interactions between individuals, with applications in fields such as biology, economics and political science. The course will introduce classical game theory, representations of games and Nash equilibria. The second part of the course will focus on evolutionary game theory, equilibrium concepts, and the evolution of cooperation.
Prerequisites: MATH035 HM or AP Statistics

MCBI118A HM  Introduction to Mathematical Biology
Credits: 1.5
Instructors: Adolph (Biology), de Pillis (Mathematics), Jacobsen (Mathematics)
Offered: Spring
Description: 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: (MATH065 HM or (MATH073 HM and MATH082 HM)) and BIOL052 HM

MCBI118B HM  Introduction to Computational Biology
Credits: 1.5
Instructors: Bush (Biology), DonaldsonMatasci (Biology), LibeskindHadas (Computer Science), Wu (Computer Science)
Offered: Spring
Description: 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: (CSCI005 HM or CSCI005GR HM) and BIOL052 HM

MCBI199 HM  Joint Colloquium for the Mathematical and Computational Biology Major
Credit: 0.5
Instructor: Staff
Offered: Fall and Spring
Description: Students registered for joint colloquium must attend a fixed number of colloquium talks during the semester in any field(s) related to their interests. The talks may be at any members of The Claremont Colleges or a nearby university and may be in any of a wide array of fields including biology, mathematics, computer science and other science and engineering disciplines including bioengineering, cognitive science, neuroscience, biophysics, and linguistics. Students enrolled in the joint colloquium are required to submit a short synopsis of each talk that they attend. No more than 2.0 credits can be earned for departmental seminars/colloquia.