2018-2019 Catalog [ARCHIVED PUBLICATION] Use the dropdown above to select the current catalog.
Mathematics Courses
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Department of Mathematics
Mathematics
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MATH015 HM - Application and Art of Calculus
Credit(s): 0.5
Instructor(s): Karp, Omar, Williams.
Offered: Fall, first half
Description: 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 Harvey Mudd Core. Students work in groups and solve calculus problems with an emphasis on applications to the sciences.
Prerequisite(s): First-year students only
Corequisite(s): MATH030B HM or MATH030G HM
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MATH030B HM - Calculus
Credit(s): 1.5
Instructor(s): Benjamin, de Pillis, Karp, Levy, 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.
Prerequisite(s): Mastery of single-variable calculus—entry by department placement only
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MATH030G HM - Calculus
Credit(s): 1.5
Instructor(s): Benjamin, de Pillis, Karp, Levy, 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.
Prerequisite(s): One year of calculus at the high school level
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MATH035 HM - Probability and Statistics
Credit(s): 1.5
Instructor(s): 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.
Prerequisite(s): MATH030B HM or MATH030G HM
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MATH040 HM - Introduction to Linear Algebra
Credit(s): 1.5
Instructor(s): 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.
Prerequisite(s): One year of calculus at the high school level
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MATH045 HM - Introduction to Differential Equations
Credit(s): 1.5
Instructor(s): Bernoff, Castro, de Pillis, Jacobsen, Levy, Su, Yong
Offered: Spring, second half
Description: 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.
Prerequisite(s): MATH030B HM or MATH030G HM
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MATH055 HM - Discrete Mathematics
Credit(s): 3
Instructor(s): 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.
Corequisite(s): MATH040 HM
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MATH055A HM - Topics in Discrete Mathematics
Credit(s): 1
Instructor(s): 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.
Prerequisite(s): By permission only
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MATH060 HM - Multivariable Calculus
Credit(s): 1.5
Instructor(s): Bernoff, Castro, Gu, Karp, Levy, 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; 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.
Prerequisite(s): (MATH030B HM or MATH030G HM ) and MATH040 HM
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MATH065 HM - Differential Equations and Linear Algebra II
Credit(s): 1.5
Instructor(s): Bernoff, Castro, Jacobsen, Levy, 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.
Prerequisite(s): MATH040 HM and MATH045 HM
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MATH070 HM - Intermediate Linear Algebra
Credit(s): 1.5
Instructor(s): 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, inner-product spaces, spectral theorems, Jordan Canonical Form, singular value decomposition, and others as time permits.
Prerequisite(s): MATH065 HM
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MATH080 HM - Intermediate Differential Equations
Credit(s): 1.5
Instructor(s): Bernoff, Castro, de Pillis, Jacobsen, Levy
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 differential equations. Topics include Existence and Uniqueness, Power Series and Frobenius Series Methods, Laplace Transform, and additional topics as time permits.
Prerequisite(s): MATH065 HM
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MATH092 HM - Mathematical Contest in Modeling/Interdisciplinary Contest in Modeling Seminar
Credit(s): 1
Instructor(s): 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.
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MATH093 HM - Putnam Seminar
Credit(s): 1
Instructor(s): 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.
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MATH094 HM - Problem Solving Seminar
Credit(s): 1
Instructor(s): 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.
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MATH104 HM - Graph Theory
Credit(s): 3
Instructor(s): 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.
Prerequisite(s): MATH040 HM and MATH055 HM
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MATH106 HM - Combinatorics
Credit(s): 3
Instructor(s): 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.
Prerequisite(s): MATH055 HM
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MATH108 PZ - History of Mathematics
Credit(s): 3
Instructor(s): 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.
Prerequisite(s): MATH030B HM or MATH030G HM
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MATH109 CM - Introduction to the Mathematics of Finance
Credit(s): 3
Instructor(s): Staff (CMC)
Offered: Alternate years
Description: 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.
Prerequisite(s): MATH065 HM
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MATH115 HM - Fourier Series and Boundary Value Problems
Credit(s): 3
Instructor(s): Bernoff, Levy, 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; 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 MATH180 HM .
Prerequisite(s): MATH065 HM
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MATH119 HM - Advanced Mathematical Biology
Credit(s): 3
Instructor(s): de Pillis, Jacobsen, Levy, 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. (Crosslisted as BIOL119 HM )
Prerequisite(s): MCBI118A HM and MCBI118B HM
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MATH131 HM - Mathematical Analysis I
Credit(s): 3
Instructor(s): 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.
Prerequisite(s): MATH055 HM
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MATH132 HM - Mathematical Analysis II
Credit(s): 3
Instructor(s): 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.
Prerequisite(s): MATH131 HM
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MATH136 HM - Complex Variables and Integral Transforms
Credit(s): 3
Instructor(s): Gu, Jacobsen, Karp, Yong
Offered: Fall
Description: 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.
Prerequisite(s): MATH065 HM
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MATH137 HM - Graduate Analysis I
Credit(s): 3
Instructor(s): Castro, Staff (Pomona), Staff (CMC)
Offered: Fall
Description: Abstract Measures, Lebesgue measure, and Lebesgue-Stieltjes measures on R; Lebesgue integral and limit theorems; product measures and the Fubini theorem; additional topics. (Crosslisted as MATH331 CG)
Prerequisite(s): MATH132 HM
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MATH138 HM - Graduate Analysis II
Credit(s): 3
Instructor(s): Castro, Omar, Staff (Pomona), Staff (CMC)
Offered: Spring
Description: Banach and Hilbert spaces; Lp spaces; complex measures and the Radon-Nikodym theorem. (Crosslisted as MATH332 CG)
Prerequisite(s): MATH137 HM or MATH331 CG
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MATH142 HM - Differential Geometry
Credit(s): 3
Instructor(s): 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).
Prerequisite(s): MATH065 HM
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MATH143 HM - Seminar in Differential Geometry
Credit(s): 3
Instructor(s): 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.
Prerequisite(s): MATH131 HM and MATH142 HM ; MATH147 HM recommended
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MATH147 HM - Topology
Credit(s): 3
Instructor(s): 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 “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.
Prerequisite(s): MATH131 HM
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MATH148 PZ - Knot Theory
Credit(s): 3
Instructor(s): 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, 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.
Prerequisite(s): MATH040 HM
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MATH152 HM - Statistical Theory
Credit(s): 3
Instructor(s): 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.
Prerequisite(s): MATH 157 HM
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MATH153 HM - Bayesian Statistics
Credit(s): 3
Instructor(s): 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.
Prerequisite(s): MATH035 HM
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MATH155 HM - Time Series
Credit(s): 3
Instructor(s): 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.
Prerequisite(s): MATH035 HM
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MATH156 HM - Stochastic Processes
Credit(s): 3
Instructor(s): Benjamin, Martonosi, Staff (CMC)
Offered: Jointly; Fall, alternate years at HMC
Description: 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.
Prerequisite(s): MATH040 HM and MATH157 HM
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MATH157 HM - Intermediate Probability
Credit(s): 2
Instructor(s): Benjamin, Martonosi, Pippenger, Su, Williams
Offered: Fall and Spring, first half
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 central-limit theorem.
Prerequisite(s): MATH035 HM
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MATH158 HM - Statistical Linear Models
Credit(s): 3
Instructor(s): 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 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.
Prerequisite(s): MATH035 HM
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MATH161 HM - Introduction to Environmental and Spatial Statistics
Credit(s): 3
Instructor(s): Srebotnjak
Description: 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.
Prerequisite(s): MATH035 HM
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MATH164 HM - Scientific Computing
Credit(s): 3
Instructor(s): Bernoff, de Pillis, Levy, 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 fast-Fourier transforms. (Crosslisted as CSCI144 HM )
Prerequisite(s): MATH065 HM and CSCI060 HM
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MATH165 HM - Numerical Analysis
Credit(s): 3
Instructor(s): Bernoff, Castro, de Pillis, Levy, 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 non-linear equations, interpolation, approximate integration (quadrature), and numerical solutions to ordinary differential equations.
Prerequisite(s): MATH065 HM
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MATH167 HM - Complexity Theory
Credit(s): 3
Instructor(s): Pippenger, Libeskind-Hadas (Computer Science), Staff (Pomona)
Offered: Fall
Description: Specific topics include finite automata, pushdown automata, Turing machines, and their corresponding languages and grammars; undecidability; complexity classes, reductions, and hierarchies. (Crosslisted as CSCI142 HM )
Prerequisite(s): (CSCI060 HM or CSCI042 HM ) and MATH055 HM
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MATH168 HM - Algorithms
Credit(s): 3
Instructor(s): Pippenger, Sweedyk (Computer Science), Libeskind-Hadas (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 pattern-matching. (Crosslisted as CSCI140 HM )
Prerequisite(s): (CSCI070 HM and CSCI081 HM ) or ((CSCI060 HM or CSCI042 HM ) and MATH131 HM ))
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MATH171 HM - Abstract Algebra I
Credit(s): 3
Instructor(s): 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.
Prerequisite(s): MATH040 HM and MATH055 HM
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MATH172 HM - Abstract Algebra II: Galois Theory
Credit(s): 3
Instructor(s): 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.
Prerequisite(s): MATH171 HM
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MATH173 HM - Advanced Linear Algebra
Credit(s): 3
Instructor(s): de Pillis, Gu, Orrison
Offered: Jointly in alternate years
Description: 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.
Prerequisite(s): MATH131 HM
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MATH174 HM - Abstract Algebra II: Representation Theory
Credit(s): 3
Instructor(s): 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.
Prerequisite(s): MATH171 HM
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MATH175 HM - Number Theory
Credit(s): 3
Instructor(s): 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.
Prerequisite(s): MATH055 HM
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MATH176 HM - Algebraic Geometry
Credit(s): 3
Instructor(s): 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.
Prerequisite(s): MATH171 HM ; Previous courses in Analysis, Galois Theory, Differential Geometry, and Topology are recommeneded
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MATH180 HM - Introduction to Partial Differential Equations
Credit(s): 3
Instructor(s): Bernoff, Castro, de Pillis, Jacobsen, Levy
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; Sturm-Liouville theory and orthogonal expansions; Bessel functions.
Prerequisite(s): MATH080 HM and MATH131 HM
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MATH181 HM - Dynamical Systems
Credit(s): 3
Instructor(s): Bernoff, de Pillis, Jacobsen, Levy, 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.
Prerequisite(s): MATH115 HM or MATH180 HM
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MATH184 HM - Graduate Partial Differential Equations
Credit(s): 3
Instructor(s): Bernoff, Castro, Jacobsen, Levy
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.
Prerequisite(s): (MATH115 HM and MATH131 HM ) or MATH180 HM ; recommended MATH132 HM
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MATH185 HM - Introduction to Wavelets and Their Applications
Credit(s): 2
Instructor(s): Staff
Description: An introduction to the mathematical theory of wavelets, with applications to signal processing, data compression, and other areas of science and engineering.
Prerequisite(s): MATH115 HM or MATH180 HM
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MATH187 HM - Operations Research
Credit(s): 3
Instructor(s): Benjamin, Martonosi, Staff (CMC), Staff (Pomona)
Offered: Fall
Description: Linear, integer, non-linear and dynamic programming, classical optimization problems, and network theory.
Prerequisite(s): MATH040 HM
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MATH188 HM - Social Choice and Decision Making
Credit(s): 3
Instructor(s): Su
Offered: Spring, alternate years
Description: 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.
Corequisite(s): MATH030B HM or MATH030G HM ; MATH055 HM recommended
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MATH189 HM - Special Topics in Mathematics
Credit(s): 1-3
Instructor(s): Staff
Description: 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.
Prerequisite(s): Dependent on topic
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MATH193 HM - Mathematics Clinic
Credit(s): 3
Instructor(s): Bernoff, Castro, de Pillis, Gu, Levy, 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, 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. Students are expected to take the two semesters of Clinic within a single academic year.
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MATH196 HM - Independent Study in Mathematics
Credit(s): 1-3
Instructor(s): Staff
Offered: Fall and Spring
Description: Readings in special topics.
Prerequisite(s): Permission of department or instructor
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MATH197 HM - Senior Thesis in Mathematics
Credit(s): 3
Instructor(s): 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.
Prerequisite(s): Permission of department
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MATH198 HM - Undergraduate Mathematics Forum
Credit(s): 1
Instructor(s): Castro, Jacobsen, Levy, 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 CS-math majors and mathematical biology majors, typically in the junior year.
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MATH199 HM - Mathematics Colloquium
Credit(s): 0.5
Instructor(s): 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.
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