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Course Descriptions

 

Engineering
  

  • ENGR164 HM - Introduction to Biomedical Engineering

    Credit(s): 3

    Orwin. The application of engineering principles to help pose and solve problems in medicine and biology. Focus on different aspects, particularly biomedical measurements, biosystems analysis, biomechanics, and biomaterials. (Spring, alternate years)

  

  • ENGR166 HM - High-Speed PC Board Design

    Credit(s): 3

    Staff. This course provides the student exposure to fundamental and practical issues in the design and fabrication of printed circuit boards (PCBs), with primary emphasis on boards for high-speed digital circuits. Students work in teams to design a high-speed PCB, which can then be fabricated and subsequently tested by the students. Upon completing this course, students should be able to use appropriate CAD tools to capture a circuit schematic, choose a board cross-section, place components on a board and route wiring. Further, the course should enable students to recognize when circuit speed/size combinations are likely to make “high-speed effects” such as reflections and cross talk important, to know how to quantify these effects and their impact on performance, and to design their boards to reduce the deleterious effects to an acceptable level. (Spring, alternate years)

    Prerequisite(s): ENGR084 HM  and (ENGR085 HM  or ENGR085A HM )
  

  • ENGR168A HM - Introduction to Fiber Optic Communication Systems

    Credit(s): 3

    Yang. This course provides the fundamentals of optics and its applications in communication systems. The physical layer of optical communication systems will be emphasized. Topics include optical materials; dispersion and nonlinear effects; polarization and interference; and the basic elements of system implementation such as laser sources, optical amplifiers, and optical detectors. The course will include a multiple channel system design. (Spring, alternate years)

  

  • ENGR171 HM - Dynamics of Elastic Systems

    Credit(s): 3

    Cha, Durón. Free and forced response of single-degree-of-freedom systems. Eigenvalue problem for multi-degree-of-freedom systems; natural modes of free vibration. Forced response of un­damped and viscously damped, multi-degree-of-freedom systems by modal analysis. (Fall)

    Prerequisite(s): ENGR083 HM  
  

  • ENGR172 HM - Structural Mechanics

    Credit(s): 3

    Bassman, Cha. Introduction to elementary structural systems: trusses, beams. Force and deflection analysis. Energy methods. Stability. Introduction to finite element methods. (Spring)

    Prerequisite(s): ENGR083 HM  
  

  • ENGR173 HM - Applied Elasticity

    Credit(s): 3

    Staff. Introduction to the concepts of stress and strain. Application to the theory of bending and torsion. Topics in elementary elasticity. (Fall, alternate years)

    Prerequisite(s): ENGR083 HM  
  

  • ENGR174 HM - Practices in Civil Engineering

    Credit(s): 3

    Little, Cardenas. The student is exposed to the practice of civil engineering through a series of case studies discussed within the context of a broad-based engineering curriculum. Engineering fundamentals related to the selection and use of construction materials, stress and strain, and to the analysis and design of structural and transportation systems may be discussed. Types and specifics of case studies vary depending upon the instructor. (Spring, alternate years)

    Prerequisite(s): ENGR059 HM , ENGR080 HM , and permission of instructor
  

  • ENGR175 HM - Dynamics of Rigid Bodies

    Credit(s): 3

    Bassman. Kinematics, mass distribution, and kinetics of systems of particles and rigid bodies. Formulation of equations of motion with: Newton/Euler equations; angular momentum prin­ciple; power, work and energy methods. Numerical solutions of nonlinear algebraic and ordinary differential equations governing the behavior of multiple degree of freedom systems. Computer simulation of multi-body dynamic systems. Construction of physical systems for comparison with simulation. (Fall)

    Corequisite(s): ENGR083 HM  
  

  • ENGR176 HM - Numerical Methods in Engineering

    Credit(s): 3

    Cha, Wang. This course focuses on the application of a variety of mathematical techniques to solve real-world problems that involve modeling, mathematical and numerical analysis, and scientific computing. Concepts, calculations and the ability to apply principles to physical prob­lems are emphasized. Ordinary differential equations, linear algebra, complex analysis, numerical methods, partial differential equations, probability and statistics, etc., are among the techniques that would be applied to problems in mechanical, electrical, chemical and civil engineering. Examples are drawn from fluid mechanics, heat transfer, vibration of structures, electromagnet­ics, communications and other applied topics. Program development and modification are expected as well as learning to use existing code. (Spring, alternate years)

    Prerequisite(s): ENGR072 HM  
  

  • ENGR179 HM - Deformation and Fracture of Solids

    Credit(s): 3

    Staff. Elements of stress and strain, elastic and plastic deformations of solid materials, fracture mechanics, strengthening mechanisms, thermal and thermo-mechanical processing, effects of microstructure, failure modes and analysis of service failures. (Fall, alternate years)

    Prerequisite(s): ENGR083 HM  and ENGR106 HM  
  

  • ENGR181 HM - New Product Development

    Credit(s): 3

    Krauss. This course will introduce the theory and practice of a process used for new product development that considers design, management and manufacturing components. Students will identify needs (market or humanitarian) amenable to an engineered product solution, select and scope the project need they will address, quantify the impact of a solution through a business case, design and develop multiple prototype solutions, validate the resulting product and solicit funding for a launch. (Spring)

    Prerequisite(s): ENGR004 HM  
  

  • ENGR182 HM - Manufacturing Planning and Execution

    Credit(s): 3

    Gokli. This course provides a fundamental understanding of manufacturing and focuses on “practical” elements of how factories are laid out, how they are optimized and how they are man­aged and measured. It introduces students to the vocabulary, processes and tools of manufactur­ing with hands-on experience. This course is designed to have one class of lectures followed by a class of hands-on exercises to effectively internalize the knowledge. The course teaches three main learning modules: shop floor management, quality management and supply chain management. (Spring)

    Prerequisite(s): ENGR004 HM  
  

  • ENGR183 HM - Management of Technical Enterprise

    Credit(s): 3

    Gokli, Little, Krauss. This course provides a fundamental understanding of management practices in a technical enterprise. Instructors teach three main learning modules: financial management, people management and company management. Students will learn processes, tools, organiza­tion and measurables in all three learning modules. (Fall)

    Prerequisite(s): ENGR004 HM  
  

  • ENGR190 HM - Special Topics in Engineering

    Credit(s): 3

    Staff. An upper division or graduate technical elective treating topics in engineering not covered in other courses, chosen at the discretion of the engineering department.

  

  • ENGR191 HM - Advanced Problems in Engineering

    Credit(s): 1-3

    Staff. Independent study in a field agreed upon by student and instructor. Credit hours to be arranged.

  

  • ENGR205 HM - Systems Simulation

    Credit(s): 3

    Bright. An examination of the use of high-speed digital computers to simulate the behavior of engineering and industrial systems. Both continuous and discrete systems are treated. (Fall)

    Prerequisite(s): ENGR101 HM  and ENGR102 HM  
  

  • ENGR206 HM - Optimization Techniques in Engineering Design

    Credit(s): 3

    Bright. Presentation of techniques for making optimum choices among alternatives; applications to engineering design problems. (Spring)

    Prerequisite(s): ENGR205 HM  
  

  • ENGR231 HM - Advanced Transport Phenomena

    Credit(s): 3

    Bright, Lape. Integrated approach to the subjects of fluid mechanics, heat transfer, and mass transfer, through the study of the governing equations common to all three fields. Applications drawn from a wide variety of engineering systems. (Spring)

    Prerequisite(s): ENGR131 HM  
  

  • ENGR240 HM - Introduction to Compressible Flow

    Credit(s): 3

    Cardenas. The effects of compressibility in the governing integral and differential equations for fluids. The effects of friction, heating and shock waves in steady one-dimensional flow. Unsteady wave motion and the method of characteristics. Two-dimensional flow over air foils, linearized potential flow and the method of characteristics for supersonic flow. (Spring, alternate years)

    Prerequisite(s): ENGR131 HM  
  

  • ENGR278 HM - Advanced Structural Dynamics

    Credit(s): 3

    Cha. Free and forced response of continuous systems, including the vibration of strings, rods, shafts, membranes, beams, and plates. One dimensional finite element methods: discretization of a continuum, selection of interpolation functions, and determining the element mass and stiffness matrices and the corresponding load vector. Introduction to special topics, including the effects of parameter uncertainties on the dynamics of periodic structures and model updating in structural dynamics. (Spring, alternate years)

    Prerequisite(s): ENGR171 HM  

Global Clinic

Students participating in Global Clinic register for the specific Clinic courses noted below, rather than the departmental Clinic course numbers in engineering, computer science, joint computer science/math, math or physics.
  

  • GLBL183 HM - Global Clinic

    Credit(s): 3

    DePillis, staff. Global Clinic is a yearlong commitment involving Harvey Mudd students and overseas collaborators, working together to find solutions to problems with international impact. Depending on the project, the Clinic team could be interdisciplinary. Permission to enroll is granted through an application process. Students from all Harvey Mudd departments are eligible to enroll; course may be substituted for the departmental Clinic course, as part of the application process required to enroll. (Fall)

  

  • GLBL184 HM - Global Clinic

    Credit(s): 3

    DePillis, staff. Global Clinic is a yearlong commitment involving Harvey Mudd students and overseas collaborators, working together to find solutions to problems with international impact. Depending on the project, the Clinic team could be interdisciplinary. Permission to enroll is granted through an application process. Students from all Harvey Mudd departments are eligible to enroll; course may be substituted for the departmental Clinic course, as part of the application process required to enroll. (Spring)


History
  

  • HIST081 HM - Science and Technology in the Early Modern World

    Credit(s): 3

    Hamilton. We will read works of natural philosophy from the 16th and 17th centuries, including selections by Vesalius, Copernicus, Galileo, Boyle, and Newton, individuals who have often been cast as crucial contributors to “The Scientific Revolution.” Engaging with historians who debate the merits of this term, we will ask whether it is possible to unite these figures and the changes they represent into one coherent intellectual and social movement.

  

  • HIST082 HM - Science and Technology in the Modern World

    Credit(s): 3

    Hamilton. An examination of several important episodes in the history of chemistry, biology, physics, and medicine from the late 18th to mid-20th centuries. We will pay particular attention to the ways in which new scientific theories have been developed and evaluated, to the impact of cultural beliefs about gender and race on science, and to fundamental debates within science and medicine about what counts as good evidence and proper methodology.

  

  • HIST127 HM - Twentieth-Century U.S. History

    Credit(s): 3

    Barron. An analysis of U.S. history from the Progressive Era to the present, with particular em­phasis on social, economic, and cultural developments and their relationships to political change.

  

  • HIST128 HM - Immigration, Ethnicity, and Race in the U. S.

    Credit(s): 3

    Barron. A study of the experiences of different ethnic groups in the U.S. from the colonial period to the present that addresses the meanings of cultural diversity in American history.

  

  • HIST131 HM - The Jewish Experience in America

    Credit(s): 3

    Barron. A consideration of the interactions between Jews and American society from the colonial period to the present. Topics include Anti-Semitism, American responses to the Holocaust, the United States and Israel, Black-Jewish relations, and the meanings of Jewish identity in contem­porary America.

  

  • HIST133 HM - Food and American Culture

    Credit(s): 3

    Barron. This course investigates the social and cultural history of food in the United States. In many ways food is the quintessential “dense social fact,” and its production and consump­tion embody many different layers of meaning. Consequently, one of the main goals of the course is to be able to look at food in a more critical, self-conscious, and theoretically and historically informed way-to problematize something that is so prosaic that we often take it for granted.

  

  • HIST150 HM - Technology and Medicine

    Credit(s): 3

    Hamilton. This course explores the increasingly technological nature of medicine in the 19th and 20th centuries, investigating the impact of new technologies on diagnostic practices, categories of disease, doctors’ professional identities, and patients’ understanding of their own bodies. Technologies studied include the stethoscope, electrotherapy devices, X-rays, ultrasound, and MRI.

  

  • HIST151 HM - Science in Fiction

    Credit(s): 3

    Hamilton. In this course, we will explore fictional texts as historical documents. Together, we will read novels from the 19th and 20th centuries in which the practice of science is central to the story being told, asking what each text reveals about cultural attitudes towards science in that time period. In addition, each student will pursue a historical research project centered on a fictional source of his or her choice.

  

  • HIST152 HM - A History of Modern Physics

    Credit(s): 3

    Hamilton. An examination of the cultural and social worlds of physics in the 19th and 20th centuries. Topics include the relationship of experiment to theory, the development of relativity and quantum mechanics, the role of physicists in the atomic bomb project, and the experiences of women in physics.

    Prerequisite(s): One college-level course in physics.

Humanities, Social Sciences, and the Arts
  

  • HSA010 HM - Critical Inquiry

    Credit(s): 3

    Staff. This seminar course introduces students to inquiry, writing, and research in HSA, through focused exploration of a particular topic selected by the instructor in each section. To encourage reflection on the place of HSA within the Harvey Mudd curriculum, the course begins with a brief unit on the history and aims of liberal arts education. Writing assignments include a sub­stantial research paper on a topic of interest chosen by the student in consultation with her or his instructor. The course ends with student research presentations in each section, followed by a Presentations Days event featuring the best presentations from across all sections. (Spring)

    Prerequisite(s): WRIT001 HM  
    Corequisite(s): WRIT001E HM  may serve as a co-requisite

Integrative Experience

The founders of the College held that “technology divorced from humanity is worse than no technology at all.” IE courses may be offered by any academic department, and they are frequently team-taught.
  

  • IE142 HM - Seminar in Mathematics and Science Education

    Credit(s): 3

    Levy and Yong (Mathematics), Dodds (Computer Science). 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?” “How does math and science education impact our society?” (Fall or Spring)

  

  • IE144 HM - Mathematics, Music, Art: Cosmic Harmony

    Credit(s): 3

    Orrison (Mathematics), Alves (Humanities, Social Sciences, and the Arts). 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. (Fall or Spring)

  

  • IE179 HM - Special Topics in Integrative Studies

    Credit(s): 3

    Staff. Course will consider issues of current importance to society.


Literature
  

  • LIT103 HM - Third Cinema

    Credit(s): 3

    Balseiro. Emerging in Latin America in the 1960s and 1970s, the notion of Third Cinema takes its inspiration from the Cuban revolution and from Brazil’s Cinema Novo. Third Cinema is the art of political film making and represents an alternative cinematic practice to that offered by mainstream film industries. Explores the aesthetics of film making from a revolutionary consciousness in three regions: Africa, Asia, and Latin America.

  

  • LIT104 HM - An Introduction to Middle English Literature

    Credit(s): 3

    Groves. A course for students interested in developing a basic ability to translate and pronounce Middle English. Works studied will include: the first fragment of Chaucer’s “The Canterbury Tales”; “Sir Orfeo”; “Sir Gawain and the Green Knight”; and selections from Malory’s “Le Morte D’Arthur.”

  

  • LIT105 HM - The Land and American Literature

    Credit(s): 3

    Groves. Explores how landscape is depicted in American literary texts and the relationship between those texts and other modes of representation (painting, cartography, photography, and film).

  

  • LIT110 HM - Shakespeare

    Credit(s): 3

    Groves. Covers selected dramatic and lyric works by Shakespeare with some attention to other Elizabethan and Jacobean writers. Final project: a public performance of a Shakespeare play.

  

  • LIT117A HM - Dickens, Hardy, and the Victorian Age

    Credit(s): 4

    Groves, Eckert. An intensive study of the work and literary development of Charles Dickens and Thomas Hardy. Readings drawn from the authors’ works and related critical, biographi­cal, and historical texts. Class travels to England over winter break; travel expenses are the responsibility of the student. (Fall and winter break)

    Prerequisite(s): Permission of instructor.
  

  • LIT144 HM - Poe Goes South: the Fantastic Short Story

    Credit(s): 3

    Balseiro. A consideration of Poe’s influence on the development of the fantastic short story in Latin America. Topics include: Poe’s reception in Europe and in the Southern Cone, Poe’s influence in the literature of magic realism in 20th-century Latin America.

  

  • LIT145 HM - Third-World Women Writers

    Credit(s): 3

    Balseiro. Focuses on the relationships between gender and identity in the writings of Third-World women as well as theoretical background on Third-World feminisms. Authors include Nawal El Saadawi, Alifa Rifaat, Mariama Ba, Bessie Head, Ana Lydia Vega, and Jamaica Kincaid.

  

  • LIT146 HM - Twentieth-Century South African Literature

    Credit(s): 3

    Balseiro. An introduction to the interactions between literature, politics, and history in 20th-century South Africa. Readings include drama, poetry, fiction, and biography, and viewings include several films and documentaries.

  

  • LIT147 HM - Writers From Africa and the Caribbean

    Credit(s): 3

    Balseiro. An examination of the themes of nation, exile, race, and gender in works by Chinua Achebe, Wole Soyinka, Ayi Jwei Armah, Yusuf Idriss, Ngugi wa Thiong’o, Nadine Gordimer, George Lamming, Jean Rhys, and Rosario Ferre, among others. Theoretical background on Third-World literature will also be covered.

  

  • LIT155 HM - Post-Apartheid Narratives

    Credit(s): 3

    Balseiro. This seminar maps the literary terrain of contemporary South Africa. Through an examination of prose, poetry, and visual material, this course offers some of the responses writers have given to the end of apartheid, to major social events such as the hearings of the Truth and Reconciliation Commission, and to the idea of a “new” South Africa.


Mathematics

(Includes mathematics courses frequently taken by HMC students at the other Claremont Colleges)
  

  • MATH015 HM - Application and Art of Calculus

    Credit(s): 0.5

    Davis, Karp, Omar, Williams. 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. (Fall, first half)

    Prerequisite(s): First-year students only
    Corequisite(s): MATH030B HM  or MATH030G HM  
  

  • MATH030B HM - Calculus

    Credit(s): 1.5

    Benjamin, de Pillis, Karp, Levy, Omar, Orrison, Su. 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. (Fall, first half)

    Prerequisite(s): Mastery of single-variable calculus—entry by department placement only
  

  • MATH030G HM - Calculus

    Credit(s): 1.5

    Benjamin, de Pillis, Karp, Levy, Orrison, Su. 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. (Fall, first half)

    Prerequisite(s): One year of calculus at the high school level
  

  • MATH035 HM - Probability and Statistics

    Credit(s): 1.5

    Benjamin, Martonosi, Omar, Orrison, Su, Williams. 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. (Fall, second half)

    Prerequisite(s): MATH030B HM  or MATH030G HM  
  

  • MATH040 HM - Introduction to Linear Algebra

    Credit(s): 1.5

    Benjamin, de Pillis, Gu, Martonosi, Omar, Orrison, Pippenger, Su, Yong. 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. (Spring, first half)

    Prerequisite(s): One year of calculus at the high school level
  

  • MATH045 HM - Introduction to Differential Equations

    Credit(s): 1.5

    Bernoff, Castro, de Pillis, Jacobsen, Levy, Su, Yong. 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. (Spring, second half)

    Prerequisite(s): MATH030B HM  or MATH030G HM  
  

  • MATH055 HM - Discrete Mathematics

    Credit(s): 3

    Benjamin, Bernoff, Orrison, Pippenger. 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. (Fall and Spring)

    Corequisite(s): MATH040 HM  
  

  • MATH060 HM - Multivariable Calculus

    Credit(s): 1.5

    Bernoff, Castro, Gu, Karp, Levy, Omar, Orrison, Su, Yong. 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. (Fall, first half, and summer)

    Prerequisite(s): (MATH030B HM  or MATH030G HM ) and MATH040 HM  
  

  • MATH065 HM - Differential Equations and Linear Algebra II

    Credit(s): 1.5

    Bernoff, Castro, Jacobsen, Levy, Martonosi. 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. (Fall, second half, and summer)

    Prerequisite(s): MATH040 HM  and MATH045 HM  
  

  • MATH070 HM - Intermediate Linear Algebra

    Credit(s): 1.5

    de Pillis, Omar, Orrison. 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. (Spring, first half)

    Prerequisite(s): MATH065 HM  
  

  • MATH080 HM - Intermediate Differential Equations

    Credit(s): 1.5

    Bernoff, Castro, de Pillis, Jacobsen, Levy. 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. (Spring, first half)

    Prerequisite(s): MATH065 HM  
  

  • MATH092 HM - Mathematical Contest in Modeling/Interdisciplinary Contest in Modeling Seminar

    Credit(s): 1

    Martonosi. 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. (Fall)

  

  • MATH093 HM - Putnam Seminar

    Credit(s): 1

    Bernoff, Omar, Pippenger, Su. 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. (Fall)

  

  • MATH094 HM - Problem Solving Seminar

    Credit(s): 1

    Bernoff, Omar. 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. (Spring)

  

  • MATH104 HM - Graph Theory

    Credit(s): 3

    Martonosi, Omar, Orrison, Pippenger. An introduction to graph theory with applications. Theory and applications of trees, matchings, graph coloring, planarity, graph algorithms, and other topics. (Alternate years)

    Prerequisite(s): MATH040 HM  and MATH055 HM  
  

  • MATH106 HM - Combinatorics

    Credit(s): 3

    Benjamin, Omar, Orrison, Pippenger. An introduction to the techniques and ideas of combinatorics, including counting methods, Stirling numbers, Catalan numbers, generating functions, Ramsey theory, and partially ordered sets. (Alternate years)

    Prerequisite(s): MATH055 HM  
  

  • MATH108 PZ - History of Mathematics

    Credit(s): 3

    Grabiner (Pitzer). 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. (Alternate years)

    Prerequisite(s): MATH030B HM  or MATH030G HM  
  

  • MATH109 CM - Introduction to the Mathematics of Finance

    Credit(s): 3

    Aksoy (CMC). 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. (Alternate years)

    Prerequisite(s): MATH065 HM  
  

  • MATH110 HM - Applied Mathematics for Engineering

    Credit(s): 1.5

    Levy, Yong, Bassman (Engineering). Applications of differential equations, linear algebra, and probability to engineering problems in multiple disciplines. Mathematical modeling, dimensional analysis, scale, approximation, model validation, Laplace Transforms. May not be included in a mathematics major program. (Spring, first half) (Also listed as ENGR072 HM )

    Prerequisite(s): MATH035 HM  and MATH065 HM  
  

  • MATH115 HM - Fourier Series and Boundary Value Problems

    Credit(s): 3

    Bernoff, Levy, Yong. 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 . (Spring)

    Prerequisite(s): MATH065 HM  
  

  • MATH119 HM - Advanced Mathematical Biology

    Credit(s): 2

    de Pillis, Jacobsen, Levy, Adolph (Biology). 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  
  

  • MATH131 HM - Mathematical Analysis I

    Credit(s): 3

    Castro, Karp, Omar, Su. 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. (Jointly; Fall semester at HMC and Pomona, Spring semester at HMC and CMC)

    Prerequisite(s): MATH055 HM  or MATH101 PO or MATH101 SC
  

  • MATH132 HM - Mathematical Analysis II

    Credit(s): 3

    Castro, Omar, Su, Radunskaya (Pomona). A rigorous study of calculus in Euclidean spaces including multiple Riemann integrals, derivatives of transformations, and the inverse function theorem. (Jointly; Fall semester at HMC, Spring semester at Pomona)

    Prerequisite(s): MATH131 HM  
  

  • MATH136 HM - Complex Variables and Integral Transforms

    Credit(s): 3

    Gu, Jacobsen, Karp, Yong. 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. (Fall)

    Prerequisite(s): MATH065 HM  
  

  • MATH137 HM - Graduate Analysis I

    Credit(s): 3

    Castro, Krieger, Grabiner (Pomona), O’Neill (CMC). Abstract Measures, Lebesgue measure, and Lebesgue-Stieltjes measures on R; Lebesgue integral and limit theorems; product measures and the Fubini theorem; additional topics. (Fall) (Crosslisted as MATH331 CG)

    Prerequisite(s): MATH132 HM  
  

  • MATH138 HM - Graduate Analysis II

    Credit(s): 3

    Castro, Krieger, Omar, Grabiner (Pomona), O’Neill (CMC). Banach and Hilbert spaces; Lp spaces; complex measures and the Radon-Nikodym theorem. (Spring) (Crosslisted as MATH332 CG)

    Prerequisite(s): MATH137 HM  or MATH331 CG
  

  • MATH142 HM - Differential Geometry

    Credit(s): 3

    Gu, Karp, Bachman (Pitzer). Curves and surfaces, Gauss curvature; isometries, tensor analy­sis, covariant differentiation with application to physics and geometry (intended for majors in physics or mathematics). (Fall)

    Prerequisite(s): MATH065 HM  
  

  • MATH143 HM - Seminar in Differential Geometry

    Credit(s): 3

    Gu. Selected topics in Riemannian geometry, low dimensional manifold theory, elementary Lie groups and Lie algebra, and contemporary applications in mathematics and physics. (Spring)

    Prerequisite(s): MATH131 HM  and MATH142 HM ; MATH147 HM  recommended
  

  • MATH147 HM - Topology

    Credit(s): 3

    Karp, Pippenger, Su, Flapan (Pomona). 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. (Jointly with Pomona; Spring semester)

    Prerequisite(s): MATH131 HM  
  

  • MATH148 PZ - Knot Theory

    Credit(s): 3

    Hoste (Pitzer). 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. (Alternate years)

    Prerequisite(s): MATH040 HM  
  

  • MATH152 HM - Statistical Theory

    Credit(s): 3

    Martonosi, Williams, Hardin (Pomona), Huber (CMC). An introduction to the general theory of statistical inference, including estimation of parameters, confidence intervals, and tests of hypotheses. (Jointly; Spring semester at Pomona and CMC)

    Prerequisite(s): MATH151 CM or MATH151  PO or MATH 157 HM  
  

  • MATH153 HM - Bayesian Statistics

    Credit(s): 3

    Williams. 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. (Spring, alternate years)

    Prerequisite(s): MATH035 HM  
  

  • MATH155 HM - Time Series

    Credit(s): 3

    Williams. 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. (Spring, alternate years)

    Prerequisite(s): MATH035 HM  
  

  • MATH156 HM - Stochastic Processes

    Credit(s): 3

    Benjamin, Martonosi, Huber (CMC). 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. (Jointly; Alternate Fall semester at HMC)

    Prerequisite(s): MATH040 HM  and (MATH151 PO or MATH151 CM or MATH157 HM )
  

  • MATH157 HM - Intermediate Probability

    Credit(s): 2

    Benjamin, Martonosi, Pippenger, Su, Williams. 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.  (Fall and Spring, first half )

    Prerequisite(s): MATH035 HM  
  

  • MATH158 HM - Statistical Linear Models

    Credit(s): 3

    Martonosi, Williams, Hardin (Pomona). 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. (Fall, alternate years)

    Prerequisite(s): MATH035 HM  
  

  • MATH164 HM - Scientific Computing

    Credit(s): 3

    Bernoff, de Pillis, Levy, Yong. 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. (Spring) (Crosslisted as CSCI144 HM )

    Prerequisite(s): MATH065 HM  and CSCI060 HM  
  

  • MATH165 HM - Numerical Analysis

    Credit(s): 3

    Bernoff, Castro, de Pillis, Levy, Pippenger, Yong. 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. (Fall)

    Prerequisite(s): MATH065 HM  
  

  • MATH167 HM - Complexity Theory

    Credit(s): 3

    Pippenger, Libeskind-Hadas (Computer Science), Bull (Pomona). Specific topics include finite automata, pushdown automata, Turing machines, and their corresponding languages and grammars; undecidability; complexity classes, reductions, and hierarchies. (Fall) (Crosslisted as CSCI142 HM )

    Prerequisite(s): (CSCI060 HM  or CSCI042 HM ) and MATH055 HM  
  

  • MATH168 HM - Algorithms

    Credit(s): 3

    Pippenger, Sweedyk (Computer Science), Libeskind-Hadas (Computer Science). 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. (Fall and Spring) (Crosslisted as CSCI140 HM )

    Prerequisite(s): MATH055 HM  and ((CSCI070 HM ; CSCI081 HM  recommended) or ((CSCI060 HM  or CSCI042 HM ) and MATH131 HM ))
  

  • MATH171 HM - Abstract Algebra I

    Credit(s): 3

    Benjamin, Karp, Omar, Orrison, Shahriari (Pomona), Sarkis (Pomona). 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. (Jointly; Fall semester at HMC and CMC, Spring semester at HMC and Pomona)

    Prerequisite(s): MATH040 HM  and MATH055 HM  
  

  • MATH172 HM - Abstract Algebra II: Galois Theory

    Credit(s): 3

    Karp, Omar, Orrison, Su, Shahriari (Pomona), Sarkis (Pomona). 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. (Jointly; Spring semester at HMC and Pomona)

    Prerequisite(s): MATH171 HM  
  

  • MATH173 HM - Advanced Linear Algebra

    Credit(s): 3

    de Pillis, Gu, Orrison. 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. (Jointly in alternate years)

    Prerequisite(s): MATH131 HM  
  

  • MATH174 HM - Abstract Algebra II: Representation Theory

    Credit(s): 3

    Karp, Omar, Orrison, Su. The topics covered will include group rings, characters, orthogonality relations, induced representations, applications of representation theory, and other select topics from module theory. (Jointly; Spring by HMC and Pomona)

    Prerequisite(s): MATH171 HM  
  

  • MATH175 HM - Number Theory

    Credit(s): 3

    Benjamin, Omar, Pippenger, Towse (Scripps). Properties of integers, congruences, Diophantine problems, quadratic reciprocity, number theoretic functions, primes. (Spring; offered jointly Fall semester at Scripps)

    Prerequisite(s): MATH055 HM  
  

  • MATH176 HM - Algebraic Geometry

    Credit(s): 3

    Karp, Omar. 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. (Fall, alternate years)

    Prerequisite(s): MATH171 HM ; Previous courses in Analysis, Galois Theory, Differential Geometry, and Topology are recommeneded
  

  • MATH180 HM - Introduction to Partial Differential Equations

    Credit(s): 3

    Bernoff, Castro, de Pillis, Jacobsen, Levy. 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. (Fall)

    Prerequisite(s): MATH080 HM  and MATH131 HM  
  

  • MATH181 HM - Dynamical Systems

    Credit(s): 3

    Bernoff, de Pillis, Jacobsen, Levy, Radunskaya (Pomona). 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. (Jointly; Fall semester at Pomona, Spring semester at HMC in alternate years)

    Prerequisite(s): MATH115 HM  or MATH180 HM  
  

  • MATH182 HM - Graduate Partial Differential Equations

    Credit(s): 3

    Bernoff, Castro, Jacobsen, Levy. 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. (Spring; offered in alternate years)

    Prerequisite(s): (MATH115 HM  and MATH131 HM ) or MATH180 HM ; recommended MATH132 HM  
  

  • MATH185 HM - Introduction to Wavelets and Their Applications

    Credit(s): 2

    Staff. 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  
  

  • MATH187 HM - Operations Research

    Credit(s): 3

    Benjamin, Martonosi, Huber (CMC), Shahriari (Pomona). Linear, integer, non-linear and dynamic programming, classical optimization problems, and network theory. (Fall)

    Prerequisite(s): MATH040 HM  
  

  • MATH188 HM - Social Choice and Decision Making

    Credit(s): 3

    Su. 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. (Spring, alternate years)

    Corequisite(s): MATH030B HM  or MATH030G HM ; MATH055 HM  recommended
  

  • MATH189 HM - Special Topics in Mathematics

    Credit(s): 1-3

    Staff. 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
  

  • MATH193 HM - Mathematics Clinic

    Credit(s): 3

    Bernoff, Castro, de Pillis, Gu, Levy, Martonosi, Williams. 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. (Fall and Spring)

  

  • MATH196 HM - Independent Study

    Credit(s): 1-5

    Staff. Readings in special topics. (Fall and Spring)

    Prerequisite(s): Permission of department or instructor 
 

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