Jun 16, 2024  
2019-2020 Catalog 
    
2019-2020 Catalog [ARCHIVED PUBLICATION] Use the dropdown above to select the current catalog.

Course Descriptions


 

Engineering

  
  • ENGR172 HM - Structural Mechanics


    Credit(s): 3

    Instructor(s): Bassman, Cha

    Offered: Spring

    Description: Introduction to elementary structural systems: trusses, beams. Force and deflection analysis. Energy methods. Stability. Introduction to finite element methods.

    Prerequisite(s): ENGR083 HM  
  
  • ENGR173 HM - Applied Elasticity


    Credit(s): 3

    Instructor(s): Staff

    Offered: Fall, alternate years

    Description: Introduction to the concepts of stress and strain. Application to the theory of bending and torsion. Topics in elementary elasticity.

    Prerequisite(s): ENGR083 HM  
  
  • ENGR174 HM - Practices in Civil Engineering


    Credit(s): 3

    Instructor(s): Cardenas

    Offered: Spring, alternate years

    Description: 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.

    Prerequisite(s): ENGR079 HM , ENGR080 HM , and permission of instructor
  
  • ENGR175 HM - Dynamics of Rigid Bodies


    Credit(s): 3

    Instructor(s): Bassman

    Description: 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.

    Corequisite(s): ENGR083 HM  
  
  • ENGR176 HM - Numerical Methods in Engineering


    Credit(s): 3

    Instructor(s): Cha, Wang

    Offered: Spring, alternate years

    Description: 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.

    Prerequisite(s): ENGR072 HM  
  
  • ENGR178 HM - High Power Rocketry


    Credit(s): 3

    Instructor(s): Spjut

    Offered: Spring

    Description: This course uses high power rockets as a vehicle for learning and demonstrating competence in modeling, experimental data collection and data analysis of rigid body and flight dynamics. In particular, students will perform 1-D analytical and numerical characterization of flight data including motor performance, testing and characterization of avionics and telemetry, develop and use models for inertial navigation and sensor fusion, and characterize structural dynamics during flight. The final project will demonstrate all of the above from data the students collect during flights of the rockets the students will construct and instrument, designed to reach Mach 1.6 and an altitude of 13,000 ft.

    Prerequisite(s): ENGR080 HM  for Engineering majors or the combination of ENGR079 HM  and permission of instructor for non-majors with the appropriate background.
    Corequisite(s): Corequisites: TRA or NAR Level 1 certification. Level 2 certification strongly recommended.
  
  • ENGR180 HM - Human Centered Design


    Credit(s): 3

    Instructor(s): Staff

    Description: This course introduces students to human-centered design approaches for innovative problem solving. Human-centered design begins with a deep understanding of people and social contexts. The course will include fundamental readings in design thinking, interactive design methods and processes, and hands-on projects. Students will learn how user research, synthesis, idea generation, and prototyping can be integrated into different phases of the design process. 

    Prerequisite(s): ENGR004 HM  
  
  • ENGR181 HM - New Product Development


    Credit(s): 3

    Instructor(s): Krauss

    Description: 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.

    Prerequisite(s): Junior or senior standing and ENGR004 HM  
  
  • ENGR182 HM - Manufacturing Planning and Execution


    Credit(s): 3

    Instructor(s): Gokli

    Offered: Spring

    Description: 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.

    Prerequisite(s): ENGR004 HM  
  
  • ENGR183 HM - Management of Technical Enterprise


    Credit(s): 3

    Instructor(s): Gokli, Krauss

    Offered: Fall

    Description: 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.

    Prerequisite(s): ENGR004 HM  and Junior standing. 
  
  • ENGR185A HM - Engineering Design and Invention


    Credit(s): 1.5

    Instructor(s): Furuya

    Offered: Fall, second half; Spring, first half

    Description: Develop a creative and innovative mindset, “thinking differently” to generate novel and patentable design ideas. Final presentation to industry panelists.

    Prerequisite(s): ENGR004 HM  
  
  • ENGR185B HM - Engineering Design and Invention II


    Credit(s): 1.5

    Instructor(s): Furuya

    Offered: Spring first and second halves

    Description: Continuation of work begun in ENGR185A HM , including the completion of the prototype developed in the prior half-semester.

    Prerequisite(s): ENGR185A HM  and permission of instructor.
  
  • ENGR187 HM - Operations Research


    Credit(s): 3

    Instructor(s): Martonosi

    Description: Linear, integer, non-linear and dynamic programming, classical optimization problems, and network theory. (Crosslisted as MATH187 HM )

    Prerequisite(s): MATH040 HM  
  
  • ENGR189 HM - Corporate Environmental Strategy and Performance Measurement


    Credit(s): 3

    Instructor(s): Srebotnjak

    Offered: Fall

    Description: This course explores how companies incorporate environmental objectives into their strategic planning. Making extensive use of actual case studies, we will focus on the management and measurement tools available to corporations, how they define priorities and actions through stakeholder engagement, and how they can drive environmental objectives at all levels. We will then extend this viewpoint to corporate sustainability, which aims to balance financial performance with environmental stewardship and social wellbeing. We will learn how to analyze and prepare a sustainability report, and take a look at the roles that government and the investor community play in the trend towards greater corporate social and environmental responsibility.

    Prerequisite(s): ENGR038 HM  or ENGR086 HM  or ENGR180 HM  or ENGR181 HM  or ENGR182 HM  or ENGR183 HM 
  
  • ENGR190 HM - Special Topics in Engineering


    Credit(s): 3

    Instructor(s): Staff

    Description: 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

    Instructor(s): Staff

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

  
  • ENGR205 HM - Systems Simulation


    Credit(s): 3

    Instructor(s): Bright

    Offered: Fall

    Description: 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.

    Prerequisite(s): ENGR101 HM  and ENGR102 HM  
  
  • ENGR206 HM - Optimization Techniques in Engineering Design


    Credit(s): 3

    Instructor(s): Bright

    Offered: Spring

    Description: Presentation of techniques for making optimum choices among alternatives; applications to engineering design problems.

    Prerequisite(s): ENGR101 HM  and ENGR102 HM   
  
  • ENGR231 HM - Advanced Transport Phenomena


    Credit(s): 3

    Instructor(s): Bright, Lape

    Offered: Spring

    Description: 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.

    Prerequisite(s): ENGR131 HM  
  
  • ENGR240 HM - Introduction to Compressible Flow


    Credit(s): 3

    Instructor(s): Cardenas

    Offered: Spring, alternate years

    Description: 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.

    Prerequisite(s): ENGR131 HM  
  
  • ENGR278 HM - Advanced Structural Dynamics


    Credit(s): 3

    Instructor(s): Cha

    Offered: Spring, alternate years

    Description: 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.

    Prerequisite(s): ENGR171 HM  

Environmental Analysis

  
  • EA010 HM - Introduction to Environmental Analysis


    Credit(s): 3

    Instructor(s): Staff

    Description: This course examines the history of environmental change, the environmental ramifications of economic and technological decisions, the impact of personal choices, and the need to evaluate environmental arguments critically. We will delve into questions such as: What is nature? How have ideas about nature varied across time and across different cultures? How have those ideas about nature influenced interactions with environments? Why doesn’t everyone have access to a clean and safe environment?

  
  • EA174 HM - Building Los Angeles


    Credit(s): 3

    Instructor(s): Groves

    Description: This course explores the complex network of urban communities in which we live in order that we might think more deeply about the relationship of the built to the natural environment. To complicate our conceptions of Los Angeles, we consider the city’s history and infrastructure and examine the social stresses and environmental pressures that result from planning decisions. We also focus on Southern California architecture and design as a profound expression of the relationship between the built and the natural, including new urbanism and the maturation of green design. As a required experiential component, the course features a substantial number of Saturday field trips. $50 fee to cover transportation costs.


History

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


    Credit(s): 3

    Instructor(s): Hamilton

    Description: 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

    Instructor(s): Hamilton

    Description: 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

    Instructor(s): Staff

    Description: 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.

  
  • HIST150 HM - Technology and Medicine


    Credit(s): 3

    Instructor(s): Hamilton

    Description: 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

    Instructor(s): Hamilton

    Description: 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

    Instructor(s): Hamilton

    Description: 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

    Instructor(s): Staff

    Offered: Spring

    Description: 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.

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

Interdisciplinary

  
  • ID048 HM - Social Justice & Equity/STEM Educ


    Credit(s): 1

    Instructor(s): Lewis, Yong

    Description: Despite many efforts over the last few decades to broaden participation in STEM (science, technology, engineering, mathematics) fields, women, African-American, Hispanic and Latinx, Native American, and Southeast Asian individuals remain underrepresented in STEM fields in the United States. Why have we not made more significant progress and what will it take to do so?  In this course, we will use critical theories (including critical race theory, feminism, Marxism, and others) to understand the entangled issues behind this and other persistent inequities. The purpose of this course is to help fulfill the HMC mission statement more completely by empowering students to be engaged, critical, and civic-minded participants who can positively impact society. This class will have a reasonable out-of-class homework requirement that will be commensurate with a one-unit course.


Leadership Studies

  
  • LEAD101 HM - Fundamentals of Leadership


    Credit(s): 3

    Instructor(s): Zorman

    Description: Successful leaders must know how to lead themselves, how to lead others, and how to lead their cause. Many diverse competencies are required to be successful in those three dimensions of leadership. This course will introduce those competencies in theory and offer plenty of opportunities to practice them. Taught through some lecture but mainly through experiential learning, group discussions, self-reflection, and enthusiastic practice in real life. This course requires students to be willing to step out of their comfort zone, to take risks and participate actively in service of personal and group learning. No pass/fail grading (i.e., no pass/no credit, credit/no credit, etc.) 

    Prerequisite(s): Junior or Senior standing
  
  • LEAD151 HM - Interpersonal Dynamics


    Credit(s): 3

    Instructor(s): Zorman

    Description: This course is designed to help students explore and understand their impact on others as well as other people’s impact on them. Students will experience in a small and intimate training group (max. 12) how changing their behavior is changing their impact on others. As a result students will learn how to authentically engage, have their intended impact, and create more productive and trusted relationships. Participation at the weekend retreat late in the semester is required to pass this course. No pass-fail grading.

    Prerequisite(s): Instructor permission and interview required

Literature

  
  • LIT035 HM - Fiction Workshop


    Credit(s): 3

    Instructor(s): Plascencia

    Offered: Fall and Spring

    Description: This course is designed as an introductory workshop focusing on the writing of fiction and the discourse of craft. Through the examination of a variety of literary traditions, stylistic and compositional approaches, and the careful reading and editing of peer stories, students will strengthen their prose and develop a clearer understanding of their own literary values and the dynamics of fiction.

  
  • LIT104 HM - An Introduction to Middle English Literature


    Credit(s): 3

    Instructor(s): Groves

    Description: 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

    Instructor(s): Groves

    Description: 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 - Performing Shakespeare


    Credit(s): 3

    Instructor(s): Groves, Dadabhoy

    Description: 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

    Instructor(s): Groves, Eckert

    Offered: Fall and Winter break

    Description: 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.

    Prerequisite(s): Permission of instructor.
  
  • LIT141 HM - Monsters in Literature


    Credit(s): 3

    Instructor(s): Dadabhoy

    Description: Our culture is fascinated by things that are weird, strange, horrifying, and grotesque. In other words, we’re fascinated by monsters, those others that stand at the margins of human, civilized society, threatening us by their very existence. Are monsters only very scary things, or do they have a social and cultural function? In this course we will take up this and other questions as we investigate the nature of the monstrous. Moreover, we will explore the libidinal charge that the recognition of the monstrous or unnatural being evokes. Thus, we will examine both the physical and psychological permutations of monstrosity. In this course, we will consider monsters in their non-human, alien, and technological forms as well as some truly terrifying human monsters.

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


    Credit(s): 3

    Instructor(s): Balseiro

    Description: 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

    Instructor(s): Balseiro

    Description: 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

    Instructor(s): Balseiro

    Description: 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

    Instructor(s): Balseiro

    Description: 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

    Instructor(s): Balseiro

    Description: 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.

  
  • LIT156 HM - Translation; or, the Foreignness of Language


    Credit(s): 3

    Instructor(s): Balseiro

    Description: This seminar is designed to introduce students to the foreignness of language through literary translation theory and its praxis. Participants will develop individual projects that will be revised and workshopped over the course of the semester. Weekly readings, including essays by theoreticians, accomplished writer-translators, and selections of multiple translations of a single text, will be used to familiarize students with a range of perspectives on translation and its relationship to writing. 

    Prerequisite(s): Students must have reading knowledge of at least one foreign language
  
  • LIT158 HM - Zora Neale Hurston: Theories of Race, Gender, and Art


    Credit(s): 3

    Instructor(s): Balseiro

    Offered: Spring

    Description: This seminar is designed to introduce students to Zora Neale Hurston as an ethnographer and fiction writer. Hurston was the first African American woman to graduate from Barnard College. Born in the South, highly educated in the North, a luminary amongst the talents of the Harlem Renaissance, and buried in an unmarked grave in her native Florida, Hurston’s writing and life offer a unique view onto notions of race, gender, art, and class in the aftermath of Reconstruction that reverberate to this day.


Mathematics

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

  
  • MATH019 HM - Calculus


    Credit(s): 3

    Instructor(s): 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, higher-order 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


    Credit(s): 1.5

    Instructor(s): 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. Half-semester course.

    Prerequisite(s): Harvey Mudd College first-year students only.
  
  • MATH030B HM - Calculus


    Credit(s): 1.5

    Instructor(s): 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.

    Prerequisite(s): Mastery of single-variable calculus—entry by department placement only
  
  • MATH030G HM - Calculus


    Credit(s): 1.5

    Instructor(s): 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.

    Prerequisite(s): One year of calculus at the high school level
  
  • 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  
  
  • 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
  
  • MATH045 HM - Introduction to Differential Equations


    Credit(s): 1.5

    Instructor(s): Bernoff, Castro, de Pillis, Jacobsen, 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  
  
  • 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  or MATH073 HM  
  
  • 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
  
  • MATH060 HM - Multivariable Calculus


    Credit(s): 1.5

    Instructor(s): 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; 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  
  
  • MATH065 HM - Differential Equations and Linear Algebra II


    Credit(s): 1.5

    Instructor(s): 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.

    Prerequisite(s): MATH040 HM  and MATH045 HM  
  
  • 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  
  
  • MATH073 HM - Linear Algebra


    Credit(s): 3

    Instructor(s): 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.

    Prerequisite(s): MATH019 HM  or equivalent
  
  • MATH080 HM - Intermediate Differential Equations


    Credit(s): 1.5

    Instructor(s): 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.

    Prerequisite(s): MATH065 HM  
  
  • MATH082 HM - Differential Equations


    Credit(s): 3

    Instructor(s): Staff

    Offered: Fall

    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. Applications to linear systems of ordinary differential equations, matrix exponential; nonlinear systems of differential equations; equilibrium points and their stability. Additional topics.

    Prerequisite(s): (MATH019 HM  and MATH073 HM ) or equivalent 
  
  • 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.

  
  • 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.

  
  • 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.

  
  • 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  or MATH073 HM ) and MATH055 HM  
  
  • 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  
  
  • 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): MATH019 HM MATH030B HM , or MATH030G HM  
  
  • 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  or (MATH073 HM  and MATH082 HM )
  
  • MATH115 HM - Fourier Series and Boundary Value Problems


    Credit(s): 3

    Instructor(s): 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; 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  or (MATH073 HM  and MATH082 HM 
  
  • MATH119 HM - Advanced Mathematical Biology


    Credit(s): 3

    Instructor(s): 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. (Crosslisted as BIOL119 HM )

    Prerequisite(s): MCBI118A HM  and MCBI118B HM  
  
  • 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  
  
  • 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  
  
  • 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  or (MATH073 HM  and MATH082 HM 
  
  • 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  
  
  • 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
  
  • 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  or (MATH073 HM  and MATH082 HM )
  
  • 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
  
  • 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  
  
  • 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  or MATH073 HM  
  
  • 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  
  
  • 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  
  
  • 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  
  
  • 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  or MATH073 HM ) and MATH157 HM  
  
  • MATH157 HM - Intermediate Probability


    Credit(s): 1.5

    Instructor(s): 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 central-limit theorem. 

    Prerequisite(s): MATH019 HM  or MATH060 HM   
  
  • 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  
  
  • 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  
  
  • MATH164 HM - Scientific Computing


    Credit(s): 3

    Instructor(s): 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 fast-Fourier transforms. (Crosslisted as CSCI144 HM )

    Prerequisite(s): (MATH065 HM  or (MATH073 HM  and MATH082 HM )) and CSCI060 HM  
  
  • MATH165 HM - Numerical Analysis


    Credit(s): 3

    Instructor(s): 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 non-linear equations, interpolation, approximate integra­tion (quadrature), and numerical solutions to ordinary differential equations.

    Prerequisite(s): MATH065 HM  or (MATH073 HM  and MATH082 HM )
  
  • MATH167 HM - Complexity Theory


    Credit(s): 3

    Instructor(s): Pippenger, Libeskind-Hadas (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 Cook-Levin Theorem. Approximability of NP-complete problems. The polynomial hierarchy, PSPACE-completeness, L and NL-completeness, #P-completeness. IP and Zero-knowledge proofs. Randomized and parallel complexity classes. The speedup, hierarchy, and gap theorems. (Crosslisted as CSCI142 HM )

    Prerequisite(s): (CSCI060 HM  or CSCI042 HM ) and MATH055 HM  
  
  • 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 ))
  
  • 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  or MATH073 HM ) and MATH055 HM  
  
  • 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  
  
  • 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  
  
  • 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  
  
  • 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  
  
  • 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 recommended
  
  • MATH178 HM - Nonlinear Data Analytics


    Credit(s): 3

    Instructor(s): 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 non-linear relationship in the data. (For example, UAVs’ data, including accelerometer and gyroscope data, obeys nonlinear kinematics and dynamics relationships, a curved 3-D 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 (non-Euclidean) 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.

    Prerequisite(s): CSCI070 HM  and (CSCI140 HM  or MATH131 HM  or MATH157 HM  or MATH168 HM )
  
  • MATH180 HM - Introduction to Partial Differential Equations


    Credit(s): 3

    Instructor(s): 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; Sturm-Liouville theory and orthogonal expansions; Bessel functions.

    Prerequisite(s): MATH080 HM  and MATH131 HM  
  
  • MATH181 HM - Dynamical Systems


    Credit(s): 3

    Instructor(s): 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.

    Prerequisite(s): MATH115 HM  or MATH180 HM  
  
  • MATH184 HM - Graduate Partial Differential Equations


    Credit(s): 3

    Instructor(s): 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.

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

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