Mathematical and Computational Biology

Mathematical and computational methods are vital to many areas of contemporary biological research, such as genomics, molecular modeling, structural biology, ecology, evolutionary biology, neurobiology, and systems biology. Conversely, biology is providing new challenges that can drive the development of novel mathematical and computational methods.

Harvey Mudd students interested in the interface between biology, mathematics, and computer science may pursue the Mathematical and Computational Biology Major, which is jointly administered by the biology, mathematics, and computer science departments.

This major prepares students for graduate studies in areas including applied mathematics, bioinformatics, computational biology, data science, genome science, mathematical biology, and diverse areas of biology, as well as employment in industry.

Harvey Mudd's Core curriculum provides mathematical and computational biology majors with a strong multidisciplinary foundation, and the College offers many opportunities for students to engage in interdisciplinary research in biomathematics, computational biology, and quantitative biology.

Students who choose this major become immersed in the scientific and intellectual cultures of biology, computer science, and mathematics, and the major is sufficiently flexible to allow students to concentrate in a particular area of interest. Students in this major have one advisor from the biology department and one advisor from either the mathematics or computer science departments. The advisors will jointly help the student plan a coherent program tailored to the student's interests and goals.

Introductory Sequence

  • BIOL054 HM

    Credit: 1

    Instructors: Ahn, McFadden, Stoebel

    Offered: Spring

    Description: Investigations in physiology, biochemistry, ecology, molecular biol­ogy, and other areas of experimental biology.

    Corequisites: BIOL023 HM and BIOL046 HM 

    Concurrent requisites: BIOL154 HM 

  • BIOL154 HM

    Credits: 3

    Instructors: Donaldson-Matasci, Stoebel

    Offered: Spring

    Description: Statistical techniques for analyzing biological data, including parametric, nonparametric, and randomization methods. Statistical aspects of experimental design with an emphasis on analyzing data collected in BIOL054 HM.

    Prerequisites: CSCI005 HM, CSCI005GR HM, or CSCI042 HM 

    Corequisites: BIOL046 HM 

    Concurrent requisites: BIOL054 HM 

  • MATH055 HM

    Credits: 3

    Instructors: Benjamin, Bernoff, Lindo, Martonosi, Orrison, Su

    Offered: Fall and spring

    Description: Topics include combinatorics (clever ways of counting things), number theory, and graph theory with an emphasis on creative problem solving and learning to read and write rigorous proofs. Possible applications include probability, analysis of algorithms, and cryptography.

    Corequisites: MATH073 HM 

  • MATH082 HM

    Credits: 3

    Instructor: 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.

    Prerequisites: (MATH019 HM and MATH073 HM) or equivalent 

  • MCBI118A HM

    Credits: 1.5

    Instructors: Adolph (Biology), de Pillis (Mathematics), Donaldson-Matasci (Biology)

    Offered: Spring

    Description: An introduction to the field of mathematical biology. Continuous and discrete mathematical models of biological processes and their analytical and computational solutions. Examples may include models in epidemiology, ecology, cancer biology, systems biology, molecular evolution, and phylogenetics.

    Prerequisites: MATH073 HM, MATH082 HM, and BIOL046 HM 

  • MCBI118B HM

    Credits: 1.5

    Instructors: Bush (Biology), Donaldson-Matasci (Biology), Wu (Computer Science)

    Offered: Spring

    Description: An introduction to the field of computational biology. Algorithms for phylogenetic inference and computational methods for solving problems in molecular evolution and population genetics.

    Prerequisites: CSCI005 HM and BIOL046 HM 

Biology Foundations

Any two of the following:

  • BIOL101 HM

    Credits: 3

    Instructor: Ahn

    Offered: Spring

    Description: The general aim will provide a broad introduction to comparative physiology. Students will learn the links between cellular & molecular mechanisms, organ systems, and organismal function in animals. Students will examine the relationship between structure and function in biology. During the process, students will be introduced to the diversity of animals and the scientific tools used to make physiological measurements.

    Prerequisites: BIOL046 HM 

  • BIOL108 HM

    Credits: 3

    Instructors: Adolph, McFadden

    Offered: Spring

    Description: Principles of organization of natural communities and ecosystems, including population dynamics, species interactions, and island biogeography. Modern experimental and mathematical approaches to ecological problems. Application of ecological principles to conservation biology, climate change, and other environmental impacts.

    Prerequisites: BIOL046 HM and MATH019 HM 

  • BIOL109 HM

    Credits: 3

    Instructors: Adolph, McFadden

    Offered: Fall

    Description: Evolutionary mechanisms, including natural selection, population genetics, speciation, and macroevolutionary processes. Modern methods of phylogenetic reconstruction. History of biological diversity and the fossil record.

    Prerequisites: BIOL046 HM and MATH019 HM 

  • BIOL113 HM

    Credits: 3

    Instructors: Hur, Schulz, Stoebel

    Offered: Fall

    Description: Molecular description of gene function in both prokaryotic and eukaryotic cells, including DNA, RNA, and protein structure; DNA replication; transcription and translation; and gene regulation.

    Prerequisites: BIOL046 HM and CHEM042 HM 

AND

  • One biology seminar
  • One biology laboratory
    •

Mathematical and Computation Courses

One of:

  • BIOL119 HM

    Credits: 3

    Instructors: Adolph, de Pillis (Mathematics), Jacobsen (Mathematics)

    Offered: Fall

    Description: Advanced study of mathematical models of biological processes, including discrete and continuous models. Examples are drawn from a variety of areas of biology, which may include physiology, sys­tems biology, cancer biology, epidemiology, ecology, evolution, and spatiotemporal dynamics.

    Prerequisites: MCBI118A HM 

  • MATH119 HM

    Credits: 3

    Instructors: Adolph (Biology), de Pillis, Jacobsen

    Description: Further study of mathematical models of biological processes, including discrete and continuous models. Examples are drawn from a variety of areas of biology, which may include physiology, systems biology, cancer biology, epidemiology, ecology, evolution, and spatiotemporal dynamics.

    Prerequisites: MCBI118A HM 

  • BIOL188 HM

    Credits: 3

    Instructor: Bush

    Offered: Fall, alternate years

    Description: Computational algorithms and methods used in the study of genomes. Lectures, dis­cussions, and computer laboratory exercises.

    Prerequisites: MCBI118B HM 

AND

One 3-credit mathematics course chosen with the advisor. Suggested mathematics course options include, but are not limited to:

  • MATH152 HM

    Credits: 3

    Instructors: Martonosi, Williams, Staff (Pomona), Staff (CMC)

    Offered: Jointly; spring semester at pomona and cmc

    Description: An introduction to the general theory of statistical inference, including estimation of parameters, confidence intervals, and tests of hypotheses.

    Prerequisites: MATH 157 HM 

  • MATH156 HM

    Credits: 3

    Instructors: 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.

    Prerequisites: MATH073 HM and MATH157 HM 

  • MATH158 HM

    Credits: 3

    Instructors: Martonosi, Williams, Staff (Pomona)

    Offered: Fall, alternate years

    Description: An introduction to linear regression including simple linear regression, multiple regression, variable selection, stepwise regression and analysis of residual plots and analysis of variance including 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.

    Prerequisites: Permission of instructor

  • MATH164 HM

    Credits: 3

    Instructors: Bernoff, de Pillis, Yong

    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.

    Prerequisites: MATH073 HM, MATH082 HM, and CSCI060 HM 

  • MATH168 HM

    Credits: 3

    Instructors: Boerkoel (Computer Science), Monta​ñez (Computer Science), Schofield (Computer Science), Stone (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.

    Prerequisites: ((CSCI070 HM and (MATH055 HM/CM/PZ/SC) and (MATH019 HM or MATH032  CM/PO/PZ/SC or MATH032S PO or MATH067 PO) and (MATH073 HM or MATH060  CM/PO/PZ/SC or MATH060C CM)) or ((CSCI060 HM or CSCI042 HM) and MATH131 HM)) or (CSCI062 PO and CSCI054  PO). CSCI081 HM is recommended.

  • MATH173 HM

    Credits: 3

    Instructors: de Pillis, Gu, Haddock, 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.

    Prerequisites: MATH131 HM 

  • MATH180 HM

    Credits: 3

    Instructors: Bernoff, Jacobsen, H. Zinn-Brooks

    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.

    Prerequisites: MATH082 HM and MATH131 HM 

  • MATH187 HM

    Credits: 3

    Instructors: Benjamin, Martonosi, Staff (CMC), Staff (Pomona)

    Offered: Fall

    Description: Linear, integer, nonlinear and dynamic programming, classical optimization problems, and network theory.

    Prerequisites: MATH073 HM 

AND

One 3 credit computer science course chosen with the advisor. Suggested computer science course options include, but are not limited to:

  • CSCI060 HM

    Credits: 3

    Instructors: Boerkoel, Breeden, Dodds, Padmanabhan, Stone, Talvitie, Trushkowsky, Wiedermann, Wu

    Offered: Fall and spring

    Description: Introduction to principles of computer science: Information structures, functional programming, object-oriented programming, grammars, logic, correctness, algorithms, complexity analysis, and theoretical limitations. Those who have completed CSCI042 HM cannot take CSCI060 HM.

    Prerequisites: CSCI005 HM or CSCI005GR HM 

  • CSCI070 HM

    Credits: 3

    Instructors: Breeden, Medero, O'Neill, Stone, Talvitie, Trushkowsky

    Offered: Fall and spring

    Description: Abstract data types including priority queues and dynamic dictionaries and efficient data structures for these data types, including heaps, self-balancing trees, and hash tables. Analysis of data structures including worst-case, average-case and amortized analysis. Storage allocation and reclamation. Secondary storage considerations. Extensive practice building programs for a variety of applications.

    Prerequisites: (CSCI060 HM or CSCI042 HM), and at least one mathematics course at the level of calculus or higher; MATH055 HM recommended

  • CSCI081 HM

    Credits: 3

    Instructors: Bang, Monta​ñez, Stone

    Offered: Fall and spring

    Description: An introduction to some of the mathematical foundations of computer science, particularly logic, automata, and computability theory. Develops skill in constructing and writing proofs, and demonstrates the applications of the aforementioned areas to problems of practical significance.

    Prerequisites: (MATH055 HM or MATH055  CM/PZ/SC), and (CSCI060 HM or CSCI042 HM), and (MATH019 HM or MATH032 CM/PO/PZ/SC or MATH032S PO or MATH067  PO), and (MATH073 HM or MATH060 CM/PO/PZ/SC)

  • CSCI123 HM

    Credits: 3

    Instructors: Kirabo, Schofield, Staff

    Offered: Fall and spring

    Description: This course dives into the technical and professional skills necessary to plan, execute, document, and present computational projects beyond a classroom. A central focus of the course is a team-based project to develop a tutorial for an existing software tool or API. A variety of exercises will help explore and build literacy in common tools and workflows in a professional computing environment. Additionally, students will discuss human-human interactions around negotiation, conflict management, peer review of both code and written work, and ethical decision-making.

    Prerequisites: CSCI070 HM 

  • CSCI133 HM

    Credits: 3

    Instructor: Trushkowsky

    Description: Fundamental models of databases: entity-relationship, relational, object-oriented. Relational algebra and calculus, query languages. Data storage, caching, indexing, and sorting. Locking protocols and other issues in concurrent and distributed data­bases.

    Prerequisites: CSCI070 HM; CSCI081 HM recommended

  • CSCI140 HM

    Credits: 3

    Instructors: Boerkoel, Monta​ñez, Schofield, Stone

    Offered: Fall and spring

    Description: Algorithm design, analysis, and correctness. Design techniques including divide-and-conquer and dynamic programming. Analysis techniques including solutions to recurrence relations and amortization. Correctness techniques including invariants and inductive proofs. Applications including sorting and searching, graph theoretic problems such as shortest path and network flow, and topics selected from arithmetic circuits, parallel algorithms, computational geometry, and oth­ers. An introduction to computational complexity, NP-completeness, and approximation algorithms. Proficiency with programming is expected as some assignments require algorithm implementation.

    Prerequisites: ((CSCI070 HM and (MATH055 HM/CM/PZ/SC) and (MATH019 HM or MATH032  CM/PO/PZ/SC or MATH032S PO or MATH067 PO) and (MATH073 HM or MATH060  CM/PO/PZ/SC or MATH060C CM)) or ((CSCI060 HM or CSCI042 HM) and MATH131 HM)) or (CSCI062 PO and CSCI054  PO). CSCI081 HM is recommended.

  • CSCI144 HM

    Credits: 3

    Instructors: Bernoff (Mathematics), de Pillis (Mathematics), Yong (Mathematics)

    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.

    Prerequisites: MATH073 HM, MATH082 HM, and (CSCI060 HM or CSCI042 HM) 

  • CSCI152 HM

    Credits: 3

    Instructor: Staff

    Description: Modeling, simulation, and analysis of artificial neural networks and their relation to biological networks. Design and optimization of discrete and continuous neural networks. Back propagation and other gradient descent methods. Hopfield and Boltzmann networks. Unsupervised learning. Self-organizing feature maps. Applications chosen from function approximation, signal processing, control, computer graphics, pattern recognition, time-series analysis. Relationship to fuzzy logic, genetic algorithms, and artificial life.

    Prerequisites: CSCI070 HM and MATH073 HM and (MATH056 HM or MATH062 HM or BIOL154 HM or MATH151 CM/PO/PZ/SC)

  • CSCI155 HM

    Credits: 3

    Instructor: Breeden

    Description: This course is an introduction to the major concepts in modern computer graphics. Students will become familiar with the technical challenges posed by the capture, display, and generation of digital images. Important concepts such as the role of specialized hardware, trade-offs in physical realism and rendering time, and the critical reading and analysis of graphics literature will be introduced.

    Prerequisites: CSCI070 HM, MATH073 HM, and (MATH056 HM or MATH062 HM or BIOL154 HM or MATH151 CM/PO/PZ/SC)

AND

  • Five credits of additional coursework in mathematics or computer science
    •

Technical Elective

  • One technical elective chosen with the advisor (3 credits): Any course related to the student's interests in the major. Possible courses satisfying this requirement could be in biology, computer science, or mathematics or in another field including (but not limited to), chemistry, bioengineering, cognitive science, neuroscience, biophysics, or linguistics.

Colloquium and Forum

  • BIOL191 HM (taken twice)

    Credit: 0.5

    Instructor: Staff

    Offered: Fall and spring

    Description: Oral presentations and discussions of selected topics including recent developments. Participants include biology majors, faculty members, and visiting speakers. Required for junior and senior biology majors. No more than 2.0 credits can be earned for departmental seminars/col­loquia.

    Prerequisites: HMC Biology (including joint majors) only.

  • MATH198 HM (preferably taken in the junior year)

    Credit: 1

    Instructors: Castro, Jacobsen, Orrison, Williams, H. Zinn-Brooks

    Offered: Fall and spring

    Description: The goal of this course is to improve students' ability to communicate mathematics, both to a general and technical audience. Students will present material on assigned topics and have their presentations evaluated by students and faculty. This format simultaneously exposes students to a broad range of topics from modern and classical mathematics. Required for all majors; recommended for all joint CS-math majors and mathematical biology majors, typically in the junior year.

  • MCBI199 HM

    Credit: 0.5

    Instructor: Staff

    Offered: Fall and spring

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

Capstone

  • Two semesters of senior thesis or Clinic, selected in consultation with the student's academic advisors (6 credits)

Sample Paths Through the Major

These paths are provided as examples; many other paths are possible, and you should work with your advisor to choose the best path for your interests.

Simple Path

Introductory Sequence (9 units)

Biology Foundations (11–12 units)

Mathematical and Computation Courses (13–14 units)

Electives, Thesis, and Colloquium (11.5 units)

Emphasis on Physiology and Modeling

Introductory Sequence (9 units)

Biology Foundations (11–12 units)

Mathematical and Computation Courses (13–14 units)

Electives, Thesis, and Colloquium (11.5 units)

Emphasis on Computational Neuroscience

Introductory Sequence (9 units)

Biology Foundations (11–12 units)

Mathematical and Computation Courses (13–14 units)

Electives, Thesis, and Colloquium (11.5 units)