# Mathematical and Computational Biology Major

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, 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 Experimental Biology Laboratory

Credit: 1

Offered: Spring

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

Corequisites: BIOL046 HM

Concurrent requisites: BIOL154 HM

• ### BIOL154 HM Biostatistics

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 Discrete Mathematics

Credits: 3

Instructors: Benjamin, Bernoff, Lindo, Martonosi, Orrison

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 Differential Equations

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 Introduction to Mathematical Biology

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 Introduction to Computational Biology

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 Comparative Physiology

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 Ecology and Environmental Biology

Credits: 3

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, human demography, and harvesting of natural resources.

Prerequisites: BIOL046 HM and MATH019 HM

• ### BIOL109 HM Evolutionary Biology

Credits: 3

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 Molecular Genetics

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 Advanced Mathematical Biology

Credits: 3

Instructors: Adolph, de Pillis (Mathematics), Jacobsen (Mathematics), Levy (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 Advanced Mathematical Biology

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 Advanced Computational Biology

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 Statistical Theory

Credits: 3

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

Offered: Jointly; spring semester at pomona and cmc

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

Prerequisites: MATH 157 HM

• ### MATH156 HM Stochastic Processes

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 Statistical Linear Models

Credits: 3

Instructors: Martonosi, Williams, Staff (Pomona)

Offered: Fall, alternate years

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

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 Algorithms

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 CSCI081 HM) or ((CSCI060 HM or CSCI042 HM) and MATH131 HM))

• ### MATH173 HM Advanced Linear Algebra

Credits: 3

Instructors: de Pillis, Gu, Orrison

Offered: Jointly in alternate years

Description: Topics from among the following: Similarity of matrices and the Jordan form, the 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 Introduction to Partial Differential Equations

Credits: 3

Instructors: Bernoff, Jacobsen, 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 Operations Research

Credits: 3

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

Offered: Fall

Description: Linear, integer, non-linear 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 Principles of Computer Science

Credits: 3

Instructors: Boerkoel, Breeden, Dodds, Stone, Trushkowsky, Wu

Offered: Fall and spring

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

Prerequisites: CSCI005 HM or CSCI005GR HM

• ### CSCI070 HM Data Structures and Program Development

Credits: 3

Instructors: Bang, Breeden, Medero, O’Neill, Stone, Talvitie, Trushkowsky, Wiedermann

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 Computability and Logic

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 and (CSCI060 HM or CSCI042 HM)

• ### CSCI121 HM Software Development

Credits: 3

Instructors: Sweedyk, Wu

Offered: Fall and spring

Description: Introduction to the discipline concerned with the design and implementation of software systems. The course presents a historical perspective on software development practice and explores modern, agile techniques for eliciting software requirements, designing and imple­menting software architecture and modules, robust testing practices, and project management. Student teams design, develop, and test a substantial software project.

Prerequisites: CSCI070 HM

• ### CSCI133 HM Database Systems

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 Algorithms

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 CSCI081 HM) or ((CSCI060 HM or CSCI042 HM) and MATH131 HM))

• ### CSCI144 HM Scientific Computing

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)

• ### CSCI151 HM Artificial Intelligence

Credits: 3

Instructors: Boerkoel, Talvitie, Wu

Description: This course presents a general introduction to the field of Artificial Intelligence. It examines the question: What does (will) it take for computers to perform human tasks? It presents a broad introduction to topics such as knowledge representation, search, learning and reasoning under uncertainty. For each topic, it examines real-world applications of core techniques to problems which may include game playing, text classification and visual pattern recognition.

Prerequisites: CSCI070 HM and (MATH062 HM or BIOL154 HM)

• ### CSCI152 HM Neural Networks

Credits: 3

Instructor: Sweedyk

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: (CSCI060 HM or CSCI042 HM) and MATH073 HM and (MATH062 HM or BIOL154 HM)

• ### CSCI155 HM Computer Graphics

Credits: 3

Instructors: Breeden, Sweedyk

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 (MATH062 HM or BIOL154 HM)

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 Biology Colloquium (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 Undergraduate Mathematics Forum (preferably taken in the junior year)

Credit: 1

Instructors: Castro, Jacobsen, Orrison, Williams, 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 Joint Colloquium for the Mathematical and Computational Biology Major

Credit: 0.5

Instructor: Staff

Offered: Fall and spring

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

## 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.