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 program tailored to the student's interests and goals.
Introductory Sequence

BIOL054 HM  Experimental Biology Laboratory
Credit: 1
Instructor:
Offered: Spring
Description: Investigations in physiology, biochemistry, ecology, molecular biology, and other areas of experimental biology.
Concurrent requisites: BIOL052 HM

BIOL154 HM  Biostatistics
Credits: 3
Instructor:
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
Concurrent requisites: BIOL052 HM

MATH055 HM  Discrete Mathematics
Credits: 3
Instructor:
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.
Concurrent requisites: MATH073 HM

MATH082 HM  Differential Equations
Credits: 3
Instructor:
Offered: Fall
Description: Modeling physical systems, firstorder ordinary differential equations, existence, uniqueness, and longterm behavior of solutions; bifurcations; approximate solutions; secondorder ordinary differential equations and their properties, applications; firstorder 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
Instructor:
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 BIOL052 HM

MCBI118B HM  Introduction to Computational Biology
Credits: 1.5
Instructor:
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 BIOL052 HM
Biology Foundations
Any two of the following:

BIOL101 HM  Comparative Physiology
Credits: 3
Instructor:
Offered: Spring
Description: Topics in the structural basis underlying general physiological mechanisms of plants and animals.
Prerequisites: BIOL052 HM

BIOL108 HM  Ecology and Environmental Biology
Credits: 3
Instructor:
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: BIOL052 HM and MATH019 HM

BIOL109 HM  Evolutionary Biology
Credits: 3
Instructor:
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: BIOL052 HM and MATH019 HM

BIOL113 HM  Molecular Genetics
Credits: 3
Instructor:
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: BIOL052 HM, CHEM023A HM, and CHEM023B HM
and
 One biology seminar
 One biology laboratory
Mathematical and Computation Courses
One of:

BIOL119 HM  Advanced Mathematical Biology
Credits: 3
Instructor:
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
Instructor:
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:
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 3credit mathematics course chosen with the advisor. Suggested mathematics course options include, but are not limited to:

MATH152 HM  Statistical Theory
Credits: 3
Instructor:
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
Instructor:
Offered: Jointly; Fall, alternate years at HMC
Description: This course is particularly wellsuited 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
Instructor:
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 oneway and twoway 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
Instructor:
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 fastFourier transforms.
Prerequisites: MATH073 HM, MATH082 HM, and CSCI060 HM

MATH168 HM  Algorithms
Credits: 3
Instructor:
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 patternmatching.
Prerequisites: (CSCI070 HM and CSCI081 HM) or ((CSCI060 HM or CSCI042 HM) and MATH131 HM))

MATH173 HM  Advanced Linear Algebra
Credits: 3
Instructor:
Offered: Jointly in alternate years
Description: Topics from among the following: Similarity of matrices and the Jordan form, the CayleyHamilton theorem, limits of sequences and series of matrices; the PerronFrobenius 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
Instructor:
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; SturmLiouville theory and orthogonal expansions; Bessel functions.
Prerequisites: MATH082 HM and MATH131 HM

MATH187 HM  Operations Research
Credits: 3
Instructor:
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  Principles of Computer Science
Credits: 3
Instructor:
Offered: Fall and Spring
Description: Introduction to principles of computer science: Information structures, functional programming, objectoriented programming, grammars, logic, logic programming, correctness, algorithms, complexity analysis, finitestate 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
Instructor:
Offered: Fall and Spring
Description: Abstract data types including priority queues and dynamic dictionaries and efficient data structures for these data types, including heaps, selfbalancing trees, and hash tables. Analysis of data structures including worstcase, averagecase 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
Instructor:
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
Instructor:
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:
Description: Fundamental models of databases: entityrelationship, relational, objectoriented. 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
Instructor:
Offered: Fall and Spring
Description: Algorithm design, analysis, and correctness. Design techniques including divideandconquer 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, NPcompleteness, 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
Instructor:
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
Instructor:
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 realworld 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:
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. Selforganizing feature maps. Applications chosen from function approximation, signal processing, control, computer graphics, pattern recognition, timeseries 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
Instructor:
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, tradeoffs 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:
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
Instructor:
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 CSmath 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:
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)
 MATH055 HM – Discrete Mathematics (3 units)
 BIOL054 HM – Experimental Biology Laboratory (1 unit)
 BIOL154 HM – Biostatistics (2 units; taken concurrently with Biology 54)
 MCBI118A HM – Introduction to Mathematical Biology (1.5 units)
 MCBI118B HM – Introduction to Computational Biology (1.5 units)
Biology Foundations (11–12 units)
 BIOL109 HM – Evolutionary Biology
 BIOL111 HM – Molecular and Cellular Biology Laboratory
 BIOL113 HM – Molecular Genetics
 BIOL189 HM – Topics in Biochemistry and Molecular Biology
Mathematical and Computation Courses (13–14 units)
 BIOL188 HM – Advanced Computational Biology (3 units)
 MATH171 HM – Abstract Algebra I (3 units)
 CSCI060 HM – Principles of Computer Science
 CSCI070 HM – Data Structures and Program Development
 CSCI140 HM – Algorithms (or MATH168 HM – Algorithms)
Electives, Thesis, and Colloquium (11.5 units)
 BIOL191 HM – Biology Colloquium
 CHEM056 HM – Organic Chemistry I
 MATH197 HM – Senior Thesis in Mathematics or BIOL193 HM – Senior Thesis Research: Biology
 MATH198 HM – Undergraduate Mathematics Forum (1 units)
 One semester of MCBI199 HM – Joint Colloquium for the Mathematical and Computational Biology Major (0.5 units)
Emphasis on Physiology and Modeling
Introductory Sequence (9 units)
 MATH055 HM – Discrete Mathematics (3 units)
 BIOL054 HM – Experimental Biology Laboratory (1 unit)
 BIOL154 HM – Biostatistics (2 units; taken concurrently with Biology 54)
 MCBI118A HM – Introduction to Mathematical Biology (1.5 units)
 MCBI118B HM – Introduction to Computational Biology (1.5 units)
Biology Foundations (11–12 units)
 BIOL101 HM – Comparative Physiology
 BIOL103 HM – Comparative Physiology Laboratory
 BIOL108 HM – Ecology and Environmental Biology
 BIOL113 HM – Molecular Genetics
 BIOL185 HM – Special Topics in Biology
Mathematical and Computation Courses (13–14 units)
 CSCI060 HM – Principles of Computer Science
 MATH119 HM – Advanced Mathematical Biology (3 units)
 MATH131 HM – Mathematical Analysis I (3 units)
 MATH180 HM – Introduction to Partial Differential Equations (3 units)
 MATH181 HM – Dynamical Systems (3 units)
Electives, Thesis, and Colloquium (11.5 units)
 BIOL191 HM – Biology Colloquium
 CHEM056 HM – Organic Chemistry I
 MATH197 HM – Senior Thesis in Mathematics or BIOL193 HM – Senior Thesis Research: Biology
 MATH198 HM – Undergraduate Mathematics Forum (1 units)
 One semester of MCBI199 HM – Joint Colloquium for the Mathematical and Computational Biology Major (0.5 units)
Emphasis on Computational Neuroscience
Introductory Sequence (9 units)
 MATH055 HM – Discrete Mathematics (3 units)
 BIOL054 HM – Experimental Biology Laboratory (1 unit)
 BIOL154 HM – Biostatistics (2 units; taken concurrently with Biology 54)
 MCBI118A HM – Introduction to Mathematical Biology (1.5 units)
 MCBI118B HM – Introduction to Computational Biology (1.5 units)
Biology Foundations (11–12 units)
 BIOL101 HM – Comparative Physiology
 BIOL103 HM – Comparative Physiology Laboratory
 BIOL109 HM – Evolutionary Biology
 BIOL113 HM – Molecular Genetics
 BIOL185 HM – Special Topics in Biology
Mathematical and Computation Courses (13–14 units)
 CSCI060 HM – Principles of Computer Science
 CSCI152 HM – Neural Networks
 CSCI153 HM – Computer Vision
 MATH119 HM – Advanced Mathematical Biology (3 units)
 MATH131 HM – Mathematical Analysis I (3 units)
Electives, Thesis, and Colloquium (11.5 units)
 BIOL191 HM – Biology Colloquium (1 unit total)
 CHEM056 HM – Organic Chemistry I
 MATH197 HM – Senior Thesis in Mathematics or BIOL193 HM – Senior Thesis Research: Biology
 MATH198 HM – Undergraduate Mathematics Forum (1 units)
 One semester of MCBI199 HM – Joint Colloquium for the Mathematical and Computational Biology Major (0.5 units)