Information found in this online edition of the 2008-09 catalog is unofficial and for informational purposes only. By authority of the dean of the College, some factual corrections to the printed version may appear here. The official document of record is the printed edition of the 2008-09 Catalog. For more information, please contact the Office of the Registrar.
Mathematical Sciences
Chair: John W. Krussel
The mathematical sciences--mathematics, statistics, and computer science--continue to play a central role in the evolution of civilization. With a focus on patterns and structure, and with methodologies based on computation and representation of information, the mathematical sciences foster coherence and understanding that enable technology and broaden insights about the world of natural science.
The goal of the department is to acquaint students with this role as it relates to developments within the mathematical sciences as well as to applications to other disciplines. The department focuses on two distinct but complementary responsibilities: the mathematical sciences as an essential component of a liberal arts education and the mathematical sciences as a major course of study.
The department's courses present the many facets of the mathematical sciences: as a way of structuring the world of knowledge, as an art form, as an enabler in other disciplines, and as a historical force. As a consequence, the department provides the requisite mathematical, computational, and statistical content and methodology for allied disciplines as well as two comprehensive major programs.
The Major Programs
The department supports three majors: one in mathematics, one in computer science and mathematics, and one in computer science.
Students intending to major in any of these programs should have four years of high school mathematics, including, at a minimum, two years of algebra, a course in geometry, and a course in precalculus mathematics (including analytical geometry and trigonometry). Most well-prepared students begin their college mathematics programs with Calculus (Mathematics 131, 132, or 233) and their college computer science programs with Computer Science I (Computer Science 171). Students who have received Advanced Placement credit in calculus or computer science should consult with a member of the department for proper placement. For students without strong backgrounds in mathematics, the department offers Elementary Functions (Mathematics 115) to prepare them for work in calculus and computer science.
Students with interest in a professional career in the mathematical sciences should plan their curriculum to meet specific goals, as follows:
For graduate study in mathematics, Abstract Algebra I and II (Mathematics 421, 422); Advanced Calculus I and II (Mathematics 441, 442); as many additional upper-division mathematics courses as possible. These students should also be aware that many graduate programs require a reading knowledge of one or two foreign languages, usually chosen from among French, German, and Russian.
For graduate study in computer science, Theory of Computation (Computer Science 465).
For graduate study in statistics or a career in actuarial science, Numerical Analysis (Mathematics 345); Probability and Statistics I and II (Mathematics 451, 452).
For teaching in secondary or middle school, Number Theory (Mathematics 315); Geometry (Mathematics 355); Abstract Algebra I (Mathematics 421); Probability and Statistics I (Mathematics 451).
For a career in industry or applied mathematics, Statistical Concepts and Methods (Mathematics 255); Numerical Analysis (Mathematics 345); Complex Variables (Mathematics 365).
Students majoring in mathematics may also earn a minor in computer science; otherwise, students may not earn more than one major or minor from the department.
Major Requirements: Computer Science
A minimum of 44 semester credits in the mathematical sciences numbered 171 and above,* including the following:
- Computer Science 171, 172, 277, 230, and 383; Mathematics 255.
- At least 20 additional semester credits in computer science numbered 200 or above.
*To apply Mathematics 490 or Computer Science 495 to a major or minor requires consent of the department chair.
Major Requirements: Computer Science And Mathematics
A minimum of 40 semester credits in the mathematical sciences numbered 171 and above,* including the following:
- Computer Science 171, 172, 277, and 383; Mathematics 215 and 225. (Computer Science 230 does not count toward this major.)
- At least 8 additional semester credits in mathematics courses numbered 200 or above.
- At least 8 additional semester credits in computer science courses at the 300 or 400* level.
*To apply Mathematics 490 or Computer Science 495 to a major or minor requires consent of the department chair.
Major Requirements: Mathematics
A minimum of 36 semester credits in mathematics courses numbered 171 and above,* including the following:
- Computer Science 171; Mathematics 215, 225, 233, and 235. (Computer Science 230 does not count toward this major.)
- At least 16 additional semester credits at the 300 or 400* level, at least 12 of which must be in mathematics courses.
*To apply Mathematics 490 or Computer Science 495 to a major or minor requires consent of the department chair.
Minor Requirements: Computer Science
A minimum of 20 semester credits, including the following:
- Sixteen semester credits in computer science courses numbered 171 and above.
- Computer Science 230 or 4 semester credits in mathematics courses numbered 115 and above.
Minor Requirements: Mathematics
A minimum of 16 semester credits in mathematics courses numbered 171 and above,* including the following:
- Mathematics 215 and 225.
- At least 4 semester credits in mathematics at the 300 or 400* level.
(For information about Lewis & Clark's 3-2 cooperative program in computer science with the OGI School of Science & Engineering, see the Engineering listing in this catalog.)
*To apply Mathematics 490 or Computer Science 495 to a major or minor requires consent of the department chair.
Honors
The honors program in the mathematical sciences usually consists of either (1) a yearlong independent research project or (2) a summer research project followed by a one-semester independent study, culminating in an appropriate oral presentation and written form. After completing the 100- and 200-level courses required for one of the majors and enrolling in at least one course at the 300 or 400 level, an interested student with a cumulative GPA of 3.500 or higher, both in the major and overall, should consult the chair or the student's advisor concerning development and completion of a project.
Resources For Nonmajors
The following courses are designed with nonmajors in mind: Review of Algebra (Mathematics 055), designed for those not prepared to take college-level mathematics, addresses second- and third-year high school mathematics.
Perspectives in Mathematics (Mathematics 103), Perspectives in Statistics (Mathematics 105), and Perspectives in Computer Science (Computer Science 107) stress connections among contemporary mathematics, statistics, computer science, and modern society.
Elementary Functions (Mathematics 115) provides experience with the functions encountered in introductory calculus or computer science courses. Statistical Concepts and Methods (Mathematics 255) introduces the main ideas of modern statistics, with applications to problems encountered in various disciplines, especially the natural sciences.
Facilities
Lewis & Clark maintains microcomputer laboratories containing Windows and Apple computers in the library, several classroom facilities, and residence halls. All Lewis & Clark students have access to this computing machinery 24 hours a day, 7 days a week, for use in assigned coursework and independent projects. In addition, the department has two labs of 40 personal computers running LINUX and a small lab of 3 to 4 computers near the faculty offices. Students are encouraged to bring their own microcomputers to campus and use them independently or as terminals to access Lewis & Clark's file servers. To assist students, Lewis & Clark supports a discount purchase program for microcomputers.
Faculty And Staff
Suanne Benowicz, director of the Math Skills Center.
Naiomi T. Cameron, assistant professor of mathematics. Enumerative combinatorics, graph theory.
Yung-Pin Chen, associate professor of statistics. Statistics, sequential designs. Probability, stochastic processes.
Peter Drake, associate professor of computer science. Artificial intelligence/cognitive science. Programming languages.
Jeffrey S. Ely, associate professor of computer science. Computer graphics, numerical analysis.
Gregory A. Fredricks, professor of mathematics. Analysis, differential geometry.
John W. Krussel, professor of mathematics. Graph theory, combinatorics, cryptography.
Jens Mache, associate professor of computer science. Operating systems, computer architecture, parallel and distributed systems, computer networks.
Elizabeth Stanhope, assistant professor of mathematics. Differential geometry, spectral geometry.
Iva Stavrov, assistant professor of mathematics. Differential geometry, algebraic topology.
Computer Science
CS 107 Perspectives In Computer Science
Staff
Content: Introduction to computer science. Topics chosen from the following: programming languages, digital logic and computer architecture, algorithms. Programming concepts including applications of loops, assignment and "if" statements, arrays, user-defined functions. Emphasis on the writing of programs illustrating these concepts. Students who have received credit (including transfer credit) for Computer Science 171 or its equivalent may not register for this course.
Prerequisite: Mathematics 055 or equivalent.
Taught: Annually, 4 semester credits. May not be taken for credit if AP Computer Science credit has been granted.
CS 171 Computer Science I
Staff
Content: Basic techniques for solving problems amenable to solution through the use of a high-level computer programming language. Emphasis on solving a problem via a program and on the skills to write programs solving complex problems. Variables, data types, branches, loops, arrays, functional decomposition.
Prerequisite: Mathematics 115 or equivalent.
Taught: Each semester, 4 semester credits.
CS 172 Computer Science II
Staff
Content: Data structures and algorithmic techniques that are fundamental in programming solutions to complex problems. Abstract data types, lists, stacks, queues, trees, graphs. Array-based and linked structures. Use and simple analysis of iterative and recursive algorithms. Introduction to object-oriented programming.
Prerequisite: Computer Science 171 or consent of instructor.
Taught: Each semester, 4 semester credits.
CS 230 Computational Mathematics
Ely
Content: Overview of the kinds of problems that arise in calculus and physics. Emphasis on computer solutions. Topics include differentiation, integration, nonlinear equations, linear systems, ordinary differential equations, approximation, curve fitting.
Prerequisites: Mathematics 115 or equivalent. Computer Science 171.
Taught: Annually, 4 semester credits.
CS 277 Computer Architecture And Assembly Languages
Ely, Mache
Content: Computer design concepts and assembly languages. Topics chosen from the following: digital logic; arithmetic/logic unit design; bus structures; VLSI implementation; SIMD, MIMD, and RISC architectures; instruction sets; memory addressing modes; parameter passing; macro facilities.
Prerequisite: Computer Science 172.
Taught: Annually, 4 semester credits.
CS 363 Operating Systems
Mache
Content: Basic principles, policies, design issues, and construction of computer operating systems. Memory management, scheduling, synchronization of concurrent processes, input-output.
Prerequisite: Computer Science 277.
Taught: Alternate years, 4 semester credits.
CS 367 Computer Graphics
Ely
Content: Two- and three-dimensional computer graphics. Line, circle, filling, windowing, clipping algorithms, three-dimensional perspective projections, hidden line removal, shading, light models.
Prerequisites: Computer Science 172. Computer science 230 or equivalent. Familiarity with trigonometry, vectors helpful.
Taught: Annually, 4 semester credits.
CS 369 Artificial Intelligence
Drake
Content: Design and construction of intelligent computer systems. Agents and environments; blind and informed search; heuristics; game play, minimax, and alpha-beta pruning; robotics; machine learning; philosophical issues including definitions of intelligence.
Prerequisite: Computer Science 172.
Taught: Alternate years, 4 semester credits.
CS 373 Programming Language Structures
Drake, Ely
Content: Organization, structure, syntax, and grammar of computer programming languages. Basic concepts and special-purpose facilities in several representative high-level languages. Manual and automatic memory management, control structures, scope of declarations, higher-order functions, macros, objectoriented programming.
Prerequisite: Computer Science 172.
Taught: Alternate years, 4 semester credits.
CS 383 Algorithm Design And Analysis
Drake, Mache
Content: Introduction to the design and analysis of algorithms. Balanced binary search trees; bit vectors; hash tables; heaps; dynamic programming; algorithms including incremental, divide and conquer, greedy, graph.
Prerequisites: Computer Science 172. Mathematics 215 or Computer Science 230.
Taught: Annually, 4 semester credits.
CS 393 Computer Networks
Mache
Content: Study of the structure, implementation, and theoretical underpinnings of computer networks. Topic areas include Internet protocols, client-server computing, distributed applications.
Prerequisites: Computer Science 172 and 277.
Taught: Alternate years, 4 semester credits.
CS 465 Theory Of Computation
Staff
Content: Basic theoretical foundations of computer science including finite state and pushdown automata, Turing machines, computability, the halting problem, regular expressions, NP-completeness, the relationship between grammars and automata.
Prerequisites: Computer Science 172. Mathematics 215.
Taught: Alternate years, 4 semester credits.
CS 467 Advanced Computer Graphics
Ely
Content: Advanced three-dimensional computer graphics. Z-buffer algorithms, Phong smooth shading, ray tracing, texture mapping, spline patches.
Prerequisite: Computer Science 367.
Taught: Alternate years, 4 semester credits.
CS 487 Advanced Algorithms
Drake, Mache
Content: Advanced study of algorithm design and implementation. Preparation for programming competitions. Topics chosen from the following: dynamic programming, graph algorithms, network flow and matching, backtracking, constructing all subsets, constructing all permutations, high-precision arithmetic, geometric algorithms.
Prerequisite: Computer Science 383.
Taught: Annually, 4 semester credits.
CS 488 Software Development
Drake
Content: Development of large software systems by teams of programmers. Problem specification, system design, testing, software frameworks, design patterns.
Prerequisite: Computer Science 373 or 383.
Taught: Alternate years, 4 semester credits.
CS 495 Topics In Computer Science
Staff
Content: Determined by student and/or faculty interest. May continue topics from an existing course or explore new areas.
Prerequisite: Consent of instructor.
Taught: Alternate years, 4 semester credits. May be taken three times for credit under different topics.
Mathematics and Statistics
MATH 055 Review Of Algebra
Benowicz
Content: Solving linear, absolute value, quadratic, exponential, and logarithmic equations. Introduction to functions and their graphs. Conic sections, polynomial operations including factoring and rules for exponents, rational and radical expressions, inequalities and systems of equations.
Prerequisite: None.
Taught: Each semester, 4 semester credits, credit-no credit. Not counted toward the 128 semester credits needed for graduation.
MATH 103 Perspectives In Mathematics
Staff
Content: For nonmajors. Selected topics illustrating mathematics as a way of representing and understanding patterns and structures, as an art, as an enabler in other disciplines, and as a historical force. Emphasis changes from semester to semester, reflecting the expertise and interests of the faculty member teaching the course. For further information consult the appropriate faculty member before registration.
Prerequisite: Mathematics 055 or equivalent.
Taught: Annually, 4 semester credits.
MATH 105 Perspectives In Statistics
Staff
Content: Data analysis, data production, statistical inference. Data analysis: methods and ideas for organizing and describing data using graphs, numerical summaries, and other statistical descriptions. Data production: methods for selecting samples and designing experiments to produce data that can give clear answers to specific questions. Statistical inference: methods for moving beyond the data to draw conclusions about some wider universe.
Note: Students who have received credit for Economics 103, Psychology 200, or AP Statistics may not take this course for credit.
Prerequisite: Mathematics 055 or equivalent.
Taught: Annually, 4 semester credits.
MATH 115 Elementary Functions
Staff
Content: The basic functions encountered in calculus, discrete mathematics, and computer science: polynomial, rational, exponential, logarithmic, and trigonometric functions and their inverses. Graphs of these functions, their use in problem solving, their analytical properties.
Prerequisite: Mathematics 055 or equivalent.
Taught: Each semester, 4 semester credits. May not be taken for credit if AP Calculus credit has been granted.
MATH 131 Calculus I
Staff
Content: Basic analytical and quantitative reasoning and problem-solving skills that depend on the concept of the limit. Continuity, the derivative and its applications, the Fundamental Theorem of Calculus, introduction to the definite integral with applications.
Prerequisite: Mathematics 115 or equivalent.
Taught: Each semester, 4 semester credits. May not be taken for credit if AP Calculus credit has been granted.
MATH 132 Calculus II
Staff
Content: Further development of the definite integral including techniques of integration, applications of the definite integral, indeterminate forms, and improper integrals. Sequences, series of constants, power series, Taylor polynomials and series, introduction to elementary differential equations.
Prerequisite: Mathematics 131 or equivalent.
Taught: Each semester, 4 semester credits. May not be taken for credit if AP Calculus BC credit has been granted.
MATH 215 Discrete Mathematics
Staff
Content: Basic techniques of abstract formal reasoning and representation used in the mathematical sciences. First order logic, elementary set theory, proof by induction and other techniques, enumeration, relations and functions, graphs, recurrence relations.
Prerequisite: Mathematics 132 or equivalent.
Taught: Each semester, 4 semester credits.
MATH 225 Linear Algebra
Staff
Content: Basic skills and concepts that evolve from the study of systems of linear equations. Systems of linear equations, Euclidean vector spaces and function spaces, linear transformations, matrices and determinants, inner product spaces, eigenvalue problems, symmetric transformations.
Prerequisite: Mathematics 132 or equivalent.
Taught: Each semester, 4 semester credits.
MATH 233 Calculus III
Staff
Content: Basic analytical and quantitative skills in the theory of functions of several variables. Partial differentiation; gradients; multiple integrals; theorems of Green, Gauss, and Stokes.
Prerequisite: Mathematics 132 or equivalent.
Taught: Annually, 4 semester credits.
MATH 235 Differential Equations
Staff
Content: Basic methods, theory, and applications of differential equations. Solutions and the qualitative behavior of solutions of linear and nonlinear differential equations and of systems of differential equations, Laplace transform methods, numerical techniques.
Prerequisite: Mathematics 132 or equivalent.
Taught: Annually, 4 semester credits.
MATH 244 Math Practicum
Benowicz
Content: Tutoring opportunities (two to four hours onsite per week) at community schools to include one-on-one tutoring or classroom aid for site supervisor. Written reports and consultation with instructor required during semester. Specific math courses or grade levels to be determined by student, site supervisor, and instructor.
Prerequisite: Consent of instructor.
Taught: Each semester, 1-2 credits, credit-no credit. May be taken twice for credit with at most 2 credits counted toward math major.
MATH 255 Statistical Concepts And Methods
Chen, Nelsen
Content: Introduction to principal statistical concepts and methods with emphasis on data. Statistical thinking, the application of statistical methods to other disciplines, and the communication of statistics, both verbally and in writing. Exploratory data analysis, random variables, regression analysis, data production, and statistical inference. Mathematical tools and skills used to address problems posed by collecting, analyzing, and modeling data.
Prerequisite: Mathematics 131 or equivalent.
Taught: Annually, 4 semester credits.
MATH 281 Putnam Exam Preparation
Stavrov
Content: Emphasis on problem-solving skills required for success on the Putnam Exam. Participation in the exam is required to earn credit.
Prerequisite: None.
Taught: Annually, 1 semester credit, credit-no credit. May be taken twice for credit.
MATH 282 Modeling Competition Preparation
Stanhope
Content: Emphasis on mathematical modeling skills required for success in the COMAP Mathematical Modeling Competition and Interdisciplinary Modeling Competition. Participation in the competition is required to earn credit.
Prerequisite: None.
Taught: Annually, 1 semester credit, credit-no credit. May be taken twice for credit.
MATH 315 Number Theory
Staff
Content: Divisibility properties of the integers, unique factorization, linear Diophantine equations, congruences, Fermat's and Wilson's theorems, arithmetic functions. Other topics selected from the following: primitive roots and indices, quadratic reciprocity, the theory of prime numbers, continued fractions, sums of squares, analytic number theory.
Prerequisite: Mathematics 215 or consent of instructor.
Taught: Alternate years, 4 semester credits.
MATH 325 Combinatorics
Cameron, Krussel
Content: Introduction to combinatorial theory, including one or more of the following: enumeration, algebraic enumeration, optimization, graph theory, coding theory, design theory, finite geometries, Latin squares, posets, lattices, Polya counting, Ramsey theory.
Prerequisites: Mathematics 215 and 225 or consent of instructor.
Taught: Alternate years, 4 semester credits.
MATH 345 Numerical Analysis
Ely
Content: Study of the theoretical basis, error analysis, and practical techniques of numerical computations. Topics chosen from among: solutions of systems of linear equations, solutions of nonlinear equations, numerical integration and differentiation, solutions of ordinary differential equations, eigenvalue problems, interpolation, approximation.
Prerequisites: Computer Science 171. Mathematics 225 and 233.
Taught: Alternate years, 4 semester credits.
MATH 355 Geometry
Staff
Content: Concepts of geometry encompassing both Euclidean and non-Euclidean geometries. Parallelism, distance, angles, triangles, other geometric notions studied from the viewpoint of logic and foundations, transformations or differential geometry.
Prerequisite: Mathematics 215 or consent of instructor.
Taught: Alternate years, 4 semester credits.
MATH 365 Complex Variables
Staff
Content: Concepts of complex analysis. Complex number system, analytic functions, integration of functions of a complex variable, power series representation, conformal mappings, residue theory.
Prerequisites: Math 233 and 235 or consent of instructor.
Taught: Alternate years, 4 semester credits.
MATH 358 Topology
Stanhope, Stavrov
Content: Concepts of topology. Set theory, metric spaces, topological spaces, continuity, compactness, connectedness, and topological equivalence.
Prerequisite: Mathematics 215 or consent of instructor.
Taught: Alternate years, 4 semester credits.
MATH 421, 422 Abstract Algebra I, II
Cameron, Krussel
Content: A two-semester sequence in abstract algebraic systems. Structure of groups, subgroups, quotient groups, homomorphisms, Fundamental Isomorphism Theorems, rings, ideals, integral domains, polynomial rings, matrix rings, fields, Galois theory, advanced topics in linear algebra.
Prerequisites: Mathematics 215 and 225 or consent of instructor.
Taught: Alternate years, 4 semester credits each.
MATH 441, 442 Advanced Calculus I, II
Fredricks, Stanhope
Content: A two-semester sequence in the theory of the calculus. Development of the ability to understand, construct, and write proofs in analysis. Limits, continuity, differentiation, integration, applications, generalizations.
Prerequisites: Mathematics 215, 225, and 233 or consent of instructor.
Taught: Alternate years, 4 semester credits each.
MATH 451, 452 Probability And Statistics I, II
Chen, Nelsen
Content: A two-semester sequence in the theory of probability and mathematical statistics. Elementary probability, discrete and continuous random variables, distributions, limit theorems, point estimation, hypothesis testing, linear models, analysis of variance, nonparametric statistics.
Prerequisites: Mathematics 215 and 233 or consent of instructor.
Taught: Alternate years, 4 semester credits each.
MATH 490 Topics In Mathematics
Staff
Content: Determined by student and/or faculty interest. May continue topics from an existing course or explore new areas.
Prerequisite: Consent of instructor.
Taught: Alternate years (contingent on student interest and faculty availability), 4 semester credits. May be taken three times for credit under different topics.