## Undergraduate Catalog

### Mathematical Sciences

###### Chair: Jens Mache

###### Administrative Coordinator: Anne Boal

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 aspects of the mathematical sciences: as a means of structuring the world of knowledge, as an art form, as an enabler of 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 three comprehensive major programs.

### Resources for Nonmajors

The following courses are designed with nonmajors in mind:

CS 102 Quantitative Reasoning is intended for those students who need more preparation for college-level mathematics and science. It replaces MATH 055. Students who do not pass Lewis & Clark's quantitative reasoning exam should enroll in this course.

MATH 103 Perspectives in Mathematics, MATH 105 Perspectives in Statistics, and CS 107 Perspectives in Computer Science stress connections among contemporary mathematics, statistics, computer science, and modern society.

MATH 115 Elementary Functions allows students to explore and become comfortable with the functions used in introductory calculus and computer science courses.

MATH 123 Mathematics for the Life Sciences introduces foundational quantitative skills that are relevant to problem solving in the life sciences.

MATH 255 Statistical Concepts and Methods introduces the main ideas of modern statistics, with applications to problems encountered in various disciplines, especially the natural sciences.

### 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 (MATH 131 Calculus I, MATH 132 Calculus II, or MATH 233 Calculus III) and their college computer science programs with CS 171 Computer Science I. 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 MATH 115 Elementary Functions 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.

**For graduate study in mathematics:**

MATH 421 | Abstract Algebra I | |

MATH 422 | Abstract Algebra II | |

MATH 441 | Real Analysis I | |

MATH 442 | Real Analysis II |

These students should take as many additional upper-division mathematics courses as possible. They 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:**

CS 465 | Theory of Computation |

**For graduate study in statistics or a career in actuarial science:**

MATH 345 | Numerical Analysis | |

MATH 451 | Probability and Statistics I | |

MATH 452 | Probability and Statistics II |

**For teaching in secondary or middle school:**

MATH 315 | Number Theory | |

MATH 355 | Geometry | |

MATH 421 | Abstract Algebra I | |

MATH 451 | Probability and Statistics I |

**For a career in industry or applied mathematics:**

MATH 255 | Statistical Concepts and Methods | |

MATH 345 | Numerical Analysis | |

MATH 365 | Complex Variables |

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:

- CS 171 Computer Science I
- CS 172 Computer Science II
- CS 230 Computational Mathematics
- CS 383 Algorithm Design and Analysis
- One of the following:
CS 277 Computer Architecture and Assembly Languages CS 393 Computer Networks - MATH 255 Statistical Concepts and Methods
- At least 20 additional semester credits in computer science numbered 200 or above.

### Major Requirements: Computer Science and Mathematics

A minimum of 40 semester credits in the mathematical sciences numbered 171 and above,* including the following:

- CS 171 Computer Science I
- CS 172 Computer Science II
- CS 383 Algorithm Design and Analysis
- One of the following:
CS 277 Computer Architecture and Assembly Languages CS 393 Computer Networks - MATH 215 Discrete Mathematics
- MATH 225 Linear Algebra
- 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.

CS 230 Computational Mathematics does not count toward this major.

### Major Requirements: Mathematics

A minimum of 36 semester credits in mathematics courses numbered 171 and above,* including the following:

- CS 171 Computer Science I
- MATH 215 Discrete Mathematics
- MATH 225 Linear Algebra
- MATH 233 Calculus III
- At least 16 additional semester credits at the 300 or 400* level, at least 12 of which must be in mathematics courses.

CS 230 Computational Mathematics does not count toward this major.

### Minor Requirements: Computer Science

A minimum of 20 semester credits, including the following:

- Sixteen semester credits in computer science courses numbered 171 and above.
- CS 230 Computational Mathematics 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:

- MATH 215 Discrete Mathematics
- MATH 225 Linear Algebra
- At least 4 semester credits in mathematics at the 300 or 400* level.

**To apply MATH 490 Topics in Mathematics or CS 495 Topics in Computer Science to a major or minor requires consent of the department chair.*

### Honors

The honors program in the mathematical sciences usually consists of either (a) a yearlong independent research project, or (b) a summer research project followed by one semester of 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.

#### Faculty

Paul T. Allen. Assistant professor of mathematics. Geometric analysis, differential equations, mathematical relativity. Ph.D. 2007, M.S. 2003 University of Oregon. B.S. 2001 University of Puget Sound.

Margot Black. Director of the Math Skills Center. M.S. 2005 University of Oregon. B.A. 2003 Lewis & Clark College.

Naiomi T. Cameron. Associate professor of mathematics. Enumerative combinatorics, graph theory. Ph.D. 2002, B.S. 1995 Howard University.

Yung-Pin Chen. Professor of statistics. Statistics, sequential designs. Probability, stochastic processes. Ph.D. 1994 Purdue University. B.S. 1984 National Chengchi University, Taiwan.

Peter Drake. Associate professor of computer science. Artificial intelligence/cognitive science. Programming languages. Ph.D. 2002 Indiana University. M.S. 1995 Oregon State University. B.A. 1993 Willamette University.

Jeffrey S. Ely. Associate professor of computer science. Computer graphics, numerical analysis. Ph.D. 1990, M.S. 1981, B.S. 1976 Ohio State University.

John W. Krussel. Professor of mathematics. Graph theory, combinatorics, cryptography. Ph.D. 1987, M.S. 1983 Colorado State University. B.A. 1977 Saint Louis University.

Jens Mache. Professor of computer science, chair of the Department of Mathematical Sciences. Operating systems, computer architecture, parallel and distributed systems, computer networks. Ph.D. 1998 University of Oregon. M.S. 1994 Southern Oregon University. Vordiplom 1992 Universitaet Karlsruhe.

Elizabeth A. Stanhope. Associate professor of mathematics. Differential geometry, spectral geometry. Ph.D. 2002, A.M. 1999 Dartmouth College. B.A. 1995 Carleton College.

Iva Stavrov. Associate professor of mathematics. Differential geometry, algebraic topology. Ph.D. 2003, M.S. 2001 University of Oregon. B.S. 1998 University of Belgrade.

Sweta Suryanarayan. Visiting assistant professor of mathematics. Ph.D. 2012 University of Washington. M.Sc. 2004 Indian Institute of Technology. B.Sc. 2002 SIES College of Arts, Science and Commerce, University of Mumbai.

#### Computer Science

**CS 102 Quantitative Reasoning**

Faculty: Ely, Schleef, Black.

Content: Cultivation of logical thinking and
problem-solving skills using mathematical models
to analyze problems and cases. Focus on
effectively reporting results and conclusions.
Application of appropriate computational
techniques, including introduction to statistical
analysis of real number data, scientific notation,
units of measurement, solving simple (systems of)
algebraic equations, rates of change, representing
data in rectangular coordinates, rules of
exponents and logarithms, logarithmic scale,
linear regression, geometry of right-angled
triangles.

Prerequisites: None.

Usually offered: Annually, fall and spring semester.

Semester credits: 2.

**CS 107 Perspectives in Computer Science**

Faculty: Mathematical Sciences Faculty.

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 and
advanced standing credit) for CS 171 or its
equivalent may not register for this course.

Prerequisites: CS 102, MATH 055, or equivalent.

Usually offered: Annually, fall and spring semester.

Semester credits: 4.

**CS 171 Computer Science I**

Faculty: Mathematical Sciences Faculty.

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.

Prerequisites: MATH 115 or equivalent.

Usually offered: Annually, fall and spring semester.

Semester credits: 4.

**CS 172 Computer Science II**

Faculty: Mathematical Sciences Faculty.

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.

Prerequisites: CS 171 or consent of instructor.

Usually offered: Annually, fall and spring semester.

Semester credits: 4.

**CS 230 Computational Mathematics**

Faculty: Mathematical Sciences Faculty.

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: MATH 115 or equivalent. CS 171.

Usually offered: Annually, fall semester.

Semester credits: 4.

**CS 277 Computer Architecture and Assembly Languages**

Faculty: Mathematical Sciences Faculty.

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.

Prerequisites: CS 172.

Usually offered: Annually, spring semester.

Semester credits: 4.

**CS 363 Operating Systems**

Faculty: Mathematical Sciences Faculty.

Content: Basic principles, policies, design issues, and
construction of computer operating systems. Memory
management, scheduling, synchronization of
concurrent processes, input-output.

Prerequisites: CS 277.

Restrictions: Sophomore standing required.

Usually offered: Alternate Years, spring semester.

Semester credits: 4.

**CS 367 Computer Graphics**

Faculty: Mathematical Sciences Faculty.

Content: Two- and three-dimensional computer graphics.
Line, circle, filling, windowing, clipping
algorithms, three-dimensional perspective
projections, hidden line removal, shading, light
models.

Prerequisites: CS 172. CS 230 or equivalent. Familiarity with trigonometry,
vectors helpful.

Restrictions: Sophomore standing required.

Usually offered: Annually, fall semester.

Semester credits: 4.

**CS 369 Artificial Intelligence**

Faculty: Mathematical Sciences Faculty.

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.

Prerequisites: CS 172.

Restrictions: Sophomore standing required.

Usually offered: Alternate Years, spring semester.

Semester credits: 4.

**CS 373 Programming Language Structures**

Faculty: Mathematical Sciences Faculty.

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, object-oriented programming.

Prerequisites: CS 172.

Restrictions: Sophomore standing required.

Usually offered: Alternate Years, fall semester.

Semester credits: 4.

**CS 383 Algorithm Design and Analysis**

Faculty: Mathematical Sciences Faculty.

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: CS 172. MATH 215 or CS 230.

Restrictions: Sophomore standing required.

Usually offered: Annually, spring semester.

Semester credits: 4.

**CS 393 Computer Networks**

Faculty: Mathematical Sciences Faculty.

Content: The structure, implementation, and theoretical
underpinnings of computer networks. Topic areas
include Internet protocols, client-server
computing, distributed applications.

Prerequisites: CS 172.

Restrictions: Sophomore standing required.

Usually offered: Alternate Years, fall semester.

Semester credits: 4.

**CS 465 Theory of Computation**

Faculty: Mathematical Science Faculty.

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: CS 172. MATH 215.

Restrictions: Sophomore standing required.

Usually offered: Alternate Years, fall semester.

Semester credits: 4.

**CS 467 Advanced Computer Graphics**

Faculty: Mathematical Sciences Faculty.

Content: Advanced three-dimensional computer graphics.
Z-buffer algorithms, Phong smooth shading, ray
tracing, texture mapping, spline patches.

Prerequisites: CS 367.

Restrictions: Sophomore standing required.

Usually offered: Alternate Years, spring semester.

Semester credits: 4.

**CS 487 Advanced Algorithms**

Faculty: Mathematical Sciences Faculty.

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.

Prerequisites: CS-383.

Restrictions: Sophomore standing required.

Usually offered: Annually, fall semester.

Semester credits: 4.

**CS 488 Software Development**

Faculty: Drake.

Content: Development of large software systems by teams of
programmers. Problem specification, system design,
testing, software frameworks, design patterns.

Prerequisites: CS 373 or CS 383.

Restrictions: Sophomore standing required.

Usually offered: Alternate Years, spring semester.

Semester credits: 4.

**CS 495 Topics in Computer Science**

Faculty: Mathematical Sciences Faculty.

Content: Determined by student and/or faculty interest. May
continue topics from an existing course or explore
new areas. May be taken three times for credit
under different topics.

Prerequisites: Consent of instructor.

Restrictions: Sophomore standing required.

Usually offered: Alternate Years, fall and spring semester.

Semester credits: 4.

#### Mathematics and Statistics

**MATH 055 Review of Algebra**

Faculty: Mathematical Sciences Faculty.

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. Credit-no credit. Not counted toward
the 128 semester credits needed for graduation.

Prerequisites: None.

Usually offered: Annually, fall, spring, and summer.

Semester credits: 4.

**MATH 103 Perspectives in Mathematics**

Faculty: Mathematical Sciences Faculty.

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.

Prerequisites: CS 102, MATH 055, or equivalent.

Usually offered: Annually, fall semester.

Semester credits: 4.

**MATH 105 Perspectives in Statistics**

Faculty: Mathematical Sciences Faculty.

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 ECON 103, PSY 200, or AP
Statistics may not take this course for credit.

Prerequisites: CS 102, MATH 055, or equivalent.

Usually offered: Annually, fall semester.

Semester credits: 4.

**MATH 115 Elementary Functions**

Faculty: Mathematical Sciences Faculty.

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. May not be
taken for credit if AP Calculus credit has been
granted.

Prerequisites: CS 102, MATH 055, or equivalent.

Usually offered: Annually, fall and spring semester.

Semester credits: 4.

**MATH 123 Mathematics for the Life Sciences**

Faculty: Kennedy, Stanhope.

Content: This course will use case studies to introduce
students to foundational quantitative skills that
are relevant to problem solving in the life
sciences. Included are topics in probability,
statistics, dynamic modeling, and algorithms.

Prerequisites: MATH 115 or equivalent; BIO 141 or BIO 151, or consent of
instructor.

Usually offered: Annually, fall semester.

Semester credits: 4.

**MATH 131 Calculus I**

Faculty: Mathematical Sciences Faculty.

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. May not be taken for credit if AP
Calculus credit has been granted.

Prerequisites: MATH 115 or equivalent.

Usually offered: Annually, fall and spring semester.

Semester credits: 4.

**MATH 132 Calculus II**

Faculty: Mathematical Sciences Faculty.

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. May not be taken for credit if AP
Calculus BC credit has been granted.

Prerequisites: MATH 131 or equivalent.

Usually offered: Annually, fall and spring semester.

Semester credits: 4.

**MATH 215 Discrete Mathematics**

Faculty: Mathematical Sciences Faculty.

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.

Prerequisites: MATH 132 or equivalent.

Usually offered: Annually, fall and spring semester.

Semester credits: 4.

**MATH 225 Linear Algebra**

Faculty: Mathematical Sciences Faculty.

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.

Prerequisites: MATH 132 or equivalent.

Usually offered: Annually, fall and spring semester.

Semester credits: 4.

**MATH 233 Calculus III**

Faculty: Mathematical Sciences Faculty.

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.

Prerequisites: MATH 132 or equivalent.

Usually offered: Annually, fall and spring semester.

Semester credits: 4.

**MATH 235 Differential Equations**

Faculty: Mathematical Sciences Faculty.

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.

Prerequisites: MATH 132 or equivalent.

Usually offered: Annually, spring semester.

Semester credits: 4.

**MATH 244 Math Practicum**

Faculty: Mathematical Sciences Faculty.

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.
Credit-no credit. May be taken twice for credit
with at most 2 credits counted toward math major.

Prerequisites: None.

Restrictions: Sophomore standing and consent required.

Usually offered: Annually, fall and spring semester.

Semester credits: 1-4.

**MATH 255 Statistical Concepts and Methods**

Faculty: Chen.

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.

Prerequisites: MATH 131 or equivalent.

Usually offered: Annually, spring semester.

Semester credits: 4.

**MATH 281 Putnam Exam Preparation**

Faculty: Stavrov.

Content: Emphasis on problem-solving skills required for
success on the Putnam Exam. Participation in the
exam is required to earn credit. Credit-no credit.
May be taken twice for credit.

Prerequisites: None.

Restrictions: Sophomore standing and consent required.

Usually offered: Annually.

Semester credits: 1.

**MATH 282 Modeling Competition Preparation**

Faculty: 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. Credit-no credit. May be
taken twice for credit.

Prerequisites: None.

Restrictions: Sophomore standing and consent required.

Usually offered: Annually, spring semester.

Semester credits: 1.

**MATH 305 Calculus IV With Applications to the Physical Sciences**

Faculty: Allen.

Content: Using techniques of multivariate calculus to
derive and study the classical linear partial
differential equations. Topics include the
calculus of variations, initial and boundary value
problems, the method of separation of variables,
Hilbert spaces, and Fourier series. Additional
topics may include special functions, the Fourier
transform, and Green's functions. Math 235 may be
taken concurrently with permission of instructor.

Prerequisites: MATH 233, MATH 235.

Restrictions: Sophomore standing required.

Usually offered: Annually, spring semester.

Semester credits: 4.

**MATH 315 Number Theory**

Faculty: Mathematical Sciences Faculty.

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.

Prerequisites: MATH 215 or consent of instructor.

Restrictions: Sophomore standing required.

Usually offered: Alternate Years, fall semester.

Semester credits: 4.

**MATH 325 Combinatorics**

Faculty: 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: MATH 215 and MATH 225 or consent of instructor.

Restrictions: Sophomore standing required.

Usually offered: Alternate Years, spring semester.

Semester credits: 4.

**MATH 345 Numerical Analysis**

Faculty: Ely.

Content: The theoretical basis, error analysis, and
practical techniques of numerical computations.
Topics chosen from the following: solutions of
systems of linear equations, solutions of
nonlinear equations, numerical integration and
differentiation, solutions of ordinary
differential equations, eigenvalue problems,
interpolation, approximation.

Prerequisites: CS 171. MATH 225. MATH 233.

Restrictions: Sophomore standing required.

Usually offered: Alternate Years, spring semester.

Semester credits: 4.

**MATH 355 Geometry**

Faculty: Mathematical Sciences Faculty.

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.

Prerequisites: MATH 215 or consent of instructor.

Restrictions: Sophomore standing required.

Usually offered: Alternate Years, fall semester.

Semester credits: 4.

**MATH 358 Topology**

Faculty: Allen, Stanhope, Stavrov.

Content: Concepts of topology. Set theory, metric spaces,
topological spaces, continuity, compactness,
connectedness, and topological equivalence.

Prerequisites: MATH 215 or consent of instructor.

Restrictions: Sophomore standing required.

Usually offered: Alternate Years, fall semester.

Semester credits: 4.

**MATH 365 Complex Variables**

Faculty: Mathematical Sciences Faculty.

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 or consent of instructor.

Restrictions: Sophomore standing required.

Usually offered: Alternate Years, fall semester.

Semester credits: 4.

**MATH 421 Abstract Algebra I**

Faculty: 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: MATH 215 and MATH 225, or consent of instructor.

Restrictions: Sophomore standing required.

Usually offered: Alternate Years, fall semester.

Semester credits: 4.

**MATH 422 Abstract Algebra II**

Faculty: 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: MATH 215 and MATH 225, or consent of instructor.

Restrictions: Sophomore standing required.

Usually offered: Alternate Years, spring semester.

Semester credits: 4.

**MATH 441 Real Analysis I**

Faculty: Stanhope, Stavrov.

Content: A two-semester sequence in mathematical analysis.
Development of the ability to understand,
construct, and write proofs in analysis. Limits,
continuity, differentiation, integration, metric
spaces, applications, generalizations.

Prerequisites: MATH 215.

Restrictions: Sophomore standing required.

Usually offered: Alternate Years, fall semester.

Semester credits: 4.

**MATH 442 Real Analysis II**

Faculty: Stanhope, Stavrov.

Content: A two-semester sequence in the theory of
mathematical analysis. Development of the ability
to understand, construct, and write proofs in
analysis. Limits, continuity, differentiation,
integration, metric spaces, applications,
generalizations.

Prerequisites: MATH 225, MATH 233, and MATH 441, or consent of instructor.

Restrictions: Sophomore standing required.

Usually offered: Alternate Years, spring semester.

Semester credits: 4.

**MATH 451 Probability and Statistics I**

Faculty: Chen.

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: MATH 215 and MATH 233, or consent of instructor.

Restrictions: Sophomore standing required.

Usually offered: Alternate Years, fall semester.

Semester credits: 4.

**MATH 452 Probability and Statistics II**

Faculty: Chen.

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: MATH 215 and MATH 233, or consent of instructor.

Restrictions: Sophomore standing required.

Usually offered: Alternate Years, spring semester.

Semester credits: 4.

**MATH 490 Topics in Mathematics**

Faculty: Mathematical Sciences Faculty.

Content: Determined by student and/or faculty interest. May
continue topics from an existing course or explore
new areas. May be taken three times for credit
under different topics.

Prerequisites: None.

Restrictions: Sophomore standing and consent required.

Usually offered: Alternate Years, fall and spring semester.

Semester credits: 4.