MATHEMATICAL SCIENCES

Associate Professors: Haley, Peluso (Chairperson), Sprechini

Assistant Professors: deSilva, Yin

Part-time Instructors: Abercrombie, Collins, Davis, Knauth 

The Department of Mathematical Sciences offers major and minor programs in computer science and mathematics, and a minor in computational science.  Interested students may want to investigate the interdisciplinary actuarial mathematics major as well. 

COMPUTER SCIENCE (CPTR)  

The B. A. Degree

The B.A. degree in computer science consists of 13 courses: MATH 216; either MATH 109 or 128 (or exemption by examination from 128); one from MATH 112, 129, or 130; CPTR 125, 246, 247, 248, 346, 445, 448, and three other computer science courses numbered 220 or above including approved internships, or MATH 338.  

The B. S. Degree

The B.S. degree in computer science consists of 17 courses: MATH 128 (or exemption by examination from 128), 129, 216 and either 214 or 332; CPTR 125, 246, 247, 248, 346, 445, 448; three other computer science courses numbered 220 or above; one of the sequences BIO 110-111, CHEM 110-111, or PHYS 225-226; and one additional course from the following list of courses: Biology course numbered 110 or above, Chemistry course numbered 110 or above, Physics course numbered 225 or above, or MATH 130, 214, 231, 233, 234, 238, 332, 333. 

Students considering graduate work in computer science should take MATH 128, 129 and 130. Recommended extra-departmental course: PHIL 225. In addition to the regular courses listed below, special courses are occasionally available.  

The following courses, when scheduled as W courses, count toward the writing intensive requirement: CPTR 246, 247, 346, and 448.  

Minor

The Department of Mathematical Sciences offers two computing minors: Computer Science and Computational Science.

 
A minor in computer science consists of Math 216, CPTR 125, 246, 247, and two other computer science courses numbered 220 or above.

A minor in computational science consists of Math 216, CPTR 125, 246, and 247; one of CPTR 321, 345, or 349; and an approved computational research project in the student’s major discipline which can be fulfilled through ASTR/PHYS 448, BIO 454, CHEM 449, Independent Study, Honors Project, Research Experience for Undergraduates (REU), or other research experience. Computational science is the study of the application of computation to the sciences.  The minor in computational science provides students with a core understanding of computer-based problem solving and prepares them to apply that computational power in their chosen discipline. 

101

MICROCOMPUTER FILE MANAGEMENT

An introduction to a file-management system, i.e. a database system that uses a single file, in the Windows environment. One-half unit of credit. This course may not be used to meet distribution requirements.  

108

COMPUTING ESSENTIALS

An introduction to the use of computers in problem solving and programming. Included are uses of spreadsheets, databases, and programming. The course teaches the use of simple techniques in areas such as number theory, algebra, geometry, statistics, and the mathematics of business and finance. The programming component of the course is currently based on the Visual Basic programming language. Emphasis is given to the processes involved in mathematical modeling and problem solving. Laboratory experience is included using current software. Prerequisite: Credit for or exemption from MATH 100.  

125

INTRODUCTION TO COMPUTER SCIENCE

Introduction to the discipline of computer science with emphasis on programming utilizing a block-structured high-level programming language. Topics include algorithms, program structure, and computer configuration. Laboratory experience is included. Prerequisite: Credit for or exemption from MATH 100.  

246

PRINCIPLES OF ADVANCED PROGRAMMING

Principles of effective programming, including structured and object oriented programming, stepwise refinement, assertion proving, style, debugging, control structures, decision tables, finite state machines, recursion, and encoding. Prerequisite: A grade of C- or better in CPTR 125.  

247

DATA STRUCTURES

Representation of data and analysis of algorithms associated with data structures. Topics include representation of lists, trees, graphs and strings, algorithms for searching and sorting. Prerequisite: A grade of C- or better in CPTR 246, or consent of instructor. Corequisite: MATH 216.  

248

PROGRAMMING LANGUAGE DESIGN

Study of modern programming language design and implementation. Paradigms studied include procedural, functional, logic, and object-oriented. Topics include syntax, semantics, data types, data structures, storage management, and control structures. Laboratory experience is included. Prerequisite: CPTR 247.

321

INTRODUCTION TO NUMERICAL ANALYSIS

Topics from the theory of interpolation; numerical approaches to approximation of roots and functions, integration, systems of differential equations, linear systems, matrix inversion, and the eigenvalue problem. Prerequisites: CPTR 125 and MATH 129; MATH 130 strongly recommended. Cross-listed as MATH 321.  

324

AUTOMATA, FORMAL LANGUAGES, AND COMPUTABILITY

The study of finite state machines, pushdown stacks, and Turing machines along with their equivalent formal language counterparts. Topics covered include results on computability, including results regarding the limits of computers and specific problems that cannot be solved. Prerequisite: MATH 216 or 234. Cross-listed as MATH 324. Alternate years.  

331

COMPUTER NETWORKS

This course introduces the following computer networking concepts: LAN, WAN, FTP, TCP/IP, HTTP, network topologies, Ethernet, OSI model, routers, switches, and wiring technologies. Students will set up a LAN using a mix of available operating systems and networking software. Prerequisite: CPTR 246.  

342

WEB-BASED PROGRAMMING

Intermediate programming on the World Wide Web. Topics covered include client/server issues in Web publishing, Java Script, VB Script, Java, Perl, and CGI. Prerequisite: CPTR 246 or consent of instructor. Alternate years.  

345

INTRODUCTION TO COMPUTER GRAPHICS

An introduction to graphics hardware and software with emphasis on the mathematics necessary to represent, transform, and display images of two- and three-dimensional objects. Subjects covered include but not limited to: three dimensional modeling and viewing, color models, and rendering. Prerequisites: CPTR 246 and either CPTR 247 or consent of instructor; MATH 130 recommended. Alternate years.  

346

COMPUTER ORGANIZATION AND MACHINE LANGUAGE

Principles of computer organization, architecture, and machine language. Topics include machine and assembly languages, internal representation of data, processor data path and control, pipelined processors, memory hierarchies, and performance issues. Laboratory experience is included. Prerequisite: A grade of C- or better in CPTR 246; CPTR 247 strongly recommended.  

349

DATABASE SYSTEMS

An in-depth introduction to the relational database model and SQL. Topics include but are not limited to: relational algebra, relational calculus, normalization, design theory of relational databases, SQL standards, and query optimization. Prerequisite: CPTR 247. Alternate years.  

441

INTRODUCTION TOARTIFICIAL INTELLIGENCE

Introduction to the theory, implementation techniques, and applications of artificial intelligence. Topics may include but are not limited to knowledge representation, problem solving, modeling, robotics, natural language analysis, and computer vision. Prerequisite: CPTR 247. Alternate years.  

442

INTRODUCTION TO ROBOTICS

Designing, building and programming mobile robots. Some advanced topics are covered which may include control theory, robotic paradigms, and vision. Teamwork is essential in all projects. Prerequisite: CPTR 247.  

445

OPERATING SYSTEMS

Detailed analysis of processes, scheduling, multithreading, symmetric multiprocessing, file management, real and virtual memory management, file and memory addressing, and distributed processing. Prerequisites: CPTR 247 and 346.  

448

ADVANCED DESIGN AND DEVELOPMENT

Individual or group research and implementation projects. Includes analysis, design, development and documentation of a significant current, relevant problem and its computer-based solution. Prerequisite: CPTR 247. Alternate years.  

470

INTERNSHIP (See index)  

N80-N89

INDEPENDENT STUDY (See index)  

490-491

INDEPENDENT STUDY FOR DEPARTMENTAL HONORS (See index)  

MATHEMATICS (MATH)

A major in mathematics consists of CPTR 125, MATH 128 (or exemption by examination from 128), 129, 130, 234, 238, 432, 434, and two other mathematics courses numbered 220 or above, one of which may be replaced by MATH 112, 214 or 216. In addition, four semesters of non-credit math Colloquium are required: two semesters each of MATH 339 and MATH 449 with at least two of the four semesters for a letter grade, one of which must be in MATH 449. All majors are advised to elect PHIL 225, 333 and PHYS 225, 226. 

The following course, when scheduled as a W course, counts toward the writing intensive requirement: MATH 234. 

Students seeking secondary teacher certification in mathematics are required to complete MATH 330 as one of the two mathematics elective courses, and are also required to take a statistics course. The statistics course requirement can be satisfied by either taking one of MATH 214 or 332 as the second mathematics elective course, or by taking MATH 123 in addition to the second mathematics elective course. PHIL 217 is recommended. See the Education section (page 103) for additional secondary certification requirements. 

Students who are interested in pursuing a career in actuarial science should consider the actuarial mathematics major.  

Minor 

A minor in mathematics consists of MATH 128 (or exemption by examination from 128), 129, and either 216 or 234; 238; one additional course selected from 130, 214, or any course numbered 200 or above; and two semesters of MATH 339, Colloquium, one taken Pass/Fail, and one taken for a letter grade. The two semesters of colloquium may be replaced by any course numbered 220 or above.

100

INDIVIDUALIZED LABORATORY INSTRUCTION IN BASIC ALGEBRA

A computer-based program of instruction in basic algebra including arithmetic and decimals, fractions, the real number line, factoring, solutions to linear and quadratic equations, graphs of linear and quadratic functions, expressions with rational exponents, algebraic functions, exponential functions, and inequalities. This course is limited to students placed therein by the Mathematics Department. One-half unit of credit.  

106

COMBINATORICS

An introduction to the analysis of counting problems. Topics include permutations, combinations, binomial coefficients, inclusion/exclusion principle, and partitions. The nature of the subject allows questions to be posed in everyday language while still developing sophisticated mathematical concepts. Prerequisite: Credit for or exemption from MATH 100.  

109

APPLIED ELEMENTARY CALCULUS

An intuitive approach to the calculus concepts with applications to business, biology, and social-science problems. Not open to students who have completed MATH 128. Prerequisite: Credit for or exemption from MATH 100.

112

FINITE MATHEMATICS FOR DECISION-MAKING

An introduction to some of the principal mathematical models, not involving calculus, which are used in business administration, social sciences, and operations research. The course will include both deterministic models such as graphs, networks, linear programming and voting models, and probabilistic models such as Markov chains and games. Prerequisite: Credit for or exemption from MATH 100.  

123

INTRODUCTION TO STATISTICS

Topics include tabular and graphical descriptive statistics, discrete and continuous probability distributions, Central Limit Theorem, one- and two-sample hypotheses tests, analysis of variance, chi-squared tests, nonparametric tests, linear regression and correlation. Other topics may include index numbers, time series, sampling design, and experimental design. Course also includes some use of a microcomputer. Prerequisite: Credit for or exemption from MATH 100.  

127

PRECALCULUS MATHEMATICS
The study of polynomial, rational, exponential, logarithmic, and trigonometric functions, their graphs and elementary properties. This course is an intensive preparation for students planning to take Calculus (MATH 128-129) or Matrix Algebra (MATH 130), or those whose major specifically requires Precalculus.  This course is taught solely as a review of topics which must be mastered by students who intend to take MATH 128 or MATH 130. Prerequisite: Credit for or exemption from MATH 100.  Not for distribution. 

128-129

CALCULUS WITH ANALYTIC GEOMETRY I - II

Differentiation and integration of algebraic and trigonometric functions, conic sections and their applications, graphing plane curves, applications to related rate and external problems, areas of plane regions, volumes of solids of revolution, and other applications; differentiation and integration of transcendental functions, parametric equations, polar coordinates, infinite sequences and series, and series expansions of functions. Prerequisite for 128: Exemption from or a grade of C- or better in MATH 127. Prerequisite for 129: exemption from or a grade of C- or better in MATH 128.  

130

INTRODUCTION TO MATRIX ALGEBRA

Systems of linear equations and matrix arithmetic. Points and hyperplanes, infinite dimensional geometries. Bases and linear independence. Matrix representations of linear mappings. The fixed point problem. Special classes of matrices. Prerequisite: MATH 127 or its equivalent.  

214

MULTIVARIABLE STATISTICS
The study of statistical techniques involving several variables. Topics include confidence intervals and hypothesis tests about means and variances, confidence intervals and hypothesis tests with simple and multiple linear regression and correlation, assessing appropriateness of linear regression models, one-and two-way analysis of variance with post hoc tests, analysis of covariance, and analysis of contingency tables. Other topics may include discriminant analysis, cluster analysis, factor analysis and canonical correlations, repeated measure designs, time series analysis, and nonparametric methods. Course also includes extensive use of a statistical package (currently SPSS). Prerequisite: A grade of C- or better in MATH 123, or a grade of C- or better in both MATH 128 and any mathematics course numbered 129 or above; or consent of instructor. 

216

DISCRETE MATHEMATICS

An introduction to discrete structures. Topics include equivalence relations, partitions and quotient sets, mathematical induction, recursive functions, elementary logic, discrete number systems, elementary combinatorial theory, and general algebraic structures emphasizing semi-groups, lattices, Boolean algebras, graphs, and trees. Prerequisite: CPTR 125 or consent of instructor.  

231

DIFFERENTIAL EQUATIONS

A study of ordinary differential equations and linear systems. Solution techniques include: reduction of order, undetermined coefficients, variation of parameters, Laplace transforms, power series, and eigenvalues and eigenvectors. A brief discussion of numerical methods may also be included. Prerequisite: A grade of C- or better in MATH 129; MATH 130 recommended.  

233

COMPLEX VARIABLES

Complex numbers, analytic functions, complex integration, Cauchy’s theorems and their applications. Corequisite: MATH 238. Alternate years.  

234

FOUNDATIONS OF MATHEMATICS

Topics regularly included are the nature of mathematical systems, essentials of logical reasoning, and axiomatic foundations of set theory. Other topics frequently included are approaches to the concepts of infinity and continuity, and the construction of the real number system. The course serves as a bridge from elementary calculus to advanced courses in algebra and analysis. Prerequisite: A grade of C- or better in MATH 129 or 130; both courses recommended.  

238

MULTIVARIABLE CALCULUS

Algebra, geometry, and calculus in multidimensional Euclidean space; n-tuples, matrices; lines, planes, curves, surfaces; vector functions of a single variable, acceleration, curvature; functions for several variables, gradient; line integrals, vector fields, multiple integrals, change of variable, areas, volumes; Green’s theorem. Prerequisites: A grade of C- or better in MATH 129, and either MATH 130 or 231.  

321

INTRODUCTION TO NUMERICAL ANALYSIS

Topics from the theory of interpolation; numerical approaches to approximating roots and functions, integration, systems of differential equations, linear systems, matrix inversion,  and the eigenvalue problem. Prerequisites: CPTR 125 and MATH 129; MATH 130 strongly recommended. Cross-listed as CPTR 321.

324

AUTOMATA, FORMAL LANGUAGES, AND COMPUTABILITY

The study of finite state machines, pushdown stacks, and Turing machines along with their equivalent formal language counterparts. Topics covered include results on computability, including results regarding the limits of computers and specific problems that cannot be solved. Prerequisite: MATH 216 or 234. Cross-listed as CPTR 324. Alternate years.  

330

TOPICS IN GEOMETRY

An axiomatic treatment of Euclidean geometry with an historical perspective. Prerequisite: MATH 234. Alternate years.  

332-333

MATHEMATICAL STATISTICS I-II

A study of probability, discrete and continuous random variables, expected values and moments, sampling, point estimation, sampling distributions, interval estimation, test of hypotheses, regression and linear hypotheses, experimental design models. Corequisite: MATH 238. Alternate years.  

338

OPERATIONS RESEARCH

Queuing theory, including simulations techniques, optimization theory, including linear programming, integer programming, and dynamic programming; game theory, including two-person zero-sum games, cooperative games, and multiperson games. Prerequisite: MATH 112 or 130. Alternate years.  

400

TOPICS IN ACTUARIAL MATHEMATICS

Study of topics selected from those covered on the examinations administered by the Society of Actuaries, with the exception of the topics already covered in MATH 332-333. Prerequisite: The prerequisite(s) for this course will depend on the particular topic being taught. With consent of the instructor, this course may be repeated for credit. 

432

REAL ANALYSIS

An introduction to the rigorous analysis of the concepts of real variable calculus in the setting of normed spaces. Topics from: topology of the Euclidean plane, completeness, compactness, the Heine-Borel theorem; functions on Euclidean space, continuity, uniform continuity, differentiability; series and convergence; Riemann integral. Prerequisites: MATH 238 and a grade of C- or better in MATH 234.  

434

ABSTRACT ALGEBRA

An integrated approach to groups, rings, fields, and vector spaces and functions which preserve their structure. Prerequisites: MATH 130 and a grade of C- or better in MATH 234.

438

SEMINAR

Topics in modern mathematics of current interest to the instructor. A different topic is selected each semester. This semester is designed to provide junior and senior mathematics majors and other qualified students with more than the usual opportunity for concentrated and cooperative inquiry. Prerequisite: Consent of instructor. One-half unit of credit. This course may be repeated for credit.  

339 & 449

MATH COLLOQUIUM

This required non-credit course for mathematics majors and minors and actuarial mathematics majors offers students a chance to hear presentations on topics related to, but not directly covered in formal MATH courses. Mathematics majors present two lectures, one during the junior year and one during the senior year. Actuarial mathematics majors and mathematics minors present one lecture during one of the semesters in which they are enrolled. A letter grade will be given in semesters in which the student gives a presentation, otherwise the grade will be P/F. Prerequisite: Junior standing or consent of instructor. One hour per week.  

470-479

INTERNSHIP (See index)  

N80-N89

INDEPENDENT STUDY (See index)  

490-491

INDEPENDENT STUDY FOR DEPARTMENTAL HONORS (See index)