Mathematics and Computer Science
Chair James P. BrumbaughSmith, Raheel Ahmad, Timothy M. Brauch, Young S. Lee, Andrew F. Rich
The Department of Mathematics & Computer Science seeks to graduate students who can: appropriately analyze a wide variety of mathematical and computing problems, understand and apply relevant theory and technology to solve realworld problems, develop and implement insightful and efficient solutions, and effectively communicate both abstract ideas and practical solutions.
Entering students take a placement test in mathematics prior to enrolling in courses. The test results in conjunction with other criteria are used to place students in an appropriate mathematics course. Advanced placement credit in calculus and statistics is possible for students who have an especially strong mathematical background.
MATHEMATICS
Courses in mathematics are designed for students who want to: acquire cultural knowledge of mathematics and its applications, apply mathematical principles of analysis and modeling in the natural and social sciences and also in industry, prepare for graduate studies in mathematics or related disciplines, and become teachers of mathematics at the precollege and college levels.
Baccalaureate Degree
Courses listed in parentheses are prerequisites.
Major in mathematics, 4244 hours: MATH 121, 122, 130, 231, 240, 251, 421, 433, three hours of 499; Nine hours of approved electives, selected from: (CPTR 105) MATH 233, 245, 306, 330, 340, 380 or 480, 385 or 485; (PHYS 210, 220) PHYS 301 or (CHEM 211 and PHYS 210, 220) CHEM 341; (ECON 221) ECON 350; (CPTR 205) CPTR 310, 499.
Majors must successfully complete the senior comprehensive evaluation prior to graduation. Details are available from the department chair.
Minor in mathematics, 25 hours: MATH 121, 130; 17 hours of electives selected from: MATH 122, 231, (CPTR 105) 233, MATH 240, 245, 251, 306, 330, 340, 421, 433, 380 or 480, 385 or 485; (PHYS 210, 220) PHYS 301 or (CHEM 211 and PHYS 210, 112) CHEM 341; (CPTR 205) CPTR 310; (ECON 221) ECON 350.
Requirements for teaching majors are available in the Office of Teacher Education.
Courses MATH
100 BASIC MATHEMATICS  2 hours
A review of topics in arithmetic including: fractions, decimals, proportions and percents, signed numbers, order of operations, approximation and rounding, unit conversion, exponents, small and large numbers, and scientific notation.
Fall.
105 BASIC ALGEBRA  2 hours
A review of topics in elementary algebra including: inequalities; graphing of equations; problem solving using linear, quadratic and exponential equations; solving equations involving exponents and roots. Prerequisite: MATH 100 or placement. Fall. January or Spring.
107 MATHEMATICS FOR ELEMENTARY TEACHERS  3 hours
A course designed especially for the teacher of elementary school mathematics. Topics include: sets, logic, problem solving, functions, intuitive geometry, transformational geometry and measurement. Prerequisite: MATH 105 or placement. Fall. Spring.
112 COLLEGE ALGEBRA  3 hours
Topics include: exponents and radicals, factoring, linear and quadratic equations, linear inequalities, graphs and functions, polynomials, exponential and logarithmic functions, and systems of linear equations. Prerequisite: placement.
113 QUANTITATIVE REASONING  3 hours
A survey of skills for understanding quantitative data in modern life. This course focuses on: interpretation (and misinterpretation) of percentages, probabilities and statistics in contemporary decisionmaking; understanding of survey and experimental results as reported in mass media; and making logical and persuasive quantitative arguments. Course is designed primarily for students seeking the B.A. degree and does not satisfy the quantitative requirement for B.S. students. This course may not be taken by students who have previous credit for (or are concurrently enrolled in) MATH 115, 210 or 240. Prerequisite: MATH 105 or placement. Spring. C1Q.
115 ELEMENTARY PROBABILITY AND STATISTICS  3 hours
A course focusing on problemsolving and decisionmaking skills using the tools of probability and statistics. Topics include: basic and conditional probabilities, probability trees, expected value, normal distributions, application of randomization to sampling and experimentation, graphical and numerical summaries of data, uses and abuses of statistical data, and introduction to confidence intervals, hypothesis testing and regression models. This course satisfies the Q requirement for both B.A. and B.S. students. This course may not be taken by students who have previous credit for (or are concurrently enrolled in) MATH 210 or 240. Prerequisite: MATH 105 or placement. Fall. Spring. C1Q.
120 PRECALCULUS  3 hours
Topics include: graphs and functions, polynomials and their zeros, complex numbers, exponential and logarithmic functions, trigonometry (functions, graphs and identities) and applications. Prerequisite: MATH 105 or placement. Fall. January.
121 CALCULUS I  4 hours
An introduction to calculus including limits, continuity, derivatives and their applications, curve sketching, integrals and the Fundamental Theorem of Calculus. Trigonometric, exponential and logarithmic functions are included. Graphing calculators will be used. Prerequisite: MATH 120 or placement. Fall. Spring. C1Q.
122 CALCULUS II  4 hours
Topics include: numerical integration, applications of integration, techniques of integration, inverse trigonometric functions, an introduction to differential equations, improper integrals, sequences and series and Taylor’s Theorem. A computeralgebra system will be used. Prerequisite: MATH 121. Fall. Spring.
130 DISCRETE MATHEMATICS  4 hours
An introduction to discrete methods used in mathematics and computer science. Principal topics covered are: logic, sets, algorithms, number theory, reasoning and proof, recursion, combinatorics, relations and graph theory. Prerequisite: MATH 120 or consent of the instructor. Spring.
210 STATISTICAL ANALYSIS  4 hours
An introduction to statistical techniques used in the social and natural sciences. Topics include: graphical and numerical summaries of data; sampling and experimental design; elementary probability; binomial, uniform, normal, student’s t, and chisquared distributions; hypothesis tests and confidence intervals for means and proportions, ANOVA, and linear regression. Statistical software is introduced during weekly lab sessions. Students are expected to be proficient in using computer applications and the campus network. This course satisfies the Q requirement for both B.A. and B.S. students. This course may not be taken by students who have previous credit for (or are concurrently enrolled in) MATH 240. Prerequisite: MATH 105 or placement.
Fall. January. Spring. C1Q.
231 MULTIVARIABLE CALCULUS  4 hours
Topics include: vector analysis in twoand threedimensional spaces, polar and spherical coordinates, curves in space; multivariable functions and their derivatives, multiple integrals, line integrals, and Green’s and Stokes’ Theorems. Prerequisites: MATH 122, 251. Spring.
233 NUMERICAL ANALYSIS  3 hours
A study of computational issues and methods used in applied mathematics and scientific computing. Topics include: computation errors; interpolation; convergence of numerical methods; approximate integration; numerical solution of ordinary differential equations; and numerical solution to systems of linear and nonlinear equations. The course is oriented toward machine computation and involves programming of various solution techniques. Prerequisite: MATH 121. Spring, odd years.
240 MATHEMATICAL STATISTICS  4 hours
Basic concepts of probability; expectation; variance, covariance, distribution functions; bivariate, marginal and conditional distributions. Treatment of experimental data; normal sampling theory; confidence intervals and test of hypotheses; introduction to regression and to analysis of variance. Prerequisite: MATH 122. Fall, odd years.
245 ORDINARY DIFFERENTIAL EQUATIONS  3 hours
Topics include: classification of differential equations; methods of solving first order equations, second and higher order linear equations, and systems of linear equations; series solutions; and existence theorems. Prerequisite: MATH 122. Spring, even years.
251 LINEAR ALGEBRA I  4 hours
Solution of linear systems, matrices and determinants, eigenvalues and eigenvectors, vector algebra, representation of lines and planes in Rn, linear transformations and mathematical models using matrix algebra. Prerequisites: MATH 121, 130; or consent of the instructor. Fall.
303 MATHEMATICS CURRICULUM AND METHODS  3 hours
The study of curriculum, methodology, computer applications, materials, and assessment appropriate for early childhood and elementary school (preK6th grades) mathematics programs. Field experience is a required component. Taken as part of the Elementary Methods Block. Prerequisites: MATH 107 and EDUC 340.
306 GEOMETRY  3 hours
A study of the logical structure and content of both Euclidean and nonEuclidean geometries. The approach to Euclidean geometry is via Hilbert’s axioms. Prerequisite: MATH 251. Fall, even years.
330 OPERATIONS RESEARCH MODELS  3 hours
Introduction to mathematical modeling processes; allocation models involving linear programming; simplex algorithm; dynamic programming; transportation models; network models; graph theory; Markov chain models; queuing theory and game theory. Prerequisite: MATH 130 or 251 or consent of instructor. January or spring, even years.
340 LINEAR ALGEBRA II  3 hours
Numerical methods for solving linear systems, the four fundamental subspaces and applications, orthogonality and approximation, eigenvectors, eigenvalues, and diagonalization of matrices and applications. Prerequisite: MATH 251. Spring, odd years.
421 REAL ANALYSIS  3 hours
Topics include: the completeness of the real number system; sequences and their limits; elementary pointset topology; and continuity and uniform continuity. The theory of series, the derivative and the Riemann integral will be treated as time permits. Prerequisites: MATH 130, 231. Fall, even years.
433 ALGEBRAIC STRUCTURES  4 hours
Basic properties of groups, rings, factor groups, ideals, quotient rings, integral domains, fields, polynomials and elementary number theory. Prerequisite: MATH 251. Fall, odd years.
475 INTERNSHIP IN MATHEMATICS  13 hours
Students work in business, industry, government or other agencies applying mathematical tools (e.g., probability, statistics, optimization) to realworld problems. Students are supervised by a professional with significant experience in such applications and also a faculty member. A written report describing the overall project and the student’s contribution will complete the course. Students must formally enroll in this course prior to beginning their work experience. Course may be repeated once for a maximum of four hours credit. Prerequisite: MATH 130, 122; permission of the department chair.
499 SENIOR PROJECT (W)  13 hours
An indepth study of some area of mathematics under the guidance of a primary and secondary faculty advisor. Students will write a thesis and give an oral presentation based on the thesis. Students will enroll either once or twice for a total of three hours credit. Prerequisite: ENG 111; permission of the department chair.
380 or 480 SPECIAL PROBLEMS  14 hours
A student who has demonstrated ability to work independently may propose a course and pursue it with a qualified and willing professor. The department chair and the vice president and dean for academic affairs must also approve. A set of guidelines is available at the Office of the Registrar.
385 or 485 SEMINAR  14 hours
An indepth consideration of a significant scholarly problem or issue. Students pursue a supervised, independent inquiry on an aspect of the topic and exchange results through reports and discussions.
COMPUTER SCIENCE
Courses in computer science are designed for students who want to: acquire a conceptual foundation for understanding and working with computers in a continuously changing field, learn practical skills in programming and software development, prepare for careers in computing in business and industry, and prepare for further study in computer science or information systems. Emphasis is placed on working with a variety of industries and software companies to provide students with realworld software experience through classroom projects, internships and senior research.
Baccalaureate Degree
Courses listed in parentheses are prerequisites.
Major in computer science, 4344 hours: CPTR 105, 205, 225, 308, 310, 314, 331, 333; three hours of CPTR 475 or 499; MATH 121, 130, 251; one course selected from: CPTR 121, 324, 410, 415; MATH 233.
Majors must successfully complete the senior comprehensive evaluation prior to graduation. Details are available from the department chair.
Minor in computer science, 2224 hours: CPTR 105, 205; MATH 130; four courses selected from : CPTR 121, 225, 308, 310, 314, 324, 331, 333, 410, 415; MATH 233.
Minor in information systems, 2630 hours: ACCT 211, BUS 111, 310; CPTR 105, 205; (MATH 120) MATH 130; two hours of BUS 106 on different topics; one course selected from: CPTR 121, 225, 308, 314.
Associate of Arts Degree
Major in computer applications, 2325 hours: CPTR 105, 205; MATH 130, 120 or 121; three hours of BUS 106 on different topics; two courses selected from CPTR 121, 221, 225, 308, 314.
Courses CPTR
105 COMPUTER PROGRAMMING I  3 hours
A first course in computer programming. Students will learn how to conceptualize, write and run programs. Programming topics include variables and types, methods, decision structures, lops, arrays, classes and objects. In addition to the syntax and semantics of programming, debugging, documentation, and programming aesthetics are also emphasized. Prerequisite: MATH 105 or higher mathematics placement.
121 WEB DEVELOPMENT  3 hours
An introductory course in developing applications for the Web. The student will develop analytical, technical, and design skills necessary for building interactive, functional, and usable websites using cutting edge tools. Topics will include: creating static web pages, clientside scripting, server management, dynamic websites using databases, graphic design, version control, typography, usability, and accessibility. Technologies used will include: HTML/XHTML, XML, RSS, JavaScript, CSS, PHP, MySQL, Apache, and Subversion. Prerequisite: CPTR 105. Fall odd years.
205 COMPUTER PROGRAMMING II  3 hours
A course focusing on advanced programming concepts emphasizing objectoriented programming. Topics include data abstraction, polymorphism and file I/O. Basic algorithmic analysis and use of data structures is also introduced. Students will write several large programs and gain an overall understanding of software development. Prerequisite: CPTR 105.
221 SOFTWARE DEVELOPMENT  4 hours
Combines a range of material related to the design, implementation and testing of software systems with the practical experience of implementing such a system as a member of a programming team. The course covers software process models, requirements, specification, design, documentation, validation and project management. In addition, it includes discussion of professional and ethical responsibilities in software development. Prerequisite: CPTR 205. Spring, odd years.
225 DATABASE PROGRAMMING  3 hours
This course introduces the fundamental topics in database design and databasebacked application development. Overall focus is on building applications with the efficient use of databases. Topics will include the relational model, SQL, dependencies, normalization, XML, JDBC, Web program. Prerequisites: CPTR 205; MATH 130.
308 COMPUTER ARCHITECTURE  3 hours
An introduction to the organization of computers. Topics include: information representation, assembly language programming, registers, linkage, I/0 and device handlers, architectural performance. Prerequisite: CPTR 205; MATH 130. Fall, even years.
310 ALGORITHMS AND DATA STRUCTURES  3 hours
This course explores the mathematical modeling of problems in computing. We will study the algorithms and data structures used for common tasks such as searching, sorting, and solving graph and geometric problems. The course will rely heavily on programming as the means for presenting the solutions. The emphasis will be on constructing correct and efficient algorithms and on analyzing their performance. Prerequisite: CPTR 205; MATH 130. Fall, odd years.
314 OPERATING SYSTEMS AND NETWORKS  4 hours
An overview of the key components and functions of computer operating systems and localarea networks. Topics include: file systems, system processes (including issues of concurrency, synchronization and deadlock), scheduling, memory management, data communications and networks. Prerequisite: CPTR 205; MATH 130. Spring, even years.
324 COMPUTER GRAPHICS  3 hours
An introduction to the theory of threedimensional (3D) computer graphics and the development of graphical applications. The student will learn concepts and techniques that form the backbone of modern computer graphics. The course will be focused on using free or opensource tools such as Processing, Blender, and the OpenGL library. Topics include: graphics hardware and software, vision, light and shading, object modeling techniques, curves and curved surfaces, textures, and shadows. Prerequisites: CPTR 105; MATH 251. Spring even years.
331 SOFTWARE DEVELOPMENT I  3 hours
Covers the design, implementation and testing of software systems. The course will introduce the current technology and tools used for software development. Topics include software process models, requirements, specification, design, documentation, validation and project management. Professional and ethical responsibilities in software development will also be included. Prerequisite: CPTR 205; MATH 130.
333 SOFTWARE DEVELOPMENT II  3 hours
This course focuses on putting software engineering theory into practice. Students will work in a team on a semesterlength project for a real customer, while applying a chosen software process model to their software development. Emphasis will be placed on structured engineering, design and usability, testing, team management, version control, customer relations and meeting project milestones. Prerequisite: CPTR 331.
410 TOPICS IN COMPUTER SCIENCE  3 or 4 hours
This course will be offered based on sufficient interest of students and faculty in particular areas of computer science. Possible topics include: artificial intelligence, numerical computation, computer graphics, expert systems, realtime systems, simulation, telecommunications, resource utilization, coding theory, UNIX and compiler design. This course requires significant independent work including a major research or programming project. Prerequisite: varies depending on topic.
415 PRINCIPLES OF PROGRAMMING LANGUAGES  4 hours
A course on the design and implementation of programming languages. Major areas are: language syntax (lexical properties, BackusNaur form, parsing), language representations (data structures, control structures, binding, execution environment, formal semantic models) and language styles (procedural, functional and objectoriented languages). Prerequisites: CPTR 205, 310. Fall, odd years.
475 INTERNSHIP IN COMPUTER SCIENCE (W)  13 hours
Students work in the computer field in the development of software or hardware algorithms or applications. Students are supervised by a computer science professional and a faculty member. A written report describing the overall project and the student’s contribution will complete the course. Students must formally enroll in this course prior to beginning work experience. Students may enroll twice for up to four hours credit. Prerequisites: two courses beyond CPTR 205; ENG 111; permission of department chair.
499 SENIOR PROJECT (W)  13 hours
Students will conduct a significant research project to consist of the development, analysis and/or implementation of an algorithm or software system, or an indepth study in some area of computer science. A formal paper as well as an oral presentation will be required. Course may be repeated once for a maximum of three hours credit. Prerequisite: ENG 111; permission of the department chair.
380 or 480 SPECIAL PROBLEMS  14 hours
A student who has demonstrated ability to work independently may propose a course and pursue it with a qualified and willing professor. The department chair and the vice president and dean for academic affairs must also approve. A set of guidelines is available at the Office of the Registrar.
385 or 485 SEMINAR  14 hours
An indepth consideration of a significant scholarly problem or issue. Students pursue a supervised, independent inquiry on an aspect of the topic and exchange results through reports and discussions.
