Academics

*Chair James P. Brumbaugh-Smith, Timothy M. Brauch, Young S. Lee, Robin R. Mitchell, Andrew F. Rich, Eva G. Sagan*

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 real-world 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, statistics, and computer science is possible for students with strong AP scores.

**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, 43 hours: MATH 121, 122, 130, 231, 240, 251, 421, 433, three hours of 499; Nine hours of approved electives, selected from: 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, 25-26 hours: MATH 121, MATH 130 or MATH 202; 17 hrs of electives from: MATH 122, MATH 210 or MATH 240 or PSYC 241; MATH 214, 231, 233, 242, 245, 251, 306, 330, 340, 380, 385, 421, 433, 480, 485; CHEM 341; CPTR 310; ECON 350; PHYS 301.

Minor in middle school mathematics, 24-26 hours: MATH 121, 130, 251, 306, 440; one course selected from MATH 214, 330, 433; one course selected from MATH 115, 210, 240.

Certificate in scientific computing; Timothy Brauch, coordinator; CPTR 105; MATH 121, 233; successful completion of an applied experience approved by the coordinator. For more about this certificate, see the certificates page.

Requirements for teaching majors are available in the Office of Teacher Education.

**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.**108 NUMBER SENSE FOR ELEMENTARY TEACHERS - 2 hours**An in-depth treatment of concepts underlying common topics in the elementary mathematics curriculum including: number theory and representation, operations and their properties, functions, and algebraic thinking. Use of selected concrete manipulatives and technology is included. Prerequisite: MATH 105 or high 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 decision-making; 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. C-1Q. Spring.

**115 ELEMENTARY PROBABILITY AND STATISTICS - 3 hours**

A course focusing on problem-solving and decision-making 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. C-1Q. Fall. January. Spring.

**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. C-1Q. Fall. Spring.

**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 computer-algebra 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. Spring.**202 MATHEMATICS FOR COMPUTER SCIENCE - 4 hours **

An introduction to mathematical methods used in computer science. Students will explore computer number representation and arithmetic, arbitrary number bases, Turing machines, number theory, relations, logic, sets, algorithmic complexity, induction, and recursion through computer applications. Prerequisites: MATH 120 or higher math placement; CPTR 113. Enrollment in CPTR 113 may be concurrent. Spring odd years.

**208 MEASUREMENT FOR ELEMENTARY TEACHERS - 2 hours **

An in-depth treatment of concepts underlying common topics in the elementary mathematics curriculum including concepts in data analysis and probability, geometry, and measurement. Use of selected concrete manipulatives and technology is included. Prerequisite: MATH 108; MATH 113, 115, 210, or PSYC 241.

**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 chi-squared 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. C-1Q. Fall. January. Spring.

**214 HISTORY OF MATHEMATICS - 3 hours**

An overview of aspects of the history of mathematics from ancient times through the development of abstraction in the nineteenth century. The course will consider both the growth of mathematical ideas and the context in which these ideas developed in various civilizations. Prerequisite: MATH 121, 130.

**231 MULTIVARIABLE CALCULUS - 4 hours**

Topics include: vector analysis in two-and three-dimensional 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 SCIENTIFIC COMPUTING - 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 non-linear equations. The course is oriented toward machine computation and involves programming of various solution techniques for problems in science, technology, engineering, and mathematics. Prerequisite: MATH 121.

**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.

**242 DATA ANALYTICS - 3 hours**A survey of quantitative techniques and computing tools used to identify patterns in massively large data sets. Such patterns are used to categorize behavioral trends and customize organizational responses, either toward specific target audiences or on an individualized basis. Applications will include areas such as: on-line behavior, social media usage, purchasing preferences, voting patterns, athletic performance, and health outcomes. Prerequisite: MATH 115, 210 or 240, or PSYC-241.

**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. 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 (preK-6th grades) mathematics programs. Field experience is a required component. Taken as part of the Elementary Methods Block. Prerequisites: MATH 107 and EDUC 340. Fall.

**306 GEOMETRY - 3 hours**

A study of the logical structure and content of both Euclidean and non-Euclidean 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.

**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 point-set 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.

** 440 SECONDARY MATHEMATICS METHODS (W) - 3 hours**

The study of standards, curriculum, teaching methods and assessment appropriate for middle and secondary school (5-12) mathematics programs. Topics will include appropriate use of mathematical technology, history of mathematics, approaches to problem solving and modes of mathematical understanding. Prerequisites: EDUC 111, EDUC 230, MATH 130, MATH 240. Enrollment in MATH 240 may be concurrent. Fall odd years.

**475 INTERNSHIP IN MATHEMATICS - 1-3 hours **

Students work in business, industry, government or other agencies applying mathematical tools (e.g., probability, statistics, optimization) to real-world 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) - 1-3 hours**

An in-depth 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: FYS or ENG 111; permission of the department chair.

**380 or 480 SPECIAL PROBLEMS - 1-4 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 - 1-4 hours**

An in-depth 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.

**SOFTWARE ENGINEERING & COMPUTER SCIENCE**

The **software engineering major** focuses on the software development process and the implementation of software systems. The foundation of software development consists of soliciting and documenting customer requirements, creative problem-solving, and effective software design. This is followed by constructing, testing, documenting and delivering professional quality software systems that are reliable, maintainable and extensible. Emphasis is placed on working with industries and software companies to provide students with real-world software experience through classroom projects, internships and senior research. Students will be prepared for successful careers in software development in a wide variety of businesses and industries. Graduates in software engineering will also be equipped to pursue a variety of graduate programs in computing.

A** minor in computer science** is offered for those desiring to be proficient at writing computer programs either for personal or workplace use, or students wishing to prepare for graduate school in computing-intensive disciplines.

**Baccalaureate Degree**

Courses listed in parentheses are prerequisites.

Major in software engineering, 47 hours: CPTR 111, 113, 225, 310, 340, 342, 420, 422, 424; IDIV 205; MATH 121, 202, 251; three hours of CPTR 477 or 499.

Majors must successfully complete the senior comprehensive evaluation prior to graduation. Details are available from the department chair.

Minor in computer science, 23-25 hours: CTPR 111, 113; MATH 130 or MATH 202; MATH 121 or MATH 251; three courses selected from CPTR 225, 310, 410, 424; MATH 233, 242.

Minor in systems analysis, 27-29 hours: CPTR 111, 113, 340, 342 or 422; BUS 111; IDIV 205; one course selected from BUS 108; CPTR 224; MATH 242; two courses selected from ACCT 211; BUS 231, 310, 447.

**Associate of Arts Degree**

Major in computer applications, 22-23 hours: BUS 108; CPTR 111, 113; MATH 120 or 121, 130; two courses selected from CPTR 121, 225, 331.

**Courses CPTR**

**105 COMPUTER PROGRAMMING - 3 hours**

An introductory course in computer programming. Students will learn how to conceptualize, write and run programs. Programming topics include variables and types, methods, decision structures, loops, 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. Spring.

**111 FOUNDATIONS OF COMPUTER SCIENCE I - 4 hours**

As a first course in Computer Science, the emphasis will be on problem solving. Students will learn to solve problems by the iterative refinement of object oriented models. Topics include simple Unified Modeling Language (UML) class diagrams, technical writing, design principles and programming using interacting classes, one dimensional arrays, program flow control, and simple I/O. An object-oriented language that supports encapsulation, polymorphism, and inheritance will be used. Prerequisite: MATH 105 or higher mathematics placement. Fall.

**113 FOUNDATIONS OF COMPUTER SCIENCE II - 3 hours**

A continuation of Foundations of Computer Science I, the emphasis will be on formalizing and extending student knowledge of analysis, design, technical writing, and implementation. Topics include reusability and change tolerance, interface design, coupling, cohesion, polymorphism, inheritance, information hiding, good programming practices, and fundamentals of algorithm/data structure design. Prerequisite: CPTR 111. Spring.

**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, client-side 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 or CPTR 111. Fall, odd years.

**225 DATABASE PROGRAMMING - 3 hours**

This course introduces the fundamental topics in database design and database-backed 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 113; MATH 130. Fall, even years

**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 113; MATH 130. Spring, odd 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 113; 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 local-area networks. Topics include: file systems, system processes (including issues of concurrency, synchronization and deadlock), scheduling, memory management, data communications and networks. Prerequisite: CPTR 113; MATH 130. Fall, odd years.

**324 COMPUTER GRAPHICS - 3 hours**

An introduction to the theory of three-dimensional (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 open-source 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 113; MATH 130. Fall, even years.

**333 SOFTWARE DEVELOPMENT II - 3 hours**

This course focuses on putting software engineering theory into practice. Students will work in a team on a semester-length 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. Spring, odd years.**340 SOFTWARE ENGINEERING METHODOLOGIES - 3 hours**

This survey course focuses on the software engineering processes of requirements engineering, architecture and design, and quality. In this course a foundation for later studies will be laid by examining the trade-offs of a variety of software development philosophies/methodologies. Prerequisite: CPTR 113. Spring even years.**342 SOFTWARE QUALITY - 3 hours**This course focuses on the software quality process. Students will learn and practice various techniques including test driven development, boundary condition testing, black and white box testing, regression testing, and system verification/validation. Prerequisite: CPTR 113. Fall odd years.

**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, real-time systems, simulation, telecommunications, resource utilization, coding theory, UNIX and compiler design. This course requires significant independent work including a major research or programming project. Course may be repeated once on a different topic. 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, Backus-Naur form, parsing), language representations (data structures, control structures, binding, execution environment, formal semantic models) and language styles (procedural, functional and object-oriented languages). Prerequisites: CPTR 205, 310.An introductory course in computer programming. Students will learn how to conceptualize, write and run programs. Programming topics include variables and types, methods, decision structures, loops, arrays, classes and objects. In addition to the syntax and semantics of programming, debugging, documentation, and programming aesthetics are also emphasized. Prerequisite: CPTR 113 and CPTR 310.

**420 SOFTWARE REQUIREMENTS ENGINEERING - 3 hours**This course focuses on the software requirements engineering process. Students will learn and practice elicitation, documentation, verification, and validation of software system requirements. Emphasis will be placed on using Unified Modeling Language (UML) and dealing with multiple audiences such as management stakeholders, end user stakeholders, and technical stakeholders. Prerequisite: IDIV 205; CPTR 340. Fall even years.

This course focuses on the software engineering process of architecture and design. Students will learn and practice creating a software system architecture and design from requirements using Unified Modeling Language (UML), architectural patterns, and design patterns. Prerequisite: CPTR 340. Spring odd years.

**475 INTERNSHIP IN COMPUTER SCIENCE (W) - 1-3 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 113; permission of department chair.**477 INTERNSHIP IN SOFTWARE ENGINEERING (W) - 1-3 hours**Students work in a professional software development environment where they engage in one or more software engineering disciplines such as requirements engineering, architecture/design, software construction or software quality. Students are supervised by a software professional and a faculty member. An oral presentation and 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. Prerequisite: Approval of Department.

**499 SENIOR PROJECT (W) - 1-3 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 in-depth 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: Permission of the department chair.

**380 or 480 SPECIAL PROBLEMS - 1-4 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 - 1-4 hours**

An in-depth 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.