The Department of Mathematical Sciences offers major and minor programs in computer science and mathematics.

The B.A. degree in computer science consists of 13 courses: MATH 216; either MATH 109 or 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 in computer science consists of 17 courses: MATH 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.

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

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.

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.

INTRODUCTION TO COMPUTER SCIENCE

Introduction to the discipline of computer science with emphasis on programming utili-zing 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.

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.

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.

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.

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. Prerequisite: CPTR 125 and MATH 129; MATH 130 strongly recommended. Cross-listed as MATH 321.

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.

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.

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.

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. Prerequisite: CPTR 246 and either CPTR 247 or consent of instructor; MATH 130 recommended. Alternate years.

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. Pre-requisite: A grade of C- or better in CPTR 246; CPTR 247 strongly recommended.

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.

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.

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.

OPERATING SYSTEMS

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

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.

INDEPENDENT STUDY (See index)

A major in mathematics consists of 10 unit courses in the mathematical sciences: CPTR 125, MATH 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. Students who are interested in pursuing a career in actuarial science should consider the actuarial mathematics major.

Students seeking secondary teacher certification in mathematics are also required to complete MATH 330, 336, and one from 123, 214 or 332, and are advised to enroll in PHIL 217. Also, all majors are advised to elect PHIL 225, 333 and PHYS 225, 226. Other courses required for certification are PSY 110, 138; EDUC 200, 446, 447, 449.

In addition to the regular courses listed below, special courses are occasionally available.
The following course, when scheduled as a W course, counts toward the writing intensive requirement: MATH 234.

A minor in mathematics consists of MATH 128, 129, and either 216 or 234; two additional courses numbered 200 or above, one of which may be replaced with MATH 130; and two semesters of MATH 339.

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.

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.

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.

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, chisquared 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

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), those in the Scholars Program, or those whose major specifically requires Precalculus. Prerequisite: Credit for or exemption from MATH 100.

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.

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.

This course is intended for prospective elementary school teachers and is required of all those seeking elementary certification. Topics include systems of numbers and numeration, computational algorithms, environmental and transformation geometry, measurement, and mathematical concept formation. Observation and participation in Greater Williamsport elementary schools. Prerequisite: PSY 138 and credit for or exemption from MATH 100. Corequisite: Any EDUC course numbered 341 or above which is specifically required for elementary certification.

MULTIVARIABLE STATISTICS

The study of statistical techniques involving several variables. Topics include multiple regression and correlation, one-and two-way analysis of variance, analysis of covariance, analysis of two- and three-way contingency tables, and discriminant analysis. Other topics may include 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 BMDP). Prerequisite: A grade of C- or better in MATH 123 or its equivalent, or MATH 332.

 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.

DIFFERENTIAL EQUATIONS

COMPLEX VARIABLES

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

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.

MULTIVARIABLE CALCULUS

Algebra, geometry, and calculus in multi-dimensional 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.

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. Prerequisite: CPTR 125 and MATH 129; MATH 130 strongly recommended Cross-listed as CPTR 321.

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.

TOPICS IN GEOMETRY

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

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.

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.

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. Prerequisite: MATH 238 and a grade of C- or better in MATH 234.

ABSTRACT ALGEBRA

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

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.

MATH COLLOQUIUM

This non-credit but required course for mathematics 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 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.

INTERNSHIP (See index)

INDEPENDENT STUDY (See index)