Mathematics

An introductory course in computer science for non-majors. The course teaches computer programming with emphasis on logical thinking, problem solving, and algorithmic development. PROCESSING or a similar programming language is used. Topics include variables, arithmetic and logical operators, graphics, user interface, built-in library calls, I/O operations, conditional statements, loops, functions, and classes. 4 SH. CC: Analytical Thought.

An introductory course in computer science for majors. Also open to nonmajors. Emphasizes computer problem-solving methods and algorithmic development. Topics include programming in Python or a comparable language, techniques of good programming style, data types, file and screen input and output, control structures, subroutines, recursion, arrays, and pointers. 4 SH. CC: Analytical Thought.

This is the second course in computer programming that builds upon functional programming developed in the prerequisite course. This class introduces object-oriented programming, stressing the importance of planning, design and optimization of object-oriented solutions to programming problems. Topics include objects, classes, constructors, inheritance, polymorphism and design. Prerequisite: CSCI-181 Principles of Computer Science. 4 SH.

This course will explore some of what computer science has to offer to the natural and social sciences. Many phenomena consist of interacting individuals that can be modeled as following a set of behavioral rules. Using a suitable computer language such as NetLogo, Repast or others, we will learn to model these phenomena. Some programming experience is helpful but not required. Prerequisites: Fulfillment of the Analytic Thought requirement, sophomore standing and completion of either the Social Interactions requirement or the Scientific Explanations requirement. Some programming experience would be helpful but is not required. 4 SH. CC: Interdisciplinary.

Second course in computer programming. Stresses the interplay between algorithms, data structures and their implementations. Topics include stacks, queues, linked lists, sorting, searching, binary trees and graphs. Prerequisite: CSCI-181 Principles of Computer Science.

Fundamentals of computer organization and machine architecture. Presents an overview of computer system organization and examines in detail the digital logic level, the register level and the operating system program interface. Uses the assembly language of an available machine for programming assignments. Prerequisite: CSCI-281 Data Structures or instructor’s permission. 4 SH.

This course provides an introduction to the concepts in the automatic extraction of implicit, previously unknown and potentially useful information from large data sets generated in commerce, science and other fields. Topics include preprocessing of the data, application of the fundamental algorithms on the prepared data and interpretation of the patterns discovered by the algorithms. Introduced are the fundamental algorithms for supervised learning, including classification and numerical prediction and unsupervised learning, which includes association rules and clustering. Prerequisites: CSCI-181 and either MATH-180 or both MATH-108 and INFS-233. 4 SH.

An introduction to the computational techniques for solving mathematical problems, focusing on one-variable calculus. Topics include roots of nonlinear equations, finding maximum and minimum, interpolation, function approximation, numerical differentiation and integration. Same as CSCI-351. Prerequisite: MATH-111 Calculus I; MATH-112 Calculus II is suggested. 2 SH.

A study of the standard numerical techniques for solving mathematical problems, focusing on multivariable calculus and linear algebra. Topics include large sparse matrices, eigensystems, solving systems of equations, multivariable interpolation, maximum and minimum of multivariable functions, multivariable numerical integration, and numerical solutions of ordinary and partial differential equations. Same as CSCI-352. Prerequisites: MATH-112 Calculus II, MATH-201 Linear Algebra and MATH-351 Numerical Computing. 2 SH.

Cryptology is the study of hiding the meaning of messages. Cryptology is an interesting venue for the study of its mathematical underpinnings (number theory, matrix algebra, probability and statistics) and as an opportunity to implement techniques by means of computer programs. We will consider monoalphabetic and polyalphabetic encryptions, public key cryptography, security, and anonymity. Same as MATH-370. Prerequisite: MATH-221 Discrete Structures. 4 SH.

Introduces the design and implementation of algorithms using an object-oriented programming language such as C++ or Java. Covers correctness and efficiency of algorithms for sorting, searching, graph problems and mathematical algorithms. Prerequisites: MATH-221 Discrete Structures and CSCI-281 Data Structures. 4 SH.

An introduction to the classical and contemporary theory of computation. Topics include the theory of automata and formal languages, computability by Turing machines and recursive functions, computational complexity and quantum computers. Same as MATH-382. Prerequisites: MATH-221 Discrete Structures and CSCI-281 Data Structures. 2 SH.

An overview of data communications and networks, including channel capacity, Ethernet, Internet protocols, DHCP, DNS, TCP, FTP, SMTP, HTTP, web servers and file sharing. Prerequisite: CSCI-181 Principles of Computer Science. 2 SH.

Further topics in networks, with an emphasis on security. Includes authentication, encryption, verification, certificates, digital signatures, attacks and defenses, privacy, and anonymity. Also covers current developments in networks. Prerequisite: CSCI-391 Data Communications and Networks I. 2 SH.

This course provides an introduction to the systematic study of algorithms and systems that improve their knowledge or performance with experience. A statistical approach that emphasizes concepts and the implementation of the methods is presented to make sense of large and complex data. Topics include linear regression, classification, resampling methods, shrinkage approaches, tree-based methods, support vector machines and clustering. Prerequisites: MATH-180 Statistical Methods (or both MATH-108 Intro to Statistics and INFS-233 Data Driven Decision Making), MATH-201 Linear Algebra, and CSCI-181 Principles of Computer Science. 4 SH.

Programming in a common application environment, such as Android apps. Creation and management of windows, dialog boxes, mouse and keyboard input, message queues, graphics and multithreading. Prerequisite: CSCI-381 Algorithms. 4 SH

The entire software development cycle is explored, from requirements gathering through analysis, design, implementation, testing and documentation procedures. This course discusses both the theory and the business-world reality of software development, with an emphasis on object-oriented methodologies. Prerequisite: CSCI-381 Algorithms or instructor’s permission. 4 SH. CC: Writing Intensive.

This course is designed to provide an experience similar to that of working in the software engineering industry. The methodologies discussed in CSCI-471 Software Engineering: Methodology are put into practice, as students work on project teams throughout one or more software development cycles. Current projects involve designing and developing software to guide a mobile robot. Prerequisites: junior standing and CSCI-471 Software Engineering: Methodology. 4 SH. Capstone. CC: Team Intensive.

Studies the principles underlying various computer languages. Uses comparisons and evaluations of multiple programming languages such as C, Python, Java, FORTRAN, HTML, Postscript, LISP and Prolog to introduce the broad principles of language design and implementation. Prerequisite: CSCI-281 Data Structures. 2 SH.

Studies the phases of compiler design, such as syntax specification, lexical analysis, parsing, symbol tables, error detection, code optimization and code generation. Term project is to write a complete compiler for a small subset of C. Prerequisites: CSCI-282 Computer Organization and MATH-221 Discrete Structures. 4 SH. Capstone.

Basic interactive graphics programming in 2D and 3D using a common graphics library such as OpenGL. Introduces fundamental hardware and software concepts to implement graphics. Covers topics of drawing points, curves, surfaces, lighting, shading, animation, geometrical transformation, representation of 3-D shapes and removal of hidden edges and surfaces as time permits. Prerequisite: CSCI-281 Data Structures and MATH-201 Linear Algebra or instructor’s permission. 2 SH.

A brief summary of the tools, techniques and applications of artificial intelligence. Introduces problem solving and knowledge representation and selects topics from techniques for constructing models, robot design, language processing, computer vision, neural networks and expert systems. Same as INFS-485. Prerequisites: CSCI-281 Data Structures, MATH-111 Calculus I, and either MATH-108 Introduction to Statistics or MATH-180 Statistical Methods. 2 SH.

Introduction to the principles of operating systems through detailed discussion of a popular operating system such as Linux, with special attention to the areas of user interface, process management and file systems. Prerequisite: CSCI-281 Data Structures. 2 SH.

A study of general operating systems principles, processes, file systems, memory management, interprocess communication, I/O and concurrent processes. Includes a programming project in which the student writes a part of an operating system. Prerequisite: CSCI-486 Introduction to Operating Systems. 2 SH.

A study of computer architecture, including logic circuits, CPU design, instruction sets, CISC, RISC, memory architecture, I/O, peripherals, pipelining, superscalar processors and multiprocessors. Includes hardware and software considerations. Prerequisite: CSCI-282 Computer Organization. 2 SH.

Experience in individual research and presentation of computer related topics. Prerequisites: senior standing and computer science department head’s permission. 4 SH. CC: Writing Intensive.

Subjects vary, depending on instructor and student interest. Example topics include software engineering, cryptography, parallel processing, digital video compression, object-oriented technologies, neural networks and others as approved. Prerequisite: Instructor’s permission. 2 or 4 SH.

Individual work for capable students under the supervision of a faculty member. Prerequisite: Instructor consent and approval of computer science department head. Regularly scheduled courses are approved for independent study only under extraordinary circumstances. 2 or 4 SH.

A research project culminating in a substantive paper on a selected topic or field in computer science or information systems by arrangement with an instructor. Prerequisite: junior or senior standing and pdepartment head’s permission. 2 or 4 SH.

Full-time employment in computer science or information systems at an industrial firm or a public service organization. Prerequisites: senior standing, appropriate background courses in computer science and department internship coordinator’s permission. Satisfactory/Unsatisfactory grade. 2, 4, or 8 SH.

Topics include algebra, functions, graphing, exponents, logarithms, exponential functions, trigonometry and solving word problems. Prerequisite: Based on placement results, some students may require a mathematics review course. 4 SH.

This is a two-semester-hour course meant to help education majors satisfy the Pennsylvania state requirement for six credits of college mathematics. Each course will cover a topic of the instructor’s choice at an introductory level. Topics so far have included Symmetry, Counting, and Math and Music. This course does not count toward a math major or minor, and particular topics may overlap enough with other math courses to bar a student from taking both. Education majors will be given priority. Prerequisite: Usually none. 2 SH.

A basic introduction to data analysis, descriptive statistics, probability, Bayes’ Theorem, distributions of random variables and topics in statistical inference. (Students may earn credit for only one of the introductory statistics courses offered by the departments of management, psychology or mathematics.) 4 SH. CC: Analytical Thought.

Differentiation and integration of polynomials, exponential, logarithmic and trigonometric functions, rules of differentiation, the Mean Value Theorem, L’Hôpital’s Rule, the Fundamental Theorem of Calculus and applications. 4 SH. CC: Analytical Thought.

Techniques of integration. Also includes improper integrals, further applications of integration and power series. Prerequisite: MATH-111 Calculus I or equivalent. 4 SH. CC: Analytical Thought.

This course provides a broad overview of introductory statistical methods and data analysis. Topics include descriptive statistics, probability, probability distributions, statistical inferences on population means and population variances, multiple comparisons, categorical data, data analysis using linear regression and multiple regression, design of experiments, and analysis of variance. 4 SH. CC: Analytical Thought.

Systems of linear equations, matrices and matrix algebra, vector spaces, linear transformations, inner product spaces, determinants, eigenvalues and eigenvectors, and selected applications. Prerequisite: MATH-111 Calculus I. 4 SH. CC: Analytical Thought.

Calculus of several variables, partial derivatives, critical points, multiple integrals, gradient, curl, divergence, Green’s, Stokes’ and Divergence Theorems. Prerequisites: MATH-112 Calculus II and MATH-201 Linear Algebra. 4 SH.

An introduction to the basic logical and set-theoretic framework of mathematics and computer science. Topics include logic, proof techniques, mathematical induction, divisibility and modular arithmetic, sets, relations, mappings, graphs, and counting principles. Prerequisite: MATH-111 Calculus I. 4 SH.

A rigorous study of the theoretical basis of (single-variable) differential and integral calculus: limits, continuity, differentiation and integration. Prerequisite: MATH-112 Calculus II and MATH-221 Discrete Structures. 2 SH.

An introduction to algebraic structures including groups, rings and fields. Prerequisites: MATH-201 Linear Algebra and MATH-221 Discrete Structures. 4 SH. CC: Writing Intensive.

A concentrated study of elementary geometry. Includes Euclidean and non-Euclidean geometries and selected topics such as symmetry, Penrose tilings, fractals, knots, mapmaking and the shape of the universe. Prerequisites: MATH-201 Linear Algebra and MATH-221 Discrete Structures. 4 SH.

An introduction to the computational techniques for solving mathematical problems, focusing on one-variable calculus. Topics include roots of nonlinear equations, finding maximum and minimum, interpolation, function approximation, numerical differentiation and integration. Same as CSCI-351. Prerequisite: MATH-111 Calculus I; MATH-112 Calculus II is suggested. 2 SH.

MATH-352 Numerical Analysis. A study of the standard numerical techniques for solving mathematical problems, focusing on multivariable calculus and linear algebra. Topics include large sparse matrices, eigensystems, solving systems of equations, multivariate interpolation, maximum and minimum of multivariable functions, multivariable numerical integration, and numerical solutions of ordinary and partial differential equations. Same as CSCI-352. Prerequisites: MATH-112 Calculus II, MATH-201 Linear Algebra and MATH-351 Numerical Computing. 2 SH.

Introduces theory, basic solution methods, qualitative analysis and applications of ordinary differential equations. Prerequisites: sophomore standing, MATH-112 Calculus II, and MATH-201 Linear Algebra or instructor’s permission. 4 SH.

Cryptology is the study of hiding the meaning of messages. Cryptology is an interesting venue for the study of its mathematical underpinnings (number theory, matrix algebra, probability and statistics) and as an opportunity to implement techniques by means of computer programs. We will consider monoalphabetic and polyalphabetic encryptions, public key cryptography, security, and anonymity. Same as CSCI-370. Prerequisite: MATH-221 Discrete Structures. 4 SH.

An introduction to the classical and contemporary theory of computation. Topics include the theory of automata and formal languages, computability by Turing machines and recursive functions, computational complexity and quantum computers. Same as CSCI-382. Prerequisites: MATH-221 Discrete Structures and CSCI-281 Data Structures. 2 SH.

Limits and continuity in the general context of metric spaces. Topics include basic point-set topology, completeness, uniform continuity, sequences and series of functions. Additional topics as time permits. Prerequisites: MATH-112 Calculus II and MATH-231 Foundations of Analysis. 4 SH. CC: Writing Intensive.

Calculus using complex numbers. Includes analytic functions and the Cauchy-Riemann equations, contour integrals, Cauchy’s Theorem, Cauchy’s Integral Formula, power and Laurent series, poles, residues, and applications. Prerequisites: MATH-211 Multivariate Calculus, and MATH-231 Foundations of Analysis. 4 SH.

A more detailed study of statistics. Topics include probability, multivariate distributions, Bayes’ Theorem, statistical inference, estimation,decision theory, hypothesis testing, linear models and experimental design. Prerequisites: MATH-211 Multivariate Calculus and either MATH-108 Introduction to Statistics or MATH-180 Statistical Methods. 4 SH.

Experience in individual research and presentation of topics in mathematics. The one-semester-hour version culminates in a presentation to an audience of faculty and students. Prerequisite: senior major or department permission. 1 or 4 SH. 4 SH version satisfies the capstone requirement.

Subject depends on students’ and instructor’s interests. Possibilities include: number theory, set theoretic foundations of mathematics, topology, graph theory, differential geometry and applied mathematics. Whether the course counts as a 400-level course for majors will be announced along with the course description. Prerequisite: Instructor’s permission. 2 or 4 SH.

Individual work for capable students under faculty supervision. Scheduled courses are approved for independent study only under extraordinary circumstances. Whether the course counts as a 400-level course for majors will be decided on an individual basis. Prerequisite: Department approval and instructor’s consent. 2 or 4 SH.

A research project leading to a substantive paper on a selected topic in mathematics. By arrangement with a department instructor. Prerequisite: Junior or senior standing and department permission. 2 or 4 SH.

Full-time mathematics-related employment at an industrial firm or a public service organization. Prerequisite: senior standing, appropriate mathematics background courses and departmental internship coordinator’s permission. Satisfactory/Unsatisfactory grade. 2, 4, or 8 SH.