Department of Mathematics and Computer Science

General overview of the many facets of computer science and information technology: Data, hardware, software, networks. System software in including operating systems and programming environments. Software engineering; program development using data structures, algoriths, files, and databases. Exposure to other topics and issues in computer science, such as data compression, security, theory of computation, computational complexity. Prerequisites: MATH 0012 or appropriate placement.

Problem solving using computers. The design and implementation of computer programs. Major areas and issues in computer science including social and ethical concerns. Problem solving and pseudocode. Formal specification and verification. Basic software engineering techniques and software reuse. Data structures. Structured types: arrays, records, files. Objects and methods. Programming in a high-level language, such as C++ or Java. Corequisite: MATH 1015.

Major issues, areas, and applications of computer science. Data structures and algorithms. Linked lists, trees and graphs. Stacks, queues, and heaps. Object-oriented programming. Problem solving and software engineering. Algorithm design, induction, recursion, and complexity. Social, economic, and ethical concerns. Programming in a high-level language, such as C++ or Java. Prerequisite: CSAS 1111. Corequisite: MATH 1501/1401.

A course in programming in C++ with emphasis on applications to the sciences and to numeric algorithms. Basics of software development (variables, control structures, functions), data structures (records, arrays, lists), dynamic structures (pointers, linked lists) and principles of object-oriented programming (fields and methods, classes, inheritance). The course will focus on creating programs for topics of interest in the natural sciences. Corequisite: MATH 1015 or equivalent.

Programming skills are important to virtually every profession. Professionals must make decisions on how to achieve goals by deciding what steps are necessary. This course is an introduction to computer programming that teaches students how to make plans, to organize their thoughts, to pay attention to detail, and to be self-critical. The main focus of the course is the design process that leads students from a problem statement and a blank page to a well-organized solution. Topics include the processing of simple forms of data, the processing of arbitrarily large data, and the process of abstraction. This course assumes no prior computer programming experience. Corequisite Math 1014, 1015, 1401 or 1501.

This course continues the study of the design and the programming processes started in CSAS 1114. Building on the abstraction skills acquired in CSAS 1114, the course focuses on new programming design techniques such as generative recursion, tail-recursion, and the changing of state variables through the use of assignment. The disciplined introduction to assigment prepares students to study modern object-oriented design and programming. Prerequisite: CSAS 1114, Corequisite: MATH 1015, 1501 or 1401.

This course is an introduction to object-oriented design and programming. Building on the knowledge gained in CSAS 1114-1115 students learn to design a system of classes to represent information. Given a system of classes and a piece of information students will be able to create objects and represent this information with data. Conversely, given an instance of a class in the system, students will be able to interpret this object as information in the real world. Topics include varieties of data, functional methods, and abstraction with classes. Prerequisite: CSAS 1114, MATH 1501/1401.

This continues the investigation of object-oriented design and programming started in CSAS 2123. Topics include circular objects, imperative methods, abstraction over data definitions, and the use of commercial programming environments for object-oriented programs. By the end of this course, students will have a solid grasp on the principles and practice of object-oriented programming. Prerequisite: CSAS 2143.

This course introduces the basic design of computing systems: CPU, memory, input and output. In addition, it provides a complete introduction to assembly language:the basics of an instruction set plus experience in assembly language programming using a RISC architecture. During the course student will gain experience using system calls and interrupt-driven programming emphasizing the interaction with the operating system. Other topics include: machine representation of integers, characters, floating point numbers, and virtual memory. Prerequisite: CSAS 1115, MATH 1611, or permission of instructor.

This course discusses data structures such as arrays, stacks, queues, lists, trees, and graphs and the algorithms that manipulate these structures. Algorithm analysis for the cost of time and space is introduced. Students will learn essential tools for designing efficient software applications, needed in all application areas of computer science, such as industrial and scientific computation and database management. Prerequisite: CSAS 1114, MATH 1611.

This course introduces the foundations of applied data mining. There is a need for extracting useful information from raw data in fields such as social and health sciences, business, the natural sciences and engineering. This course covers the fundamental ideas and algorithms of data mining. Furthermore, it teaches applying data mining techniques in order to extract useful information from data. Standard software for data mining will be used. The course is intended for any student desiring an introduction to data mining.

Signature III course with substantial computer science or related content, typically interdisciplinary and perhaps team-taught, taught on an experimental basis with topics to be determined by the instructor(s) in cooperation with the University Core Curriculum process. See Co-op Adviser.Crosslisted with PSYC 3698 and CORE 3490 Engaging the World

See Co-op Adviser.

Interdependence of operating systems and architectures. System structure and system evaluation. Emphasis on memory management: addressing, virtual memory, paging, segmentation and secondary storage; processes management: scheduling, context switching, priority, concurrency and deadlock; and resource management: memory, secondary storage, buses and printers. Prerequisite: CSAS 2122.

Introduction to principles of programming languages and nonprocedural, non-object-oriented programming. Programming language concepts, including higher-order functions, first-class functions, recursion, tail-recursion and iteration, tree-recursion; issues of pure versus impure languages in relation to performance, implementation and ease of abstraction; environments, parameter passing, and scoping. Structure, the syntax, and implementation of languages, illustrated using interpreters. Emphasis on programming in a language such as Scheme or Prolog; individual programming assignments and team project. Prerequisite: CSAS 2122.

The course presents an overview of topics in and related to logic, including development of formal logic and an axiomatic first-order logic. It explores the history of mathematics and logic in the Catholic Intellectual and wider Western Traditions, as well as the mutual interactions of mathematics, philosophy and religion. It then considers extensions of first-order logic, and provable limits to knowledge: the three unsolvable problems of Euclidean geometry, and examples from Gödel, Turing, Arrow, quantum physics, and others

Principles of computer and networking. The layered model of a computer network and its implementation. Standard protocols. Applications. Mathematical principles and theory. Team and individual programming projects. Prerequisite: CSAS 2122 or permission of instructor.

Special topics and problems in various branches of computer science. Prerequisites: At least five CSAS courses, including CSAS 2122, or permission of chair.

Prerequisites: At least five CSAS courses, including CSAS 2122, or permission of chair.

Prerequisites: At least five CSAS courses, including CSAS 2122, or permission of chair.

Prerequisites: At least five CSAS courses, including CSAS 2122, or permission of chair.

Prerequisites: At least five CSAS courses, including CSAS 2122, or permission of chair.

Prerequisites: At least five CSAS courses, including CSAS 2122, or permission of chair.

Different definitions of and approaches to artificial intelligence. Problems, problems spaces and search techniques; special emphasis on heuristic search, including hill climbing, best-first search and A*. The role of knowledge and knowledge representation issues. Programming and AI application. Introductory survey paper. Prerequisites: CSAS 3113, MATH 2611.

Introduction to the theory of finite state automata and their equivalence to regular expressions and regular grammars; pushdown automata and context-free languages; context-sensitive grammars and Turing machines; determinism and nondeterminism; issues of complexity including P and NP; and issues of computability including Turing computable versus Turing decidable, the Halting problem and other incomputable problems. Prerequisites: CSAS 2122, MATH 2611.

Modern relational databases. Relational algebra, views and queries, normal forms and normalization, tuning and optimization. The entity-relationship model and database design. Overview of other approaches, especially object-oriented databases, data warehouses and data mining, distributed databases and very large applications. Group project, both design and implementation, in an SQL-based environment, such as an SQL Workbench. Prerequisites: CSAS 2121, MATH 1611 or permission of department chair. MATH 2611 recommended.

The software universe and the role of software engineering. Project, process, and product. Approaches to system and software engineering; software architectures, including component-oriented and service-oriented architectures. Traditional and object-oriented approaches to software engineering; the modern approach, modeling languages and patterns; agile and extreme programming. Requirements elicitation and analysis and system specification; risk analysis; use cases. Knowledge management for requirements elicitation and risk analysis. Design of a software system using patterns and incremental iterative refinement. Complementary approaches, including aspects and interfaces with databases. Security and other non-behavioral considerations. Development of an initial prototype.

Design and implementation of a software application. Design patterns and aspects. User and component interfaces. Approaches for software quality assurance: validation and verification, testing, static analysis and model checking. Verification, validation, and testing. Approaches to verification – theorem proving, model checking, and others. Principles and theory of testing; white box and black box testing. Unit, integration, stress, and acceptance tests. Test metrics and test coverage. Testing tools. Maintenance: corrective, preventative, adaptive, and perfective changes. Software configuration management. Technical and business management of large software projects. Technical and business metrics. Cost estimation, scheduling, and staffing – connection to risk analysis. Subcontractors, vendors and collaborators; outsourcing in software projects. Software engineering for web applications and real-time systems.

Computer Graphics Visualization is used throughout society, including science, engineering, enterprises, politics, art, etc., for visualizing data and processes. Visualization is crucial for mining usable information from the ever increasing amounts of data and ever more complex procedural relationships of today’s society. This course introduces the foundations for computer graphics visualization: basics of visual thinking and perception, techniques for visualization, such as maps, time series, trees, graphs, etc., and applications, such as in medical imaging, biochemistry, social sciences, etc. The course also teaches developing visualizations using a standard programming system. Visualizations will be demonstrated using online material, such as Many Eyes or Google Maps. Prerequisite: CSAS 4121 or permission or instructor.

Topics covered: review of arthimetic skills, simplifying algebraic expressions, exponents, equations, polynomials, graphing, factoring, square roots, algebraic fractions and elementary word problems. Successful completion of this class will satisfy the Developmental Math requirements. Prerequisite: MATH 0011 or appropriate placement.

A 3-credit lab linked with specified sections of MATH 1014 required for students whose placement indicated the need for additional mathematics skills mastery. Topics covered: review of arithmetic skills, simplifying algebraic expressions, exponents, equations, polynomials, graphing, factoring, radical expressions, algebraic fractions and elementary word problems.

The real number system, algebraic manipulations, solving equations and inequalities, exponents and radicals, functions and graphing. Prerequisite: MATH 0012 or appropriate placement.

The real number system, functions, polynomial functions and equations, exponential and logarithmic functions, trigonometric functions (graphs, applications, identities and equations), analytic geometry. Prerequisite: MATH 1014 or appropriate placement.

Nature of statistics. Descriptive statistics, graphical methods, measures of central tendency and variability. Probability, correlation and regression, sampling distributions. Inferential statistics, estimation and hypothesis testing, tests of independence and nonparametric statistics. Use of computer statistical packages. Prerequisite: MATH 0012 or appropriate placement.

Introduction to traditional and contemporary mathematical ideas in logic, number theory, geometry, probability and statistics. Historical and cultural development of these topics, as well as connections to other disciplines and various problem-solving strategies are included. Prerequisite: MATH 0012 or appropriate placement.

Applications of statistics in the social sciences. Analysis and interpretation of statistical models. Sampling techniques, common flaws and errors in sampling and in using statistics. Descriptive statistics, levels of measurement, measures of central tendency and dispersion. Contingency tables and measures of association for categorical variables. Correlation and linear regression. Probability and frequency distributions. Parametric and nonparametric inferential statistics. Confidence intervals and hypothesis testing. Prerequisite: MATH 0012 or appropriate placement.

For students in the School of Business. Functions and linear models, systems of linear equations, linear programming, sets and counting, probability, random variables and statistics, quadratic functions, introduction to the derivative, marginal analysis, maximum and minimum problems, the mathematics of finance. Specific and real-world applications to problems illustrate each topic. Prerequisite: MATH 0012 or appropriate placement.

Implicit differentiation, related rates, differential equations, improper integrals and probability density functions, partial derivatives and applications and multiple integrals. Introduction to matrix theory, solution of systems of linear equations and linear programming. Prerequisite: MATH 1303.

Real numbers, functions, elements of plane analytic geometry, limits, continuity, derivatives, differentiation of algebraic functions, applications of the derivative, antiderivatives, definite integral and Fundamental Theorem of Calculus. Applications using computer software packages. Prerequisite: MATH 1015 or appropriate placement.

Applications of integration. Differentiation of trigonometric and exponential functions and their inverses. Techniques of integration. Improper integrals, indeterminate forms, polar coordinates and vectors. Applications using computer software packages. Prerequisite: MATH 1401.

Real numbers, proof by induction, functions, definition by recursion, limits, continuity, derivatives and applications, definite integral, Fundamental Theorem of Calculus and inverse functions. Applications using computer software packages. Emphasis on theory. Prerequisite: MATH 1015 or appropriate placement.

Applications of integration, polar coordinates, techniques of integration, infinite series, conics, two-dimensional vectors and differential equations. Applications using computer software packages. Emphasis on theory. Prerequisite: MATH 1401 or 1501.

Basic counting rules, permutations, combinations, Pigeonhole principle, inclusion-exclusion, generating functions, recurrence relations, graphs, digraphs, trees and algorithms. Prerequisite: MATH 1015 or appropriate placement

Oriented toward direct application to research problems in the sciences. Collecting and organizing data, design of experiments, standard distributions, statistical tests and procedures used in hypothesis testing. A discursive treatment of the probability theory necessary to understand statistical tests is included but minimized. Emphasis on statistical inference and developing an awareness of statistical methods in a given situation. Prerequisite: MATH 1401.

Elements of solid analytic geometry, parametric equations, vector-valued functions, partial differentiation, multiple integrals, line integrals and surface integrals. Applications using computer software packages. Prerequisite: MATH 1411.

Vectors in space, vector-valued functions, partial differentiation, multiple integrals, vector analysis, and line and surface integrals. Applications using computer software packages. Emphasis on theory. Prerequisite: MATH 1511.

Introduction to statistics. Levels of measurement; central tendency and dispersion; accuracy, precision, error and bias. Probability spaces, random variables, and sampling. Counting: principles, permutations and combinations, combinatorics. Continuous and discrete probability, conditional probability and expectation. Approaches for summarizing and visualizing statistical information. Univariate, bivariate, and multivariate distributions; standard continuous and discrete distributions, including Binomial, Poisson, Exponential, Normal and Chi-Square distributions; introduction to moment generating functions. The Central Limit Theorem. Overview of confidence intervals and hypothesis testing. Independence and association, correlation and regression, and the Chi-Square test. Use of software packages such as Maple, Excel, and/or StatCrunch for statistics. Prerequisite: MATH 1401 or MATH 1501, and MATH 1611. (Note: Students cannot receive credit for both MATH 2711 and MATH 2111.)

First order and linear second order differential equations, matrices and linear equation systems, eigenvalues and eigenvectors, and linear systems of differential equations. Separable partial differential equations.

Matrix algebra, determinants, solutions of systems of linear equations, Rn, abstract vector spaces, linear transformations, inner product spaces and eigenvectors. Prerequisites: MATH 2611.

Topics essential for computer science selected from traditional linear algebra and Calculus II. The material is presented in a constructive and algorithmic way to increase relevance for computer science students. The students will implement relevant mathematical algorithms in a programming language taught during the freshman or sophomore year. Students will acquire skills that are essential for designing efficient software applications, needed in industrial and scientific applications of computer science.

The development of mathematical ideas in various cultures, civilizations, and eras including Ancient Greece, Medieval China, the Renaissance, Era of Descartes and Fermat, Era of Newton and Leibniz, as well as the logical foundations and the use of the computer in Modern Mathematics. Prerequisite: MATH 2511 and MATH 1611.

The course presents an overview of topics in and related to logic, including development of formal logic and an axiomatic first-order logic. It explores the history of mathematics and logic in the Catholic Intellectual and wider Western Traditions, as well as the mutual interactions of mathematics, philosophy and religion. It then considers extensions of first-order logic, and provable limits to knowledge: the three unsolvable problems of Euclidean geometry, and examples from Gödel, Turing, Arrow, quantum physics, and others

This course introduces discrete graphs and their applications, with emphasis on applications. It covers the fundamental structures of and algorithms on discrete graphs, teaching students how to use graph algorithms to extract useful information from graph and network data, how to model complex processes using graph theoretic techniques, and how to investigate and validate resulting models in order to test graph models and make predictions.

Analytic functions, elementary functions and mappings, integrals, Cauchy’s integral theorem and formula, power series, residues and poles. Prerequisite: MATH 2511. 3 credits

Existence theorems, graphical methods, phase plane analysis, boundary value problems and selected topics. Prerequisites: MATH 2511, MATH 2813.

Structure of R1 and Rn. Sets, equivalence classes, countability; compactness and connectedness; continuity, differentiability and integrability. Theory of series. Pointwise and uniform convergence. Prerequisites: MATH 2411 or 2511; MATH 2813.

Construction and use of mathematical models in operations research. Classical techniques for optimization of functions of one and several variables. Linear programming problem and simplex method for their solutions. Applications to practical problems. Prerequisites: MATH 2511, MATH 2813.

Combinatorial methods and discrete structures. Topics may include enumeration techniques, subsets and designs, partitions, generating functions and recurrence relations; codes and graphs. Prerequisites: MATH 1611, MATH 2813 or MATH 2814.

Graphs, trees and digraphs. Various properties are discussed and may include connectivity, colorability, planarity, matchings, extremal graph theory, spanning trees, and reliability. Applications to real world problems will be introduced.

This course introduces fundamental matrces and matrix algorithms used in applied mathematics, and essential theorems and their proofs. It covers matrices used in linear optimization, solving systems of linear differential equations, and modeling of stochastic processes. It also covers implementing matrx algorithms with mathematical software,

Overall emphases on modeling, on concepts and theory, and on standard statistical tools and approaches. Review of probability spaces, random variables, and sampling. Continuous and discrete probability, moment generating functions, standard distributions. Functions of random variables. The Law of Large Numbers and the Central Limit Theorem. Point estimation, confidence intervals and hypothesis testing. The power of a test. Correlation and regression; the Chi-Square Test. Use of software packages such as Maple, Excel and/or StatCrunch/SPSS for statistics. Prerequisites: Either MATH 2111 or MATH 2711, and either MATH 2813 or MATH 2814.

The course presents an overview of topics in and related to actuarial math, including the time value of money, annuities, and amortization. It looks at financial mathematics in terms of bonds, internal rate of return, and term structure of interest rates. It then considers financial calculus with discrete financial models, market models, risk free assets with a concentration on bonds and money markets, and risky assets. Finally, the course introduces financial engineering including the Black-Scholes Equations using probabalistic methods and applications to options and derivatives.

Vector spaces and algebras, unitary and orthogonal transformations, characteristic equation of a matrix, the Jordan canonical form. Bilinear, quadratic and Hermitian forms. Spectral theorem. Prerequisite: MATH 2813.

Introduction to algebraic structures: monoids, groups, rings and fields. Examples are given, and the elementary theory of these structures is described. Prerequisite: MATH 2813.

Seminars and discussions designed to integrate readings of mathematical literature with both oral and written presentations.

Topics chosen from among operations research, optimization, including an introduction to the calculus of variations, combinatorics, discrete mathematics, Fourier analysis, integral equations, partial differential equations. Students acquire some experience.

Prerequisite: permission of department chair.

Prerequisite: permission of department chair.

Prerequisite: permission of department chair.

Independent study on a select topic completed under the supervision of the instructor.

Analytic functions, elementary functions and mappings, integrals, Cauchy's integral theorem and formula, power series, residues and poles. Prerequisite: MATH 2511.

Consequences of continuity, differentiability and integrability in Rn; introduction to metric spaces. Lebesgue integration.

Advanced topics in probability and statistics or its application, selected by the instructor. Possible topics include, but are not limited to: advanced statistical modeling, stochastic models, applications to actuarial science and reliability, statistical data analysis and visualization, simulation and validation, design of experiments.

The course presents an overview of topics in and related to financial calculus and financial engineering, including portfolio management, hedging strategy, and risk management. It will introduce Brownian Stochastic Processes and Martingales and Continuous Financial Models. It then considers extensions of optimal portfolios and risk management, including swaps and currency forward contracts.

Further properties of groups and fields, with a section on the applications of finite fields. Galois theory, the theory of the solution of algebraic equations.

Individual research project applying skills developed in Junior Seminar (MATH 3912) under the guidance of faculty adviser. Grade is ordinarily based on oral and written presentations. Prerequisites: MATH 3912 and permission of department chair.

Special topics and problems in various branches of mathematics. Prerequisite: permission of department chair.