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**Jesse X. Yu, Ph.D.**

**ChairpersonAssociate Professor of Math and Computer Science**

The Mathematics Program offers a Bachelor of Arts in Mathematics, a minor in Mathematics, and a minor in Computer Science.

The Mathematics program is broad and is designed to accommodate the diversity of student needs and interests. The student is led to seek an understanding of the place of mathematics in our culture, and in particular to appreciate its relationship to the physical and social sciences. The primary goal of the mathematics curriculum is to develop the attitudes of mind and analytical skills required for efficient use and understanding of mathematics. By earning a Bachelor of Arts degree in Mathematics, students prepare to pursue their chosen professions with distinction, whether it be graduate study, a career in industry, or one in mathematics education.

The mission of the Mathematics Program is to promote competence in both mathematical and computer sciences and to foster the ability to apply mathematics and computer technology to related fields.

The goals of the Mathematics program at the College of Saint Elizabeth are:

- To offer a rigorous and diverse set of courses that will enable students to acquire knowledge and competency in the major field of mathematics;
- To prepare students for the use of mathematics and computer technology in a professional capacity, as a basis for advanced study, and for continued professional development;
- To provide all students the opportunity to learn mathematics and computer technology, to develop analytical skills, to improve quantitative thinking, and to recognize the usefulness of mathematics and computer technology;
- To support the liberal arts environment of the College by providing all students the opportunity to appreciate the beauty of mathematics and computer technology as they apply to the student's major field of study and the world around them.

A student who completes the major requirements in the Mathematics program will have:

- Acquired in-depth knowledge of, and a high level of competency in the major field of study;
- Learned various problem solving strategies including the use of technologies and their applications
- Acquired the necessary skills to pursue a career in the major field of study or a related field
- Demonstrated the ability to clearly and effectively communicate ideas in the major field of study.

Graduates of the Mathematics Program are equipped with the mathematics skills needed to engage in a successful career. Career opportunities for mathematics majors are ample. The Program takes great pride in the fact that our students find strong placements in graduate school, in primary and secondary education, and in business as well as computer-related fields.

**Core Requirements**

- MATH151 Calculus I (4)
- MATH153 Calculus II (4)
- MATH253 Calculus III (4)
- MATH255 Linear Algebra (4)
- MATH403 Abstract Algebra (4)
- MATH453 Introduction to Real Analysis (4)
- CS115 Fundamentals of Computer and Programming (4)
- MATH480 Senior Seminar (1)

Total: 29 credits

In addition to the mathematics core courses, students must choose at least three courses from the following list.

- MATH301 Probability Theory
- MATH305 Geometry
- MATH309 Differential Equations
- MATH315 Mathematical Statistics
- MATH321 Discrete Mathematics
- MATH337 Applied Mathematics
- MATH351 Number Theory
- MATH421 Numerical Analysis
- MATH457 Special Topics in Mathematics
- MATH491 Independent Study
- MATH495 Professional Internship

Total: 12 credits

Total credits for the Bachelor of Arts in Mathematics: 41**Capstone Requirement**

Students will fulfill the capstone requirement by successful completion of the Mathematical Comprehensive Experience which includes a written examination, an oral presentation and Math 480 Senior Seminar course.

- CS 115 Fundamentals of Computers and Programming (4)
- CS 117 Introduction to Object Oriented Programming (4)
- CS 217 Data Structures and Algorithms (4)

And two of the following computer science elective courses with a grade of C or better:

- CS235 Computer Architecture and Organization (4)
- CS307 Database Management (4)
- CS313 Cryptography (4)
- CS319 Computer Operating Systems (4)
- CS325 Web Programming (4)
- CS345 Principles of Computer Security (4)
- CS357 Software Engineering (4)
- CS421 Numerical Analysis (4)
- CS425 Fundamentals of Programming Languages (4)
- CS431 Computer Graphics (4)
- CS435 Artificial Intelligence (4)
- CS437 Computer Networks (4)
- CS457 Special Topics (4)
- CS491 Independent Study (4)
- CS495 Professional Internship

Total: 20 credits

A student who wants to minor in mathematics must complete Math 151 Calculus I, Math 153 Calculus II, and any other three courses from the following mathematics courses with a grade of C or above:

- MATH119 Elementary Statistics
- MATH253 Calculus III
- MATH255 Linear Algebra
- MATH301 Probability Theory
- MATH305 Geometry
- MATH309 Differential Equations
- MATH315 Mathematical Statistics
- MATH321 Discrete Mathematics
- MATH337 Applied Mathematics
- MATH351 Number Theory
- MATH403 Abstract Algebra
- MATH421 Numerical Analysis
- MATH453 Real Analysis
- MATH457 Special Topics in Mathematics

Total: 20 credits

The Certificate in Cyber Security program (pending notification of New Jersey Presidents Council) at the College of Saint Elizabeth is aimed to equip students with knowledge and skills for employment in the computer security or related fields. Credits earned in CSE's Certificate in Cyber Security Program can be applied toward a B.S. in Computer Science.**Courses:**

- JUS 101 Introduction to Justice Studies (2)
- CS 115 Fundamentals of Computers and Programming (4)
- CS 117 Introduction to Object-Oriented Programming (4)
- CS 313 Cryptography (4)
- CS 345 Principles of Computer Security (4)
- CS 457 Special Topics – Digital Crimes (3)

Total: 20 credits

This course covers the essentials of college algebra, presented in the context of real world applications, including linear programming, mathematical modeling, compound interest, and fractals. Pre-Requisie: MATH096 and/or Basic Algebra Placement. Restricted to first time students in the EOF summer program.

The primary focus of this course is the development of students' logical thinking and problem solving skills through the study of fundamentals of computer, the Internet and technologies used on the Internet. Topics include computer hardware components; operating systems; software; representation of information in computer; Internet; technologies and languages used to create web pages as well as the ethical and security issues using the Internet. Students will write programs and create a simple personal web site. Satisfies Cluster 3 General Education requirement. (Spring)

This course provides the foundation to students interested in computer science and information systems. It helps develop logical thinking and problem solving skills through the study and use of Java programming language. Topics include computer hardware and software, binary system, algorithms and their role in problem solving, flowcharting, program design, coding, debugging, testing and documentation. Satisfies Cluster 3 General Education requirement. (Fall, night)

This course continues CS 115 with an emphasis on object-oriented design principles and programming language features that support object orientation. It applies software engineering techniques to the design and implementation of programs using Java programming language with emphasis on data abstraction and encapsulation; inheritance and code reuse; polymorphisms, and program design. Prerequisites: CS 115 or permission of the instructor. (Spring, night)

Descriptive statistics, single variable and bivariate data, probability distributions, binomial and normal distributions, estimation, confidence intervals, hypothesis testing, correlation, regression, statistical inferences of more than one population, t-distribution, Chi-square distribution, and ANOVA. Applications in Business, social and behavioral sciences will be presented. Appropriate statistical software will be utilized.

Study of real world applications of mathematics and mathematical models using problems chosen from the areas of graph theory, planning and scheduling, linear programming, probability and statistics, election theory, voting systems, fair division, savings and borrowing models, symmetry and patterns, and information science.

Elements of set theory; numeration, whole number, rational number and real number systems; problem solving. Term project according to major, e.g., computer project, historical paper, micro-teaching for education majors. Taken concurrently with ED 355 for education junior majors.

Functions, analytic geometry, graphing including linear and quadratic functions, polar coordinates, polynomial, exponential, and trigonometric functions, applications of trigonometric functions, and complex numbers. An appropriate Computer Algebra System (CAS) will be utilized. Open to students who have had only three years of high school mathematics or who have approval of the chairperson.

Limits, Continuity, Rules of Differentiation, Implicit Differentiation, Related Rates, Maxima and Minima, Rolle?s Theorem, Mean Value Theorem, Curve Sketching, Definite and Indefinite Integrals, Fundamental Theorem of Calculus, applications of definite integrals, and derivatives of Transcendental Functions. An appropriate Computer Algebra System (CAS) will be utilized. Prerequisite: four years of high school mathematics or Math 149 or approval of the chairperson.

Techniques of integration, Applications of definite integrals, improper integrals, sequences and series. An appropriate Computer Algebra System (CAS) will be utilized. Prerequisite: Math 151.

Rigorous study of basic data structures of lists, stacks and queues, and algorithms for their implementation; study of trees, graphs and networks; abstract data structures and their implementation in an object oriented environment; program design, testing, documentation and verification. Prerequisite: CS 117.

Organization and structuring of the major hardware components of computers; function of, and communication between, the components; fundamentals of logic design. Processor design and implementation of modern architecture theories. Prerequisite: CS 117.

Vectors in two and three dimensions, functions of several variables, partial derivatives, gradient, directional derivative, optimization, Lagrange multipliers, double and triple integrals, line integrals, vector analysis, Green?s, Stokes?, and Divergence Theorems. An appropriate Computer Algebra System (CAS) will be utilized. Prerequisite: Math 153.

Systems of linear equations, matrices and determinants, vectors, vector spaces and subspaces, nullspace, row space and column space, linear transformations, eigenvalues and eigenvectors, and inner products. An appropriate Computer Algebra System (CAS) will be utilized. Prerequisite: four years of high school mathematics or approval of chairperson.

Elements of combinatorial analysis, basic rules and axioms of probability, random variables, probability distributions, expected values, moments and moment-generating functions, functions of random variables, and method of distribution functions. Prerequisite: Math 253.

Axiomatic systems, finite geometries, foundations of Euclidean geometry, non-Euclidean geometries, hyperbolic geometry, fractals, and applications of Geometry. Prerequisite: Math 153.

This course introduces the concepts and design principles used in database management. It provides an overview of principles of physical and logical database design, query languages, relational design theory, file structures, transaction management, entity relationships; hierarchical, network and relational models; data dependencies, integrity, reliability, security, and applications in a relational database. Prerequisite: CS 117.

Existence and uniqueness theorems for ordinary differential equations, solutions of first order equations, linear differential equations of higher order, systems of differential equations, series solutions, Laplace Transforms, and applications. An appropriate Computer Algebra System (CAS) will be utilized. Prerequisite: MATH 153 or permission of instructor.

This course provides the foundation of computer security including authentication, confidentiality, integrity, and non-repudiation and the mechanisms to achieve them as well as the underlying mathematical basics. Topics include various cryptographic algorithms such as secret key cryptography, public-key cryptography and hash functions, key management, certificates, public-key infrastructure, digital signatures, non-repudiation, and authentication as well as the use of cryptography for anonymizing communication, voting and digital cash. Prerequisite: CS117 or permission of the instructor.

Central Limit Theorem, Sampling distributions, estimation, hypothesis testing, applications, regression and correlation, analysis of variance, contingency tables, categorical data, linear Models, and Chi-Square distribution. Appropriate statistical software will be utilized. Prerequisite: Math 301.

Introduction to the major concepts of operating systems, principles of system organization, process management, memory management and recovery procedures; case studies of several operating systems. Prerequisites: CS 231 and 235 or permission of the instructor.

Foundations of set theory and logic including quantifiers, truth tables, and valid vs. invalid arguments; introduction to proof-writing including direct and indirect methods of proof; additional topics include algorithms, combinatorics, relations, countable and uncountable sets, graph theory, functions, sequences, and trees. Prerequisite: MATH 255 or permission of the instructor.

A selection of topics from applied mathematics including, but not limited to, Fourier analysis, optimization (linear programming), linear transformations, partial differential equations, and other topics determined by faculty interests. An appropriate Computer Algebra System (CAS) will be utilized. Prerequisite: Math 253.

Introduction to the basic concepts of number theory including divisibility, prime numbers, number theoretic functions, linear congruences, continued fractions, Prime Number Theorem, Chinese Remainder Theorem, groups of units, Euler?s function, arithmetic functions, and Riemann Zeta Function. Prerequisite: Math 153.

Group and subgroup theory, Permutation Groups, Cosets, Direct Products, Homomorphisms, Isomorphisms, Factor Groups, Cyclic Groups, Rings, Fields, and Integral Domains. Prerequisite: Math 253

Foundations of set theory and logic including quantifiers, truth tables, and valid vs. invalid arguments; introduction to proof-writing including direct and indirect methods of proof; additional topics include algorithms, combinatorics, relations, countable and uncountable sets, graph theory, functions, sequences, and trees. Prerequisite: MATH 255 or permission of the instructor.

This is an introduction to numerical methods with emphasis on algorithm construction, analysis, implementation and their uses in solving mathematical problems on computer. Topics include round-off error, zeros of functions, interpolation and polynomial approximation, direct solvers for linear systems, numerical differentiation and integration, solutions of ordinary differential equations. Additionally, students will learn good programming techniques and implement algorithms using mathematical software uniting theory with practice. Prerequisites: MATH 255 and MATH 153

Formal study of programming language specification and analysis, syntax and semantics, comparison of language features, and run-time considerations. Prerequisite: CS 217.

Introduction to the basic principles for the design, use, and understanding of computer graphics; types of graphic hardware; transformations, windowing, and clipping; algorithms for creating and manipulating graphic displays. Prerequisite: CS 217 and MATH 155 or permission of the instructor.

Basic concepts and techniques of AI including internal representation, search problems and strategies, first-order logic, game playing, knowledge based systems, consideration of active research areas and applications. Prerequisite: CS 217.

A study of the principles and design of computer networks. Topics include network structures and architectures; protocols; flow control; error handling; routing; and network security. Prerequisite: CS 319 or permission of the instructor.

Principles, techniques and tools used in writing compilers for programming languages, including LL (1) grammars and parsers, LR parsing, symbol table construction, and run-time storage organization. Includes the development of a complete, working compiler for a specified subset of a programming language. Prerequisite: CS 425 or permission of the instructor.

Properties of the real number system including the Completeness Axiom, metric spaces, and the topology of the real line; sequences, convergence, function limits, continuous functions, the derivative, the Riemann integral, sequences and series of functions, and uniform convergence. Prerequisite: Math 253.

The study of an area of mathematics, such as topology or complex analysis, not offered on a regular basis in the mathematics curriculum. Specific topics will be determined by student and faculty interests. Prerequisite: Senior majors or the approval of the chairperson.

The study of an area in computer science, such as network security, game design or wireless applications, not offered on a regular basis in the computer science curriculum. Specific topics will be determined by student and faculty interests. Prerequisite: Senior majors or the approval of the program chair.

Topics not ordinarily covered in the mathematics major curriculum will be presented. Students must submit a research paper on each topic with a maximum three topics being covered during the semester. In addition, students will give an oral presentation to the seminar class on one aspect from each paper. Senior seminar is part of the Mathematics Comprehensive Experience offered only to graduating seniors meeting once per week during fall semesters. Prerequisite/Co-requisite: Math 403 or Math 453 or Math 457.

Open to junior and senior mathematics majors who have a minimum 3.0 GPA in mathematics or who have approval of chairperson.

Open to junior and senior computer science majors who have a minimum 3.0 GPA in computer science or who have approval of the Program Chairperson. Variable credit, students can register 2 or 3 credits.

Placement of a student with a business or professional organization engaged in some aspect of mathematics. Open to juniors and seniors in the Mathematics and Computer Science department with departmental approval. Credit to be determined, with a maximum of six credits to be earned over two semesters.

Placement of a student with a business or professional organization engaged in some aspect of computer science. Open to juniors and seniors in the Mathematics and Computer Science program with program approval. A maximum of three credits permitted within the 36 credit major requirement; an additional three elective credits will be allowed. Variable credit, students can register 1-4 credits.