**Chairperson: Gary S. Krenz, Ph.D.**

marquette.edu/mscs/

The Department of Mathematics, Statistics and Computer Science offers a unique interdisciplinary learning environment with areas of study ranging from pure and applied mathematics to computer science, statistics and mathematics education.

The Mathematics major (MATH) explores the interplay between the pure theory and the practical applications of mathematics. The mathematics curriculum can be tailored to an individual's interests with a focus in pure mathematics, applied mathematics or actuarial science, statistics, as well as, secondary education. In any case, the curriculum is designed to provide technical skills for growth within the discipline and for success in a wide variety of careers.

The Computer Science major (COSC) provides students with an understanding of the central ideas and methods used to solve real problems with software. Students will practice the many skills required to build computer systems that address problems in scientific, engineering, and business domains. Most of all, the major aims to prepare students for long-term success in a rapidly changing field that provides the computer technology underpinning our modern world.

The Computational Mathematics major (COMA) blends the subjects of computer science and applied mathematics providing a balance, which would otherwise require a double major to achieve. Furthermore, the curriculum teaches the skills necessary for careers in today's technical environment.

The Mathematics for Elementary School Teachers major (MELT) is for College of Education students who are seeking teaching certification at the elementary school level, while obtaining strong mathematical preparation. This program is designed to prepare “mathematics specialists” who provide vision, focus and leadership in elementary schools.

## Major in Mathematics

The major in mathematics consists of 39 credit hours of mathematics courses, including five required math courses (18 credit hours); one math sequence (two courses - 6 credit hours); at least one course from each of the three groups (Group 1- Pure Mathematics, Group 2 - Applied Mathematics and Group 3 - Statistics, for a total of 9 credit hours); and two courses (6 credit hours) of upper division MATH courses.

**Note: **

- Students majoring in mathematics must also complete the following course in computer science: COSC 1010 Introduction to Computer Programming.

Required Mathematics Courses: | ||

MATH 1450 | Calculus 1 | 4 |

MATH 1451 | Calculus 2 | 4 |

MATH 2350 | Foundations of Mathematics | 3 |

MATH 2450 | Calculus 3 | 4 |

MATH 3100 | Linear Algebra and Matrix Theory | 3 |

Choose one of the following sequences: | 6 | |

Abstract Algebra 1 and Abstract Algebra 2 | ||

Intermediate Analysis 1 and Intermediate Analysis 2 | ||

Intermediate Analysis 1 and Complex Variables | ||

Intermediate Analysis 1 and Topology | ||

Foundations of Geometry and Concepts in Geometry and Calculus from an Advanced Standpoint | ||

Theory of Differential Equations and Elementary Partial Differential Equations | ||

Applied Combinatorial Mathematics and Theory of Optimization | ||

Theory of Probability and Mathematical Statistics | ||

Choose at least one additional course from each of the three groups listed below: | 9 | |

Group 1 - Pure Mathematics | ||

Abstract Algebra 1 | ||

Abstract Algebra 2 | ||

Intermediate Analysis 1 | ||

Intermediate Analysis 2 | ||

Complex Variables | ||

Theory of Numbers | ||

Foundations of Geometry | ||

Topology | ||

Group 2 - Applied Mathematics | ||

Operational Methods in Physics and Engineering | ||

Theory of Differential Equations | ||

Elementary Partial Differential Equations | ||

Numerical Analysis | ||

Mathematical Modeling and Analysis | ||

Theory of Optimization | ||

Applied Combinatorial Mathematics | ||

Group 3 - Statistics | ||

Theory of Probability | ||

Mathematical Statistics | ||

Statistical Methods | ||

Biostatistical Methods and Models | ||

Time Series Analysis | ||

Regression Analysis | ||

Choose 6 credit hours of upper-division MATH courses. | 6 | |

Total Credit Hours | 39 |

**Note:**

- Occasionally MATH 4931 Topics in Mathematics or Statistics may be approved as a substitute within a student’s program of study for an above listed course.

### Typical Program for Mathematics Major

Freshman | |||
---|---|---|---|

First Term | Hours | Second Term | Hours |

ENGL 1001 | 3 | ENGL 1002 | 3 |

Foreign Language | 3-4 | Foreign Language | 3-4 |

HIST 1001 or 1002 | 3 | History or Individual and Social Behavior | 3 |

MATH 1450 | 4 | MATH 1451 | 4 |

Individual and Social Behavior | 3 | Elective | 3 |

16-17 | 16-17 | ||

Sophomore | |||

First Term | Hours | Second Term | Hours |

MATH 2450 | 4 | MATH 3100 | 3 |

MATH 2350 | 3 | Literature | 3 |

Literature | 3 | Natural Science | 4 |

Natural Science | 4 | PHIL 1001 | 3 |

Elective | 3 | Elective | 3 |

17 | 16 | ||

Junior | |||

First Term | Hours | Second Term | Hours |

MATH Sequence (part 1) | 3 | MATH Sequence (part 2) | 3 |

MATH Group 1 (Pure) | 3 | MATH Group 3 (Statistics) | 3 |

COSC 1010 | 4 | PHIL 2310 | 3 |

THEO 1001 | 3 | Electives | 6-9 |

Electives | 3-6 | ||

16-19 | 15-18 | ||

Senior | |||

First Term | Hours | Second Term | Hours |

MATH Group 2 (Applied) | 3 | MATH elective (upper division) | 3 |

MATH Elective (upper division) | 3 | Theology (third level) | 3 |

Philosophy (upper division) | 3 | Diverse Cultures elective | 3 |

Theology (second level) | 3 | Electives | 6-9 |

Electives | 3-6 | ||

15-18 | 15-18 | ||

Total credit hours: 126-140 |

**Note:** A minimum of 128 credits is required for the degree.

### Department of Public Instruction Certification for Mathematics Majors

To pursue Department of Public Instruction certification, College of Education students are required to fulfill the requirements of a mathematics major (39 credit hours of mathematics courses) as listed below. In addition to the 39 credit hours, students must complete an introductory computer science course (4 credit hours) and the mathematics teaching methodology course (3 credit hours) for a total of 46 credit hours as listed below.

**Notes: **

- Students majoring in mathematics must also complete COSC 1010 Introduction to Computer Programming
- MATH 4020 The Teaching of Mathematics is required as part of the state certification program and must be completed before student teaching.
- From the beginning of their work toward a degree, students should consult with both the department adviser for Mathematics Education and the Director of Teacher Education in the College of Education about the appropriate sequence of courses.

Required Mathematics Courses: | ||

MATH 1450 | Calculus 1 | 4 |

MATH 1451 | Calculus 2 | 4 |

MATH 2350 | Foundations of Mathematics | 3 |

MATH 2450 | Calculus 3 | 4 |

MATH 3100 | Linear Algebra and Matrix Theory | 3 |

MATH 4420 & MATH 4030 | Foundations of Geometry and Concepts in Geometry and Calculus from an Advanced Standpoint | 6 |

Required Group Courses: | ||

Group 1 - Pure Mathematics | ||

MATH 4120 | Abstract Algebra 1 | 3 |

Group 2 - Applied Mathematics | ||

MATH 4630 | Mathematical Modeling and Analysis | 3 |

Group 3 - Statistics | ||

MATH 4720 | Statistical Methods | 3 |

Additional Mathematics Courses: | ||

MATH 4670 | Applied Combinatorial Mathematics | 3 |

or MATH 4700 | Theory of Probability | |

MATH 4040 | Concepts in High School Algebra and Number Theory from an Advance Standpoint | 3 |

Total Credit Hours | 39 |

## Minor in Mathematics

The minor in mathematics consists of 24 credit hours of mathematics courses, including four required math courses (15 credit hours) and an additional 9 credit hours of upper division math courses as listed below:

Required Courses: | ||

MATH 1450 | Calculus 1 | 4 |

MATH 1451 | Calculus 2 | 4 |

MATH 2450 | Calculus 3 | 4 |

MATH 2350 | Foundations of Mathematics | 3 |

or MATH 2451 | Differential Equations | |

Electives - Choose at least nine additional hours of upper-division MATH courses. | 9 | |

Total Credit Hours | 24 |

### Department of Public Instruction Certification for Mathematics Minor

To pursue Department of Public Instruction certification for a minor in mathematics, College of Education students are required to complete eight required MATH courses (26 credit hours)as well as completing MATH 4020 (3 credit hours), for a total of 29 credit hours as listed below.

Required Courses: | ||

MATH 1450 | Calculus 1 | 4 |

MATH 1451 | Calculus 2 | 4 |

MATH 2350 | Foundations of Mathematics | 3 |

MATH 3100 | Linear Algebra and Matrix Theory | 3 |

MATH 4040 | Concepts in High School Algebra and Number Theory from an Advance Standpoint | 3 |

MATH 4120 | Abstract Algebra 1 | 3 |

MATH 4420 | Foundations of Geometry | 3 |

MATH 4720 | Statistical Methods | 3 |

The following must be completed before student teaching: | ||

MATH 4020 | The Teaching of Mathematics | 3 |

Total Credit Hours | 29 |

## Major in Computer Science

The major in computer science consists of nine required COSC courses (29 credit hours) and 12 credit hours of upper-division COSC courses, for a total of 41 credit hours of COSC courses. In addition, each student must complete four required MATH courses (14 credit hours) and an additional 3 credit hours of upper-division MATH courses for a total of 17 credit hours of mathematics courses.

Required Computer Science Courses: | ||

COSC 1010 | Introduction to Computer Programming | 4 |

COSC 1020 | Object-Oriented Software Design | 4 |

COSC 2100 | Data Structures and Algorithms 1 | 3 |

COSC 2200 | Hardware Systems | 3 |

COSC 3100 | Data Structures and Algorithms 2 | 3 |

COSC 3250 | Operating Systems | 3 |

COSC 3410 | Programming Languages | 3 |

COSC 4920 | Principles of Design | 3 |

COSC 4998 | Senior Design Project | 3 |

Electives - Choose 12 credit hours of upper-division COSC courses. | 12 | |

Required Mathematics Courses: | ||

MATH 1450 | Calculus 1 | 4 |

MATH 1451 | Calculus 2 | 4 |

MATH 2100 | Discrete Mathematics | 3 |

MATH 3100 | Linear Algebra and Matrix Theory | 3 |

Mathematics Elective - Choose 3 additional hours of upper-division MATH courses. | 3 | |

Total Credit Hours | 58 |

### Typical Program for Computer Science Majors

Freshman | |||
---|---|---|---|

First Term | Hours | Second Term | Hours |

COSC 1010 | 4 | COSC 1020 | 4 |

MATH 1450^{*} | 4 | MATH 1451 | 4 |

Foreign Language | 3-4 | Foreign Language | 3-4 |

HIST 1001 or 1002 | 3 | History/Individual and Social Behavior | 3 |

ENGL 1001 | 3 | ENGL 1002 | 3 |

17-18 | 17-18 | ||

Sophomore | |||

First Term | Hours | Second Term | Hours |

COSC 2100 | 3 | COSC 3100 | 3 |

COSC 2200 | 3 | COSC 3250 | 3 |

MATH 2100 | 3 | MATH 3100 | 3 |

Individual and Social Behavior | 3 | PHIL 1001 | 3 |

THEO 1001 | 3 | Literature | 3 |

15 | 15 | ||

Junior | |||

First Term | Hours | Second Term | Hours |

COSC 3410 | 3 | Computer 3xxx/4xxx | 3 |

Computer 3xxx/4xxx | 3 | MATH 3xxx/4xxx | 3 |

Literature | 3 | PHIL 2310 | 3 |

Natural Science | 3-4 | Natural Science | 3-4 |

Elective | 3 | Elective | 3 |

15-16 | 15-16 | ||

Senior | |||

First Term | Hours | Second Term | Hours |

COSC 4920 | 3 | COSC 3xxx/4xxx | 3 |

COSC 3xxx/4xxx | 3 | COSC 4998 | 3 |

Philosophy (upper division) | 3 | Theology (third level) | 3 |

Theology (second level) | 3 | Diverse Cultures | 3 |

Electives | 6 | Elective | 3 |

18 | 15 | ||

Total credit hours: 127-131 |

**Note:** A minimum of 128 credits is required for the degree.

* | Potential computer science majors who have taken a university-level calculus course in high school should discuss with the department the possibility of credit by examination for MATH 1450 Calculus 1. |

## Minor in Computer Science

The minor in computer science consists of 20 credit hours of computer science courses, including four required COSC courses (14 credit hours) and 6 additional credit hours of upper-division COSC elective courses. In addition, each student must complete a required MATH course (3 credit hours) as listed below:

Required Courses: | ||

COSC 1010 | Introduction to Computer Programming | 4 |

COSC 1020 | Object-Oriented Software Design | 4 |

COSC 2100 | Data Structures and Algorithms 1 | 3 |

COSC 2200 | Hardware Systems | 3 |

Electives - Choose 6 credit hours of upper-division COSC courses. | 6 | |

Required Mathematics Course: | ||

MATH 2100 | Discrete Mathematics | 3 |

Total Credit Hours | 23 |

## Minor in Software Development

The minor in software development consists of 20 credit hours of computer science courses, including four required COSC courses (14 credit hours) and 6 additional credit hours of upper-division COSC elective courses. In addition, each student must complete a required MATH course (3 credit hours) as listed below:

Required Courses: | ||

COSC 1010 | Introduction to Computer Programming | 4 |

COSC 1020 | Object-Oriented Software Design | 4 |

COSC 2100 | Data Structures and Algorithms 1 | 3 |

COSC 4860 | Component-Based Software Construction | 3 |

Electives - Choose 6 credit hours of upper-division COSC courses. | 6 | |

Required Mathematics Course: | ||

MATH 2100 | Discrete Mathematics | 3 |

Total Credit Hours | 23 |

## Major in Computational Mathematics

The major in computational mathematics consists of 50 credit hours of computer science and mathematics courses as listed below:

Required Computer Sciences Courses: | ||

COSC 1010 | Introduction to Computer Programming | 4 |

COSC 1020 | Object-Oriented Software Design | 4 |

COSC 2100 | Data Structures and Algorithms 1 | 3 |

COSC 2200 | Hardware Systems | 3 |

Computer Science Elective: Choose one of the following. | 3 | |

Operating Systems | ||

Programming Languages | ||

Required Mathematics Courses: | ||

MATH 1450 | Calculus 1 | 4 |

MATH 1451 | Calculus 2 | 4 |

MATH 2350 | Foundations of Mathematics | 3 |

MATH 2450 | Calculus 3 | 4 |

MATH 3100 | Linear Algebra and Matrix Theory | 3 |

MATH 4540 | Numerical Analysis | 3 |

MATH 4630 | Mathematical Modeling and Analysis | 3 |

MATH 4710 | Mathematical Statistics | 3 |

or MATH 4720 | Statistical Methods | |

Mathematics Electives: Choose two of the following. | 6 | |

Intermediate Analysis 1 | ||

Complex Variables | ||

Theory of Differential Equations | ||

Elementary Partial Differential Equations | ||

Theory of Optimization | ||

Applied Combinatorial Mathematics | ||

Theory of Probability | ||

Biostatistical Methods and Models | ||

Time Series Analysis | ||

Regression Analysis | ||

Total Credit Hours | 50 |

### Typical Program for Computational Mathematics Majors

Freshman | |||
---|---|---|---|

First Term | Hours | Second Term | Hours |

COSC 1010 | 4 | COSC 1020 | 4 |

MATH 1450 | 4 | MATH 1451 | 4 |

ENGL 1001 | 3 | ENGL 1002 | 3 |

Foreign Language | 3-4 | Foreign Language | 3-4 |

HIST 1001 or 1002 | 3 | History/Individual and Social Behavior | 3 |

17-18 | 17-18 | ||

Sophomore | |||

First Term | Hours | Second Term | Hours |

COSC 2200 | 3 | COSC 2100 | 3 |

MATH 2450^{2,3} | 4 | MATH 3100 | 3 |

MATH 2350^{2,3} | 3 | PHIL 1001 | 3 |

Individual and Social Behavior | 3 | Electives | 6 |

Elective | 3 | ||

16 | 15 | ||

Junior | |||

First Term | Hours | Second Term | Hours |

COSC 3410 (or elective) | 3 | COSC 3250 (or elective) | 3 |

Mathematics elective | 3 | Mathematics elective | 3 |

Literature | 3 | Literature | 3 |

Natural Science | 4 | Natural Science | 4 |

THEO 1001 | 3 | PHIL 2310 | 3 |

16 | 16 | ||

Senior | |||

First Term | Hours | Second Term | Hours |

MATH 4540 | 3 | MATH 4710 or 4720 | 3 |

MATH 4630 | 3 | Theology (third level) | 3 |

Philosophy (upper division) | 3 | Diverse Cultures | 3 |

Theology (second level) | 3 | Electives | 6-9 |

Electives | 3-6 | ||

15-18 | 15-18 | ||

Total credit hours: 127-135 |

**Note:** A minimum of 128 credits is required for the degree.

## Major in Mathematics for Elementary School Teachers (MELT)

This major is for students in the College of Education enrolled in the middle childhood/early adolescence teacher education program (grades 1-8). The major in mathematics for elementary teachers consists of twelve required mathematics courses for a total of 36 credit hours as listed below.

**Note:**

- From the beginning of their work toward a degree, students should consult with both a department adviser and the director of teacher education in the College of Education about the appropriate sequence of courses. University and state requirements for teacher certification are described in the College of Education section of this bulletin.

Required Courses: | ||

MATH 1450 | Calculus 1 | 4 |

MATH 1451 | Calculus 2 | 4 |

MATH 2030 | Problem Solving and Reasoning for Teachers | 3 |

MATH 2031 | Number Systems and Operations for Elementary Teachers | 2 |

MATH 2032 | Algebra and Geometry for Teachers | 2 |

MATH 2350 | Foundations of Mathematics | 3 |

MATH 3100 | Linear Algebra and Matrix Theory | 3 |

MATH 4300 | History of Mathematical Ideas | 3 |

MATH 4320 | Theory of Numbers | 3 |

MATH 4420 | Foundations of Geometry | 3 |

MATH 4630 | Mathematical Modeling and Analysis | 3 |

MATH 4720 | Statistical Methods | 3 |

Total Credit Hours | 36 |

### Typical Program for Mathematics for Elementary School Teachers Majors

Freshman | |||
---|---|---|---|

First Term | Hours | Second Term | Hours |

ARSC 1020 | 4 | ARSC 1021 | 4 |

EDUC 1210 | 3 | EDUC 1220 | 3 |

ENGL 1001 | 3 | ENGL 1002 or COMM 1100 | 3 |

Foreign Language 1 | 4 | Foreign Language 2 | 4 |

MATH 1450 | 4 | MATH 1451 | 4 |

Service Learning | |||

18 | 18 | ||

Sophomore | |||

First Term | Hours | Second Term | Hours |

EDUC 2227 | 3 | HIST 1301, 1401, or 1501 | 3 |

POSC 2201 | 3 | EDUC 2330 | 3 |

Literature elective | 3 | PHIL 1001 | 3 |

MATH 2350 | 3 | MATH 3100 | 3 |

HIST 1101 | 3 | MATH 4300 or 4320 | 3 |

THEO 1001 | 3 | THEO 2000 | 3 |

Field Experience 1 | |||

18 | 18 | ||

Junior | |||

First Term | Hours | Second Term | Hours |

PHIL 2310 | 3 | EDUC 3240 | 3 |

EDUC 4347 | 4 | EDUC 4317 | 3 |

EDUC 4217 | 3 | EDUC 4357 | 4 |

EDUC 4337 (must be taken for 3 cr. hrs.) | 3 | MATH 2031 | 2 |

MATH 2030 | 3 | EDUC 1964 | 1 |

MATH 4420 | 3 | MATH 4300 or 4320 | 3 |

Field Experience 2 | MATH 4630 | 3 | |

Field Experience 3 | |||

19 | 19 | ||

Senior | |||

First Term | Hours | Second Term | Hours |

EDUC 4297 | 4 | EDUC 4966 (must be taken for 15 cr. hrs.) | 15 |

EDUC 4540 | 3 | ||

EDUC 4964 | 4 | ||

MATH 2032 | 2 | ||

EDUC 2964 | 1 | ||

MATH 4720 | 3 | ||

Senior Level Practicum | |||

17 | 15 | ||

Total credit hours: 142 |

**Note:**

- A minimum of 128 credits is required for the degree.
- EDUC 4337 Teaching Elementary Social Studies must be taken for 3 cr. hrs.
- EDUC 4966 Student Teaching: Elementary/Middle must be taken for 15 cr. hrs.

### Computer Science Courses

**COSC 1000. Introduction to Computer Science. 3 cr. hrs.**

Introduction to the science behind today's computerized society. Emphasis placed on understanding the breadth and current status of computer science rather than the development of skills. Topics include machine architectures, operating systems, networking, algorithms and their development, programming languages, artificial intelligence, and data representation systems. (Previous computer experience is not required.) Prereq: Two years of college preparatory mathematics. This course satisfies the computer option in the Arts and Sciences core curriculum.

**COSC 1010. Introduction to Computer Programming. 4 cr. hrs.**

Introduction to abstraction, algorithmic thinking, simulation and testing for computer-based problem solving. Students will learn a high-level programming language and use tools developed by computer scientists and software engineers to solve problems. No prior programming experience is assumed. 3 hrs. lecture, 2 hrs. lab. Two years of college preparatory mathematics required.

**COSC 1020. Object-Oriented Software Design. 4 cr. hrs.**

Software development using Java. Topics include classes and interfaces as design patterns, the Java API, current object-oriented design methodologies, an introduction to the Internet and the development of Web applications. Projects involve the development of graphical interfaces and net-centric applications. 3 hrs. lecture, 2 hrs. lab. Prereq: COSC 1010 or advanced placement.

**COSC 2010. Data Structures for Engineers. 3 cr. hrs.**

The study of popular data structures such as lists, stacks, queues and trees and their related algorithms. Prereq: COSC 1010 or EECE 1610; knowledge of JAVA. Credit will not be given for both COSC 2010 and COSC 2100.

**COSC 2100. Data Structures and Algorithms 1. 3 cr. hrs.**

Introduction to algorithm analysis and complexity theory presented in the context of data structures and the algorithms used to manipulate them. Includes introduction to traditional data structures, indexing, hashing and time and space complexity. Prereq: COSC 1020; MATH 2100 which may be taken concurrently.

**COSC 2200. Hardware Systems. 3 cr. hrs.**

Introduction to computer architecture and machine level programming. Topics include combinational and sequential binary logic, assembly languages, memory management, caching, pipelining, bus architecture, interrupts and I/O processing. Course may consist of a 3 hr. lecture or a 2 hr. lecture and 2 hr. lab. Prereq: COSC 1020 and MATH 2100, which may be taken concurrently.

**COSC 3100. Data Structures and Algorithms 2. 3 cr. hrs.**

Types of algorithms such as divide-and-conquer, greedy, probabilistic, graph traversal, heuristic, and parallel algorithms. Computational complexity including time and space complexity, and the P=NP problem. Prereq: COSC 2100 or COSC 2010.

**COSC 3250. Operating Systems. 3 cr. hrs.**

Fundamental concepts of operating systems including process control and scheduling, synchronization, memory management, file systems, device control, and the boot process. Course may consist of a 3 hr. lecture or a 2 hr. lecture and 2 hr. lab. Prereq: COSC 2200 and COSC 2100 or COSC 2010.

**COSC 3410. Programming Languages. 3 cr. hrs.**

A comparative study of programming paradigms and representative programming languages. Topics include binding times, control of data, control of execution, execution environment, the role of language as an organizational tool, modularization, and the concept and significance of universal programming languages. Prereq: COSC 2100 or COSC 2010.

**COSC 3550. Programming Computer Games. 3 cr. hrs.**

Algorithms, data structures, and tricks used to program arcade-style video games written in Java. Topics include 2D animation, sprites, interaction, music/sound, 3D worlds, network games. Underlying issues include graphical user interfaces, multi-threaded applications, real-time concerns, use of APIs, and client-server applications. Prereq: COSC 2200 and COSC 2100 or COSC 2010.

**COSC 3810. Software Design and Analysis. 3 cr. hrs.**

Issues involved in the design and implementation of large software systems. Software lifecycle, software design methodologies, human factors analysis, project management. Prereq: COSC 2100 or COSC 2010.

**COSC 3977. Problem Solving -- Programming. 1 cr. hr.**

Students will study and implement computing problems, examine their solutions, apply classical algorithms, and formulate strategies for teamwork and problem solving in a programming contest environment. This course is a preparation for the ACM International Collegiate Programming Contest. S/U grade assessment. Prereq: Cons. of instr.

**COSC 4110. Formal Languages and Computability. 3 cr. hrs.**

Regular languages, finite state automata, and lexical analysis; context free languages, push-down automata, parsing, and the rudiments of LL and LR parsers; general phrase-structure languages, Turing machines, the Chuch-Turing thesis, the halting problem, universal programming languages. Prereq: COSC 3100.

**COSC 4290. Real-Time and Embedded Systems. 3 cr. hrs.**

Focuses on event-driven programming, real-time scheduling, and synchronization; worst-case execution time analysis and deadline analysis; real-time operating systems and real-time programming languages. Prereq: COSC 3250 or COEN 4820 or equivalent system programming experience.

**COSC 4300. Networks and Internets. 3 cr. hrs.**

Focuses on data communication and network protocols, including the TCP/IP protocol suite; Internet transport, packet switching and routing; network programming and network applications. May consist of a 3 hr. lec. or a 2 hr. lec. and 2 hr. lab. Prereq: COSC 3250 or COEN 4820 or equivalent system programming experience.

**COSC 4400. Compiler Construction. 3 cr. hrs.**

Lexical analysis, parsing, code generation, and optimization. Includes theoretical foundations and the practical concerns of implementation. Prereq: COSC 2200 and COSC 3410; or COSC 3410 and COSC 2010.

**COSC 4600. Fundamentals of Artificial Intelligence. 3 cr. hrs.**

An introduction to the broad field of artificial intelligence. Topics include problem solving by searching, knowledge representation, reasoning, planning, decision making, learning, perception, and language processing. Offered alternate fall terms. Prereq: COSC 2100 or COSC 2010; and COSC 2200.

**COSC 4610. Data Mining. 3 cr. hrs.**

Techniques for extracting and evaluating patterns from large databases. Introduction to knowledge discovery process. Fundamental tasks including classification, prediction, clustering, association analysis, summarization, and discrimination. Basic techniques including decision trees, neural networks, statistics, partitional clustering, and hierarchical clustering. Offered alternate spring terms. Prereq: COSC 4600 or COEN 4850; and COSC 4800.

**COSC 4800. Principles of Database Systems. 3 cr. hrs.**

Topics include database concepts and architecture, data modeling, formal query languages such as relational algebra, commercial query language SQL, database access from application programs and a brief examination of advanced concepts including transactions, distributed databases, security and XML. Prereq: COSC 2100 or COSC 2010.

**COSC 4860. Component-Based Software Construction. 3 cr. hrs.**

Introduction to software components in the context of the object-oriented paradigm. Component development, component selection and adaptation/customization, component deployment and assembly/integration, and system architecture. Industry standards such as JavaBeans, CORBA Component Model, and Microsoft COM/DOM/COM+. Prereq: COSC 1020 or COSC 2010; and MATH 2100.

**COSC 4920. Principles of Design. 3 cr. hrs.**

Fundamentals of structured software design and development applied in a multi-disciplinary, team-based project environment. Teams create project definition and specification based on user needs. Activities focus on software lifecycle, design methodologies, human factor analysis, teamwork, customer interaction, project management and effective communication. Work culminates in a technically and economically viable proposal for future development. (This course specifies and designs a project for implementation in COSC 4998.) Prereq: MATH 1400 or 1451; MATH 2100 or 2350; COSC 3250; COSC 3100; and Sr. stndg.

**COSC 4931. Topics in Computer Science. 1-3 cr. hrs.**

Topics selected from one of the various branches of computer science. Specific topics to be announced in the Schedule of Classes.

**COSC 4953. Undergraduate Seminar. 3 cr. hrs.**

Designed to initiate a selected group of qualified undergraduates into the techniques and discipline of scholarly research by concentrated work in a restricted field. Emphasis on critical reading and analysis of sources. Specific subjects to be announced in the Schedule of Classes. Prereq: Cons. of dept. ch.

**COSC 4987. Co-op Work Period. 0 cr. hrs.**

Students work full-time during fall or spring terms in a cooperative education program work assignment approved in advance by the department. Responsibilities include relevant academic content. Grading and credits are accomplished by registering for COSC 4988 during the following term. Fee. Prereq: Jr. stndg. SNC/UNC grade assessment.

**COSC 4988. Co-op Grading Period. 1 cr. hr.**

Grading for preceding co-op work assignment is accomplished by completing a report on the work assignment, a report on academic material related to the work assignment, and other materials as required. Grading is completed during the school term following the work assignment. May be taken more than once, but a maximum of 2 credits may be counted toward a major in the department. Prereq: Jr. stndg. and COSC 4987.

**COSC 4995. Independent Study in Computer Science. 1-3 cr. hrs.**

Directed reading and/or research in computer science under a member of the staff. Prereq: Cons. of dept. ch.

**COSC 4998. Senior Design Project. 3 cr. hrs.**

Given initial design and project specification, focus is on detailed software design, prototyping and testing of design concepts in a realistic multi-disciplinary team environment. "Team-based activities" result in implementation of a software system in support of a project and culminate in a working prototype satisfying user needs and software specification. Final report documents prototype details and verifies resulting project meets needs and specifications. (This course implements project specified and designed in COSC 4920.) Prereq: MATH 1400 or 1451; MATH 2100 or 2350; COSC 3250; COSC 3100; and Sr. stndg.

**COSC 4999. Senior Thesis. 2 cr. hrs.**

Preparation of a thesis by approved students under the direction of an adviser from the staff. Prereq: Cons. of dept. ch.

### Mathematics Courses

**MATH 105. Intermediate Algebra. 2 cr. hrs.**

Designed for students with deficient mathematical backgrounds. Basic arithmetic and algebraic operations on integers, polynomials, rational numbers and expressions. Linear equations and inequalities, quadratic equations. Relations and functions. Not applicable to the total number of hours required for graduation. Prereq: Cons. of dept. ch.

**MATH 1100. College Algebra. 3 cr. hrs.**

Precalculus mathematics including basic algebraic operations, equations, inequalities, complex numbers, graphs, functions, zeros of polynomials, systems of equations, and matrices. Offered every term. Prereq: Two years of college preparatory mathematics including a year each of algebra and geometry. Does not count toward Math-Logic-Computer requirement in the Arts and Sciences College Curriculum.

**MATH 1101. Trigonometry and Analytic Geometry. 3 cr. hrs.**

A continuation of MATH 1100 covering precalculus mathematics including trigonometric functions and their properties, trigonometric identities and equations, applications of trigonometry, vectors, polar coordinates, exponential and logarithmic functions, and conic sections. Prereq: MATH 1100 or equivalent. Equivalent is one year of high school geometry and the equivalent of MATH 1100 in high school courses. Does not count toward the Math-Logic-Computer requirement in the Arts and Sciences College Curriculum.

**MATH 1300. The Nature of Mathematics. 3 cr. hrs.**

Concepts of mathematics for liberal arts students. Emphasis on understanding and appreciating concepts rather than developing computational skills. For example, such topics as the historical development of ideas, role of abstraction, and relationship between different areas of mathematics is given precedence over performance of arithmetic and algebraic manipulations. Prereq: Two years of college preparatory mathematics.

**MATH 1390. Finite Mathematics. 3 cr. hrs.**

Mathematics of finance, including simple and compound interest, present and future value of ordinary annuities, sinking funds, and amortization schedules. Matrices, linear systems and linear programming. Combinatorics and elementary probability theory. Prereq: MATH 1100 or equivalent. Equivalent is three years of college preparatory mathematics.

**MATH 1400. Elements of Calculus. 3 cr. hrs.**

The basic concepts and techniques of differential and integral calculus. Applications and examples chosen primarily from economics, biology, the social and behavioral sciences and business. Prereq: MATH 1100 or equivalent. Equivalent is three years of college preparatory mathematics.

**MATH 1410. Calculus for the Biological Sciences. 3 cr. hrs.**

Fundamental concepts and techniques of differential and integral calculus, logarithmic, exponential and trigonometric functions, examples and applications from biology and medicine. Prereq: MATH 1100 or equivalent. Equivalent is three years of college preparatory mathematics.

**MATH 1450. Calculus 1. 4 cr. hrs.**

Functions of one variable, limits and continuity. The derivative and the definite integral with applications. Prereq: MATH 1101 or equiv. Equivalent is three to four years of college preparatory mathematics including topics listed in description of MATH 1101.

**MATH 1451. Calculus 2. 4 cr. hrs.**

The transcendental functions. Techniques of integration including numerical methods. Elementary differential equations. Infinite sequences and series, Taylor Series. Prereq: MATH 1450.

**MATH 1455. Calculus 2 for Biomedical and Civil Engineers. 4 cr. hrs.**

Techniques of integration, including numerical methods. Infinite sequences and series, including Taylor Series. Analytic-Geometry including parametric equations, vectors and vector functions. The differential and integral calculus of functions of several variables. Restricted to students in BIEN or CEEN. Prereq: MATH 1450.

**MATH 1700. Modern Elementary Statistics. 3 cr. hrs.**

Fundamental theory and methods of statistics without calculus. Descriptive statistics, elements of probability theory, estimation, tests of hypotheses, regression, correlation, introduction to computer methods of statistical tabulation and analysis. This course is recommended for students seeking a general introduction to statistical concepts and is not intended to be a final course in statistics for students who need a thorough working knowledge of statistical methods. Prereq: MATH 105 or equivalent. Equivalent is two years of college preparatory mathematics. May not be taken for credit by students who have received college credit for another probability or statistics course.

**MATH 2030. Problem Solving and Reasoning for Teachers. 3 cr. hrs.**

Mathematical content and processes for teachers. Mathematical techniques and ways of thinking are used to enhance mathematical power. Multiple ways of organizing and analyzing data, reasoning and communication skills, and multiple problem-solving strategies are used to solve nonroutine problems. In the process, elementary mathematical ideas are expanded and deepened. Restricted to students in the teacher preparation program. Prereq: Two years of college preparatory mathematics.

**MATH 2031. Number Systems and Operations for Elementary Teachers. 2 cr. hrs.**

Mathematical content and processes for elementary teachers. Uses a problem solving approach. Integrates mathematics content with teaching methods and learning theory. In-depth study of whole and rational number systems including analyses of algorithms for addition, subtraction, multiplication, and division. Provides a framework for the meaningful teaching of place value, whole numbers, exponents, fractions, decimals, percents, ratios, proportions, probability, and data analysis. Restricted to students in the elementary teacher preparation program. Prereq: EDUC 1964, which must be taken concurrently, and MATH 2030.

**MATH 2032. Algebra and Geometry for Teachers. 2 cr. hrs.**

Mathematical content and processes for teachers. Uses a problem solving approach. Integrates mathematics content with teaching methods and learning theory. In-depth study of the growth of algebraic and geometric reasoning. Provides a framework for the meaningful teaching of integers, patterns, algebraic expressions, functions, equations, graphs, spatial visualization, polygons and polyhedra, similarity and congruence, conjectures and deductions in geometry, and mathematical modeling. Restricted to students in the teacher preparation program. Prereq: EDUC 2964, which must be taken concurrently, and MATH 2031.

**MATH 2100. Discrete Mathematics. 3 cr. hrs.**

Introduction to set theory, logic, mathematics induction, finite state machines, graph theory, modular arithmetic, Boolean algebra, and coding theory. Applications in computer science are emphasized. Two years of college preparatory mathematics required. May not be taken for credit by those who have completed MATH 2350.

**MATH 2105. Discrete Mathematics for Engineers. 3 cr. hrs.**

Counting methods. The algebra of sequences, generating functions, and recurrences. The algebra of finite state machines and semigroups. Relations, graphs, posets, and trees. Path and flow problems. Prereq: MATH 2451. Credit will not be given for both MATH 2105 and either MATH 2100 or MATH 2350.

**MATH 2350. Foundations of Mathematics. 3 cr. hrs.**

Introduction to set theory, logic, mathematical induction, graph theory, modular arithmetic, and higher mathematical thinking through proof and applications. Mathematical proof is emphasized. Prereq: MATH 1400, MATH 1410 or MATH 1450.

**MATH 2450. Calculus 3. 4 cr. hrs.**

Three-dimensional analytic geometry including parametric equations, vectors and vector functions. The differential and integral calculus of functions of several variables. Prereq: MATH 1451.

**MATH 2451. Differential Equations. 4 cr. hrs.**

Methods and techniques applicable to first order, nth order, and systems of first order differential equations. Eigenvalues, eigenvectors, the Wronskian, Laplace transforms, linearization, and phase portraits. Prereq: MATH 2450.

**MATH 2455. Differential Equations for Biomedical and Civil Engineers. 3 cr. hrs.**

Methods and techniques for solving differential equations and systems of differential equations, with applications to biomedical and civil engineering. Restricted to students in BIEN or CEEN. Prereq: MATH 2450 or MATH 1455.

**MATH 3100. Linear Algebra and Matrix Theory. 3 cr. hrs.**

N-dimensional vector spaces, bases and coordinate systems, linear transformations and matrices, systems of equations, characteristic values, applications to differential equations and geometry. Prereq: MATH 2100, MATH 2350, or MATH 2451.

**MATH 3520. Operational Methods in Physics and Engineering. 3 cr. hrs.**

Functions of a complex variable. Laplace and Fourier transforms and applications. Introduction to the calculus of variations. Prereq: MATH 2450.

**MATH 3977. Problem Solving: Putnam Competition. 1 cr. hr.**

Students will study mathematical problems, examine their solutions and formulate general problem solving methods and techniques. The course is a preparation for the Putnam Mathematical Competition. S/U grade assessment. Prereq: Cons. of instr.

**MATH 4020. The Teaching of Mathematics. 3 cr. hrs.**

Historical background, problems, curricular materials, and teaching procedures in the various areas of mathematics pertinent to the needs of a secondary school mathematics teacher. In addition, a three-hour time block on one day each week between 8 a.m. and 3 p.m. must be kept free for clinical experience. Prereq: EDUC 2227 and either MATH 4120 or MATH 4420, which may be taken concurrently. Admission to the College of Education.

**MATH 4030. Concepts in Geometry and Calculus from an Advanced Standpoint. 3 cr. hrs.**

Topics chosen primarily from geometry and calculus, taught from an advanced standpoint to enrich and deepen the student's understanding. Emphasis on alternative approaches, generalizations, historical contexts and connections with prior mathematical studies. Prereq: MATH 4420 and six additional hrs. of upper division MATH courses and cons. of dept. ch.

**MATH 4040. Concepts in High School Algebra and Number Theory from an Advance Standpoint. 3 cr. hrs.**

Topics closely related to the high school mathematics curriculum, chosen primarily from algebra and number theory, taught from an advanced standpoint to enrich and deepen the student's understanding. Emphasis on alternative approaches, generalizations, historical contexts and connections with prior mathematical studies. Offered alternate spring terms. Course is offered for graduate credit only to students enrolled in MSST. Prereq: MATH 4120 and cons. of dept. ch.

**MATH 4120. Abstract Algebra 1. 3 cr. hrs.**

Sets, mappings, operations on sets, relations and partitions. A postulational approach to algebraic systems including semigroups, groups, rings and fields. Homomorphisms of groups and rings, number systems, polynomial rings. Prereq: MATH 2350.

**MATH 4121. Abstract Algebra 2. 3 cr. hrs.**

A continuation of MATH 4120 with emphasis on groups, rings, fields, and modules. Prereq: MATH 4120.

**MATH 4200. Intermediate Analysis 1. 3 cr. hrs.**

Limits and continuity, differentiability, Riemann integration. Topology of N-dimensional spaces. Prereq: MATH 2451 or MATH 3100.

**MATH 4201. Intermediate Analysis 2. 3 cr. hrs.**

Transformations of N-spaces, line and surface integrals, sequences and series, uniform convergence. Prereq: MATH 4200.

**MATH 4210. Complex Variables. 3 cr. hrs.**

Complex numbers, analytic functions, differentiation, series expansion, line integrals, singularities, and residues. Prereq: MATH 2450.

**MATH 4300. History of Mathematical Ideas. 3 cr. hrs.**

Topics selected from the following: development of the number system (need for irrational and complex numbers); development of geometry including the effects of the discovery of non-Euclidean geometry; limit concept; need for axiomatic structures; twentieth-century problems. Current mathematics research and place of mathematics in today's world. Prereq: Jr. stndg. or cons. of dept. ch.

**MATH 4320. Theory of Numbers. 3 cr. hrs.**

Integers, unique factorization theorems, arithmetic functions, theory of congruences, quadratic residues, partition theory. Prereq: MATH 2100 or MATH 2350.

**MATH 4420. Foundations of Geometry. 3 cr. hrs.**

Modern postulational development of Euclidean and non-Euclidean geometries. Prereq: MATH 2100 or MATH 2350.

**MATH 4450. Topology. 3 cr. hrs.**

Topological spaces, mappings, metric spaces, product and quotient spaces. Separation axioms, compactness, local compactness and connectedness. Prereq: MATH 2350.

**MATH 4500. Theory of Differential Equations. 3 cr. hrs.**

Existence and uniqueness theorems, linear and non-linear systems, numerical techniques, stability. Prereq: MATH 2451 or MATH 3100.

**MATH 4510. Elementary Partial Differential Equations. 3 cr. hrs.**

Fourier series, method of separation of variables, eigenfunction expansions, application of eigenfunctions to partial differential equations, Green's functions and transform methods. Prereq: MATH 2451 or MATH 3100.

**MATH 4540. Numerical Analysis. 3 cr. hrs.**

Numerical solution of algebraic and transcendental equations, linear systems and the algebraic eigenvalue problem, interpolation and approximation, numerical integration, difference equations, numerical solution of differential equations, and finite difference methods. Prereq: COSC 2200, COSC 2100 and either MATH 1400 or MATH 1451; or COSC 2010 and MATH 1451; or COEN 1610 and MATH 1451.

**MATH 4630. Mathematical Modeling and Analysis. 3 cr. hrs.**

Construction and analysis of mathematical models from biological, behavioral, and physical sciences. Prereq: MATH 2451, MATH 2455 or MATH 3100.

**MATH 4650. Theory of Optimization. 3 cr. hrs.**

Fundamental theorems describing the solution of linear programs and matrix games. Minimax, duality, saddle point property, simplex and specialized algorithms. Zero sum games, transportation and assignment problems, applications to economics. Prereq: MATH 2451 or MATH 3100.

**MATH 4670. Applied Combinatorial Mathematics. 3 cr. hrs.**

Permutations and combinations, recurrence relations, inclusion and exclusion, Polya's theory of counting, graph theory, transport networks, matching theory. Prereq: MATH 2100 or MATH 2350.

**MATH 4700. Theory of Probability. 3 cr. hrs.**

Random variables, distributions, moment generating functions of random variables, various derived probabilistic models and applications. Recommended, with MATH 4710, for students in mathematics, engineering, and the physical and behavioral sciences. Prereq: MATH 2450.

**MATH 4710. Mathematical Statistics. 3 cr. hrs.**

Sampling theory and distributions, estimation and hypothesis testing, regression, correlation, analysis of variance, non-parametric methods, Bayesian statistics. Prereq: MATH 4700.

**MATH 4720. Statistical Methods. 3 cr. hrs.**

Probability, discrete and continuous distributions. Treatment of data, point and interval estimation, hypothesis testing. Large and small sample method, regression, non-parametric methods. An introductory applications-oriented course recommended for students who wish to acquire a basic understanding of statistical methods. Prereq: MATH 1400, MATH 1410 or MATH 1450. May not be taken for credit by those who have completed MATH 4710.

**MATH 4740. Biostatistical Methods and Models. 3 cr. hrs.**

Introduction to the statistics of life science and the use of mathematical models in biology. Data analysis and presentation, regression, analysis of variance, correlation, parameter estimation and curve fitting. Biological sequence analysis, discrete and continuous mathematical models and simulation. Credit will not be given for both MATH 4720 and MATH 4740. Prereq: One semester of calculus.

**MATH 4760. Time Series Analysis. 3 cr. hrs.**

Basic concepts of probability. Stationary time series. Autocorrelation and spectrum. Descriptive methods for time series data. ARMA and ARIMA models: estimation and forecasting. Identification and diagnostic techniques. Periodogram and spectral analysis. Use of softwares for time series analysis. Offered alternate spring terms. Prereq: MATH 2450 or equivalent.

**MATH 4780. Regression Analysis. 3 cr. hrs.**

Basic concepts of statistical inference, simple linear regression, multiple linear regression, diagnostic analysis, selecting the best equation, stepwise methods, nonlinear regression, use of statistical software. Offered alternate spring terms. Prereq: MATH 4720 or equivalent.

**MATH 4931. Topics in Mathematics or Statistics. 1-3 cr. hrs.**

Topics selected from one of the various branches of mathematics or statistics. Specific topics to be announced in the Schedule of Classes.

**MATH 4953. Undergraduate Seminar. 3 cr. hrs.**

Designed to initiate a selected group of qualified undergraduates into the techniques and discipline of scholarly research by concentrated work in a restricted field. Emphasis on critical reading and analysis of sources. Specific subjects to be announced in the Schedule of Classes. Prereq: Cons. of dept. ch.

**MATH 4987. Co-op Work Period. 0 cr. hrs.**

Students work full-time during fall or spring terms in a cooperative education program work assignment approved in advance by the department. Responsibilities include relevant academic content. Grading and credits are accomplished by registering for MATH 4988 during the following term. Fee. Prereq: Jr. stndg. SNC/UNC grade assessment.

**MATH 4988. Co-op Grading Period. 1 cr. hr.**

Grading for preceding co-op work assignment is accomplished by completing a report on the work assignment, a report on academic material related to the work assignment, and other materials as required. Grading is completed during the school term following the work assignment. May be taken more than once, but a maximum of two credits may be counted toward a major in the department. Prereq: Jr. stndg. and MATH 4987.

**MATH 4995. Independent Study in Mathematics. 1-3 cr. hrs.**

Directed reading and/or research in Mathematics under a member of the staff. Prereq: Cons. of dept. ch.

**MATH 4999. Senior Thesis. 2 cr. hrs.**

Preparation of a thesis by approved students under the direction of an adviser from the staff. Prereq: Cons. of dept. ch.

# On this page

- Major in Mathematics
- Typical Program for Mathematics Major
- Department of Public Instruction Certification for Mathematics Majors
- Minor in Mathematics
- Major in Computer Science
- Minor in Computer Science
- Minor in Software Development
- Major in Computational Mathematics
- Major in Mathematics for Elementary School Teachers (MELT)
- Computer Science Courses
- Mathematics Courses

# College of Arts and Sciences

- Degrees Offered
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- Academic Regulations
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