Mathematics

# Mathematics

**MAT 098 Elementary Algebra 3 SH**

First order linear equations, algebraic techniques including manipulation of algebraic expressions, solution of linear equations and inequalities, graphing of linear equations and applications. This three-credit course carries no academic credit and does not satisfy the general education requirement in mathematics/computer science. Offered summer and intersession.

**MAT 100P Intermediate Algebra Plus 4 SH**

In this course students will use an online adaptive learning technology to master the skills needed for a foundation in mathematics for further work in the field. Students will be required to attend classes regularly and an additional 2 hours of computer assisted work within the Emporium will also be required. This will be a self-paced course but still afford students the opportunity to work with faculty on a one-to-one basis, in addition to a lecture setting. This class format will allow the student to potentially complete the course at a pace quicker than the standard semester and fulfill the remedial requirement of the Board of Regents in one semester, instead of two. *Prerequisite:* SAT math test score below 500.

**MAT 100 Intermediate Mathematics 3 SH**

Manipulating and simplifying polynomials and rational expressions; algebraic techniques including solution of first and second degree algebraic equations and inequalities; solution of systems of equations and inequalities; graphing of linear equations and applications; exponential functions and logarithms. Three free elective credits will be earned; the course does not satisfy the general education requirement in mathematics/computer science. Admission by successful completion of MAT 098 or placement testing. Every semester.* Not open to students who have passed a General Education Mathematics course.*

**MAT 105 Foundations of Mathematics I 4 SH **

Designed for and required of students preparing to teach in the elementary schools. Topics to include number systems and their properties, the set-theoretic basis for computation, mathematical problem-solving, developing mathematically correct and clear explanations of mathematical ideas, and diagnosis of student error patterns. Assumes a background in mathematics that includes algebra and geometry. Every semester.* Prerequisite: *“C” or higher in MAT 100 or appropriate placement score. **General Education: Mathematics (if MAT 106 is successfully completed). **

**MAT 106 Foundations of Mathematics II 4 SH**

Designed for and required of students preparing to teach in the elementary schools. Topics to include problem-solving, geometry and measurement, probability and statistics, and applications. Assumes a background in mathematics that includes algebra and geometry. Every semester. *Prerequisite:* “C” or higher in MAT 100 or appropriate placement score. **General Education: Mathematics (if MAT 105 is successfully completed). **

**MAT 110 Great Ideas in Mathematics 3 SH**

In this course students will explore the ways in which mathematics touches on or is used within other fields of study. This may include exploring the history of mathematics and how it influenced and was influenced by other events in history. It may look at a survey of topics in mathematics such as the golden ratio or the Fibonacci sequence and where they appear in the world or the interesting philosophical issues that they raise. Or, it may look at the ways in which mathematics arises in music or is used in theatrical set design. Independent of the specific area to be studied, in every section students will demonstrate an ability to understand and explain mathematical concepts and appreciate the role of mathematics in the world. For details on a specific section students should see the outline for that section. Every semester. *Prerequisite:* “C” grade or better in MAT 100 or appropriate placement. **General Education: Mathematics; Competency: Quantitative Reasoning.**

**MAT 113 Introduction to the History of Mathematics** **3 SH**

This course offers a brief overview of the history of mathematics. It gives a general picture of the history of mathematics with a few specific units focused on significant individuals, events and ideas. Mathematics has a long and rich history, the knowledge of which can enhance understanding and appreciation for the subject as well as give insight into the cultures and times in which the discoveries were made. Students will be expected to be able to perform basic algebraic computations. Every fall. *Prerequisite:* An “A” in MAT 098 or a pass in MAT 100 or appropriate math placement. **General Education: Mathematics.**

**MAT 115 Introduction to Biostatistics 3 SH**

An introduction to the practices of statistics, for health and other science majors, which emphasizes elementary data analysis, probability and inference. Topics include correlation, regression, probability models, estimation, and hypothesis testing. Examples will focus on biological and health sciences. Students will be expected to use appropriate technology, such as statistics calculators or computer software. Not open to students who have passed MAT 120. Every semester. *Prerequisite: *“C” or higher in MAT 100 or appropriate test score.** General Education: Mathematics; Competency: Quantitative Reasoning.**

**MAT 118 Elementary Applied Mathematics 3 SH
**Matrix algebra and systems of linear equations (matrix operations, solutions of systems of linear equations, and applications); Linear Programming (graphical and simplex methods and their applications to multivariable optimization problems with a linear objective function under multiple linear inequality constraints); and financial mathematics/theory of interest (time value of money and annuities/cash flows with payments that are non-contingent). Conceptual understanding, not theoretical treatment, intuition, and skill acquisition as well as applications to business and the social sciences will be emphasized. Additional topics at the discretion of the instructor: Brief introduction to the notions of average and instantaneous rates of change. Every semester.

*Prerequisite:*“C” or higher in MAT 100 or appropriate test score.

**General Education: Mathematics; Competency: Quantitative Reasoning.****MAT 120 Elementary Statistics 3 SH
**An introduction to the practices of statistics, for non-science or math majors, which emphasizes elementary data analysis and inference. Topics include correlation, regression, probability models, estimation, and hypothesis testing. Examples will be selected from many fields, such as anthropology, business, medicine, psychology, sociology, and education. Students will be expected to use appropriate computer software. Not open to students who have passed MAT 115. Every semester.

*Prerequisite:*“C” grade or higher in MAT 100 or appropriate test score.

**General Education: Mathematics; Competency: Quantitative Reasoning.****MAT 127 Introduction to Cryptology 3 SH**

When messages are sent over public media, such as the internet, there is a need to protect (encrypt) the information contained in those messages from unauthorized viewers. And, when your adversaries send messages you may have need to break into their secrets (decrypt). This course is an introduction to cryptology focusing on the mathematics used to encrypt and decrypt messages.* Prerequisite:* “C” grade or higher in MAT 100 or appropriate placement. **General Education: Mathematics; Competency: Quantitative Reasoning.**

**MAT 133 Precalculus 3 SH**

The functions needed for the study of calculus are presented from a numerical, graphical and algebraic point of view. Polynomial, exponential, logarithmic and trigonometric functions are included. Graphics calculators are used throughout the course. Not open to students who have passed any calculus course. Summer semester. *Prerequisite: *“B” grade or higher in MAT 100 or appropriate test score. **General Education: Mathematics; Competency: Quantitative Reasoning.**

**MAT 135 Differential Business Calculus and Applications 3 SH**

A survey of fundamental concepts of differential calculus, the subject that studies change. In particular, real-valued functions of one variable and their limits, continuity, derivatives, and applications to non-linear optimization and other business problems. Also, partial derivatives of real-valued functions of more than one variables and the method of Lagrange multipliers for the solution of non-linear optimization problems with equality constrains. Conceptual understanding, not theoretical treatment, intuition, and skill acquisition as well as applications to business and the social sciences will be emphasized. *Prerequisite:* C or higher in MAT 100 or appropriate placement score. *MAT 118 highly recommended, but may be taken concurrently.* Not open to students who have passed any of MAT 170, MAT 171, or MAT 181. **Competency: Quantitative Reasoning.**

**MAT 141 Foundational Discrete Mathematics 3 SH**

An in-depth introduction to discrete structures and processes such as counting techniques, sequences, indexed summations, introductory propositional and predicate logic, introductory induction and recursion, sets, relations, functions, and connections among these topics. *Prerequisite:* “B” or better in MAT 100 or general education placement. *Competency: Quantitative Reasoning.*

**MAT 150, 151 Mathematics Seminar I and II**** 0.5 SH each **

During the first semester, MAT 150 is designed to introduce mathematics majors to the university and the math department. Through this course they will learn about the breadth of topics that constitute mathematics and the particular interests of the mathematics faculty. They will also learn how to navigate and utilize the resources available to them through the university and they will become familiar with what is expected of them as college students. In the second semester, students will not only hear lectures from mathematics faculty, but will also be responsible for preparing and presenting material. The seminar is required of first-year math majors. Students may take each semester of the seminar a maximum of one time for credit. MAT 150, fall semester, MAT 151, spring semester. *Prerequisite*: For MAT 150: Declared major in mathematics or MAT 100 or general education mathematics placement. Prerequisite: For MAT 151: MAT 150; Grading: MAT 150, “P/F”; MAT 151, “A”-“F.” May not be used toward general education mathematics requirement. May not be used toward mathematics elective credit. **Competency: First Year.**

**MAT/CS 165 Introductory Discrete Mathematics 4 SH
**An introduction to discrete structures and processes such as counting, algorithms, proof, induction and recursion through the study of logic, sets, relations and functions. Sufficient theory is introduced for applications to graph theory and elementary computer science. Every semester.

*Prerequisite:*grade of C or better in MAT 133 or MAT 170 or equivalent.

**General Education: Mathematics.****MAT 170 Calculus with Precalculus Part I 4 SH**

This course is an introduction to the concepts of functions, their derivatives and their integrals from algebraic, graphical, and numerical points of view. The concentration in this course will be on algebraic functions. Appropriate technology will be used in this course. Knowledge and proficiency with elementary algebra will be assumed. *Prerequisite:* Grade of “B” or higher in MAT 100 or appropriate placement.** General Education: Mathematics; Competency: Quantitative Reasoning.**

**MAT 171 Calculus with Precalculus Part II 4 SH**

This course is a continued exploration of the fundamental tools of calculus. The second course in a sequence introduces more functions, their derivatives, and their anti-derivatives. There is a continued emphasis on graphical, algebraic and numerical viewpoints. Appropriate technology will be used in this course. Knowledge and proficiency with algebra will be assumed. *Prerequisite:* MAT 170. Completion of MAT 170 and 171 counts as MAT 181 with regard to prerequisite in subsequent courses. **General Education: Mathematics; Competency: Quantitative Reasoning.
**

**MAT 181 Calculus I 4 SH**

Calculus I will introduce students to the ideas and applications of single variable differential calculus and to the foundations of single variable integral calculus. This will include, but not be limited to, the definitions and applications of limits, continuity, the derivative, and the definite and indefinite integral. Students will be expected both to become proficient with basic skills and to demonstrate an understanding of the underlying principles of the subject. Students should expect to make appropriate use of technology in this course. Knowledge of Precalculus will be assumed, in particular knowledge of lines, polynomials, rational functions, trigonometric functions, and exponential and logarithmic functions. Students are also expected to be proficient with algebra. *Prerequisite: *MAT 133 or appropriate placement.** General Education: Mathematics; Competency: Quantitative Reasoning.**

**MAT 182 Calculus II 4 SH**

Calculus II will introduce students to a variety of new techniques of integration, to some applications of integration, and to sequences and series. Students will be expected both to become proficient with basic skills and to demonstrate an understanding of the underlying principles of the subject. Students should expect to make appropriate use of technology in this course. Knowledge of Calculus I will be assumed, in particular knowledge of the rules and concepts behind differentiation and basic integration. Prerequisite: MAT 181: Calculus I. *Prerequisite:* MAT 181 or appropriate placement. **General Education: Mathematics; Competency: Quantitative Reasoning.**

**MAT 185 Mathematics with Symbolic Computation 3 SH
**The course provides hands-on experience in mathematical computations with Computer Algebra System (CAS). It covers techniques for solving certain typical classes of problems appropriate for undergraduate mathematics as well as analysis of simple models in sciences with computer assistance. Introduction to a particular CAS is included. Emphasis is on analysis and implementation of mathematical algorithms and visualization of results of computations.

*Prerequisite:*MAT 171 or MAT 181.

**Competency: Quantitative Reasoning.**

MAT 207 Proofs 3 SH

MAT 207 Proofs 3 SH

An introduction to the theory and practice of reading and writing mathematical proofs, using theorems and problems in number theory as a source of examples.

*Prerequisite:*“C” or better in MAT 141.

**MAT 211 The Mathematical Laboratory 3 SH**

Topics will be selected from the background material for elementary and middle-school mathematics, including functions, measurement, geometry and problem-solving. Manipulative materials will be used throughout this course. Recent topics pulled from mathematical journals may also be included. Spring semester of even-numbered years. *Prerequisite:* MAT 105 or MAT 106.

**MAT 212 Mathematics in the Middle Grades 3 SH **

This course will focus on mathematical content and pedagogy related to the middle grades. It will include curricular connections from elementary to middle school level mathematics and from middle to secondary school level mathematics. Nationally recognized content and process standards will be incorporated throughout the course. Spring semester of odd-numbered years. *Prerequisite*: MAT 105 or MAT 106 or declared B.S. Math Secondary Education major with Sophomore standing.** **

**MAT 222 Introductory Statistics 3SH
**A rigorous introduction to the concepts and practice of statistics for math and science majors, with emphasis on developing statistical literacy through data analysis. This data-driven course will cover the following topics: descriptive and inferential statistics, sampling distributions, estimation, hypothesis testing, regression, correlation and analysis of variance. Statistical software will be used throughout the class.

*Prerequisite:*A minimum grade of C in MAT 171 or a minimum grade of C in MAT 181.

**MAT 242 Foundations of Geometry 3 SH**

Elementary geometry, primarily from the point of view of transformations: postulates, isometries, congruence, similarity, triangles and circles, area and perimeter, informal three-space geometry. This course is designed for elementary education majors majoring in mathematics and for secondary education majors.* Prerequisite:* Junior standing in an education program or permission of instructor. Fall semester. **General Education: Mathematics.**

**MAT 250 Mathematical Modeling 3 SH**

This courses addresses the ways in which mathematics and mathematical thinking serve as a model for understanding real world phenomena. The purpose of this course is to prepare students to apply upper-level mathematics to other problems outside the realm of mathematics. Students also learn how to incorporate mathematics in technical reports. Fall semester of even-numbered years. *Prerequisite*: MAT 182. **General Education: Mathematics.**

**MAT 251 Posing and Solving Problems in Mathematics 3 SH
**Posing and solving problems is a course in heuristics, the art of inventing or discovering solutions to problems in the absence of routines that make those solutions readily attainable. General methods for discovering solutions to such problems will be presented. Fall semester of odd-numbered years.

*Prerequisite*: MAT 182.

**General Education: Mathematics.****MAT 272 Introduction to Linear Algebra 3 SH**

Topics will be selected from: systems of linear equations, vector spaces, basic operations for matrices, determinants, bilinear and quadratic functions and forms, linear transformations on a vector space, and others. Spring semester. *Prerequisite*: MAT 182. **General Education: Mathematics.**

**MAT 281 Calculus III 4 SH**

The study of multivariable and vector calculus, including partial derivatives, multiple integrals and applications. Space curves, vector fields, and line integrals will be introduced. Students will be expected both to become proficient with basic skills and to demonstrate an understanding of the underlying principles of the subject. Students should expect to make appropriate use of technology in this course. Graphical, numerical and algebraic points of view will be emphasized. Every semester. *Prerequisite*: MAT 182 with a grade of “C” or better or MAT 181/171 with a grade of “B” or better and concurrent registration in MAT 182. **General Education: Mathematics.**

**MAT 282 Ordinary Differential Equations 3 SH**

The classification and techniques of solving differential equations from algebraic, graphical, and data-based points of view. Modeling of problems that lead to differential equations from biological and physical sciences. Graphing and symbolic-manipulating computer tools are used throughout the course. Spring semester. *Prerequisite*: MAT 182. **General Education: Mathematics.**

**MAT 298 Faculty Developed Study 1–4 SH
**

**MAT 299 Student Developed Study 1–6 SH**

**MAT 304 Discrete Mathematics for Computer Science 2 SH**

A continuation of MAT 141 Foundational Discrete Mathematics, intended for students majoring in Computer Science and other computing-related disciplines. Review and extension of the topics from the areas of sets, relations and functions, logic, and graph theory. In-depth introduction to proof techniques with computing-related examples. *Prerequisite*: MAT 141 with a grade of C or better.

**MAT 332 Introduction to Applied Mathematics 3 SH
**This course is an introduction to selected topics in areas of applied mathematics. The students will be exposed to models used to understand real world phenomena. Technology and written communication will be emphasized.

*Prerequisite:*“C” or better in MAT 222 and MAT 272.

**MAT 342 Topics in Geometry 3 SH**

The central theme of the course is the study of many different geometries, rather than a single geometry. The focus will be on those geometries that have been developed since 1800 with references back to the geometry of Euclid. Spring semester. *Prerequisite*: MAT 242 or permission of the instructor. **General Education: Mathematics. **

**MAT 351 Independent Study 3 SH**

Designed for students who show above-average ability and interest in mathematics. It allows the student to study advanced topics not included in the standard course offerings. Approval of mathematics department is required.

**MAT/CS 359 Introduction to Theory of Computation 3 SH **

Basic theoretical principles embodied in formal languages, automata and computability. Spring semester of even-numbered years. *Prerequisite*: Grade of C or better in MAT 171 or MAT 181 and C grade or better in MAT/CS 165. **General Education: Mathematics. **

**MAT 363 History of Mathematics 3 SH**

A survey of the historical development of mathematics designed to help students develop their own philosophy of mathematics as well as their answer to the question, “What is mathematics?” Spring semester of even-numbered years. *Prerequisite*: MAT 182. **General Education: Mathematics. **

**MAT 375 Algebraic Structures 3 SH**

In order to have a proper foundational understanding of the numbers and algorithms we use every day one must have knowledge of groups, rings, and fields. This course will introduce the basic ideas in groups, rings, and fields. There will be particular emphasis on field extensions, factorization, and transformations. Students will learn about the fundamental algebraic structures behind the algorithms for arithmetic and polynomials. They will also understand how one number system is developed from another. *Prerequisite:* C or better in MAT 207 and MAT 272.

**MAT 382 Complex Variables 3 SH**

Continuity, differentiability, analyticity, line integration and power series within the context of the complex number system. Residues and poles, conformal mapping, analytic continuation and most of the well-known classical theorems associated with the theory of complex variables. Fall semester of even-numbered years. *Prerequisite*: MAT 381. **General Education: Mathematics. **

**MAT 383 Introduction to Analysis 3 SH**

This course is a first course in advanced calculus. Students are introduced to the theory of calculus of real valued functions. The course will focus on formal definitions and proof in analysis. Topics covered include limits, continuity, convergence, differentiation and integration. *Prerequisites:* MAT 207 and MAT 182.

**MAT/ED 386 Secondary Education Professional Development School Experience 1 SH
**

*See ED/MAT 386*

**MAT/ED 449 Teaching Mathematics in the Secondary Schools 3 SH **

*See ED/MAT 449*

**MAT 450, 451 Senior Seminar I and II 1.5 SH each **

This is a two-semester capstone experience for all math majors. During the first semester all students will study several topics that are not covered elsewhere in the curriculum. Students will be expected to read, present and write expository reports on these topics. During the second semester, students will study a topic in more depth, culminating in a senior project. The student will be expected to present the project as a formal written report and an oral presentation to the faculty, other seminar participants and other interested majors. MAT 450, fall semester; MAT 451, spring semester. *Prerequisite*: Senior standing in B.A. Mathematics program.

**MAT 453 Senior Seminar Experience 3 SH**

In this course students will study topics not covered elsewhere in the curriculum. They may be given the topics which they are to study or they may be encouraged to explore new avenues from topics they have previously studied. All students will be expected to read, present, and write expository reports on these topics. *Prerequisite:* senior standing and a grade of “C” or better in one 300-level course. **Competency: Writing III.**

**MAT 467 Topics in Mathematics 3 SH**

This course is an opportunity for students to pursue in greater depth topics introduced in other courses or topics not included in other courses. The topic would vary from semester to semester. Typical topics might be mathematical models, combinatorics, field theory, algebraic topology, decision theory, harmonic analysis, wavelets, etc.* Prerequisite:* “C” or better in MAT 332 or 375 or 383 as appropriate to the topic determined by the department. May be repeated for credit with different topics.

The following courses also have been approved and are offered periodically:

MAT 222 Intermediate Statistics

MAT 356 Introduction to Operations Research

MAT 381 Advanced Calculus

MAT 400 Applied Mathematics