**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 3 SH course carries no academic credit and does not satisfy the general education requirement in mathematics/computer science. Grade--standard A-F. Every semester.

**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. Grade—standard A-F. Admission by successful completion of MAT 098 or placement testing. Every semester.

**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. *Prerequisites:* C or higher in MAT 100 or appropriate placement score.

**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. *Prerequisites:* C or higher in MAT 100 or appropriate placement score.

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

This is a survey course designed to acquaint the student with mathematical ideas not normally encountered at the precollege level. The course conveys something about the nature of mathematics - its methods, uses and roles in society - through an elementary treatment of topics such as rubber-sheet geometry, number theory, astronomy, modular arithmetic or art. Every semester. *Prerequisite: *A in MAT 098 or MAT 100 or appropriate test score. **General Education: CS/Mathematics.**

**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. Knowledge of this history enhances understanding and appreciation for the subject as well as giving some insight into the cultures and times in which the discoveries were made. Students will be expected to be able to perform basic algebraic computations. *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**

Primary focus is on statistical comprehension of the research aspects of current nursing, medical and other health-related literature through an understanding of statistics utilizing the computer. Not open to students who have passed MAT 120. Every semester. *Prerequisite:* C or higher in MAT 100 or appropriate test score. **General Education: CS/Mathematics.**

**MAT 118 Elementary Applied Mathematics 3 SH**

Fundamental mathematical tools useful in the study of business and the social sciences, including matrices and polynomial calculus. Not open to students who have completed MAT 181 or 135. Every semester. *Prerequisite: * C or higher in MAT 100 or appropriate test score. **General Education: CS/Mathematics.**

**MAT 120 Elementary Statistics 3 SH**

An introduction to the practice of statistics that emphasizes elementary data analysis and inference. Topics include correlation, regression, probability models, estimations, hypothesis testing of various parameters and analysis of variance. Examples will be selected from many fields, such as anthropology, business, medicine, psychology, the natural sciences, 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 or higher in MAT 100 or appropriate test score. **General Education: CS/Mathematics.**

**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. This course is an introduction to cryptology focusing on the mathematics used to encrypt and decrypt messages. Grade—standard A-F. Spring semester. *Prerequisites:* A in MAT 098, or MAT 100, or appropriate test scores. **General Education: CS/ Mathematics.**

**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. Every semester. *Prerequisite: *B or higher in MAT 100 or appropriate test score. **General Education: CS/Mathematics.**

**MAT 135 Concepts of Calculus 3 SH**

A survey of fundamental concepts of calculus: limits, derivatives, integrals and applications pertaining to the study of business and the social sciences. Emphasis will be on concepts, not on theoretical treatment. Not open to students who have passed MAT 181. *Prerequisite:* MAT 100 or appropriate test score. **General Education: CS/Mathematics.**

**MAT 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: *MAT 133 or equivalent. **General Education: CS/Mathematics.**

**MAT 170 Calculus of Polynomials 3 SH**

An introduction to the concept of a function and its derivative from algebraic, graphical, and data-based points of view. The concentration in this course will be on linear, polynomial, and power functions. Technology, such as graphing calculators and computer algebra systems, will be used in this course. Grade—standard A-F. Every semester. *Prerequisites:* B or higher in MAT 100 or placement in general education math. **General Education: CS/Mathematics.**

**MAT 171 Calculus I with Review 4 SH**

A continued exploration of the fundamental tools of calculus. This second course in a sequence introduces more functions and their derivatives, and also introduces integrals. There is a continued emphasis on graphical, algebraic and data based viewpoints. Technology, such as graphing calculators and computer algebra systems, will be used in this course. Grade—standard A-F. Every semester. *Prerequisites:* MAT 170. Satisfies mathematics general education requirement and counts as Math 181 with regard to prerequisites in subsequent courses.

**MAT 181 Calculus I 4 SH**

An introduction to the two fundamental tools of calculus — derivatives and integrals—from algebraic, graphical and data-based points of view. Calculus is presented as a problem-solving tool with applications to the physical and social sciences. Graphing and symbolic-manipulating calculator and computer tools are used throughout the course. Every semester. *Prerequisite:* MAT 133 or equivalent. **General Education: CS/Mathematics.**

**MAT 182 Calculus II 4 SH**

An extension of the study begun in calculus I with greater emphasis on differentiation and integration skills and techniques. Topics include methods of integration, approximating methods and infinite sequences and series. Graphing and symbolic-manipulating calculator and computer tools are used throughout the course. Every semester. *Prerequisite: *MAT 181 or MAT 171. **General Education: CS/Mathematics.**

**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. Every spring. *Prerequisite:* MAT 105 or 106.

**MAT 220 Intermediate Statistics 3 SH**

A second course in statistical methods that stresses analysis of multivariate data applications from social and natural sciences, business, health and medical sciences or education. Some familiarity with computers is assumed, since statistical software will be used throughout. Prerequisite: a first course in statistical methods, e.g., MAT 115, MAT 120, MIS 121, PSY 204. Odd spring semester. General Education: CS/Mathematics.

**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: CS/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. Even fall. *Prerequisite:* MAT 182. **General Education: CS/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. Odd fall. *Prerequisite: *MAT 182. **General Education: CS/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: CS/Mathematics.**

**MAT 281 Calculus III 4 SH**

The study of multivariable and vector calculus, including partial derivatives, multiple integrals and applications. Emphasis on the graphical, numerical and algebraic points of view as developed in Calculus I and Calculus II will be continued. Fall semester. *Prerequisite: *MAT 182. **General Education: CS/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: CS/Mathematics.**

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

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

**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. Prerequisite: MAT 242 or permission of the instructor. Spring semester.

**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 356 Introduction to Operations Research 4 SH **

This course includes topics in classical optimization, linear programming, probabilistic simulation and the network analysis. These techniques are applied to mathematical problems in business and society. Theoretical aspects of problems are considered, aided by computer use. *Prerequisite:* CS 143 or 170 and MAT 182. Odd fall semester.

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

Basic theoretical principles embodied in formal languages, automata and computability. *Prerequisite: *MAT 181, 163 or 165, and either CS 143 or 170. Even spring semester.

**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?” *Prerequisite:* MAT 182. Even spring semester.

**MAT 381 Advanced Calculus 3 SH**

Topics selected to enhance the student’s understanding of analysis: point set topology, metric spaces, continuity, integration theory, uniform convergence, power series. *Prerequisite:* MAT 281. Even spring semester.

**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. Even fall semester. *Prerequisite: *MAT 381.

**MAT/ED 385 Methods of Teaching int he Secondary Schools 3 SH**

Method of Teaching in the Secondary Schools is designed to help prospective teacher education candidate develop and/or refine the planning, implementation, assessment, and reflection skills and dispositions necessary to be an effective classroom teacher in grades 7-12. Candidates will be introduced to those methods and materials needed for effective teaching in the secondary shcool; analysis of research and current learning theory, along with a required observation/participation component in a secondary school. Candidates will use Connecticut State Departmetn of Education documents and standards for effective teaching as bases for observation and practice teaching opportunities. Every fall. *Prerequisite:* Admission to the Professional Secondary Teacher Education Program, and approval by the Chairperson of the Education and Education Psychology Department. *Co-Requisite: * Registration in Secondary Education Professional Semester.

**MAT/ED 386 Secondary Education Professional Development**

** School Experience 1 SH **

Students who are enrolled in the Secondary Education Professional Semester are placed in public school classrooms for 10 days during the Professional Semester. They work with students under the direction of public school classroom teachers. In addition, they receive supervision from Arts and Science faculty. Students apply what they are learning in Professional Semester courses in 7-12 classrooms. Every fall. *Co-requisite: * Enrollment in the Secondary Education Professional Semester. Grading: Pass/Fail.

**MAT 400 Applied Mathematics 3 SH**

This course will investigate the applications of mathematics to areas of human endeavor where quantification is possible. The mathematical descriptions so obtained may then be used to predict future states, make logical choices and obtain a deeper understanding of the systems and phenomena under study. Differential equations and other mathematical skills will be used to investigate topics in the natural and behavioral sciences. Even fall semester. *Prerequisite: MAT 282.*

**MAT 410, 411 Mathematical Statistics I & II 3 SH each sem. **

A two-semester course that introduces the major distributions used in classical statistics, e.g., binomial, normal and chi square, and develops the mathematical theory basic to an understanding of them. Estimation theory, hypothesis testing, regression analysis and analysis of variance will be presented, and applications will be given. MAT 410 odd fall and MAT 411 even spring. *Prerequisite:* MAT 120; MAT 281 for MAT 410; MAT 410 for MAT 411.

**MAT 416 Introduction to Abstract Algebra 3 SH**

This course deals with the mapping operation and relations of sets, as well as other axiomatic treatment of numbers. It includes some study of groups, integral domains and fields. *Prerequisite:* MAT 281. Fall semester.

**MAT 431, 432 Numerical Analysis I & II 3 SH each sem. **

The study of numerical methods associated with systems of linear equations, eigenvalues, polynomial and transcendental equations, and solutions of differential equations; the theory of interpolation and functional approximation; techniques of numerical differentiation and integration. Also included are the topics of least squares and nonlinear functional optimization, the analysis of types of errors, and computational speed. Computer implementation of numerical methods will be emphasized throughout the course. MAT 431 even fall and MAT 432 odd spring. *Prerequisite: *MAT 272 for MAT 431; MAT 431 for 432.

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

This course provides candidates for teacher certification with an understanding of the methods and materials needed to become effective teachers of mathematics at the secondary school level. Candidates are introduced to assessment methods and learn to integrate current instructional technologies into their teaching. Emphasis is placed on making content knowledge accessible to diverse student populations found in public schools. Candidates develop lesson plans and units of instruction and practice delivering instruction. In addition, they examine current curricular reform movements and consider their impact on mathematics education in the secondary school. The implications of state, national, and international testing movements and state and national standards are considered. This course will be taught by a member of the Mathematics Department. Candidates must receive a grade of B or higher in order to enroll in student teaching. *Prerequisite: * Admission to the Professional Secondary Education Teacher Preparation Program. *Co-requisite:* Registration in secondary education professional semester courses.

**MAT 481, 482 Wavelet Analysis I & II 3 SH each sem. **

A basic introduction to wavelet transformation and related mathematics with application of signal processing, data compression, digital communication, and wavelet-based diagnosis. Wavelet Analysis II will continue with more advanced topics in wavelet transformations, with applications in image analysis, object-oriented wavelet analysis using appropriate computer software, and numerical solutions of differential equations. MAT 481 odd spring and MAT 482 odd fall.

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