# Mathematics Courses

MT 010 - Fundamentals of Mathematics I

(Credits: 3.00)

This course is an extensive review of the fundamentals of mathematics. The topics covered include arithmetic of whole numbers, fractions, decimals and signed numbers; ratios, rates and proportions; percents; elementary descriptive statistics; applications for business and consumer math; and an introduction to algebra. Use of a scientific calculator is taught and strongly encouraged. Although assessed for three credits, this course does not carry University credit.

MT 095 - Algebra Basics

(Credits: 3.00)

This course reviews many of the topics covered in a traditional first course in algebra. These topics include real numbers, linear equations, exponents and polynomials, linear graphs and linear systems. Quadratic expressions and solving quadratic equations by factoring are introduced. Although assessed for three credits, this course does not carry University credit. Prerequisite: Placement results or MT 010 .

MT 102 - Math for Elementary/Middle School Teachers I

(Credits: 3.00)

This is course is designed for teachers who will be teaching in the elementary grades (1-9). The content of this course reflects the Common Core Standards for Mathematics. Students will study estimation, computation, number systems and number theory, geometry, measurement, probability, statistics, fractions, decimals, percents, number patterns and relationships, and algebra.

MT 103 - Math for Elementary/Middle School Teachers II

(Credits: 3.00)

This course continues the investigation of the grades 1-9 mathematics content using problem solving, critical thinking strategies and methodology. Students will become familiar with current applications of mathematics. Technology is an integral part of the course. Students will learn to examine, represent, invent, transform, conjecture, justify, apply, and communicate mathematics in cooperative group and individual situations. This course examines the mathematical curriculum found in the Common Core Standards for Mathematics. Prerequisite: MT 102 or departmental approval.

MT 104 - Mathematics for Early Childhood Teachers I

(Credits: 3.00)

This is a mathematics content course that is designed for teachers who will be teaching in early childhood education. The content of this course reflects the Common Core Standards for Mathematics. Students will study mathematical processes, sets, functions, logic, whole numbers, integers, fractions, geometry, number theory, and measurement, and are expected to use appropriate math vocabulary. Students also will be immersed in various problem-solving situations, both individually and cooperatively. Corequisite: CA 207, ECUE 211.

MT 105 - Mathematics for Early Childhood Teachers II

(Credits: 3.00)

This is the second mathematics content course that is designed for teachers who will be teaching in Early Childhood Education. Students will continue to study mathematical processes, sets, functions, logic, whole numbers, integers, and fractions; expand their knowledge of geometry, number theory and measurement; and be expected to use appropriate math vocabulary. Students will be immersed in various problem-solving situations, both individually and cooperatively. Prerequisite: MT 104. Corequisite: ECUE 291, ECUE 398, EN 201.

MT 107 - Intermediate Algebra

(Credits: 3.00)

Intermediate Algebra is designed to address, at the college level, intermediate algebra topics. These topics include properties of real numbers, solving and graphing linear equations and inequalities, quadratic equations and inequalities, and solving exponential equations. The concepts of function and conic sections also will be introduced, time permitting. Prerequisite: Placement results or MT 095 .

MT 109 - Mathematics: A Human Endeavor

(Credits: 3.00)

This course covers a broader view of mathematics than computation. Topics include inductive and deductive reasoning, patterns in number sequences, logic, set theory and discussions of infinity, systems of numbers, graph theory, explorations in geometry, methods of counting, probability and statistics. The focus of this course is to view the nature of mathematics as an organized, beautiful body of thought. Prerequisite: Placement results or MT 095.

MT 120 - Applied Statistics

(Credits: 3.00)

Basic statistical methods are discussed and practiced in this course. Topics include displaying and describing distributions, measures of center and spread, correlation and linear regression, methods of gathering data through sampling and statistical experiments, sampling distributions, the normal distribution and the central limit theorem, confidence intervals for proportions and means, hypothesis testing for proportions and means, and comparing two proportions and two means. Prerequisite: Placement results or MT 107 (previously MT 115) .

MT 140 - Visual Mathematics

(Credits: 3.00)

The links between mathematics and the arts are many and date back to prehistory. This course is intended for those students majoring in the fine arts (including music as well as the visual arts). The mathematical content of this course is explicitly linked to important ideas in art, music, and graphic design. Topics include similar triangles and proportions; musical intervals and ratios, the development of three-dimensional thinking and a mathematical analysis of perspective; fractals, logarithms, and fractal dimension; Fibonacci numbers, the Golden Ratio, quadratic equations, and limits; and computer representation of art. Prerequisite: ART 101, art major.

MT 195 - College Algebra

(Credits: 3.00)

This course provides an overview of the fundamental concepts of algebra. Topics include linear and quadratic equations and inequalities; the Cartesian plane and graphing; using a graphing utility; functions; graphs and models; polynomial and rational functions; exponential and logarithmic functions; systems of equations, inequalities and matrices. Prerequisite: Placement results or MT 107 (previously MT 115).

MT 209 - College Algebra and Trigonometry

(Credits: 4.00)

This course is an investigative study of topics in algebra, trigonometry, and analytical geometry that are needed by students who will continue their study in calculus or the natural sciences. Topics include coordinate and analytic geometry; factoring and simplification of expressions; solving equations and systems of equations; and a broad study of the representations and properties of linear, polynomial, rational, exponential, logarithmic, and trigonometric functions. Prerequisite: Placement results or MT 107 (previously MT 115).

MT 210 - Calculus I

(Credits: 4.00)

Calculus is a transition course from lower-division courses to upper-division mathematics and computer science courses. Students will extend their experience with functions as they study the fundamental concepts of calculus: limits, difference quotients and the derivative, Riemann sums and the definite integral, antiderivatives, indefinite integrals and the Fundamental Theorem of Calculus. Students will review and extend their knowledge of trigonometry and basic analytic geometry. Important objectives of the calculus sequence are to develop and strengthen the students' problem-solving skills and to teach them to read, write, speak and think in the language of mathematics. In particular, students will learn how to apply the tools of calculus to a variety of problem situations. Prerequisite: Placement results or strong background in algebra and some familiarity with trigonometry (high school trigonometry and advanced algebra or MT 209).

MT 211 - Calculus II

(Credits: 4.00)

This course is a continuation of MT 210. While the first semester focuses on differential calculus, this course focuses on integral calculus. Students will extend their experience with functions, limits, Riemann sums, the definite integral, antiderivatives, and the Fundamental Theorem of Calculus. This course includes an introduction to sequences and series. Prerequisite: MT 210.

MT 212 - Calculus III

(Credits: 4.00)

This course builds on the foundations laid in Calculus I and II. Topics include a review of infinite sequences and series; vectors and the geometry of space; vector functions; partial derivatives; multiple integrals; and vector calculus. Prerequisite: MT 211.

MT 215 - Selected Topics

(Credits: 1.00 - 4.00)

This is a study of a particular topic in the field of mathematics. This course may be taken more than once, but no more than a total of four credits apply toward the major. Prerequisite: MT 210, departmental approval.

MT 217 - Accelerated Calculus

(Credits: 5.00)

This course offers students who have had some calculus an intense, fast-paced, one-semester course covering the material in MT 210-211, Calculus I and II. This course is appropriate for students who have taken an Advanced Placement calculus course in high school, and do not place into MT 212 Calculus III. This would also be a good course for students in the Master of Arts in Teaching (MAT) program who are seeking teacher certification for mathematics. This course covers limits, difference quotients, a conceptual development and definition of derivative, Riemann sums, a conceptual development and definition of the definite integral, antiderivatives, the Fundamental Theorem of Calculus, and an introduction to sequences and series. This is an ambitious course; the intention is to cover the material of two four-credit courses in one semester. The student will be challenged to grow in mathematical maturity, and to develop and strengthen problem-solving skills while reading, writing, and thinking in the language of mathematics. Prerequisite: Placement results or strong background in algebra, some familiarity with trigonometry, a previous course in calculus (e.g.., AP calculus), and department approval.

MT 315 - Discrete Mathematical Structures

(Credits: 3.00)

Topics include logical reasoning, truth tables, and Boolean algebra; modular arithmetic, mathematical induction, and properties of the integers; functions, relations, and equivalence relations; an introduction to proofs and proof writing; and an introduction to graph theory. Also listed under CS 315. Prerequisite: MT 209 or departmental approval.

MT 320 - Geometry

(Credits: 3.00)

This one-semester introduction to Euclidean and non-Euclidean geometries serves as an introduction to mathematical proof. Through an exploration of properties of plane geometry and Euclid's Postulates, students will develop skill in logical mathematical reasoning, and learn to develop good mathematical proofs. The importance of axiomatic reasoning is developed through experiences with some non-Euclidean geometries. While not a teaching methods course, practical ways to implement geometry into the middle/high school curriculum are modeled through the use of dynamic geometry software. Prerequisite: MT 209 or departmental approval.

MT 322 - Topics in Geometry

(Credits: 3.00)

This course offers a variety of geometrical topics which may include taxicab geometry, conic sections, four-dimensional space, trigonometry in the unit circle, the geometry of the sphere, and geometric patterns in art. The subjects are determined by the instructor and the needs of the students. Prerequisite: Departmental approval.

MT 325 - Linear Algebra

(Credits: 3.00)

This course offers the student a concrete introduction to linear algebra, including vector spaces in two-, three-, and high-dimensions; bases of vector spaces; eigenvalues and eigenvectors; linear transformations; matrices; determinants; and the solution of systems of linear equations. This is the first semester in a two-semester sequence; the second course, MT 425 Abstract Algebra, builds on the content of this first course to develop the concept of algebra structures. Prerequisite: MT 210, MT 211 or equivalent, MT 315 or MT 320.

MT 365 - Data Analysis and Interpretation

(Credits: 3.00)

Exploratory data analysis is used to introduce basic concepts of descriptive and inferential statistics, and to foster the ability to reason statistically. Topics include summarizing and presenting categorical and quantitative data; descriptive statistics and graphical presentation of data; assessing statistical significance; probability and counting methods; sampling from populations; investigations of discrete and continuous probability distributions; hypergeometric, binomial, and normal probability distributions; point and interval estimation of population parameters; and hypothesis testing. While not a teaching methods course, practical ways to implement statistics into the middle/high school curriculum will be modeled using manipulatives, computer simulations and relevant computer software. Prerequisite: MT 209 or department approval.

MT 400 - Independent Study/Internships

(Credits: 2.00)

This involves the independent study of the particular subject under the direction of a faculty member. Independent study can be terminated at the discretion of the faculty member if the student does not progress at a rate which meets minimum expectations. Prerequisite: B (3.0) average in mathematics courses, junior or senior standing, consent of the department head and the cooperating faculty member prior to registration for the course.

MT 401 - Seminar

(Credits: 4.00)

This is a culminating experience for majors in mathematics who are near the end of their program of studies. The objectives of this seminar are to review fundamental concepts of mathematics; provide opportunities for students to integrate, synthesize and/or extend their knowledge base in mathematics; develop collaborative problem-solving skills in a peer group; and explore career opportunities available to graduates in mathematics. A faculty member acting as a facilitator will provide a list of topics to be covered on the exam and some problems for class discussion. Readings in mathematical history or philosophy may also be required. Students will be expected to play a major role in planning and carrying out activities to meet the course objectives. This course is normally taken in a student's final year of upper-division coursework in the major. Prerequisite: Senior standing, MT 212 and departmental approval.

MT 410 - Mathematical Modeling

(Credits: 3.00)

Mathematical modeling is a mathematical tool for solving real-world problems. In this course, students study a problem-solving process. They learn how to identify a problem, construct or select appropriate models, figure out what data needs to be collected, test the validity of a model, calculate solutions, and implement the model. Emphasis lies on model construction in order to promote student creativity and demonstrate the link between theoretical mathematics and real-world applications. Prerequisite: MT 211.

MT 421 - Topology

(Credits: 3.00)

This one-semester introduction to topology is intended for strong mathematics majors. The goal is to introduce the student to basic concepts of topology, open and closed sets, topological spaces, product spaces, continuity, homeomorphisms, connectedness, compactness, separation properties and metric spaces. Students are challenged to become fluent in logical mathematical reasoning. They learn to read and write good mathematical proofs and to clearly articulate mathematical concepts and processes. By studying the problems and methods of topology, students learn ways that mathematicians have grappled with describing intrinsic qualitative properties of space, that is, properties that are independent of size, location or space. This should not be the student's first course in doing mathematical proofs. A student who has a grade of A in MT 315 or MT 320 should be well-prepared for this course. Prerequisite: Departmental approval.

MT 425 - Abstract Algebra

(Credits: 3.00)

This course is a study of sets, mappings, operations, relations, partitions, and basic algebraic structures, including groups, rings, integral domains, fields, and vector spaces. This is the second course in a two-semester sequence which introduces the student to algebraic structures; it builds on the introduction to vector spaces which is begun in the first course, MT 325 Linear Algebra. Prerequisite: MT 315 or MT 320, and MT 325.

MT 450 - Numerical Analysis

(Credits: 3.00)

Numerical analysis, particularly applied numerical analysis, is concerned with obtaining numerical solutions to problems which do not lend themselves to solution by ordinary mathematical analysis. Since calculators and digital computers do not really use real numbers, numerical problems are compounded when such tools are used to do the number crunching. Often, the only way to get an idea of the solution is to approximate the problem in such a way that numbers representing the solution can be produced. The purpose of this course is to introduce the student to some modern numerical methods, to improve the student's skills in using the computer as a tool to solve numerical problems, to increase the student's awareness of problems inherent in obtaining numerical solutions, and to make the student a more discerning consumer of numerical solutions and software which claims to produce numerical solutions. Prerequisite: The student should have completed three semesters of calculus and have a working knowledge of a higher-level programming language. A student who has a grade of A in MT 210 and MT 211 may seek approval of the instructor..

MT 460 - Introduction to Complex Analysis

(Credits: 3.00)

Calculus ordinarily covers a wide range of topics involving real-valued functions. Complex analysis extends these topics to the system of complex numbers. Topics covered in this introductory course include the algebra of complex numbers; various representations of complex numbers (points, vectors, polar forms); analytical functions; exponential, trigonometric and logarithmic functions; complex integration; and series representations for analytic functions. Prerequisite: MT 212 or departmental approval.

MT 470 - Theory of Probability and Statistics

(Credits: 3.00)

Through a study of theory and applications, this course introduces the theoretical underpinnings of the basic concepts of probability and sampling distributions, estimation, tests of hypotheses, regression, and correlations. Prerequisite: MT 211 and MT 365.