# Course Descriptions

## Prefix: MAT

**Note: Exceptions to any prerequisite must be made by the Department Chair.**

### 090 Pre-Entry Math (3)

This course prepares a student to take MAT 091 or MAT 093. A variety of individualized strategies are used, including computer-aided instruction, and one-on-one tutoring. The course does not fulfill distribution or degree requirements. CR/NC option only. Placement in this course is by appropriate score on the math SAT or ACT test.

### 091 Preparatory Mathematics I (3) (formerly MAT 100A)

Introduction to algebra; polynomials, factoring, solving linear and quadratic equations. Emphasis on problem solving skills. The course prepares students for MAT 107, 152 or 201 and does not fulfill distribution or degree requirements. CR/NC option available. Placement in this course is by appropriate score on the math SAT or ACT test or by a skills assessment.

### 093 Preparatory Mathematics II (3) (formerly MAT 100B)

Graphs, systems of linear equations, inequalities, fractional and radical expressions, fractional, radical and quadratic equations; emphasis on problem solving skills. This course prepares students for MAT 095 or MAT 108 or MAT 152 and does not fulfill distribution or degree requirements. CR/NC option available. Placement in the course is by appropriate score on the math SAT or ACT test or by a skills assessment.

### 095 Preparatory Mathematics III (3) (formerly MAT 100C)

Basic properties of real and complex numbers, equations and inequalities, coordinates and graphs, equations, graphs of lines, and systems of equations. The course prepares science majors to take Precalculus courses, but does not fulfill distribution or degree requirements. CR/NC option available. Placement in this course is by appropriate score on the math SAT or ACT test.

### 097 Pre-College Mathematics Review (6)

A review of high school mathematics required for college level work. Topics include sets, real numbers, equations, and inequalities, polynomials, rational expressions, exponents and radicals, quadratic equations and inequalities, coordinate geometry, systems of linear equations and inequalities. This course does not satisfy distribution or degree requirements. CR/NC option available. Placement in this course is by appropriate math SAT or ACT score or by a skills assessment.

### 107 General Education Mathematics (3) (formerly MAT 101)

Nature and application of mathematics for liberal arts students. Topics selected from algebra, geometry, logic, numeration systems, probability, and statistics, as required by the State of Florida CLAST examination. Prerequisite: MAT 091 or appropriate math SAT or ACT score or by a skills assessment.

### 108 Precalculus Mathematics for Business (3)

Equations and inequalities; systems of equations and inequalities; exponential and logarithmic functions and their graphs; vectors, matrices, linear programming. Prerequisite: MAT 093 or appropriate math SAT or ACT score.

### 109 Precalculus Mathematics I (3)

Functions and their graphs; polynomial, algebraic, exponential, and logarithmic functions, roots of algebraic equations, conic sections, nonlinear equations and inequalities. Prerequisite: two years of high school algebra, geometry and MAT 095 or appropriate math SAT or ACT score.

### 110 Precalculus Mathematics II (3)

Trigonometric functions of angles and of real numbers, trigonometric identities and equations, polar coordinates. Prerequisite: MAT 109 with a grade of C or above, or appropriate math SAT or ACT score.

### 120 Mathematics and Art (3)

An analysis of the interplay between mathematics and art. Emphasis will be made on the discovery and analysis of numerical relations, geometric patterns, and algebraic structures. This is a mathematics course that draws its content from an analysis of art throughout key periods of history and the present. Prerequisites: At least two semesters of high school algebra or one semester of high school geometry or college-level mathematics.

### 152 Elementary Probability and Statistics (3)

Sampling, tables and graphs, elementary probability, special discrete and continuous random variables, linear correlation and regression, contingency tables, hypothesis testing. Prerequisite: MAT 091 or 093 or satisfactory math SAT or ACT score.

### 201 Fundamentals of Mathematics I (3)

Introduction to problem solving, exploration of patterns; functions; numeration systems, whole numbers and operations; integers and operations, integer exponents; divisibility, prime and composite numbers, greatest common divisor, least common multiple, modular arithmetic; rational numbers and operations; proportional reasoning. Emphasis on problem solving. Prerequisite: MAT 091 or appropriate math SAT or ACT scores; education majors only.

### 202 Fundamentals of Mathematics II (3)

Logic, sets, set operations; decimals and operations, real numbers; Pythagorean Theorem; equations, Cartesian coordinate system, equation of a line, percent, interest; introduction to probability and statistics. Emphasis on problem solving. Prerequisite: MAT 201 with a grade of C or above; education majors only.

### 203 Geometry for Teachers (3)

Informal plane and space geometry; measurements, perimeter, area, volume; metric system; congruence, similarity, constructions; translations, rotations, reflections, symmetries, tessellations; use of appropriate software. Emphasis on problem solving. Prerequisite: MAT 202 with a grade of C or above; education majors only.

### 210 Calculus with Applications (3)

Applications of calculus to business, social and behavioral sciences. Limits of functions, derivative as the rate of change, marginal cost, marginal revenue. Curve sketching, maximization and optimization, elasticity. Integration, density function, consumers and producers surplus, annuities, exponential and logistic growth. Not acceptable for the Mathematics or Computer Science major. Prerequisite: MAT 108 or appropriate math SAT or ACT score.

### 211 Calculus I (4)

Limits of functions and approximation; differentiation and integration of elementary functions; maxima and minima applications. Prerequisite: MAT 110 with a grade of C or above, or appropriate math SAT or ACT score.

### 212 Calculus II (4)

Advanced techniques of differentiation and integration; polar coordinates, sequences and series. Prerequisite: MAT 211 with a grade of C or above.

### 213 Calculus III (4)

Multivariable calculus; functions of several variables; partial derivatives; multiple integration; theorems of Green, Gauss and Stokes; introduction to linear differential equations. Prerequisite: MAT 212 with a grade of C or above.

### 230 Statistical Methods I (3)

Introduction to the description and analysis of data. Exploratory graphical methods. Data summarization methods. Probability, sampling, expectation. Statistical inference for means and proportions. Statistical software will be widely used. Prerequisites: MAT 110 or 152 or equivalent.

### 240 History and Philosophy of Science (3)

The course examines scientific and mathematical thought from an historical and philosophical perspective. The connection among the disciplines of physics, mathematics, and chemistry will be highlighted. The development of scientific thought throughout history will be studied and paradigm shifts will be emphasized. (Honors Option)

### 252 Statistics with Applications I

Continuation of MAT 152. Hypothesis testing, regression and correlation, chi-square and F distributions, nonparametric statistics. Emphasis on applications to social and behavioral sciences. Prerequisite: MAT 152 or equivalent.

### 253 Discrete Mathematics I (3)

Sets, counting, methods of proof. Logic. Relations, types of relations, functions, types of functions. Recursive functions. Prerequisite: MAT 110.

### 254 Discrete Mathematics II (3)

Systems of linear equations, matrices, matrix operations. Graphs, lattices, Boolean algebras, regular expressions, finite state automata. Decidability, formal languages and grammars. Computational complexity. Prerequisite: MAT 253.

### 300 Special Topics (3)

Contents to be determined each semester by the Department to meet needs of the program and/or of the students. Prerequisite: Departmental approval.

### 310 Advanced Calculus I (3)

Functions, sequences, limits. Continuity, uniform continuity. Differentiation. Series, Uniform convergence. Prerequisite: MAT 213.

### 311 Advanced Calculus II (3)

Continuation of MAT 310. Riemann-Stieltjes integral; functions of several variables, partial differentiation; multiple integrals. Prerequisite: MAT 310.

### 314 Differential Equations (3)

Linear differential equations; systems of differential equations; solutions by series and by numerical methods; applications. Prerequisite: MAT 212.

### 321 Topics in Geometry (3)

Geometric shapes and measurement: primitive areas and volumes. Properties of lines and triangles: properties of incidence and parallelism, similarity and congruence of triangles. Circles: central and inscribed angles, chords, secants and tangents. Transformation Geometry: geometric transformations, translations, reflections, rotations and related groups. Prerequisites: MAT 211 and MAT 253.

### 330 Statistical Methods II (3)

Continuation of MAT 230. Statistical inference, analysis of variance, correlation and regression analysis, categorical data, design of experiments. Statistical software will be widely used. Prerequisite: MAT 230.

### 331 Algebraic Structures (3)

Groups, Lagrange's theorem, homomorphisms. Rings, integral domains, field of quotients, polynomial rings, unique factorization domains. Fields and finite field extensions. Prerequisites: MAT 332 or MAT 462 acceptable, but both preferred.

### 332 Linear Algebra (3)

Systems of linear equations, matrices, vector spaces, linear transformations, determinants. Quadratic forms, eigenvalues and eigenvectors. Prerequisites: MAT 211 and MAT 253.

### 356 Statistics for Science (3)

Analysis of data, histograms, measures of central tendency and of dispersion. Probability, normal curve. Statistical tests; hypothesis testing. This course is designed for science majors (Biology, Physics, Chemistry, Computer Science, Mathematical Sciences). Prerequisite: MAT 211.

### 374 Theory of Computation (3)

A study of mathematical, engineering and linguistic foundations of theoretical computer science: abstract machines and languages, formal grammars, finite-state machines, finite-state languages, automata, Turing machines, recursive functions. Prerequisite: MAT 254.

### 414 Methods of Mathematical Physics (3)

Fourier analysis, special functions, calculus of variations. Selected partial differential equations. Integral equations. Prerequisites: MAT 213 and MAT 314.

### 415 Introduction to Real Analysis (3)

The real numbers, real functions. Measure theory. The Lebesgue integral. Prerequisite: MAT 311.

### 416 Introduction to Complex Analysis (3)

Analytic functions, Cauchy-Riemann conditions. Complex integration, Cauchy's theorem and integral formula. Power series, Laurent series. Calculus of residues and applications. Prerequisite: MAT 213.

### 440 Mathematical Modeling (3)

Basic training in the development of mathematical models for real-world phenomena using probability, statistics and differential equations. Prerequisites: CS 232, MAT 314.

### 441 Introduction to Topology (3)

Axiom of choice, topological spaces, metric spaces. Compactness, connectedness. Separation properties, quotient spaces. Compactification. Prerequisite: MAT 213.

### 451 Probability Theory (3)

Probability spaces, distribution functions, central limit theorem, conditional probability. Prerequisites: MAT 213.

### 452 Mathematical Statistics (3)

Sampling theory, statistical inference, hypothesis testing. Prerequisite: MAT 451.

### 456 Numerical Analysis (3)

A survey of numerical and computational methods for solving algebraic problems. Zero location, maxima and minima, Newton's methods, vector and matrix operations, characteristic value problem, numerical approximation to differential equations. Use of computer algorithms and programming is involved. Prerequisites: MAT 314 and 332.

### 462 Number Theory (3)

The integers, congruences, multiplicative functions, primitive roots, quadratic residues, reciprocity, diophantine equations, applications to cryptology. Prerequisites: MAT 211 and MAT 253.

### 471 History of Mathematics (3)

People and ideas that have shaped the mathematical sciences throughout history. Contemporary problems and leading contributions. Emphasis on activities for secondary school mathematics classroom, which incorporate the historical viewpoint. Prerequisite: MAT 211.

### 359, 459 Independent Study (3) (3)

Opportunity for extensive research in areas of special interest to the student. Prerequisites: Dean's and Department Chair's approval.

### 476 Teaching Mathematics in the Middle and Secondary School (3)

Methods of mathematics teaching for the prospective middle and secondary school teacher. Prerequisite: 21 credits in mathematics, including MAT 211.

### 487 Undergraduate Mathematics

Seminar (1-3 credits)

Topics will be chosen according to student and faculty interest. Presentations of papers on original work or advanced material to be discussed under a faculty moderator. Prerequisites: Junior or senior standing and Department Chair's approval.

### 499 Internship (3-12)

Practical experience within a professional setting. Prerequisites: Senior status (90+ credit hours); 2.50 overall GPA; all documentation must be completed before the end of the semester preceding the internship. Prior approval of Department Chair and Dean required.