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Mathematics & Statistics

Unless otherwise noted, the courses listed are offered during both fall and spring semesters. Course offerings during the summer vary from year to year.

The following codes by a course title signify that a course fulfills part of the stated requirement.

CAMA |
FKL Core Curriculum Mathematics Requirement |

CAQR |
FKL Core Curriculum Quantitative Reasoning Requirement |

**MAC 1105 — COLLEGE ALGEBRA — CAMA (3)**
[Syllabus]

Concepts of the real number system, functions, graphs, and complex numbers. Analytic skills for solving linear, quadratic, polynomial, exponential, and logarithmic equations. Mathematical modeling of real-life applications.

**Prerequisite(s):**
C (2.0) or better in MAT 1033, ** or** SAT Math score of 490 or better,

**MAC 1114 — PRECALCULUS TRIGONOMETRY (2)**

Angles, trigonometric functions, properties and graphs of trigonometric functions, right triangles, laws of sines and cosines. (No credit for students with credit in MAC 1147.)

**Prerequisite(s):** C (2.0) or better in MAC 1105, ** or** SAT Math score of 570 or better,

**MAC 1140 — PRECALCULUS ALGEBRA (3)**

Review of functions and graphs. Polar coordinates; Analytic geometry, including conic sections and rotation of axes; Systems of equations, including matrix algebra and determinants; Sequences and series; Binomial theorem. (No credit for students with credit in MAC 1147. Students should either have taken MAC 1114 previously or be taking it concurrently.)

**Prerequisite(s):** C (2.0) or better in MAC 1105, ** or** SAT Math score of 550 or better,

**MAC 1147 — PRECALCULUS ALGEBRA AND TRIGONOMETRY — CAMA (4)**
[Syllabus]

This is an accelerated combination of MAC 1114 and MAC 1140. Students in this course should already have seen some trigonometry. (No credit for students with credit in MAC 1114 or MAC 1140.)

**Prerequisite(s):** C (2.0) or better in MAC 1105, ** or** SAT Math score of 550 or better,

**MGF 1106 — FINITE MATHEMATICS — CAMA (3)**
[Syllabus]

Concepts and analytical skills in areas of logic, linear equations, linear programming, mathematics of finance, permutations and combinations, probability, and descriptive statistics.

**Prerequisite(s):** C (2.0) or better in MAT 1033, ** or** SAT Math score of 440 or better,

**MGF 1107 — MATHEMATICS FOR LIBERAL ARTS — CAMA (3)**

This terminal course is intended to present topics which demonstrate the beauty and utility of mathematics to the general student population. Among the topics which might be included are: Financial Mathematics, Linear and Exponential Growth, Numbers and Number Systems, Elementary Number Theory, Voting Techniques, Graph Theory, and the History of Mathematics.

**Prerequisite(s):** C (2.0) or better in MAT 1033, ** or** SAT Math score of 440 or better,

**MAC 2233 — BUSINESS CALCULUS — CAMA (3)**
[Syllabus]

Linear equations and functions, mathematics of finance, differentiation and integration of algebraic, trigonometric, exponential and logarithmic functions with applications to business, finance, and economics. (No credit for math majors or students with credit in MAC 2241, MAC 2281, or MAC 2311.)

**Prerequisite(s):** C (2.0) or better in MAC 1105, ** or** C (2.0) or better in MAC 1140,

**MAC 2241 — LIFE SCIENCES CALCULUS I — CAMA (3)**
[Syllabus]

Differentiation and integration of algebraic, trigonometric, exponential, and logarithmic functions with applications to life sciences. (No credit for math majors or students with credit in MAC 2233, MAC 2281, or MAC 2311.)

**Prerequisite(s):** C (2.0) or better in MAC 1114, ** or** C (2.0) or better in MAC 1147,

**MAC 2242 — LIFE SCIENCES CALCULUS II — CAMA (3)**
[Syllabus]

Techniques of integration, differential equations, functions of several variables, series and Taylor polynomials. (No credit for math majors or students with credit in MAC 2282 or MAC 2312.)

**Prerequisite(s):** C (2.0) or better in MAC 2241.

**Note:** Prior to Fall 2013, this was a 4-hour course.

**MAC 2281 — ENGINEERING CALCULUS I — CAMA (4)**
[Syllabus]

Differentiation, limits, differentials, extrema, indefinite integrals. (No credit for students with credit in MAC 2233, MAC 2241, or MAC 2311.)

**Prerequisite(s):** C (2.0) or better in MAC 1114 ** and** C (2.0) or better in MAC 1140,

**MAC 2282 — ENGINEERING CALCULUS II — CAMA (4)**
[Syllabus]

Techniques of integration for trigonometric, exponential, and logarithmic functions, series, polar coordinates, applications. (No credit for students with credit in MAC 2242 or MAC 2312.)

**Prerequisite(s):** C (2.0) or better in MAC 2281.

**MAC 2283 — ENGINEERING CALCULUS III (4)**
[Syllabus]

Functions of several variables, partial derivatives, vector algebra, applications. (No credit for students with credit in MAC 2313.)

**Prerequisite(s):** C (2.0) or better in MAC 2282.

**MAC 2311 — CALCULUS I — CAMA (4)**
[Syllabus]

Limits, derivatives, applications. (No credit for students with credit in MAC 2233, MAC 2241, or MAC 2281.)

**Prerequisite(s):** C (2.0) or better in MAC 1114 ** and** C (2.0) or better in MAC 1140,

**MAC 2312 — CALCULUS II — CAMA (4)**
[Syllabus]

Antiderivatives, the definite integral, applications, series, trigonometric, exponential, and logarithmic functions. (No credit for students with credit in MAC 2242 or MAC 2282.)

**Prerequisite(s):** C (2.0) or better in MAC 2311.

**MAC 2313 — CALCULUS III (4)**
[Syllabus]

Integration, polar coordinates, conic sections, vectors, indeterminate forms, and improper integrals. (No credit for students with credit in MAC 2283.)

**Prerequisite(s):** C (2.0) or better in MAC 2312.

**MAP 2302 — DIFFERENTIAL EQUATIONS (3)**
[Syllabus]

First-order linear and nonlinear differential equations, higher-order linear equations, applications.

**Prerequisite(s):** MAC 2283 ** or** MAC 2313.

**MAD 3107 — DISCRETE MATHEMATICS (3)**

An introduction to some of the aspects of discrete mathematics that are fundamental to digital computing. Topics include: sets, numbers, algorithms, Boolean algebra, computer arithmetic, elementary combinatorics, and an introduction to graph theory. (No credit towards Mathematics major.)

**Prerequisite(s):** MAC 2281 ** or** MAC 2311.

**MAS 3105 — LINEAR ALGEBRA (3)** [Syllabus]

Linear systems, matrix algebra, vector spaces, linear independence, inner product spaces, Gram-Schmidt algorithm, linear transformations and matrix representations, determinants, eigenvalues, diagonalization, quadratic forms.

**Co-prerequisite(s):** MAC 2283 ** or** MAC 2313,

**MAS 3108 — ALGEBRA CONNECTIONS (3)**

This course will provide prospective teachers with experiences that will help them develop the specialized content knowledge needed to support the teaching of mathematics in middle level education.

**Prerequisite(s):** MAC 2311

**MAS 3156 — VECTOR CALCULUS (3)**

Implicit and inverse function theorems, parametrized surfaces, submanifolds on Euclidean space, exterior calculus of differential forms, differentiation of vector fields, line and surface integrals, Stokes' Theorem, elementary continuous groups.

**Prerequisite(s):** MAC 2283 ** or** MAC 2313

**MAS 3205 — NUMBER CONCEPTS CONNECTIONS (3)**

This course will provide prospective teachers with experiences in number theory that will help them develop the specialized content knowledge needed to support the teaching of mathematics in middle level education.

**Prerequisite(s):** MAC 2311

**MGF 3301 — BRIDGE TO ABSTRACT MATHEMATICS (3)**

Techniques and logic of the construction of proofs. Topics will be selected from propositional logic, set theory, relations and functions, equivalence relations, Boolean algebra, cardinality, and limits.

**Co-prerequisite(s):** MAC 2283 ** or** MAC 2313

**MTG 3207 — GEOMETRY CONNECTIONS (3)**

This course will provide prospective teachers with experiences in geometry that will help them develop the specialized content knowledge needed to support the teaching of mathematics in middle level education.

**Prerequisite(s):** MAC 2311

**MTG 3212 — GEOMETRY (3)**

Emphasis on axiomatics, advanced Euclidean geometry, elements of projective geometry, non-Euclidean geometry. (No credit towards Mathematics major.)

**Prerequisite(s):** MAC 2281 ** or** MAC 2311.

**COP 4313 — SYMBOLIC COMPUTATIONS IN MATHEMATICS (3)**

Students will write programs to solve problems in various areas of mathematics, including calculus and linear algebra, with symbolic programming systems such as Maple, Mathematica, or Macsyma.

**Prerequisite(s):** MAP 2302 ** and** MAS 3105.

**MAA 4211 — INTERMEDIATE ANALYSIS I (3)**

Sequences, series, metric spaces, continuity, differentiation.

**Prerequisite(s):** MAC 2313 ** and** MGF 3301

**MAA 4212 — INTERMEDIATE ANALYSIS II (3)**

Riemann-Stieltjes integration, uniform convergence, and related topics. (No credit for students with credit in MAA 5306.)

**Prerequisite(s):** MAA 4211.

**Suggested Textbook:** *Principles of Mathematical Analysis* by Rudin, Third Edition, McGraw-Hill Higher Education

**Note:** This course is only taught in the spring semester.

**MAA 4402 — COMPLEX VARIABLES (3)**

Complex numbers, Cauchy-Riemann equations, analytic and conformal functions, power series, Cauchy Integral Theorem, Cauchy Integral Formula, residue theory. (No credit for students with credit in MAA 5405.)

**Prerequisite(s):** MAP 2302

**Suggested Textbooks:**

*Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics* by Saff & Snider, Third Edition, Prentice Hall

*Complex Variables and Applications* by Brown & Churchill, Eighth Edition, McGraw-Hill

**Note:** This course is only taught in the spring semester.

**MAD 4203 — INTRODUCTION TO COMBINATORICS (3)**

Fundamental principles of counting. Topics include bijective proofs, arrangements and permutations, sets and multisets, the Principle of Inclusion-Exclusion, partitions, generating functions, recurrence relations, and the Polya theory of counting.

**Prerequisite(s):** MGF 3301

**Suggested Textbook:** *A Walk Through Combinatorics*, by Miklos Bona, Third Edition, World Scientific, 2011

**Note:** This course is only taught in the fall semester.

**MAD 4301 — INTRODUCTION TO GRAPH THEORY (3)**

Fundamental principles of Graph Theory, including isomorphism, trees and connectivity, Eulerian circuitry, Hamiltonicity, matching theory, planarity, graph colorings, Ramsey theory, and graph algorithms.

**Prerequisite(s):** MGF 3301

**Suggested Textbook:** *A Walk Through Combinatorics*, by Miklos Bona, Third Edition, World Scientific, 2011

**Note:** This course is only taught in the spring semester.

**MAD 4401 — NUMERICAL ANALYSIS I (3)**

Interpolation and quadrature, finite differences, numerical solution of algebraic and transcendental equations, numerical solution of differential equations, computer techniques.

**Prerequisite(s):** MAP 2302 ** and** MAS 3105.

**MAD 4402 — NUMERICAL ANALYSIS II (3)**

Numerical linear algebra, approximation theory, eigenvalue approximation, systems of nonlinear equations, boundary value problems.

**Prerequisite(s):** MAD 4401.

**Note:** This course is only taught in the spring semester.

**MAD 4471 — INTRODUCTION TO CRYPTOGRAPHY AND CODING THEORY (3)**

Cryptology combines the studies of cryptography, the creating of masked messages, and cryptanalysis, the unraveling of masked messages. Coding theory is the study of coding schemes used to detect and correct errors that occur during the data transmission.

**Prerequisite(s):** MAS 3105 ** and** MGF 3301

**MAD 4504 — THEORY OF COMPUTATION (3)**

Mathematical aspects of alphabets and languages. Chomsky's hierarchy. Grammars. Regular languages, grammars and finite state machines. Context-free languages and grammars. Turing machines and languages. Decidability. Inductive definition of functions and basic computable functions. Introduction to computational complexity.

**Prerequisite(s):** MGF 3301 ** or** MAD 3100.

**MAP 4202 — OPTIMIZATION (3)**

Linear and nonlinear programming, the simplex method, duality and sensitivity, constrained and unconstrained optimization.

**Prerequisite(s):** MAP 2302 ** and** MAS 3105.

**MAP 4341 — INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS (3)**

Separation of variables, Fourier series, Sturm-Liouville problems, initial boundary value problems, Bessel functions and Legendré polynomials.

**Prerequisite(s):** MAP 2302 ** and** MAS 3105.

**MAS 4214 — ELEMENTARY NUMBER THEORY (3)**

Divisibility, prime numbers, Fundamental Theorem of Arithmetic, Diophantine equations, the algebra of congruences, number functions, and other selected topics. (No credit towards Mathematics major.)

**Prerequisite(s):** MAC 2282 ** or** MAC 2312.

**MAS 4301 — ELEMENTARY ABSTRACT ALGEBRA I (3)**

An introduction to the basic algebraic structures: groups, rings, integral domains and fields; homeomorphisms, and isomorphisms.

**Prerequisite(s):** MGF 3301 ** and** MAS 3105.

**MAS 4302 — ELEMENTARY ABSTRACT ALGEBRA II (3)**

Continuation of MAS 4301. Advanced topics in abstract algebra, including ring theory and field theory; introduction to Galois theory.

**Prerequisite:** MAS 4301.

**Suggested Textbook(s):** *A First Course in Abstract Algebra*, 7th ed, by John B. Fraleigh, 2002.

**Supplemental:** *A Book of Abstract Algebra*, by Charles C. Pinter, Dover Books on Mathematics, 2009.

*Algebra*, 2nd ed., by Michael Artin, 2010

*Abstract Algebra: Theory and Applications*, by Tom Judson, 2013.

**Note:** This course is only taught in the spring semester.

**MAT 4906 — INDEPENDENT STUDY (1-4)**

Specialized independent study determined by the student's needs and interests. The written contract required by the College of Arts & Sciences specifies the regulations governing independent study. (S/U only. May be repeated.)

**Prerequisite(s):** CI

**Note:** This course requires the approval of the Associate Chair.

**MAT 4930 — SELECTED TOPICS IN MATHEMATICS (1-4)**

The course content will depend on the interest of faculty members and student demand.

**Prerequisite(s):** CI

**MAT 4937 — MATHEMATICS MAJORS SEMINAR (1)**

Directed discussions on a variety of topics of interest to mathematics majors, including career opportunities in mathematics. (S/U only. May not be repeated.)

**Prerequisite(s):** MAS 4301

**Note:** This seminar is not currently offered at USF.

**MAT 4970 — MATHEMATICS SENIOR THESIS (3)**

Course restricted to mathematics majors. (S/U only.)

**Prerequisite(s):** Admission to Mathematics Honors Program ** and** CC.

**MHF 4403 — THE EARLY HISTORY OF MATHEMATICS (3)**

A study of the history and development of mathematics and its cultural impact from the formation of number systems to the Renaissance. (No credit for students with credit in MHF 5402.)

**Prerequisite(s):** MAC 2312 ** and** upper-level standing.

**MHF 4406 — THE HISTORY OF MODERN MATHEMATICS (3)**

Traces the development of mathematical ideas in Western culture. (No credit for students with credit in MHF 5405.)

**Prerequisite(s):** MAC 2313 ** and** upper-level standing.

**MTG 4214 — MODERN GEOMETRY (3)**

Topics will be selected from modern plane geometry. Möbius geometry, elliptic and hyperbolic geometry.

**Co-prerequisite(s):** MAS 4301 ** or** CI.

**MTG 4254 — DIFFERENTIAL GEOMETRY (3)**

The intrinsic geometry of curves and surfaces will be explored using fundamental concepts and techniques from classical differential geometry.

**Prerequisite(s):** MAC 2313 ** or** MAC 2283, MAP 2302, MAS 3105

**MTG 4302 — INTRODUCTION TO TOPOLOGY (3)**

Metric spaces, completeness, topological spaces, subspaces, product spaces, continuity, homeomorphisms, connectedness, compactness, separation axioms, countability axioms.

**Prerequisite(s):** MAC 2313 ** and** MGF 3301

**STA 2023 — INTRODUCTORY STATISTICS I — CAQR (3)**

Descriptive and Inferential Statistics; Principles of Probability Theory, Discrete and Continuous Probability Distributions: Binomial Probability Distribution, Poisson Probability Distribution, Uniform Probability Distribution, Normal Dist and more. (No credit for students with credit in QMB 2100 or STA 2122. No credit towards Mathematics major.)

**Prerequisite(s):** C (2.0) or better in MAT 1033, ** or** SAT Math score of 440 or better,

**STA 3024 — INTRODUCTORY STATISTICS II (3)**

Factorials, ANCOVA; multiple curvilinear regression; response surfaces; Latin squares, Split Plots, incomplete designs; distribution free methods.

**Prerequisite(s):** STA 2023

**Suggested Textbooks:**

*Introduction to the Practice of Statistics* by Moore & McCabe, Fifth Edition, W H Freeman

*The Joy of Statistics: Learning with Real World Data* by Tsokos & Wooten, Kendall Hunt

**STA 3027 — STATISTICS AND PROBABILITY CONNECTIONS (3)**

This course will provide prospective teachers with experiences in statistics and probability theory that will help them develop the specialized content knowledge needed to support the teaching of mathematics in middle level education.

**Prerequisite(s):** MAC 2311

**STA 4102 — COMPUTATIONAL METHODS FOR APPLIED STATISTICS (3)**

This course introduces fundamentals of the R and SAS statistical software packages. Topics include data manipulation, graphs, regression, ANOVA, hypothesis testing, and non-parametric tests.

**Prerequisite(s):** STA 3024

**Note:** This course is only offered in the fall semester.

**STA 4222 — SAMPLE SURVEY DESIGN (3)**

The course covers common statistical survey design methods, including random sampling, stratified sampling, systematic sampling, and cluster sampling. Other topics include bias and non-sampling errors.

**Prerequisite(s):** STA 3024

**Note:** This course is only offered during the spring semester of even years.

**STA 4321 — INTRODUCTION TO MATHEMATICAL STATISTICS I (3)**

Basic statistical methods. Estimation, hypothesis testing, regression, ANOVA, and nonparametric theory and methods.

**Prerequisite(s):** MAC 2313 ** or** MAC 2283

**STA 4322 — INTRODUCTION TO MATHEMATICAL STATISTICS II (3)**

Point Estimators, Goodness-of-Fit Tests, Linear Regression Models, Design of Experiments, Analysis of Variance (ANOVA), Bayesian Estimation and Inference, Nonparametric Tests, amd Empirical Methods.

**Prerequisite(s):** STA 4321

**Suggested Textbook:** *Mathematical Statistics with Applications* by Ramachandran & Tsokos, Academic Press

**STA 4442 — INTRODUCTION TO PROBABILITY (3)**

Introduction to probability theory using calculus. Basic ideas of probability and random variables, discrete probability functions, continuous probability densities, joint distributions, transformations of random variables, moments and generating functions of random variables, and limit theorems.

**Prerequisite(s):** MAC 2313 ** or** MAC 2283

**STA 4502 — NONPARAMETRIC STATISTICAL METHODS (3)**

This course covers the fundamental concepts, and provides examples, of nonparametric statistical methods. Topics to be covered include sample testing, estimation methods, layout models, correlation and regression models, and goodness-of-fit tests.

**Prerequisite(s):** STA 3024

**Note:** This course is only offered in the spring semester.

**STA 4504 — CATEGORICAL DATA ANALYSIS (3)**

Fundamental concepts and examples of categorical data analysis. Topics include description and interference using proportions and odd ratios, multi-way contingency tables, logistic regression and other generalized linear models, and log linear models.

**Prerequisite(s):** STA 3024

**Note:** This course is only offered in the spring semester of odd years.

**STA 4702 — MULTIVARIATE STATISTICAL METHODS (3)**

This course covers the fundamental concepts of multivariate analysis. Topics to be covered include Matrix theory and distributions (normal, \(t\), chi-squared, \(F\)), inference about multivariate means and inference about covariance structure.

**Prerequisite(s):** STA 3024

**Suggested Textbook:** *Applied Multivariate Statistical Analysis* by Johnson & Wichern, Sixth Edition, Prentice Hall

**Note:** This course is only offered in the fall semester.

**STA 4852 — APPLIED TIME SERIES (3)**

This course covers the fundamental concepts, estimations, and hypothesis testing of discrete time series models. The models will be developed using the autoregressive and moving average processes. Numerous examples will be provided.

**Prerequisite(s):** STA 3024

**Suggested Textbook:** *Introduction to Time Series Analysis and Forecasting* by Montgomery, Jennings, & Kulahci, Wiley

**Note:** This course is only offered in the fall semester.

**STA 4930 — SELECTED TOPICS IN STATISTICS (1-4)**

The course content will depend on the interest of faculty members and student demand.

**Prerequisite(s):** CI