USF Mathematics -- Undergraduate Course Descriptions

Undergraduate Courses

COP 4313 -- SYMBOLIC COMPUTATIONS IN MATHEMATICS -6A (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 -6A (4)

Sequences, series, metric spaces, continuity, differentiation.

Prerequisite(s): MAC 2313 and MGF 3301 and MAS 3105.

MAA 4212 -- INTRODUCTION TO REAL ANALYSIS -6A (3)

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

Prerequisite(s): MAA 4211.

MAA 4402 -- COMPLEX VARIABLES -6A (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

MAC 1105 -- COLLEGE ALGEBRA -6A -QM (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, or ACT Math score of 21 or better, or Elementary Algebra CPT score of 90 or better, or College-Level Math CPT of 40 or better.

MAC 1114 -- PRECALCULUS TRIGONOMETRY -6A (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 550 or better, or ACT Math score of 24 or better, or College-Level Math CPT of 60 or better.

MAC 1140 -- PRECALCULUS ALGEBRA -6A -QM (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, or ACT Math score of 24 or better, or College-Level Math CPT of 60 or better.

MAC 1147 -- PRECALCULUS ALGEBRA AND TRIGONOMETRY -6A -QM (4)

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, or ACT Math score of 24 or better, or College-Level Math CPT of 60 or better.

MAC 2233 -- BUSINESS CALCULUS -6A -QM (4)

Linear equations and functions, mathematics of finance, differentiation and integration of algebraic 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, or C (2.0) or better in MAC 1147, or SAT Math score of 590 or better, or ACT Math score of 26 or better, or College-Level Math CPT score of 78 or better.

MAC 2241 -- LIFE SCIENCES CALCULUS I -6A -QM (4)

Differentiation and integration of algebraic, trigonometric, exponential, and logarithmic functions with applications to biological 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, or SAT Math score of 650 or better, or ACT Math score of 29 or better, or College-Level Math CPT score of 90 or better, and knowledge of trigonometry.

MAC 2242 -- LIFE SCIENCES CALCULUS II -6A -QM (4)

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.

MAC 2281 -- ENGINEERING CALCULUS I -6A -QM (4)

Limits, differentiation, 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, or C (2.0) or better in MAC 1147, or SAT Math score of 650 or better, or ACT Math score of 29 or better, or College-Level Math CPT score of 90 or better, and knowledge of trigonometry.

MAC 2282 -- ENGINEERING CALCULUS II -6A -QM (4)

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 -6A (4)

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 -6A -QM (4)

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

MAC 2312 -- CALCULUS II -6A -QM (4)

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 -6A (4)

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.

MAD 3100 -- DISCRETE MATHEMATICS -6A (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.

MAD 4401 -- NUMERICAL ANALYSIS -6A (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 4504 -- THEORY OF COMPUTATION -6A (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 2302 -- DIFFERENTIAL EQUATIONS -6A (3)

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

Prerequisite(s): MAC 2283 or MAC 2313.

MAS 3105 -- LINEAR ALGEBRA -6A (4)

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, and MGF 3301.

MAS 4156 -- VECTOR CALCULUS -6A (4)

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 2313 and MGF 3301 and MAS 3105.

MAS 4214 -- ELEMENTARY NUMBER THEORY -6A (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 -6A (3)

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

Prerequisite(s): MGF 3301 and MAS 3105.

MAT 2930 -- SELECTED TOPICS IN MATHEMATICS (1-4)

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

Prerequisite(s): CI.

MAT 2936 -- TECHNOLOGY SEMINAR -6A (1)

A two contact hour/week technology seminar designed to acquaint students majoring in mathematics, physics, and other sciences with the computer tools necessary for scientific communication and document preparation. (S/U only. May not be repeated.)

Prerequisite(s): None.

MAT 4906 -- INDEPENDENT STUDY -6A (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.

MAT 4930 -- SELECTED TOPICS IN MATHEMATICS -6A (1-4)

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

Prerequisite(s): CI.

MAT 4937 -- MATHEMATICS MAJORS SEMINAR -6A (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.

MAT 4970 -- MATHEMATICS SENIOR THESIS -6A (3)

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

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

MGF 1106 -- FINITE MATHEMATICS -6A -QM (3)

Topics include mathematical logic, sets, counting techniques, probability, statistics, and geometry.

Prerequisite(s): C (2.0) or better in MAT 1033, or SAT Math score of 440 or better, or ACT Math score of 19 or better, or Elementary Algebra CPT score of 72 or better.

MGF 1107 -- MATHEMATICS FOR LIBERAL ARTS -6A -QM (3)

Topics include voting techniques, graph theory, fair division, scheduling, and linear and exponential growth.

Prerequisite(s): C (2.0) or better in MAT 1033, or SAT Math score of 440 or better, or ACT Math score of 19 or better, or Elementary Algebra CPT score of 72 or better.

MGF 1108 -- SELECTED TOPICS IN LIBERAL ARTS MATHEMATICS -6A (3)

Topics in this course are similar to those in MGF 1106 or MGF 1107. This course may be repeated for credit with the consent of the instructor.

MGF 1116 -- MATHEMATICAL EXPERIENCE -6A (3)

Introduction to some important and interesting basic ideas in mathematics with an emphasis on a mathematical way of thinking. Concepts such as definitions, axioms, and proofs are explained. Examples from number theory, combinatorics, algebra, and geometry are used. Some topics are presented in their historical context and their impact on the development of mathematics is discussed.

MGF 1131 -- CHAOS AND FRACTALS -6A -QM (3)

Computer experiments in the behavior of functions under iteration: periodicity, attractors, stability, complex numbers, Cantor set, fractional dimension, sensitive dependence.

Prerequisite(s): C (2.0) or better in MAT 1033, or SAT Math score of 440 or better, or ACT Math score of 19 or better, or Elementary Algebra CPT score of 72 or better.

MGF 3301 -- BRIDGE TO ABSTRACT MATHEMATICS -6A -QM (4)

An introduction to the axiomatic nature of mathematics through topics in areas such as set theory, algebra, and calculus. The rigor of precise definitions, theorems, and proofs will be emphasized.

Co-prerequisite(s): MAC 2283 or MAC 2313, and MAS 3105.

MHF 4403 -- THE EARLY HISTORY OF MATHEMATICS -6A -XMW (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 -- HISTORY OF MODERN MATHEMATICS -6A -XMW (3)

Traces the development of mathematical ideas from the Renaissance to the 19th century. (No credit for students with credit in MHF 5405.)

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

MTG 3212 -- GEOMETRY -6A (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.

MTG 4214 -- MODERN GEOMETRY -6A (3)

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

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

MTG 4302 -- INTRODUCTION TO TOPOLOGY -6A (3)

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

Prerequisite(s): MAC 2313 and MGF 3301 and MAS 3105.

STA 1022 -- BASIC STATISTICS -6A -QM (3)

Basic philosophy of statistical thinking. Acquisition of data. Techniques for organizing and presenting statistical data. Sample mean, variance, and standard deviation. Statistical decisions--estimation and hypothesis testing. Design of experiments, linear association and prediction. Statistical software. (No credit towards Mathematics major.)

Prerequisite(s): C (2.0) or better in MAT 1033, or SAT Math score of 440 or better, or ACT Math score of 19 or better, or Elementary Algebra CPT score of 72 or better.

STA 2023 -- INTRODUCTORY STATISTICS I -6A -QM (4)

Descriptive statistics, basic probability principles, discrete and continuous probability distributions: binomial, normal, t, and chi-square; point estimation, confidence limits and hypothesis testing. Emphasis on applications to social sciences, life sciences, physical sciences, engineering, and business. (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, or ACT Math score of 19 or better, or Elementary Algebra CPT score of 72 or better.

STA 3024 -- INTRODUCTORY STATISTICS II -6A (3)

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

Prerequisite(s): STA 2023 or CC.

STA 4321 -- ESSENTIALS OF STATISTICS -6A (3)

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

Prerequisite(s): STA 4442.

STA 4442 -- INTRODUCTION TO PROBABILITY -6A (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, and MGF 3301.

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