USF 1998-99 Undergraduate Catalog - Pages 143 - 146
CGS 3414 PROBLEM SOLVING USING PASCAL OR C -6A (3)
CR: MAS 3105. Introduction to Pascal or C with special emphasis on its applications to mathematics.
COP 4313 SYMBOLIC COMPUTATIONS IN MATHEMATICS -6A (3)
PR: MAP 2302 and MAS 3105. 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.
MAA 4211 INTERMEDIATE ANALYSIS I -6A (4)
PR: MAS 4301. Sequences, series, metric spaces, continuity, differentiation.
MAA 4212 INTERMEDIATE ANALYSIS II -6A (3)
PR: MAA 4211. Riemann-Stieltjes integration, uniform convergence, and related topics.
MAA 4402 COMPLEX VARIABLES -6A (3)
PR: MAS 4301 or CI. Complex numbers, Cauchy-Riemann equations, analytic and conformal functions, power series, Cauchy IntegralTheorem, Cauchy Integral Formula, residue theory. (No credit for students with credit in MAA 5405.)
MAA 5306 REAL ANALYSIS I (3)
PR: MAA 4211. Sets and functions, measure theory, measurable functions, Lebesque integrations and limit theorems.
MAA 5307 REAL ANALYSIS II (3)
PR: MAA 5306. Continuation of MAA 5306, including functions of bonded variation, product measures and Fubibi's theorem, differentiation, LP spaces.
MAA 5405 APPLIED COMPLEX ANALYSIS (3)
PR: CI. Complex numbers, analytic and harmonic functions. Series. Contour integrals, residue theory. Conformal mappings. (A survey course emphasizing techniques and applications.)
MAC 2102 COLLEGE ALGEBRA -6A -QM (3)
PR: Two years of high school algebra. 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.
MAC 2114 COLLEGE TRIGONOMETRY -6A (2)
PR: Two years of high school algebra. Angles, Trigonometric functions, properties and graphs of trigonometric functions, right triangles, laws of sines and cosines, polar coordinates. (No credit for students with credit in MAC 2132.)
MAC 2132 COLLEGE ALGEBRA AND TRIGONOMETRY -6A -QM (4)
PR: Two years of high school algebra. Real numbers and their properties, algebraic expression, equations and inequalities, functions, polynominals, exponential and logarithmic functions. Angles, trigonometric functions, properties and graphs of trigonometric functions, right triangles, laws of sines and cosines, polar coordinates. (No credit for MAC 2132 for students with credit in MAC 2233 or MAC 2102.)
MAC 2230 BUSINESS CALCULUS -6A -QM (4)
PR: Three years of high school mathematics including two years of algebra or MAC 2102. Linear equations and functions, mathematics of finance, differentiation and integration of algebraic functions with applications to business, finance, and economics. (No credit for mathematics majors or students with credit in MAC 2233, MAC 2281, or MAC 2311.)
MAC 2233 ELEMENTARY CALCULUS I -6A -QM (4)
PR: Three years of high school mathematics including two years of algebra or MAC 2102. Differentiation and integration of algebraic functions with applications, exponential and logarithmic functions. MAC 2233-MAC 2234 are primarily for students from biological and social sciences. (No credit for mathematics majors or students with credit in MAC 2230, MAC 2281, or MAC 2311.)
MAC 2234 ELEMENTARY CALCULUS II -6A -QM (3)
PR: MAC 2230 or MAC 2233. Techniques of integration, differential equations, functions of several variables, series and Taylor polynomials. (No credit for mathematics majors or students with credit in MAC 2282 or MAC 2312.)
MAC 2281 ENGINEERING CALCULUS I -6A -QM (3)
PR: Two years of high school algebra, and a semester of trigonometry or MAC 2132. A year of high school geometry is recommended. Limits, differentiation, differentials, extrema, indefinite integral. (No credit for students with credit in MAC 2230, MAC 2233, or MAC 2311.)
MAC 2282 ENGINEERING CALCULUS II -6A -QM (3)
PR: MAC 2281 or CC. Techniques of integration, trigonometric, log, and exponential functions, series, polar coordinates, applications. (No credit for students with credit in MAC 2234 or MAC 2312.)
MAC 2283 ENGINEERING CALCULUS III -6A (3)
PR: MAC 2282 or CC. Functions of several variables, partial derivatives, vector algebra, applications. (No credit for students with credit in MAC 2313.)
MAC 2311 CALCULUS I -6A -QM (4)
PR:Two years of high school algebra, and a semester of trigonometry or MAC 2132. A year of high school geometry is recommended. Limits, derivatives, applications. (No credit for students with credit in MAC 2230, MAC 2233, or MAC 2281.)
MAC 2312 CALCULUS II -6A -QM (4)
PR: MAC 2311 with a grade of “C” or better or CC. Antiderivatives, the definite integral, applications, series, log, exponential and trig functions. (No credit for students with credit in MAC 2234 or MAC 2282.)
MAC 2313 CALCULUS III -6A (4)
PR: MAC 2312 with a grade of “C” or better or CC. Integration, polar coordinates, conic sections, vectors, indeterminate forms and improper integrals. (No credit for students with credit in MAC 2283.)
MAD 3100 DISCRETE MATHEMATICS -6A (3)
PR: MAC 2281 or MAC 2311. 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.
MAD 4401 NUMERICAL ANALYSIS -6A (4)
PR: MAS 3105; ability to program a digital computer. Interpolation and quadrature, finite differences, numerical solution of algebraic and transcendental equations, numerical solution of differential equations, computer techniques.
MAD 4504 THEORY OF COMPUTATION -6A (3)
PR: MGF 3301 or MAD 3100. Mathematical aspects of alphabets and languages. Chomsky’s hierarchy. Grammars. Regular languages, grammars and finite states machines. Context-free languages and grammars. Turing machines and languages. Decidability. Inductive definition of functions and basic computable functions. Introduction to computational complexity.
MAD 5101 LISP: PROGRAMMING WITH ALGEBRAIC APPLICATIONS (3)
PR: MHF 5306 or MAD 6510 or MAS 5311 or CI. Programming in LISP, functional languages, foundations of Lambda Calculus and algebraic applications (theorem proving and game playing).
MAD 5305 INTRODUCTION TO GRAPH THEORY (3)
PR: CI. Brief introduction to classical graph theory (4-color theorem, etc.), directed graphs, connected digraphs, condensations, incidence matrices, Polya’s Theorem, networks.
MAE 5875 ABSTRACT ALGEBRA FOR TEACHERS (3)
PR: MAS 4301 and bachelor’s degree or CC. Groups, fields, vector spaces as they relate to high school algebra and geometry. (No credit for mathematics majors.)
MAE 5877 MATHEMATICAL ANALYSIS FOR TEACHERS (3)
PR: MAC 2313 and bachelor’s degree or CC. Advanced consideration of limits continuity, derivatives, differentials. (No credit for Mathematics majors.)
MAP 2302 DIFFERENTIAL EQUATIONS -6A (3)
PR: MAC 2283 or MAC 2313. First order linear and nonlinear differential equations, higher order linear equations, applications.
MAP 5316 ORDINARY DIFFERENTIAL EQUATIONS I (3)
PR: MAP 2302 or CI. Existence and uniqueness theory, properties of solutions, linear systems, stability theory, Sturm-Liouville theory.
MAP 5317 ORDINARY DIFFERENTIAL EQUATIONS II (3)
PR: MAP 5316 and MAA 5307 or CI. Topics selected from fixed point theory, comparison theory, oscillation theory, Poincare-Bendixson Theory, Lyapunov functions, eigenfunction expansions.
MAP 5345 APPLIED PARTIAL DIFFERENTIAL EQUATIONS (3)
PR: MAP 5407 or CI. Separation of variables, the heat equation, wave equation, Laplace’s equation, classification, Green’s functions, with emphasis on applications.
MAP 5407 METHODS OF APPLIED MATHEMATICS (3)
PR: MAP 2302 or CI. Sturm-Liouville theory, Fourier series, Green’s functions, matrix methods for linear systems of ordinary differential equations, and topics from calculus of variations, control theory, numerical solutions of differential equations.
MAS 3105 LINEAR ALGEBRA -6A (3)
PR: MGF 3301. CR: MAC 2283 or 2313. Linear systems, matrix algebra, vector spaces, linear independence, inner product spaces, Gram-Schmidt algorithm, linear transformations and matrix representations, determinants, eigenvalues, diagonalization, quadratic forms.
MAS 4124 NUMERICAL LINEAR ALGEBRA -6A (3)
PR: MAS 3105. This course will consider efficient and stable numerical methods for dealing with matrix computations such as the solution of systems, calculation eigenvalues and vectors, least squares, and so on.
MAS 4156 VECTOR CALCULUS -6A (3)
PR: MAS 3105, and MAC 2313 or MAC 2283. Implicit and inverse function theorems, parametrized surfaces, submanifolds of Euclidean space, exterior calculus of differential forms, differentiation of vector fields, line and surface integrals, Stokes’ Theorem, elementary continuous groups.
MAS 4214 ELEMENTARY NUMBER THEORY -6A (3)
PR: MAC 2312. Divisibility, prime numbers, Fundamental Theorem of Arithmetic, Diophantine equations, the algebra of congruences, number functions and other selected topics.
MAS 4301 ELEMENTARY ABSTRACT ALGEBRA -6A (3)
PR: MAS 3105. An introduction to the basic algebraic structures: groups, rings, integral domains, and fields; homomorphisms and isomorphisms.
MAS 5107 ADVANCED LINEAR ALGEBRA (3)
PR: MAS 4301 or CI. CR: MAS 5311. The study of finite dimensional vector spaces over arbitrary fields. Topics covered include dual spaces, canonical forms for linear transformations, inner product spaces, orthogonal, unitary and self-adjoint operators and quadratic forms.
MAS 5215 NUMBER THEORY (3)
PR: MAS 4301 or CI. Fundamental theorem of arithmetic, modular arithmetic, Chinese remainder theorem, Mersenne primes, perfect numbers, Euler-Fermat theorem, pseudoprimes, primitive roots, law of quadratic reprocity, factorization and primality testing algorithms.
MAS 5311 ALGEBRA I (3)
PR: MAS 4301 or CI. Group theory: Sylow theorems, classification of groups of small order. Ring theory: ideals, quotient rings, polynomial rings, Euclidean domains, quotient rings, polynomial rings, Euclidean domains, principal ideal domains and unique factorization.
MAS 5312 ALGEBRA II (3)
PR: MAS 5311 or CI. Continuation of MAS 5311. Finitely generated modules over a principal ideal domain, basic field theory, finite fields, Galois theory.
MAT 2930 SELECTED TOPICS IN MATHEMATICS (1-4)
PR: CI. The course content will depend on the interest of faculty members and student demand.
MAT 2936 TECHNOLOGY SEMINAR -6A (1)
A two contact hour/week technology seminar to acquaint students majoring in mathematics, physics, and other sciences with the computer tools necessary in scientific communication and document preparation. (S/U only. May not be repeated.)
MAT 4906 INDEPENDENT STUDY -6A (1-4)
PR: CI. Specialized independent study determined by the student’s needs and interests. The written contract required by the College of Arts and Science specifies the regulations governing independent study. May be repeated. (S/U only.)
MAT 4930 SELECTED TOPICS IN MATHEMATICS -6A (1-4)
PR: CI. The course content will depend on the interest of faculty members and student demand.
MAT 4937 MATHEMATICS MAJORS SEMINAR -6A (1)
PR: MAS 4301. Directed discussions on a variety of topics of interest to mathematics majors, including carreer opportunities in mathematics. (S/U only. May not be repeated.)
MAT 4970 MATHEMATICS SENIOR THESIS -6A (3)
PR: Admission to Mathematics Honors Program and CC. Course restricted to mathematics majors. (S/U only.)
MAT 5932 SELECTED TOPICS -6A (1-4)
PR: CI. Each course covers a single topic outside the usual curriculum.
MGF 2131 CHAOS AND FRACTALS -6A -QM (3)
PR: High school algebra and trigonometry. Computer experiments in the behavior of functions under iteration: periodicity, attractors, stability, complex numbers, Cantor set, fractional dimension, sensitive dependence.
MGF 2202 FINITE MATHEMATICS -6A -QM (3)
PR: Two years of high school algebra. Concepts and analytical skills in areas of logic, linear equations, linear programming, mathematics of finance, permutations and combinations, probability, and descriptive statistics.
MGF 3301 BRIDGE TO ABSTRACT MATHEMATICS -6A -QM (3)
PR: MAC 2311 or MAC 2281. 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
MHF 4403 THE EARLY HISTORY OF MATHEMATICS -6A -XMW (3)
PR: MAC 2312 and upper-level standing. A study of the history and development of mathematics and its cultural impact from the formation of number systems to the Renaissance.
MHF 5306 MATHEMATICAL LOGIC AND FOUNDATIONS I (3)
PR: MAS 4301 or CI. Two-course sequence covering: predicate calculus and classical model theory; transfinite set theory and the system ZFC; recursion theory and decidability.
MHF 5405 HISTORY OF MODERN MATHEMATICS (3)
PR: MAC 2313. Traces the development of mathematical ideas in Western culture. Special emphasis is placed on those concepts which led to the Calculus. This course is open to majors and non-majors alike.
MTG 4212 GEOMETRY -6A (4)
PR: MGF 3301 or CI. Emphasis on axiomatics, advanced Euclidean geometry, elements of projective geometry, non-Euclidean geometries.
MTG 4302 INTRODUCTION TO TOPOLOGY -6A (3)
PR: MAS 4301. Metric spaces, completeness, topological spaces, subspaces, product spaces, continuity, homeomorphisms, connectedness, compactness, separation axioms, countability axioms.
MTG 5256 DIFFERENTIAL GEOMETRY (3)
PR: MAA 4211, MAS 3105. Exterior calculus, differentiable manifolds, integration of differential forms, surfaces in 3-space, covariant derivative, curvature, matrix groups.
MTG 5316 TOPOLOGY I (3)
PR: MAA 4211. Topological spaces, continuity, homeomorphisms, connectedness, compact spaces, separation axioms, product spaces.
MTG 5317 TOPOLOGY II (3)
PR: MTG 5316. The fundamental group; elements of homotopy theory and homology theory
STA 2022 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 for mathematics majors.)
STA 2023 INTRODUCTORY STATISTICS I -6A -QM (4)
PR: Two years of high school algebra. 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. Students who successfully complete this course may not also receive credit for QMB 2150 or STA 2122. (No credit for Mathematics Majors.)
STA 3024 INTRODUCTORY STATISTICS II -6A (3)
PR: STA 2023 or CC. Factorials, ANCOV; multiple curvilinear regression; response surfaces; Latin squares, Split Plots, incomplete designs; distribution free methods.
STA 4321 INTRODUCTION TO STATISTICS -6A (3)
PR: STA 4442. Basic statistical methods. Estimation, hypothesis testing, regression, ANOVA, and nonparametric theory and methods.
STA 4442 INTRODUCTION TO PROBABILITY -6A (3)
PR: MAC 2313 or MAC 2283. 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.
STA 5166 COMPUTATIONAL STATISTICS I (3)
PR: STA 4321, CGS 3422 or CC. Statistical analysis of data by means of statistics package programs. Regression, ANOVA, discriminant analysis, and analysis of categorical data. Emphasis is on inter-relation between statistical theory, numerical methods, and analysis of real life data. STA 5228 SAMPLING TECHNIQUES (3)
PR: STA 4321 or CI. Sampling versus total enumeration. Planning of a survey. Statistical sampling methods and their analysis; simple, stratified, systematic cluster, and double and multistage sampling. Use of auxiliary information in sampling. Ratio and regression estimates. Case study.
STA 5326 MATHEMATICAL STATISTICS (3)
PR: STA 5446. Sample distribution theory, point and interval estimation, optimality theory, statistical decision theory and hypothesis testing.
STA 5446 PROBABILITY THEORY I (3)
PR: STA 4442 and MAA 4211 or CI. Axioms of probability, random variables in Euclidean spaces, moments and moment generating functions, modes of convergence, limit theory for sums of independent random variables.
STA 5526 NON-PARAMETRIC STATISTICS (3)
PR: STA 5326, CC. Topics may include: classical nonparametric statistical theory, nonparametric density estimation, nonparametric regression, generalized additive models, nonparametric pattern recognition, classification and regression trees.
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Karen M. Hall - webCat@ugs.usf.edu
Effective Date: Semester I, 1998
http://www.ugs.usf.edu/catalogs/9899/cdmath.htm