USF 1995-96 Undergraduate Catalog - Pages 176 - 178
CGS 3422 COMPUTER APPLICATIONS OF MATHEMATICS -6A (3)
CR: MAS 3103. Introduction to FORTRAN (WATFIV) with special emphasis on its applications to Mathematics.
COP 4213 MATHEMATICAL PROBLEM SOLVING USING PASCAL -6A (3)
PR: MAS 3103, and the ability to program at least one other language. The highly structured programming language PASCAL is used to solve numerical and non-numerical problems in mathematics involving graph theory, combinatorics, and number theory. Non-numerical data structures and algebraic manipulation are emphasized.
MAA 4211 MULTIVARIATE CALCULUS -6A (4)
PR: MAC 3313 or MAC 3283 with a grade of "C" or better, MAS 4301 and MAS 3103. Vector-valued functions, multiple integrals, line and surface integrals.
MAA 4212 INTERMEDIATE ANALYSIS -6A (4)
PR: MAA 4211. A theoretical treatment of differential and integral calculus of one and several variables. Emphasis on techniques of proof.
MAA 5306 REAL ANALYSIS I (3)
PR: MAA 4212. Riemann-Stieltjes integrals, uniform convergence, Fourier series, Lebesgue measure and integration on R.
MAA 5307 REAL ANALYSIS II (3)
PR: MAA 5306. Metric spaces, Banach spaces, and function spaces; measure and integration on abstract 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 3233 or MAC 2102.)
MAC 3233 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 3233-MAC 3234 are primarily for students from Biological Sciences, Social Sciences and Business. (No credit for math majors or students with credit in MAC 3281 or MAC 3311).
MAC 3234 ELEMENTARY CALCULUS II -6A -QM (4)
PR: MAC 3233. Techniques of integration, differential equations, functions of several variables, series and Taylor polynomials. (No credit for Mathematics majors or students with credit in MAC 3282 or MAC 3312.)
MAC 3281 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. Differentiation, limits, differentials, extrema, indefinite integral. (No credit for students with credit in MAC 3233 or MAC 3311.)
MAC 3282 ENGINEERING CALCULUS II -6A -QM (3)
PR: MAC 3281 or CC. Definite integral, trigonometric functions, log, exponential, series, applications. (No credit for students with credit in MAC 3234 or MAC 3312.)
MAC 3283 ENGINEERING CALCULUS III -6A (3)
PR: MAC 3282 or CC. Techniques of integration, numerical methods, analytic geometry, polar coordinates, Vector algebra, applications. (No credit for students with credit in MAC 3313.)
MAC 3311 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 3233 or MAC 3281.)
MAC 3312 CALCULUS II -6A (4)
PR: MAC 3311 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 3234 or MAC 3282.)
MAC 3313 CALCULUS III -6A (4)
PR: MAC 3312 with a grade of "C" or better or CC. Integration, polar coordinates, conic sections, vectors, indeterminate forms and proper integrals. (No credit for students with credit in MAC 3283.)
MAD 3100 DISCRETE MATHEMATICS -6A (3)
PR: MAC 3281 or MAC 3311. 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 3103; 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 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 3103 and 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 3313 and bachelor's degree or CC. Advanced consideration of limits continuity, derivatives, differentials. (No credit for Mathematics majors.)
MAP 4302 DIFFERENTIAL EQUATIONS -6A (3)
PR: MAC 3283 or MAC 3313. First order linear and nonlinear differential equations, higher order linear equations, applications.
MAP 5316 ORDINARY DIFFERENTIAL EQUATIONS I (3)
PR: MAP 4302, MAA 4211, 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 4302 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 3103 LINEAR ALGEBRA -6A (3)
CR: MAC 3282 or 3312. Linear equations, matrices, real vector spaces, relationship between linear transformations and matrices, determinants, inner product spaces, eigenvalues and eigenvectors.
MAS 4124 NUMERICAL LINEAR ALGEBRA -6A (3)
PR: MAS 3103. 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 ANALYSIS -6A (3)
PR: MAC 3313 or MAC 3283 or CI. The algebra and calculus of vectors, line and surface integrals, Divergence Theorem, Stokes' Theorem, generalized coordinates, applications. (No credit for both MAA 4211 and MAS 4156.)
MAS 4214 ELEMENTARY NUMBER THEORY -6A (3)
PR: MAC 3312. 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: MAC 3312 or MAC 3282. An introduction to basic set theory: sets, functions, and relations. An introduction to the basic algebraic structures: groups, rings, and fields. Homomorphisms and isomorphisms. A rigorous treatment of the real and complex number systems.
MAS 5107 ADVANCED LINEAR ALGEBRA (3)
PR: MAS 3103, MAS 4301 (or MHF 4102) 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 3103 and 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 3103 and MAS 4301, or CI. Group theory: Sylow theorems; classification of groups of small order. Ring theory: ideals, 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 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 Sciences 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)
Directed discussions on a variety of topics of interest to math majors, including carreer opportunities in mathematics. May be repeated up to 2 credit hours. (S/U only.)
MAT 4939 MATHEMATICS HONORS SEMINAR -6A (1)
PR: Admission to Mathematics Honors Program or CC. Directed discussions on a variety of topics of mathematical interest. May be repeated up to 8 credit hours. (S/U only.)
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 2130 MODERN MATHEMATICS WITH MICROCOMPUTERS -6A (4)
PR: Two years of high school algebra. Topics in finite math, real vs. computer number systems, inequalities, functions, graphs, introduction to BASIC programming and microcomputers, exact and approximate solutions of algebraic equations, probability, computer simulations of models.
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.
MHF 4102 LOGIC AND SET THEORY -6A (3)
PR: MAC 3311 or MAC 3281, or CI. First half: An introduction to the Propositional and Predicate Calculi, concentrating on proofs. Second half: An introduction to naive set theory, up to cardinal numbers, concentrating on sets of numbers.
MHF 4403 THE EARLY HISTORY OF MATHEMATICS -XMW (3)
PR: MAC 3312 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 3313. 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: MAC 3311. Emphasis on axiomatics, advanced Euclidean geometry, elements of projective geometry, non-Euclidean geometries.
MTG 5256 DIFFERENTIAL GEOMETRY (3)
PR: MAA 4211, MAS 3103. Exterior calculus, differentiable manifolds, integration of differential forms, surfaces in 3-space, covariant derivative, curvature, matrix groups.
MTG 5316 TOPOLOGY I (3)
PR: MAA 4212. 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 (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: MINITAB. (No credit for Mathematics majors.)
STA 3023 INTRODUCTORY STATISTICS I -6A -QM (4)
PR: Two years of high school algebra. Descriptive statistics, basic probability principles, discrete and continuous probability distributions: binomial, Poisson, uniform, normal, t, chi-square and F; point estimation, confidence limits, hypothesis testing, correlation analysis and linear regression. 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 3122. (No credit for Mathematics Majors.)
STA 3024 INTRODUCTORY STATISTICS II -6A (3)
PR: STA 3023 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 methods.
STA 4442 INTRODUCTION TO PROBABILITY -6A (3)
PR: MAC 3313, MAS 4301. Introduction to probability theory using calculus. Basic ideas of probability and random variables, discrete probability functions, continuous probability densities including normal, gamma, x (Greek letter Chi), and Weibull, and transformations of random variables.
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 4212 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. Theory and methods of non-parametric statistics, order statistics, tolerance regions and their applications.
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Margaret R. Martinroe - webCat@ugs.usf.edu
Publication Date: June 1, 1995
http://www.ugs.usf.edu/catalogs/9596/cdmath.htm