USF 1997-98 Undergraduate Catalog - Pages 93 - 95 | Course Descriptions |
The Department of Mathematics offers a diversity of courses designed not only to enable the student to pursue a profession in mathematics itself, but also to enhance the student’s competence in the fields of engineering, the physical sciences, the life sciences, and the social sciences. The department offers programs leading to the B.A., M.A., and Ph.D. degrees. The undergraduate program emphasizes the broad nature of modern mathematics and its close associations with the real world. The program is designed to prepare students for entry into graduate school or careers in industry or secondary education.
The Department of Mathematics consists of 31 full-time faculty members, whose areas of interest include: algebra, applied mathematics, approximation theory, celestial mechanics, complex analysis, dynamical systems, functional analysis, graph theory, logic, number theory, ordinary differential equations, partial differential equations, potential theory, probability theory, real analysis, statistics, theoretical computer science, and topology.
The courses taken to satisfy the requirements below will constitute the major program referred to in the general graduation requirements of the College of Arts and Sciences. A minimum of 12 hours of 4000 level or higher mathematics courses must be taken in residency and must be applicable to the major.
1. Mathematics Requirement (Min. 45 cr. hrs.)
Majors must complete the following core courses:
In addition, majors must complete three (3) courses from the following electives:
Special topics courses, listed under MAT 4930, or other 5000-level mathematics courses can also be taken as electives, with the approval of an undergraduate advisor. In addition, one elective of high mathematical content can be taken from another department, with the approval of an undergraduate advisor and the chairman.
An undergraduate advisor will work with the student in recommending electives which are appropriate for the student’s interests and goals.
The following is a typical mathematics course program for mathematics majors:
MAC 2311 Calculus I - 4
MAC 2312 Calculus II - 4
MAT 2936 Technology Seminar - 1
MAC 2313 Calculus III - 4
MGF 3301 Bridge to Abstract Mathematics - 3
MAP 2302 Differential Equations - 3
MAS 3105 Linear Algebra - 3
MAS 4301 Elementary Abstract Algebra - 3
COP 4313 Symbolic Computations in Mathematics - 3
STA 4442 Introduction to Probability - 3
Elective - 3-4
MAA 4211 Intermediate Analysis I - 4
Elective - 3-4
MAT 4937 Mathematics Majors Seminar - 1
Elective - 3-4
2. Mathematics-related Courses (6-8 cr. hrs.)
Majors, except for majors in mathematics for teaching, must take two courses with laboratories in the Departments of Biology, Chemistry, Geology, or Physics that are required courses for the major within those departments.
Majors will not receive credit toward graduation for the following courses: AST 3033, GEB 2111, GEB 3121, PHY 2020, STA 2023, STA 2122
Majors wishing to take a course in statistics should take STA 4321.
The minor in mathematics is open to all students. Students with majors in the sciences, engineering, business, and the social sciences are particularly encouraged to pursue the minor. A student wishing to receive a minor in mathematics must meet the following course requirements (minimum of 24 cr. hrs.):
1. Required Courses (18 cr. hrs.)
Either
Also, both of the following:
2. Elective Courses (Min. 6 cr. hrs.)
Any 2 courses (3 or more credit hours each) which are required or elective for the major in mathematics.
For information concerning the degree programs for secondary school teachers, see the description given in the Mathematics Education section of this catalog.
The Department of Mathematics offers specialized technical concentrations within the general Bachelor of Arts degree in mathematics that emphasize a subfield of Environmental Science. These concentrations are more structured than the general B.A. program and require additional study in a related field comparable to earning a minor in that field. This cross disciplinary training prepares the student for a career in Environmental Science. Furthermore, the student is able to pursue graduate work in either mathematics or the related field.
1. Mathematics requirement
Completion of the mathematics major, including
2. Supporting courses
3. Biology courses
1. Mathematics requirement
Completion of the mathematics major, including
2. Chemistry courses
And either
1. Mathematics requirement
Completion of the mathematics major, including
The student must complete one of the sequences
2. Supporting courses
3. Geology courses
And either
This program is designed for superior students having a solid background in high school mathematics and the ability to handle a fast paced, challenging program leading to a BA and MA degree in mathematics in four to five years.
The program meets all the requirements for the BA degree, but requires the students to take those 5000 and 6000 level courses required for the MA degree during the last two years in the program. By awarding up to 20 hours of dual credit (undergraduate and graduate), the student also uses these courses to satisfy the requirements for the MA in mathematics.
For admission to the program, a student must have completed at least 30 hours of college credit including 8 hours of 3000-level or above mathematics courses; have an overall grade point average of 3.0 or above; and have a grade point average of 3.5 or above in all mathematics courses taken at the 3000-level or above. Further information is available on request from the Department of Mathematics (974-2643).
The program is designed for students who wish to obtain a B.A. degree that will indicate unusual strength in the field of mathematics. Successful completion of the program will be prominently displayed on the student’s diploma and will be recorded on the official U.S.F. transcript of the student’s work.
Students are eligible for admission to the program when they
Applications are submitted to the Undergraduate Committee of the Department of Mathematics.
The requirements for a B.A. degree in mathematics with honors are as follows:
Students wishing to transfer to USF should complete the A.A. degree at the community college. Some courses required for the major may also meet General Education Requirements thereby transferring maximum hours to the university. A minimum of 60 semester hours must be completed at the university unless prior approval is secured.
A student who transfers without an A.A. degree and has fewer than 60 semester hours of acceptable credit must meet the university’s entering freshman requirements including ACT or SAT test scores, GPA, and course requirements. The transfer student should also be aware of the immunization, foreign language, and continuous enrollment policies of the university.
Students should complete the following prerequisite courses listed below at the lower level prior to entering the University. If these courses are not taken at the community college, they must be completed before the degree is granted. Unless stated otherwise, a grade of “C” is the minimum acceptable grade.
Students must also complete two laboratory-based science courses, 4 - 8 semester hours total, from the respective science majors: Biology, Chemistry, or Physics.
USF 1997-98 Undergraduate Catalog - Page 105
USF 1997-98 Undergraduate Catalog - Pages 139 - 141
CGS 3422 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, 1997
http://www.ugs.usf.edu/catalogs/9798/math.htm