2005-06 Undergraduate Catalog

**Course Descriptions**

College of Liberal Arts and Sciences

MAA 4102 Introduction to Advanced Calculus for Engineers and Physical Scientists 1

Credits: 3; Prereq: grade of C or better in MAC 2313 or MAC 3474 and in MAS 4105 or MAS 3114.

Theory of real numbers, functions of one variable, sequences, limits, continuity and differentiation; continuity and differentiability of functions of several variables. MAA 4102 is not recommended for students who plan to do graduate work in mathematics; these students should take MAA 4211. (Note: credit will be given for at most one of MAA 4102, MAA 4211 or MAA 5104.)

MAA 4103 Introduction to Advanced Calculus for Engineers and Physical Scientists 2

Credits: 3; Prereq: grade of C or better in MAA 4102.

A continuation of MAA 4102. Theory of integration, transcendental functions and infinite series. MAA 4102 is not recommended for students who plan to do graduate work in mathematics; these students should take MAA 4212. (Note: credit will be given for at most one of MAA 4103, MAA 4212 and MAA 5105.)

MAA 4211 Advanced Calculus 1

Credits: 3; Prereq: grade of C or better in MAS 4105.

An advanced treatment of limits, differentiation, integration, series; calculus of functions of several variables. (Note: credit will be given for at most one of MAA 4211, MAA 4102 and MAA 5104.)

MAA 4212 Advanced Calculus 2

Credits: 3; Prereq: grade of C or better in MAA 4211, taken the previous semester.

A continuation of MAA 4211. (Note: credit will be given for at most for one of MAA 4212, MAA 4103 and MAA 5105.)

MAA 4226 Introduction to Modern Analysis 1

Credits: 3; Prereq: grade of C or better in MAS 4105.

Topology of metric spaces, numerical sequences and series, continuity, differentiation, the Riemann-Stieltjes integral, sequences and series of functions, the Stone-Weierstrass, theorem, functions of several variable, Stokes' theorem, the Lebesgue theory. (Note: credit will be given for at most one of MAA 4226 and MAA 5228.)

MAA 4227 Introduction to Modern Analysis 2

Credits: 3; Prereq: grade of C of better in MAA 4226, taken the previous semester.

A continuation of MAA 4226. (Note: credit will be given for at most for one of MAA 4227 and MAA 5229.)

MAA 4402 Functions of a Complex Variable

Credits: 3; Prereq: grade of C or better in MAC 2313 (or MAC 3474) and in MAP 2302.

Complex numbers, analytic functions, Cauchy-Riemann equations, harmonic functions, elementary functions, integration, Cauchy-Goursat theorem, Cauchy integral formula, infinite series, residues and poles, conformal mapping. (Note: credit will be given for at most one of MAA 4402 and MAA 5404.)

"Credit" here means credit toward graduation, General Education requirements, the College of Liberal Arts and Sciences' Basic Distribution requirements, and the Writing and Math requirement.

MAC 1105 Basic College Algebra

Credits: 3.

Entry-level algebra for college students. (M) (MR) (See note above)

MAC 1114 Trigonometry

Credits: 2.

Exponential and logarithmic functions, trigonometry, analytic and additional applications of trigonometry. (M) (MR) (See note above)

MAC 1140 Precalculus Algebra

Credits: 3.

College algebra, functions, coordinates geometry, exponential and logarithmic functions. (M) (MR) (See note above)

MAC 1147 Precalculus: Algebra and Trigonometry

Credits: 4.

College algebra, functions, coordinates geometry, exponential and logarithmic functions, and trigonometry. This fast-paced course is designed as a review of algebra and trigonometry to prepare the student for calculus. This course assumes prior knowledge of intermediate algebra (Algebra II) and trigonometry. (M) (MR) (See note above)

MAC 2233 Survey of Calculus 1

Credits: 3; Prereq: strong background in precalculus.

A geometric and heuristic approach to calculus; differentiation and integration of simple algebraic and exponential functions; applications to graphing, marginal analysis, optimization, and areas and volumes. (M) (MR) (See note above)

MAC 2234 Survey of Calculus 2

Credits: 3; Prereq: grade of C or better in MAC 2233, or equivalent.

Sequences, geometric and Taylor series; systems of linear equations, Gaussian elimination, matrices, determinants and vectors; partial differentiation, multiple integrals; applications to marginal analysis, least-squares and Lagrange multipliers. (M) (MR)

MAC 2311 Analytic Geometry and Calculus 1

Credits: 4; Prereq: strong background in precalculus.

Introduction to analytic geometry; limits; continuity; differentiation of algebraic, trigonometric, exponential, and logarithmic functions; applications of the derivative; inverse trigonometric functions; differentials; introduction to integration; and the fundamental theorem of calculus. (Note: credit will be given for at most one of MAC 2233, MAC 2311 and MAC 3472.) (M) (MR)

MAC 2312 Analytic Geometry and Calculus 2

Credits: 4; Prereq: grade of C or better in MAC 2311 or MAC 3472.

Techniques of integration; applications of integration; differentiation and integration of inverse trigonometric, exponential and logarithmic functions; and sequences and series. (Note: credit will be given for at most one of MAC 2312, MAC 2512 and MAC 3473.) (M) (MR)

MAC 2313 Analytic Geometry and Calculus 3

Credits: 4; Prereq: grade of C or better in MAC 2312 or MAC 2512 or MAC 3473.

Solid analytic geometry, vectors, partial derivatives, multiple integrals. (Note: credit will be given for at most one of MAC 2313 and MAC 3474.) (M) (MR)

MAC 2512 Calculus 2 for Advanced Placement Students

Credits: 4; Prereq: Advancement Placement credit for MAC 2311.

A calculus course for entering freshmen who have Advanced Placement Calculus AB credit for MAC 2311. MAC 2512 covers those topics in MAC 2311 and MAC 2312 not included or only partially covered in the AP Calculus AB curriculum. Some topics from the AP curriculum are reviewed briefly in the first part of the semester. The combination of AP Calculus AB and MAC 2512 has the same content as the sequence MAC 2311-2312. Calculus 2 topics to which the student has been exposed in AP Calculus AB are covered more quickly in MAC 2512 than in MAC 2312. (Note: credit will be given for at most one of MAC 2312, MAC 2512, and MAC 3473.) (M) (MR)

MAC 3472 Honors Calculus 1

Credits: 4; Prereq: strong background in precalculus.

The topics covered in the MAC 34723473/3474 sequence closely parallel those covered in MAC 2311/2312/2313 but are treated in greater depth. (Note: credit will be given for at most one of MAC 2311 and MAC 3472.) (M) (MR)

MAC 3473 Honors Calculus 2

Credits: 4; Prereq: grade of C or better in MAC 3472 or MAC 2311.

A continuation of MAC 3472. (Note: credit will be given for at most one of MAC 2312, MAC 2512 and MAC 3473.) (M) (MR)

MAC 3474 Honors Calculus 3

Credits: 4; Prereq: grade of C or better in MAC 2312, MAC 2512 or MAC 3473.

A continuation of MAC 3473. (Note: credit will be given for at most one of MAC 2313 and MAC 3474.) (M) (MR)

MAD 3107 Discrete Mathematics

Credits: 3; Prereq: grade of C or better in MAC 2312, MAC 2512 or MAC 3473.

Logic, sets, functions. Algorithms and complexity; integers and algorithms. Mathematical reasoning and induction. Counting principles; permutations and combinations; discrete probability. Advanced counting techniques and inclusion-exclusion.

MAD 4203 Introduction to Combinatorics 1

Credits: 3; Prereq: grade of C or better in MAC 2312, MAC 2512 or MAC 3473. Some experience with theorems and proofs is recommended.

Permutations and combinations, binomial coefficients, inclusion-exclusion, recurrence relations, Fibonacci sequences, generating functions, graph theory. (M)

MAD 4204 Introduction to Combinatorics 2

Credits: 3; Prereq: grade of C or better in MAC 2312, MAC 2512 or MAC 3473. Some experience with theorems and proofs is recommended.

Matching theory, block designs, finite projective planes and error-correcting codes. This course does not require the student to have taken MAD 4203.

MAD 4401 Introduction to Numerical Analysis

Credits: 3; Prereq: experience with a scientific programming language, and a grade of C or better in MAS 3114 or in MAS 4105.

Numerical integration, nonlinear equations, linear and non-linear systems of equations, differential equations, and interpolation.

MAE 3811 Mathematics for Elementary School Teachers 2

Credits: 3; Prereq: passing score on the MAE 3811 Prerequisite Exam. Refer to
www.math.ufl.edu/course_guides/mae/3811.html.

Properties of and operations with rational numbers; ratio; proportion; percentages; an introduction to real numbers; elementary algebra; informal geometry and measurement; and an introduction to probability and descriptive statistics. Note: this course is open only to students whose majors are in the College of Education.

MAP 2302 Elementary Differential Equations

Credits: 3; Prereq: grade of C or better in MAC 2312, MAC 2512 or MAC 3473.

First-order ordinary differential equations, theory of linear ordinary differential equations, solution of linear ordinary differential equations with constant coefficients, the Laplace transform and its application to solving linear ordinary differential equations. (M) (MR)

MAP 3170 Introduction to Actuarial Mathematics

Credits: 3; Prereq: grade of C or better in MAC 2312, MAC 2512 or MAC 3473.

Amount function, simple and compound interest, present value, dollar-weighted and time-weighted rates, force of interest, discrete and continuous annuities, bonds, amortization, capitalization, and applications.

MAP 4102 Probability Theory and Stochastic Processes 2

Credits: 3; Prereq: grade of C or better in STA 4321.

Random walks and Poisson processes, martingales, Markov chains, Brownian motion, stochastic integrals and Ito's formula.

MAP 4305 Differential Equations for Engineers and Physical Scientists

Credits: 3; Prereq: grade of C or better in MAP 2302 and in either MAS 3114 or MAS 4105.

This is a second course in differential equations. Topics are systems of linear differential equations, stability theory and phase plane analysis, power series solutions of differential equations, Sturm-Liouville boundary-value problems and special functions. (Note: credit will be given at most for one of MAP 4305 and MAP 5304.)

MAP 4341 Elements of Partial Differential Equations

Credits: 3; Prereq: grade of C or better in MAP 2302 and in MAP 4305.

Introduction to second-order linear partial differential equations (heat, wave and Laplace equations), separation of variables in PDEs, Sturm-Liouville eigenvalue problems, method of eigenfunction expansions (Fourier analysis), Green's functions. Possible introduction to first-order PDEs and the method of characteristics. (Note: credit will be given for at most one of MAP 4341 and MAP 5345.)

MAP 4403 Mathematical Methods for Engineers

Credits: 3; Prereq: grade of C or better in MAC 2313 (or in MAC 3474) and in MAP 2302.

Complex variables, including derivatives and integrals, singularities, Taylor/Laurent series and residues; linear algebra, including Gaussian elimination, determinants, inversion, linear independence, eigenvalues and eigenvectors, and (time permitting) QR decomposition, systems of differential equations; (time permitting) numerical methods, including roots of equations, numerical integration, and numerical optimization.

MAP 4413 Fourier Series and Transforms 1

Credits: 3; Prereq: grade of C or better in MAC 2313 (or MAC 3474) and in MAP 2302; MAP 4305 recommended.

Introduction to linear systems and transforms; Laplace, Fourier and Z transforms and their mutual relationship; convolutions. Operational calculus; computational methods including the fast Fourier transform; second-order stationary processes and their autocorrelation functions; and problems of interpolation, extrapolation, filtering and smoothing of second-order stationary processes.

MAS 3114 Computational Linear Algebra

Credits: 3; Prereq: experience with a scientific programming language, and a grade of C or better in MAC 2312 (or in MAC 2512 or in MAC 3473).

Linear equations, matrices and determinants. Vector spaces and linear transformations. Inner products and eigenvalues. This course emphasizes computational aspects of linear algebra. (M) (MR)

MAS 3300 Numbers and Polynomials

Credits: 3; Prereq: grade of C or better in a UF math course; this requirement is waived for transfer students with junior standing.

This course emphasizes theorems and proofs. Topics include algebraic and order properties of the real numbers, introduction to number theory, rational numbers and their decimal expansions, uncountability of the real numbers, complex numbers, irreducible polynomials over the integral, rational, real and complex numbers, elementary theory of equations. Taking one (but not both) of MAS 3300 and MHF 3202 is required of mathematics majors. MAS 3300 is also particularly useful for prospective secondary-school mathematics teachers. (M) (MR)

MAS 4105 Linear Algebra 1

Credits: 4; Prereq: grade of C or better in MAC 2313 or MAC 3474 and in MAS 3300 or MHF 3202.

Linear equations, matrices, vector spaces, linear transformations, determinants, eigenvalues, inner-product spaces. This course includes both theory and computational skills. The student is expected to develop the ability to reason through, and coherently write up, proofs of theorems. For math majors, this course serves as a transition from a study of techniques into more conceptual math; for engineering and science majors, it serves also as a coherent foundation in linear algebra.

MAS 4107 Linear Algebra 2

Credits: 4; Prereq: grade of C or better in MAS 4105.

Further topics in linear algebra. (MR)

MAS 4124 Introduction to Numerical Linear Algebra

Credits: 3; Prereq: experience with a scientific programming language, and a grade of C or better in MAS 3114 or MAS 4105.

Topics in linear algebra most useful in applications with emphasis on the numerical methods involved: direct and iterative solutions to systems of linear equations; matrix norms; Householder transformations; singular value decomposition; least squares and the generalized inverse; QR method for computing eigenvalues; condition number of linear systems and eigensystems.

MAS 4156 Introduction to Vector Analysis

Credits: 3; Prereq: grade of C or better in MAC 2313 or in MAC 3474.

Review of vector algebra, lines, planes and space curves; vector fields, their divergence and curl; line, surface, and volume integrals, the Divergence Theorem and Stokes' Theorem. (Note: credit will be given for at most one of MAS 4156 and MAS 5157.)

MAS 4203 Introduction to Number Theory

Credits: 3; Prereq: grade of C or better in MAC 2312 or in MAC 2512 or in MAC 3473; MAS 3300 recommended.

An introduction to elementary number theory and its applications to computer science and cryptology. Divisibility, primes, Euclidean Algorithm, congruences, Chinese Remainder Theorem, Euler-Fermat Theorem, primitive roots. Selected applications to decimal fractions, continued fractions, computer file storage and hashing functions, and public-key cryptography. (M)

MAS 4301 Abstract Algebra 1

Credits: 3; Prereq: grade of B or better in MAS 3300 or in MHF 3202, or a grade of C or better is MAS 4105.

Sets and mappings, groups and subgroups, homomorphisms and isomorphisms, permutations, rings and domains, arithmetic properties of domains, fields. This course requires facility in writing proofs.

MAS 4302 Abstract Algebra 2

Credits: 3; Prereq: grade of C or better in MAS 4301.

Further topics in abstract algebra.

MAT 4905 Individual Work

Credits: 1 to 3; can be repeated for up to 10 credits. Prereq: grade of C or better in MAC 2313 (or in MAC 3474) and permission of undergraduate coordinator.

For special topics not obtainable in the regular course offerings.

MAT 4930 Special Topics in Mathematics

Credits: 1 to 3; can be repeated for up to 16 credits. Prereq: permission of undergraduate coordinator.

Qualified undergraduates will take part in seminars or classes on special topics.

MGF 1106 Mathematics for Liberal Arts Majors 1

Credits: 3; Students who have received credit for MGF 1202 will not receive credit for MGF 1106.

This course is designed for non-science and non-business majors who need to fulfill their Gordon Rule and General Education math requirements. The course includes an introduction to set theory, logic, number theory, probability, statistics, graphing, and linear programming. (M) (MR)

MGF 1107 Mathematics for Liberal Arts Majors 2

Credits: 3.

A General Education course that demonstrates the beauty and utility of mathematics. Topics include financial management, linear and exponential growth, mathematics in the arts and discrete mathematics. This course does not require the student to have taken MGF 1106. (M) (MR)

MHF 3202 Sets and Logic

Credits: 3; Prereq: grade of C or better in a UF math course.

Examples of sets, operations on sets, set algebra, Venn diagrams, truth tables, tautologies, applications to mathematical arguments and mathematical induction. Taking one (but not both) of MAS 3300 and MHF 3202 is required of mathematics majors. MHF 3202 can also be very useful for prospective and in-service secondary-and middle school teachers. (M) (MR)

MHF 3404 History of Mathematics

Credits: 3; Prereq: grade of C or better in MAS 2312, MAC 2512 or MAC 3473.

An introduction to the history of mathematics. The course includes a historical discussion of selected mathematical topics. (M) (MR)

MHF 4102 Elements of Set Theory

Credits: 3; Prereq: grade of C or better in MAS 4105.

The basic axioms and concepts of set theory. Students present proofs. (Note: credit will be given for at most one of MHF 4102 and MHF 5107.)

MHF 4203 Foundations of Mathematics

Credits: 3; Prereq: grade of C or better in MAS 4105.

Models and proofs. Foundations of the real and natural numbers, algorithms, Turing machines, undecidability and independence. Examples and applications in algebra, analysis, geometry and topology. (Note: credit will be given for at most one of MHF 4203 and MHF 5207.)

MHF 4404 History of Mathematics

Credits: 3.

An introduction of mathematics. The course includes a historical discussion of selected mathematical topics. (M) (MR)

MTG 3212 Geometry

Credits: 3; Prereq: grade of C or better in MAC 2312, MAC 2512 or MAC 3473.

An axiomatic treatment of topics in Euclidean, non-Euclidean, projective geometry, and (time permitting) fractal geometry. This course is particularly useful for prospective secondary-school mathematics teachers. (M) (MR)

MTG 3214 Euclidean Geometry

Credits: 3; Prereq: grade of C or better in MAC 2312, MAC 2512 or MAC 3473.

Axiomatic structure of Euclidean geometry: congruence, parallelism, area, similarity, circles, polygons, medians, constructions, solid geometry, spherical and hyperbolic geometry. This course is particularly useful for prospective secondary-school mathematics teachers.

MTG 4302 Elements of Topology 1

Credits: 3; Prereq: grade of C or better in MAS 4105.

The basic concepts of general topology. (Note: credit will be given for at most one of MTG 4302 and MTG 5316.)

MTG 4303 Elements of Topology 2

Credits: 3; Prereq: grade of C or better in MTG 4302.

Continuation of MTG 4302. (Note: credit will be given for at most one of MTG 4303 and MTG 5317.)

**General Education Categories**

- Composition (C)
- Mathematical Sciences (M)
- Humanities (H)
- Social and Behavioral Sciences (S)
- Physical (P) and Biological (B) Sciences
- International and Diversity focus (I)

**Symbols Used in Course Descriptions**

**(WR)**indicates the course satisfies the writing requirement.

The Schedule of Courses lists the amount of writing credit per course section.**(MR)**indicates the course satisfies the math requirement.indicates the course may be taken on an S-U basis.*††*