MAA 4102 Introduction to Advanced Calculus for Engineers and Physical Scientists 1
Credits: 3; Prereq: MAC 2313 or MAC 3474, and MAS 4105 or MAS 3114, both with minimum grades of C.
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 and MAA 5104.)
MAA 4103 Introduction to Advanced Calculus for Engineers and Physical Scientists 2
Credits: 3; Prereq: MAA 4102 with minimum grade of C.
A continuation of the advanced calculus for engineers and physical scientists sequence. 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.)
Credits: 3; Prereq: MAS 4105 with minimum grade of C.
An advanced treatment of limits, differentiation, integration and series. Course includes calculus of functions of several variables. (Note: Credit will be given for, at most, one of MAA 4211, MAA 4102 and MAA 5104.)
Credits: 3; Prereq: MAA 4211 with minimum grade of C, taken the previous semester.
A continuation of the advanced calculus sequence in limits, differentiation, integration and series. (Note: Credit will be given for, at most, one of MAA 4212, MAA 4103 and MAA 5105.)
MAA 4226 Introduction to Modern Analysis 1
Credits: 3; Prereq: MAA 4212 with minimum grade of C.
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 variables, Stokes' theorem and the Lebesgue theory. (Note: Credit will be given for, at most, MAA 4226 or MAA 5228.)
MAA 4227 Introduction to Modern Analysis 2
Credits: 3; Prereq: MAA 4226 with minimum grade of C, taken the previous semester.
A continuation of the modern analysis sequence discussing the 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 variables, Stokes' theorem and the Lebesgue theory. (Note: Credit will be given for, at most, MAA 4227 or MAA 5229.)
MAA 4402 Functions of a Complex Variable
Credits: 3; Prereq: MAC 2313 or MAC 3474, and MAP 2302, both with minimum grades of C.
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, MAA 4402 or MAA 5404.)
Information About Precalculus and Calculus. A student can receive, at most:
- four credits for MAC 1147 and MAC 1140
- four credits for MAC 1147 and MAC 1114
- five credits for MAC 1140 and MAC 1114
- five credits for MAC 1147, MAC 1140 and MAC 1114.
- If both MAC 2233 and MAC 2311 (or MAC 3472) are taken, credit will be given only for MAC 2311 (or MAC 3472).
Credit, as used above, refers to credit toward graduation, general education requirements, the College of Liberal Arts and Sciences' basic distribution requirements and the writing and math requirements.
Credits: 3.
An online entry-level algebra course for college students. (M) (MR)
Credits: 2.
Exponential and logarithmic functions, trigonometry and analytic and additional applications of trigonometry. (M) (MR) (See calculus note above)
Credits: 3.
College algebra, functions, coordinate geometry, exponential and logarithmic functions. (M) (MR) (See calculus note above)
MAC 1147 Precalculus: Algebra and Trigonometry
Credits: 4.
College algebra, functions, coordinate 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 2) and trigonometry. (M) (MR) (See calculus note above)
Credits: 3; Prereq: Any of the following: minimal acceptable score on the online mathematics placement exam; a minimum grade of C in a MAC course numbered 1140 or higher; AP credit for MAC 2311; IB credit for a MAC course numbered 1140 or higher. Any course grades, AP or IB scores used to meet this prerequisite must be on file at UF by registration.
A geometric and heuristic approach to calculus; differentiation and integration of simple algebraic and exponential functions; applications to graphing, marginal analysis, optimization, areas and volumes. (M) (MR) (See calculus note above)
Credits: 3; Prereq: MAC 2233 with minimum grade of C, or the 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: Any of the following: minimal acceptable score on the online mathematics placement exam; a grade of C in a MAC course numbered 1147 or higher; AP credit for MAC 2311; IB credit for a MAC course numbered 1147 or higher. Any course grades, AP or IB scores used to meet this prerequisite must be on file at UF by registration.
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: MAC 2311 or MAC 3472 with a minimum grade of C.
Techniques of integration; applications of integration; differentiation and integration of inverse trigonometric, exponential and logarithmic functions; 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: MAC 2312, MAC 2512 or MAC 3473 with a minimum grade of C.
Solid analytic geometry, vectors, partial derivatives and multiple integrals. (Note: Credit will be given for, at most, MAC 2313 or MAC 3474.) (M) (MR)
MAC 2512 Calculus 2 for Advanced Placement Students
Credits: 4; Prereq: AP 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, which is 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 MAC 2311/2312 sequence. 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)
Credits: 4; Prereq: strong background in precalculus.
The topics covered in the MAC 3472/3473/3474 sequence closely parallel those covered in MAC 2311/2312/2313, but are treated in greater depth. (Note: Credit will be given for, at most, MAC 2311 or MAC 3472.) (M) (MR)
Credits: 4; Prereq: MAC 3472 or MAC 2311 with a minimum grade of C.
A continuation of the honors calculus sequence. (Note: Credit will be given for, at most, one of MAC 2312, MAC 2512 and MAC 3473.) (M) (MR)
Credits: 4; Prereq: MAC 2312, MAC 2512 or MAC 3473 with a minimum grade of C.
A continuation of the honors calculus sequence. (Note: Credit will be given for, at most, MAC 2313 or MAC 3474.) (M) (MR)
Credits: 3; Prereq: MAC 2312, MAC 2512 or MAC 3473 with a minimum grade of C.
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: MAC 2312 or MAC 2512 or MAC 3473, and MAS 3300 or MHF 3202, both with minimum grades of C.
Permutations and combinations, binomial coefficients, inclusion-exclusion, recurrence relations, Fibonacci sequences, generating functions and graph theory. (M)
MAD 4204 Introduction to Combinatorics 2
Credits: 3; Prereq: MAC 2312 or MAC 2512 or MAC 3473, and MAS 3300 or MHF 3202, both with minimum grades of C.
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: MAS 3114 or MAS 4105 with a minimum grade of C and experience with a scientific programming language.
Numerical integration, nonlinear equations, linear and nonlinear systems of equations, differential equations and interpolation.
MAE 3811 Mathematics for Elementary School Teachers 2
Credits: 3. Prereq: College of Education majors only.
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.
MAP 2302 Elementary Differential Equations
Credits: 3; Prereq: MAC 2312, MAC 2512 or MAC 3473 with a minimum grade of C.
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 2483 Mathematical Methods for Natural Sciences
Credits: 4; Prereq: MAC 2311.
Introduction to basic mathematical methods and computer modeling used in the natural sciences, including data representation and analysis, basic statistics and probability, linear algebra, stochastic and deterministic processes and optimization. Theoretical concepts will be integrated with real-life applications and computer medeling projects.
MAP 4102 Probability Theory and Stochastic Processes 2
Credits: 3; Prereq: STA 4321 with a minimum grade of C.
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: MAP 2302, and MAS 3114 or MAS 4105, both with minimum grades of C.
The second course in differential equations. Topics include 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 for, at most, MAP 4305 or MAP 5304.)
MAP 4341 Elements of Partial Differential Equations
Credits: 3; Prereq: MAP 2302 and MAP 4305 with minimum grades of C.
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) and Green's functions. Possible introduction to first-order PDEs and the method of characteristics. (Note: Credit will be given for, at most, MAP 4341 or MAP 5345.)
MAP 4403 Mathematical Methods for Engineers
Credits: 3; Prereq: MAC 2313 or MAC 3474, and MAP 2302, both with minimum grades of C.
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.
Credits: 3; Prereq: MAC 2313 or MAC 3474, and MAP 2302, and MAS 3114 or MAS 4105, all three with minimum grades of C.
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.
MAP 4484 Modeling in Mathematical Biology
Credits: 3; Prereq: MAP 2302, and MAS 3114 or MAS 4105, both with minimum grades of C.
Mathematical models of biological systems. Topics include models of growth, predator-prey populations, competition, the chemostat, epidemics, excitable systems and analytical tools such as linearization, phase-plane analysis, Poincare-Bendixson theory, Lyapunov functions and bifurcation analysis.
Credits: 3; Prereq: MAC 2312, MAC 2512 or MAC 3473 with a minimum grade of C and experience with a scientific programming language.
Linear equations, matrices and determinants. Vector spaces and linear transformations. Inner products and eigenvalues. This course emphasizes computational aspects of linear algebra. (M) (MR)
Credits: 3; Prereq: a UF math course at the 2000 level or above with a minimum grade of C; this requirement is waived for transfer students with junior standing.
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; and elementary theory of equations. Taking one, but not both, of MAS 3300 or MHF 3202 is required of mathematics majors. MAS 3300 is also particularly useful for prospective secondary-school mathematics teachers. (M) (MR)
Credits: 4; Prereq: MAC 2313 or MAC 3474, and MAS 3300 or MHF 3202, both with minimum grades of C.
Linear equations, matrices, vector spaces, linear transformations, determinants, eigenvalues and 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, 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.
Credits: 3; Prereq: MAS 4105 with a minimum grade of C.
Additional topics in linear algebra. (MR)
MAS 4124 Introduction to Numerical Linear Algebra
Credits: 3; Prereq: MAS 3114 or MAS 4105 with a minimum grade of C and experience with a scientific programming language .
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: MAC 2313 or MAC 3474 with a minimum grade of C.
Review of vector algebra, lines, planes and space curves; vector fields, divergence and curl; line, surface, and volume integrals, the Divergence Theorem and Stokes' Theorem. (Note: Credit will be given for, at most, MAS 4156 or MAS 5157.)
Credits: 3; Prereq: MAC 2312, MAC 2512 or MAC 3473 with a minimum grade of C; 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 and primitive roots. Selected applications to decimal fractions, continued fractions, computer file storage and hashing functions, and public-key cryptography. (M)
Credits: 3; Prereq: MAS 3300 or MHF 3202 with a minimum grade of B, or MAS 4105 with a minimum grade of C.
Sets and mappings, groups and subgroups, homomorphisms and isomorphisms, permutations, rings and domains, arithmetic properties of domains, and fields. This course requires facility in writing proofs.
Credits: 3; Prereq: MAS 4301 with a minimum grade of C.
Additional topics in abstract algebra.
Credits: 3; Prereq: MAC 2311 and UFTeach Step 1. Coreq: MAC 2312.
Group activities designed to strengthen knowledge of secondary mathematics, especially topics from precalculus and the transition to calculus, including contexts that can be modeled using linear, exponential, polynomial or trigonometric functions. Topics will include conic sections, parametric equations and polar equations. Explorations will involve multiple representations, transformations and data analysis techniques, and will be facilitated by various technologies.
Credits: 1 to 3; can be repeated with a change in content up to 10 credits. Prereq: MAC 2313 or MAC 3474 with a minimum grade of C and undergraduate coordinator permission.
Special topics not obtainable in regular course offerings.
Credits: 1 to 3; can be repeated with a change in content up to 16 credits. Prereq: undergraduate coordinator permission.
Qualified undergraduates will take part in seminars or classes on special topics.
Credits: 1 to 15; can be repeated with a change in content up to 15 credits. Prereq: undergraduate adviser permission.
This course provides a mechanism by which coursework taken at a foreign university as part of an approved study abroad program can be recorded on the UF transcript and counted toward graduation.
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.
Course is designed for non-science and non-business majors who need to fulfill the writing and math 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)
Credits: 3; Prereq: a UF math course at the 2000 level or above with a minimum grade of C.
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 or 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)
Credits: 3; Prereq: MAS 2312, MAC 2512 or MAC 3473 with a minimum grade of C.
Introduction to the history of selected mathematical topics. (M)
Credits: 3; Prereq: MAS 4105 with a minimum grade of C.
Basic axioms and concepts of set theory. Students present proofs. (Note: Credit will be given for, at most, MHF 4102 or MHF 5107.)
Credits: 3; Prereq: MAS 4105 with a minimum grade of C.
Models and proofs. Foundations of 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, MHF 4203 or MHF 5207.)
Credits: 3; Prereq: MAC 2312, MAC 2512 or MAC 3473 with a minimum grade of C.
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)
Credits: 3; Prereq: MAC 2312, MAC 2512 or MAC 3473 with a minimum grade of C.
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.
Credits: 3; Prereq: MAS 4105 with a minimum grade of C.
Basic concepts of general topology. (Note: Credit will be given for, at most, MTG 4302 or MTG 5316.)
Credits: 3; Prereq: MTG 4302 with a minimum grade of C.
Continuation of the basic concepts of general topology. (Note: Credit will be given for, at most, MTG 4303 or MTG 5317.)