Course Descriptions
MAA 4211 - Vector Analysis - 3 credit(s)
Differential and integral calculus of vector fields Topics include vector fields, total derivative of a vector field, Taylor series, linearization, curl and divergence, flows and the transport theorem, line and surface integrals, Gauss' and Stokes' theorems, differential forms, Navier-Stokes equations, applications to fluid flows.
Prerequisite(s): MAC 2313 and MAS 3105 with minimum grade of C
MAA 4226 - Analysis I- 3 credit(s)
Fundamentals of differential and integral calculus, with rigorous development emphasis on those aspects necessary to understand interchange of limits. Topics include sequences of real numbers, limits and continuity, intermediate value property, derivatives, Mean Value Theorem, Riemann integral, sequences and series of functions, uniform convergence, interchange of limit theorems.
Prerequisite(s): MAC 2313 with a minimum grade of C and MHF 2191 with a minimum grade of C
MAA 4227 - Analysis II- 3 credit(s)
Introduction to fundamental concepts of analysis necessary for graduate study in mathematics. Topics include topology of metric spaces, Heine-Borel theorem, sequences and continuity in metric spaces, spaces of functions, introduction to measure and Lebesgue integral.
Prerequisite(s): MAA 4226 with a minimum grade of C
MAA 4402 - Complex Variables - 3 credit(s)
Introduction to the general theory of functions of one complex variable. Topics include algebra of complex numbers, analytic functions, Cauchy-Riemann equations, Taylor and Laurent series, line and contour integral, poles of functions, integration theorems, residues and the Residue Theorem, conformal mappings and Riemann surfaces, Riemann mapping theorem.
Prerequisite(s): MAC 2313 and MAP 2302 with a minimum grade of C
MAC 1105 - College Algebra - 3 credit(s)
General course in techniques of algebraic representation and solution of problems. Topics will include review of properties of exponents and radicals, functions and functional notation, symbolic, graphical, and numerical representation of functions and equations, polynomial, exponential and logarithmic functions, systems of equations and inequalities, matrix representation of linear systems, matrix methods for solving systems of equations.
Prerequisite(s): MAT 1033 with a minimum grade of C or STA 2023 with a minimum grade of C
MAC 1147 - Precalculus - 4 credit(s)
Survey of the basic properties of classes of functions commonly used in applications. Topics may include polynomial, trigonometric, exponential, logarithmic, conic sections, matrices, mathematical induction, and polar coordinates.
Prerequisite(s): MAC 1105 with a minimum grade of C
MAC 2157 - Analytic Geom with Trig - 3 credit(s)
Trigonometry and analytic geometry, with applications. Topics include trigonometric functions, graphs of trig functions, identities, solving triangles, vectors, polar coordinates, conic sections, equations of conics, eccentricity and polar equations, parametric curves. This course is designed to meet teacher certification requirements for middle grades mathematics.
Prerequisite(s): MAC 1105 with a minimum grade of C
MAC 2233 - Elementary Calculus - 3 credit(s)
Introduction to the techniques of calculus of primary use to business students. Topics include: differentiation and integration of algebraic functions with applications, exponential and logarithmic functions with applications to finance and economics. This course is NOT equivalent to MAC 2311.
Prerequisite(s): MAC 1105 with a minimum grade of C
MAC 2311 - Calculus I - 4 credit(s)
Introduction to the primary concepts and techniques of differential and integral calculus. Topics include limits and continuity, the derivative, differentiation and integration of algebraic and trigonometric functions, linearization of functions, Mean Value theorem, antidifferentiation, extrema and curve sketching, area and the definite integral, fundamental theorem.
Prerequisite(s): MAC 1147 or MAC 2157 with a minimum grade of C
MAC 2312 - Calculus II - 4 credit(s)
Continuation of MAC 2311. Topics include integration by substitution, inverse functions, exponential and logarithmic functions, inverse trig functions, solids an surfaces of revolution, arc length, techniques of integration, parametric curves and polar coordinates, power series, Taylor's theorem. Emphasis on conceptual understanding and modeling of physical phenomena.
Prerequisite(s): MAC 2311 with a minimum grade of C
MAC 2313 - Calculus III - 4 credit(s)
Continuation of MAC 2312. Topics include vectors in the plane and 3-space, topics from plane and solid analytic geometry, curves in space, tangential and normal acceleration, directional derivatives and the gradient, tangent and normal to surfaces, extrema of multivariable functions, Lagrange multipliers, double and triple integrals, integration in cylindrical and spherical coordinates. Emphasis on conceptual understanding and modeling of physical phenomena.
Prerequisite(s): MAC 2312 with a minimum grade of C
MAC 2332 - Integrated Math II - 4 credit(s)
Topics in this course include derivatives and antiderivatives, parametric curves, position, velocity, and acceleration, kinematics, slope fields, Euler's method, exponential growth and decay, logarithms, optimization, integration by substitution, introduction to differential equations, general theory of limits and L'Hopital's Rule.
Prerequisite(s): MAC 2331 with a minimum grade of C
MAC 2333 - Integrated Math III - 4 credit(s)
Topics in this course include integration by parts and partial fraction decomposition, linear spaces and linear differential equations, Inverse trig functions and trig substitutions, numerical integration, polar coordinates, power series, series solutions of differential equations, line integrals and work, lengths of curves.
Prerequisite(s): MAC 2332 with a minimum grade of C
MAC 2334 - Integrated Math IV - 4 credit(s)
Among the topics included in this course are curvature, tangent and normal acceleration, functions of several variables, partial differentiation, Picard iteration, tangent plane and differentials, quadratic forms and quadratic surfaces, extrema of functions of two variables, multiple integrals, cylindrical and spherical coordinates, and change of variable in multiple integrals.
Prerequisite(s): MAC 2333 with a minimum grade of C
MAD 3107 - Discrete Mathematics - 3 credit(s)
Introduction to concepts of discrete mathematics, as used by computer scientists. Topics include symbolic logic and Boolean algebra, propositional and predicate calculus, sets, functions, and relations, enumeration and counting principles, introduction to graphs, trees, spanning trees, shortest path and matching algorithms, finite state automata, Turing machines.
Prerequisite(s): MAC 2312 with a minimum grade of C
MAD 4301 - Graph Theory - 3 credit(s)
Introduction to the theory and applications of graphs. Topics include definitions and basic properties, Euler and Hamilton circuits and applications, connectivity, spanning trees and enumeration problems, cycle space and application to networks, matching algorithms and applications, shortest path problems, planar graphs and dual graphs, coloring problems and algorithms network flows, max flow-min cut theorem, Ramsey theory.
Prerequisite(s): MHF 2191 with a minimum grade of C and MAS 3105 with a minimum grade of C
MAD 4401 - Numerical Analysis - 3 credit(s)
Introduction to basic concepts and methods of numerical approximation, with emphasis on error estimates and computer algorithms. Topics include numerical differentiation and integration, solution of initial value problems, interpolation and quadrature, numerical solution of algebraic and transcendental equations, systems of equations, finite differences, introduction to finite element methods.
Prerequisite(s): MAC 2313 with a minimum grade of C
MAD 4504 - Theory of Computation - 3 credit(s)
Mathematical principles of the theory of computation and computer science. Topics include finite and infinite state machines, regular expressions and their recognition automata, pushdown automata, Turing machines, grammars and parsing, recursive functions, decidability and unsolvability, halting problem.
Prerequisite(s): MHF 2191 with a minimum grade of C and MAD 3107 with a minimum grade of C
MAP 2302 - Differential Equations - 3 credit(s)
An introduction to differential equations and their applications, based upon a knowledge of calculus. Topics to include: initial value problems of the first- order, numerical solutions, systems of differential equations, linear differential equations, Laplace transforms, series solutions.
Prerequisite(s): MAC 2312 with a minimum grade of C
MAP 3161 - Mathematics for Science and Engineering - 4 credit(s)
Intermediate theory of linear algebra and differential equations with applications. Topics include: eigenvectors and generalized eigenvectors, invariant subspaces, canonical forms, special matrices: unitary, symmetric, quadratic forms and positive-definite matrices, applications of matrix methods to systems of DE, phase plane and equilibria of linear and nonlinear systems, and Laplace transform. Emphasis is on techniques and applications to modeling and representation of physical systems.
Prerequisite(s): MAC 2313 with a minimum grade of C and MAP 2302 with a minimum grade of C
MAP 3162 - Probability and Statistics - 4 credit(s)
Introduction to mathematical aspects of probability and statistics. Topics include discrete and continuous probability distributions, random variables and their distributions, sums and transformations of random variables, limit theorems, hypothesis testing and confidence intervals, general linear statistical models, regression and ANOVA, nonparametric statistics, introduction to queuing theory.
Prerequisite(s): MAC 2313 with a minimum grade of C and MAS 2121 with a minimum grade of C
MAP 3163 - Operations Research I - 3 credit(s)
Introduction to mathematical aspects of decision science and operations research. Topics include systems of inequalities and linear programming, simplex algorithm, sensitivity analysis, integer programming, branch and bound methods, graph and network models, shortest paths, matchings, network flows, duality theory, introduction to game theory.
Prerequisite(s): MAC 2313 with a minimum grade of C and MAS 3105 with a minimum grade of C
MAP 4101 - Probab & Stochastic Processes - 3 credit(s)
MAP 4101 covers fundamental notions of mathematical theory of probability and probabilistic modeling of random processes. Topics include: expectation, conditional probability and expectation, characteristic functions, central limit theorem, sums of random variables, laws of large numbers, random walks and Poisson processes, Brownian motion, Markov processes, introduction to queuing theory, applications. Students will be expected to develop and write computer simulations as part of the course.
Prerequisite(s): MAP 3162 with a minimum grade of C-
MAP 4231 - Operations Research II - 3 credit(s)
Linear programming, linear program models of problems, integer programming, branch and bound methods, queuing, CPM and PERT, network flows, duality principles in modeling and problem solving, statistical models in OR.
Prerequisite(s): MAP 3163 with a minimum grade of C
MAP 4314 - Dynamical Systems - 3 credit(s)
Topics include discrete dynamical systems: fixed points and stability, bifurcations, classification of equilibria, self-similarity, fractals. Continuous dynamical systems: kneading, bifurcations, attractors, limit cycles and their classification, chaotic behavior.
Prerequisite(s): MAP 3161 with a minimum grade of C
MAP 4341 - Partial Differential Equations - 3 credit(s)
Elements of the classical theory of partial differential equations. Topics include classification of PDEs and boundary value problems, Fourier series and transform, separation of variables, Fourier series solution of wave and heat equations, d'Alembert's solution and change of variables, transform methods, applications.
Prerequisite(s): MAP 3161 with a minimum grade of C
MAS 2121 - Linear Ops & Diff Equations - 4 credit(s)
Elements of linear algebra and linear differential equations. Topics include matrices and matrix operations, Gaussian elimination and LU factorization, determinants, vector spaces, basis, independence, orthogonality and Gram-Schmidt process, linear transformations and matrices, differential operators, eigenvalues and eigenvectors, diagonalization, Markov chains, systems of differential equations, matrix methods for systems of DE, Runge-Kutta methods, Laplace transform.
Prerequisite(s): MAC 2312 with a minimum grade of C
MAS 3105 – Linear Algebra – 3 credit(s)
Introduction to the basic concepts and theorems of linear algebra. Toics include matrices and determinants, matrix operations and canonical factorizations, Gauss-Jordan elimination, vector spaces, linear transformations, basis, independence, orthogonality, eigenvalues and eigenvectors, similarity, Diagonalization, and an introduction to Markov chains.
Prerequisite(s): MAC 2313 with a minimum grade of C
MAS 4106 - Matrix Analysis - 3 credit(s)
Topics include exponential matrices, unitary and positive-definite matrices, QR, polar, and singular value decompositions, matrix norms, perturbation methods for eigenvalues, numerical methods for matrix equations (with error analysis), weighted least squares, Kalman filtering, introduction to Hilbert space.
Prerequisite(s): MAS 3105 with a minimum grade of C and MHF 2191 with a minimum grade of C
MAS 4214 - Elementary Number Theory - 3 credit(s)
Basic principles of algebraic number theory. Topics include divisibility and residues, congruences, primes, pseudoprimes and primality tests, systems of congruences and Chinese remaindering, multiplicative functions, continued fractions.
Prerequisite(s): MHF 2191 with a minimum grade of C
MAS 4301 - Abstract Algebra I - 3 credit(s)
Introduction to fundamental concepts of modern algebra. Topics include group axioms, subgroups, Lagrange's Theorem, homomorphism, quotient groups, permutation and symmetry groups, rings, integral domains and fields, rings of polynomials, field of quotients.
Prerequisite(s): MHF 2191 with a minimum grade of C
MAS 4302 - Abstract Algebra II - 3 credit(s)
Continuation of MAS 4301. Topics include subgroups and Sylow theorems, homomorphisms and quotient groups, ideals in rings, principal ideal domains and Euclidean domains, quotient rings, fields and extension fields. Emphasis is on skills and topics needed for graduate study in mathematics.
Prerequisite(s): MAS 4301 with a minimum grade of C
MAS 4730 – Computational Technology – 2 credit(s)
Training in formulating and solving problems with the aid of a computer algebra system. A wide-ranging selection of exercises will be address with Maple 10 or a similar system.
Prerequisite(s): MAC 2312 with a minimum grade of C.
MAS 5215 - Number Theory - 3 credit(s)
Course will feature an accelerated review of elementary concepts in sufficient detail to support a more intensive study of the classical problems in algebraic number theory. Permission of instructor required.
MAT 1033 - Intermediate Algebra - 3 credit(s)
Reinforcement and development of algebra skills needed for further study in mathematics. Topics include operations with polynomials and rational expressions, radicals, rational exponents, linear and quadratic equations, linear inequalities, systems of equations, functions, and applications. This course does not count toward completion of FGCU general education or Gordon Rule requirements.
MAT 4906 - Independent Study - 1 to 4 credit(s)
Individual study by a student under the direction of an instructor. Topics are selected on an individual basis, and cannot duplicate existing FGCU courses. Credit hours may vary. Students must obtain an access code from the instructor in order to register for the course.
MAT 4930 - Special Topics - 1 to 4 credit(s)
Topics of current or special interest. Topics may vary according to interest and needs of instructor and students. Credit hours may vary. Prerequisites may vary depending on the content of the course; students must consult with instructor before registering.
MAT 4937 - Senior Seminar - 2 credit(s)
Senior capstone course involving a variety of problem-solving activities and/or research projects to provide an integrative experience within the discipline. (Senior Standing)
Prerequisite(s): MAT 4940 - Internship - 1 to 4 credit(s)
MAT 4940 - Internship - 1 to 4 credit(s)
MAT 4940 is a practical application of knowledge in an external setting. Credit hours may vary. Departmental approval required. Grading criteria to be jointly determined by supervising faculty member and supervisor at place of employment.
MAT 5932 - Special Topics Math - 1 to 3 credit(s)
Topics of current or special interest. Topics may vary according to interests and needs of students. May be repeated for credit if topics are substantially different from prior offerings. Permission of instructor required to enroll.
MGF 1106 - Finite Mathematics - 3 credit(s)
A survey course of various topics in mathematics, intended for students pursuing a degree in a nonscientific field. Topics will come from the general areas of combinations, probability and statistics, history of mathematics, geometry, set theory, and logic.
Prerequisite(s): MAT 1033 with a minimum grade of C
MGF 1107 - General Mathematics - 3 credit(s)
A survey course of various topics in mathematics, intended for students pursuing a degree in a nonscientific field. Topics will come from the general areas of financial mathematics, exponential growth, number systems and number theory, history of mathematics, and graph theory.
Prerequisite(s): MAT 1033 with a minimum grade of C
MHF 2191 - Mathematical Foundations - 3 credit(s)
Introduction to axiomatic systems and techniques of proof, in preparation for upper-level study in mathematics. Topics include: symbolic logic, boolean algebra, set theory, countable and uncountable sets, techniques of proof, functions and relations, mathematical induction, group axioms. Emphasis is on preparing the student to read and write mathematical proofs, and to work with abstract definition and axioms.
Prerequisite(s): MAC 2312 with a minimum grade of C
MHF 4400 – Mathematics and Society – 3 credits
Examination of the role of mathematics as a scientific enterprise promoting the advancement of society. Topics included may vary from semester to semester, but will generally focus on the historical influence of mathematics on the development of civilization, the philosophy of mathematics itself, the ethical issues confronting mathematicians, and the unique nature of the profession as a human endeavor.
Prerequisite(s): Senior standing.
MHF 4404 - History of Math - 3 credit(s)
The evolution of mathematical thought and methods from antiquity through the Renaissance. Topics include development of the concepts of number, quantity, and magnitude, algebraic techniques and symbolic notation, solution of polynomial equations, the evolution of the concept of proof, development of numeration systems, history of number theory and congruences, and notions of infinity and infinitesimals. Mathematical ideas and practice in European, African, Mesoamerican, and Asian cultures will be considered.
Prerequisite(s): MAC 2312 with a minimum grade of C
MHF 5405 - History of Math - 3 credit(s)
Development of mathematical concepts of antiquity through the Renaissance, with emphasis on those having the most influence on contemporary mathematical paradigms and practice. Mathematical notions from Western, Mesoamerican, African, Asian cultures will be considered. Students will be expected to complete an independent research project as part of the course requirements. Permission of instructor required.
MTG 3216 - Geom with Lin Algebra - 3 credit(s)
Study of Euclidean and non-Euclidean geometries, utilizing techniques of linear algebra. Topics include overview of synthetic geometry, vectors and matrices, linear transformations and isometries, orthogonality, vector space methods in Euclidean and projective geometry, non-Euclidean geometries, applications to computational geometry and computer graphics.
Prerequisite(s): MAC 2311 with a minimum grade of C
STA 2023 - Statistical Methods - 3 credit(s)
Basic concepts of probability, data collection, organization and presentation, descriptive statistics, parameter estimation for normally distributed r.v., confidence intervals, hypothesis testing (t and chi- square tests) and regression. Emphasis will be on developing conceptual understanding, model selection, and interpretation skills.
Prerequisite(s): (MAT 1033 with a minimum grade of C or MAC 1105 with a minimum grade of C or MGF 1106 with a minimum grade of C or MAC 1147 with a minimum grade of C or MAC 2233 with a minimum grade of C)
STA 2037 - Statistics with Calculus - 3 credit(s)
Calculus-based introduction to statistics. Basic concepts of probability, data collection, organization and presentation, descriptive statistics, random variables and their distributions, parameter estimation, confidence intervals, hypothesis testing (t and chi-square tests). Emphasis will be on developing conceptual understanding, model selection, and interpretation skills.
Prerequisite(s): MAC 2311 with a minimum grade of C
STA 2122 - Social Science Statistics - 3 credit(s)
Intermediate course covering applied statistical analysis including analysis of variance, probability theory, correlation, non-parametric, and regression methods.
Prerequisite(s): PSY 2012 with a minimum grade of C and STA 2023 with a minimum grade of C
STA 4234 - Intro. to Regression Analysis - 3 credit(s)
Study of theory and applications of regression analysis. Topics include: general linear model, parameter estimation, residual analysis, polynomial and logarithmic regression, model identification, applications to biological and social sciences.
Prerequisite(s): MAP 3162 with a minimum grade of C
