# Math Courses

## Math Courses @ FAMU

List of undergraduate and graduate level math courses offered at Florida A&M University.

#### 1000 Level Courses (6)

MAC 1105  College Algebra (3 hrs)
Topics: functions and functional notation, domains and ranges of functions, graphs of functions and relations, operations on functions, inverse functions, linear, quadratic and rational functions, absolute value and radical functions, algebraic techniques, linear and quadratic equations, functions, and inequalities, complex numbers, logarithms and exponential properties, systems of equations and inequalities, combinations and Binomial Theorem.

MAC 1114  Algebra and Trigonometry (3 hrs)
Prereq: MAC 1105
Topics: trigonometric functions, properties, graphs, inverse trigonometric functions, properties, graphs, trigonometric identities, conditional trigonometric equations, solutions to triangles, vector algebra, parametric equations, polar coordinates.

MAC 1147  Pre-Calculus Mathematics (3 hrs)
Prereq: Trigonometry (high-school) and MAC 1105
Topics: polynomial, rational, and other algebraic functions, their properties and graphs, polynomial and; rational inequalities, exponential and morganatic functions , their properties and graphs, conic sections, Binomial Theorem, trigonometric functions, their properties and graphs, inverse trigonometric functions, their properties and graphs, trigonometric identities, conditional trigonometric equations, solutions of triangles, vector algebra, parametric equations, polar coordinates, applications.

MAT 1033  Intermediate Algebra (3 hrs – elective credit)
Topics: polynomial, rational, and other algebraic functions, their properties and graphs, polynomial and; rational inequalities, exponential and morganatic functions

MGF 1118  Selected Topics in College Mathematics (1 hr – elective credit)
Topics: symbolic logic and analysis of valid reasoning; informal geometry, elementary probability and statistics; algebra review (individualized). This course is designed primarily for CLAST preparation of students who have not taken MGF 1108 or MAD 2120 or MGF 1107.

MGF 1106  Liberal Arts Mathematics I (3 hrs)
Topics: systematic counting, probability, statistics, history of mathematics, sets, geometry, logic.

MGF 1107  Liberal Arts Mathematics II (3 hrs)
Topics: financial mathematics, linear and exponential growth, numbers and number systems, history of mathematics, elementary number theory, voting techniques, graph theory.

#### 2000 Level Courses (8)

MAC 2233  Business Calculus  (3 hrs)
Prereq: MAC 1105
Topics: limits, continuity, differential techniques of logarithmic and exponential functions, application of derivatives, curve sketching; integration and applications.

MAC 2311  Calculus with Analytic Geometry I (4 hrs)
Prereq: MAC 1147 or the combination of MAC 1114 and MAC 1105.
Topics: limits; continuity; differentiation techniques; introduction to integration; curve sketching; areas between curves; theory augmented by applications from a variety of disciplines.

MAC 2312  Calculus with Analytic Geometry II (4 hrs)
Prereq: MAC 2311
Topics: techniques of integration, approximate integration and Simpson's Rule, application of the integral to volumes, moments, centroids, etc., conic sections, parametric equations and polar coordinates, infinite series.

MAC 2313  Calculus with Analytic Geometry III (5 hrs)
Prereq: MAC 2312
Topics: solid analytic geometry, vectors in 3-space, partial derivatives and applications, multiple integrals, line and surface integrals, topics from plane solid analytic geometry, directional derivatives and curvature, differential calculus of functions of several variables.

MAD 2120 Finite Mathematics (3 hrs)
Topics: matrix operations; systems of linear equations and inequalities; linear programming and the simplex method; symbolic logic; probability theory; counting techniques; elementary graph theory; descriptive statistics.

MAP 2302  Differential Equations (3 hrs)
Prereq: MAC 2313
Topics: methods of solutions of ordinary differential equations, linear equations and systems of linear equations, separation of variables, integrating factors, linear differential equations, undetermined coefficients, variation of parameters, solution by series, Laplace transform, successive approximation and applications, boundary value problems.

MTG 2206  College Geometry (3 hrs)
Prereq: MAC 1105
Topics: emphasizes Euclidean geometry and its relationship to logic, trigonometry, and coordinate geometry, the problems proofs, constructions, and graphs involve line segments, angles, triangles and polygons, parallel and perpendicular lines, slope of lines, circles, and similarity, presented in terms of right triangle relationships, logic is the basis for deductive reasoning in proofs of theorems, lines and other geometric figures are graphed in the rectangular coordinate system.

STA 2023  Probability and Statistics (3 hrs)
Prereq: MAC 1105
Topics: probability theory; random variables; hypothesis test ing; confidence intervals; small sample methods; correlation; simple linear regression, nonparametric statistics.

#### 3000 Level Courses (7)

MAD 3401  Numerical Analysis (3 hrs)
Prereq: MAC 2313
Topics: solutions to scalar nonlinear and finite difference equations; numerical differentiation and integration; numerical solution of initial values problems for ordinary differential equations, error and convergence; general interpolation problems, interpolation and quadrature, numerical solutions of algebraic and transcendental equations.

MAP 3130  Difference Operators (3 hrs)
Prereq: MAC 1105 and MAD 2120
Topics: difference operators, introduction to difference equations, linear difference equations with constant coefficients, examples from social sciences, Z–transforms, Cobweb cycles, generating functions, matrix methods.

MAP 3305  Engineering Mathematics I (3 hrs)
Prereq: MAC 2313
Topics: linear algebra, determinants, matrices, eigenvalues, and eigenvectors. Ordinary differential equations, including systems of first-order equations.

MAP 3306  Engineering Mathematics II  (3 hrs)
Prereq: MAC 1105
Topics: vector calculus, solution of partial differential equations by separation of variables, Sturm-Louisville problems, Fourier series, complex numbers, Cartesian tenors.

MAP 3341  Partial Differential Equations (3 hrs)
Prereq: MAP 2302
Topics: solution of first-order partial differential equations, classification of linear second-order partial differential equations, separation of variables, initial value and initial boundary value problems.

MAS 3105  Linear Algebra  (3 hrs)
Prereq: MAC 2313
Topics: Major topics: investigation of systems of linear equations, matrices, vector spaces, linear transformations, determinants, eigenvalues, inner product spaces.

STA 3034  Mathematical Statistics  (3 hrs)
Prereq: MAC 2311
Topics: probability, random variables, hypothesis testing, estimation.

#### 4000 Level Courses (14)

MAA 4211  Advanced Calculus I  (3 hrs)
Prereq: MAC 2313
Topics: real number system, functions, sequences, limits and continuity, fundamental theorems and bounded sequences, Cauchy criterion, point sets, open, closed, compact and connected sets, derivatives, Rolle’s Theorem, law of mean, Hospital’s Rules and intermediate forms.

MAA 4212  Advanced Calculus II  (3 hrs)
Prereq: MAA 4211
Topics: Riemann integral, fundamental theorem of integral calculus, infinite series, power series, uniform convergence, functions of several variables, partial differentiation, multiple integrals, improper integrals, Fourier series and orthogonal functions.

MAA 4402  Complex Variables (3 hrs)
Prereq: MAC 2313
Topics: Complex num bers; functions; continuity; derivatives; elementary functions; line and con tour integrals; Cauchy formula; representation by power series and classification of singularities.

MAD 4203  Combinatorial Analysis (3 hrs)
Prereq: MAC 2313
Topics: permutations and combinations, binomial coefficients, inclusion-exclusion, linear recurrence relations, generating functions, block designs, difference sets, existence and non-existence theorems, systems of distinct representatives, introduction to graphs.

MAE 4360  Methods of Teaching Middle and Secondary Mathematics (4 hrs)
Prereq: MAC 2313
Topics: Curriculum materials and methods used in teach ing in middle and secondary schools.

MAP 4103  Mathematical Modeling (3 hrs)
Prereq: MAP 2302
Topics: mathematical models of problems in the social, life, physical, and/or management sciences, methods of solution including Laplace transforms, Fourier Series, calculus of variations, and other techniques for solving differential equations.

MAS 4301  Abstract Algebra I  (3 hrs)
Prereq: MAS 3105
Topics: groups, subgroups, homomorphism theorems, rings, integral domains and quotient fields, quotient groups, polynomial rings, ideals, quotient rings, subrings,  extension fields and finite fields.

MAS 4203  Introduction to Number Theory (3 hrs)
Prereq: MAC 2312
Topics: mathematical induction; linear Diophantine equa tions and congruence, Chinese Remainder theorem, theorems of Euler, Fermat, and Wilson, divisibility and divisibility tests, greatest common divisor, division and Euclidean algorithms, primes, number-theoretic functions.

MAT 4906  Directed Individual Study  (1 – 6 hrs)
Prereq: Consent of Mathematics Chairperson.
Topics: Independent study or research under supervision of faculty member in various topics.

MHF 4202  Foundations of Mathematics (3 hrs)
Prereq: MAC 1105
Topics: sets, operations on sets, set algebra, Venn diagrams, truth tables, tautologies, applications to mathematical arguments, general techniques of mathematical induction.

MTG 4212  Modern Pure Geometry (3 hrs)
Prereq: MAC 2313
Topics: fundamental concepts of Euclidean Geometry treated in specialization of projective geometry. Postulate of projectivity, Quadrangles, Theorems of Desargues, Pappus and Pascal. Harmonic sets, postulates of separation, matrices, cross ratio, affine and homothetic transformations, Non-Euclidean geometry (Geometry of Bolyai-Lobachevsky).

MTG 4302  Elementary Topology (3 hrs)
Prereq: MAC 2313
Topics: topological spaces and properties, compactness, metric spaces and continuous functions; general topological spaces, the topological spaces and topological properties. Hausdorff spaces; connectedness.

STA 4202  Design and Analysis of Experiments I (3 hrs)
Prereq: STA 3034, MAS 3105 preferred
Topics: analysis of variance, blocking, factorial experiment, incomplete blocks, multiple comparisons, confounding, variance components.

STA 4603  Mathematical Techniques of Operations Research  (3 hrs)
Prereq: MAC STA 3034 and MAS 3105
Topics: inventory theory, dynamic programming, queuing theory, network analysis, Markov chains, computer simulation.

#### 5000 Level Courses (12)

MAP 5345 Partial Differential Equations  (3 hrs)
Prereq: MAC 2313
Topics: solutions of first-order, quasi-linear partial differential equations, classification and reduction of normal form of linear second-order equations, separation of variables, Sturm-Louisville problems, Fourier series, Fourier integral, Fourier transforms, applications to initial value and initial boundary value problems

MAS 5145 Linear Algebra (3 hrs)
Prereq: MAS 3105
Topics: review of linear algebra, applications of matrices, practical methods of matrix computation, computations using Guassian elimination, Fredholm alternative, choice of pivots, modified systems, unitary transformations and applications, eigenspaces, Schur, QR, and singular value decomposition, similarity transformations, defective matrices, Jordan form, iterative solutions, norms of matrices, quadratic forms and variational principles.

MAS 5204 Number Theory (3 hrs)
Prereq: MAC 2313
Topics: mathematical induction, linear Diophantine equations and congruences, Chinese remainder theorem, Euler-Fermat theorems, quadratic reciprocity law.

MAS 5311 Algebraic Structures  (3 hrs)
Prereq: MAS 4301
Topics: groups, direct products, linear algebras, rings, fields extensions of rings and fields, Galois theory

MAS 5317 Structures of the Real Number System  (3 hrs)
Prereq: MAC 2313
Topics: concepts in set theory, relations and their properties, evaluation of numeration systems, integers, rational and irrational numbers, the field of real numbers, introduction to the theory of matrices.

MAS 5328 Group Theory in the Physical Sciences (3 hrs)

MAT 5907 Directed Individual Study  (1 – 6 hrs)
Prereq: Consent of Mathematics Chairperson.
Topics: Independent study or research under supervision of faculty member in various topics.

MAT 5932 Topics in Mathematics  (3 hrs)
Topics: Course centers around current interest or of special interest to students or instructors. Topics or focus vary.

MAT 5939 Seminar in Mathematics  (3 hrs)
Topics: Course centers around current interest or of special interest to students or instructors. Topics or focus vary.

MHF 5206  Structures and Concepts of Arithmetic  (3 hrs)
Prereq: MAC 2313
Topics: Zermelo-Frankel axioms for set theory, finite and infinite sets, ordinal numbers, cardinal numbers, the Axiom of Choice and some of its equivalents.

MTG 5220 Logic and Geometry (3 hrs)
Prereq: MAC 2313
Topics: foundations of mathematical logic and geometry, sentential logic, survey of fundamental concepts of non-metric geometry, metric geometry in development of geometry as a mathematical system.

STA 5155  Liberal Statistical Inference  (3 hrs)
Prereq: STA 3034
Topics: nature and importance of statistics, descriptive statistics, probability theory and sampling distribution, experimental designs and data analysis, introduction to matrix algebra, regression analysis, introduction to times series analysis.