## Mathematical Sciences

## Undergraduate Courses

**MTH 0111 INTERMEDIATE ALGEBRA** (3 credits). Basic operations on real numbers, algebraic expressions, linear equations, inequalities, exponents, polynomials, factoring, rational functions, roots, radicals, quadratic equations and quadratic functions. Credit cannot be applied toward any Florida Tech degree.

**MTH 1000 PRECALCULUS** (4 credits). Algebra and trigonometry that are used to develop the skills needed in calculus. Required for students who have minimal algebra and/or trigonometry preparation, or whose placement test indicated such a need. (Requirement: Passing score on placement exam or prerequisite course.) Prerequisites: MTH 0111 or MTH 0111.

**MTH 1001 CALCULUS 1** (4 credits). Functions and graphs, limits and continuity, derivatives of algebraic and trigonometric functions, chain rule; applications to maxima and minima, and to related rates. Exponential logarithmic, circular and hyperbolic functions: their inverses, derivatives and integrals. (Requirement: High school algebra and trigonometry, and a passing score on the placement test, or prerequisite course.) Prerequisites: MTH 1000.

**MTH 1002 CALCULUS 2** (4 credits). Integration and applications of integra¬tion, further techniques of integration, improper integrals, limits, l’Hospital’s rule, sequences and series, numerical methods, polar coordinates and introductory dif¬ferential equations. Prerequisites: MTH 1001.

**MTH 1603 APPLIED CALCULUS AND STATISTICS** (3 credits). Includes derivatives and integrals, and their applications, and probability and statistics, and their applications. Credit cannot be applied toward any Florida Tech degree that requires MTH 1001. Prerequisites: MTH 1000.

**MTH 1701 COLLEGE ALGEBRA** (3 credits). Real-number system; arithmetic operations with polynomials, special products and factoring; linear, fractional and quadratic equations; inequalities, exponents, radicals and absolute values; functions and graphs; and complex numbers, logarithms, logarithmic and exponential functions. Credit can only be applied toward business, communication, humanities, management, psychology or computer information systems degrees at Florida Tech. (Requirement: Passing score on placement exam or prerequisite course.) Prerequisites: MTH 0111

**MTH 1702 APPLIED CALCULUS** (3 credits). Elements of differential and integral calculus with application to business, economics, management and the social and life sciences, as well as maxima, minima, rates, exponential growth and decay, and some techniques of integration. Prerequisites: MTH 1000 or MTH 1701.

**MTH 1801 TRIGONOMETRY REVIEW** (1 credit). Reviews trigonometric topics necessary for calculus, including trigonometric functions, graphs, identities and solving trigonometric equations. May be taken with MTH 1001. (Requirement: High school trigonometry and appropriate score on placement test.)

**MTH 2001 CALCULUS 3** (4 credits). Cylindrical and spherical coordinates, vectors, functions of several variables, partial derivatives and extrema, multiple integral, vector integral calculus. Prerequisites: MTH 1002.

**MTH 2051 DISCRETE MATHEMATICS** (3 credits). Formulation of precise definitions and their negations using propositional and predicate logic; argument analysis and proof techniques including induction; number theory; and sets, relations, functions, directed graphs and elementary counting arguments. (Requirement: Passing score on placement test or prerequisite course.) Prerequisites: MTH 1000 or MTH 1001 or MTH 1702.

**MTH 2201 DIFFERENTIAL EQUATIONS/LINEAR ALGEBRA** (4 credits). First-order differential equations, linear differential equations with constant coefficients, first-order systems of differential equations with constant coefficients, numerical methods, Laplace transforms, series solutions, algebraic systems of equations, matrices, determinants, vector spaces, eigenvalues and eigenvectors. Prerequisites: MTH 1002.

**MTH 2202 LINEAR ALGEBRA FOR DIFFERENTIAL EQUATIONS** (1 credit). Includes systems of equations, matrices, determinants, vector spaces, eigenvalues, and eigenvectors. Supplements differential equations. (Requirement: Instructor approval.) Prerequisites: MTH 1002.

**MTH 2332 PRIMER FOR BIOMATH** (1 credit). Introduces the separate languages of mathematics and biology such that students from the different disciplines can efficiently develop a biomath glossary to communicate with one another. Focuses on the current research projects in biology and ecology, and the relevant mathematical analysis. (Requirement: Instructor approval.) Prerequisites: MTH 1000.

**MTH 2401 PROBABILITY AND STATISTICS** (3 credits). Random variables, expectations, sampling and estimation of parameters, normal and other distributions and central-limit theorem, tests of hypothesis, linear regression and design experiments. Prerequisites: MTH 1002.

**MTH 3051 COMBINATORICS AND GRAPH THEORY** (3 credits). Elementary and advanced counting techniques including permutations, combinations, multisets, inclusion-exclusion, generating functions, recurrence relations and topics in graph theory including graphs, trees, binary tree, graph traversals and network flow. Prerequisites: MTH 1001, MTH 2051.

**MTH 3101 COMPLEX VARIABLES** (3 credits). Algebra of complex numbers, elementary analytic functions, complex integration, series representations for analytic functions, residue theory and conformal mapping and its applications. Prerequisites: MTH 2001.

**MTH 3102 INTRODUCTION TO LINEAR ALGEBRA** (3 credits). Includes vectors and matrices, linear equations, vector spaces and subspaces, orthogonality, determinants, eigenvalues and eigenvectors, and linear transformations. Introduces students to solution and manipulation of matrix equations using a standard package of mathematical software. Prerequisites: MTH 1002.

**MTH 3210 INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS** (3 credits).Inclueds heat, wave and Laplace equations, initial and boundary value problems of mathematical physics and Fourier series. Also covers Dirichlet problem and potential theory, Dalambert’s solutions for wave equation, Fourier and Laplace transforms, and Poisson integral formula. Also includes PDEs in higher dimensions and special functions of mathematical physics. Prerequisites: MTH 2001, MTH 2201.

**MTH 3301 FINITE DIFFERENCES AND FINITE ELEMENTS** (3 credits). Numerical methods for BVPs in one and two dimensions; finite difference methods for solving PDEs, finite element methods, variational formulation and Galerkin approximations for ODEs and two-dimensional PDEs, and writing programs. Prerequisites: CSE 1502 or CSE 1503 or CSE 2050, MTH 3201.

**MTH 3311 APPLIED NUMERICAL METHODS** (3 credits). Numerical methods, use and modification of existing software and computer arithmetic, linear systems of equations, interpolation, numeric quadrature, linear least-squares data fitting, eigenvalues, solutions of nonlinear equations. Prerequisites: CSE 1502 or CSE 1503 or CSE 2050, MTH 1002.

**MTH 3663 MATHEMATICAL METHODS FOR BIOLOGY AND ECOLOGY** (3 credits). Examines biological processes and mathematically reformu¬lates the biological information into linear and nonlinear systems, and differential equations, and studies these formulations via matrix algebra, numerical techniques, approximation theory, stability and bifurcation analysis. (Requirement: Junior standing and instructor approval.) Prerequisites: BIO 2332 or MTH 2332, MTH 1002.

**MTH 3993 SELECTED TOPICS ON BIOSTOCHASTICS** (3 credits). Studies the influence of stochasticity on biological processes using statistical methods and Markov processes to analyze vital biological rates, including mutation rates for disease-associated DNA repeats, organismal growth and per-capita survival. (Requirement: Instructor approval.) Prerequisites: MTH 1002, BIO 2332 or MTH 2332.

**MTH 4051 ABSTRACT ALGEBRA** (3 credits). Groups, cyclic groups, permutation groups, isomorphisms, cosets and Lagrange’s theorem, rings, integral domains, vector spaces, and fields. Prerequisites: MTH 3102.

**MTH 4082 INTRODUCTION TO PARALLEL PROCESSING** (3 credits). Introduces parallel algorithm development, architectures for parallel computers, programming paradigms SIMD and MIMD for shared and distributed memory computers. Presents parallel algorithms for matrix computations, sorting and searching, and various numerical algorithms. Includes analysis of performance of parallel algorithms and scalability of algorithms. (Requirement: Programming ability in FORTRAN or C.) Prerequisites: CSE 1502 or CSE 1503 or CSE 2010 or CSE 2050.

**MTH 4101 INTRODUCTORY ANALYSIS** (3 credits). Rigorous treatment of calculus. Includes sequences and series of real numbers, limits of functions, topology of the real line, continuous functions, uniform continuity, differentiation, Riemann integration, sequences and series of functions, Taylor’s theorem; uniform convergence and Fourier series. Prerequisites: MTH 2001 or MTH 2201.

**MTH 4105 TOPOLOGY** (3 credits). Metric and topological spaces, continuity, homeomorphism connectedness, compact spaces, separation axioms, product spaces, homeotypic and fundamental group. Prerequisites: MTH 2051, MTH 3102.

**MTH 4201 MODELS IN APPLIED MATHEMATICS** (3 credits). Allows students to formulate and construct mathematical models that are useful in engineering, physical sciences, biological sciences, environmental studies and social sciences. (Requirement: Junior standing.) Prerequisites: MTH 2201.

**MTH 4311 NUMERICAL ANALYSIS** (3 credits). Introduces numerical methods for solving equations in one variable, polynomial approximation, interpola¬tion, numerical differentiation and integration, initial-value problems for ODE and direct methods for solving linear systems. Prerequisites: CSE 1502 or CSE 1503 or CSE 2050, MTH 2201.

**MTH 4320 NEURAL NETWORKS** (3 credits). Includes basic existence theory, differential and integral inequalities, qualitative and quantitative theory, and Lyapunov’s second method. Prerequisites: CSE 1502 or CSE 1503 or CSE 2050, MTH 2201.

**MTH 4801 ADVANCED GEOMETRY** (3 credits). Topics in Euclidean and non-Euclidean geometry with an emphasis on proofs and critical thinking. Satisfies the state of Florida requirement for teacher certification in mathematics. (Requirement: Instructor approval or prerequisite course.) Prerequisites: MTH 2001.

**MTH 4920 SPECIAL TOPICS IN APPLIED MATHEMATICS** (3 credits). Selected topics from mathematics. Content varies from year to year depending on the needs and interests of the students and expertise of the instructor. (Requirement: Instructor approval.)

**MTH 4990 UNDERGRADUATE RESEARCH** (3 credits). Participation in a research project under the direction of a faculty member. (Requirement: Instructor approval.) (Q)