NSU 2014-2015 Undergraduate Catalog

403 Nova Southeastern University • Undergraduate Student Catalog • 2014–2015 COURSE DESCRIPTIONS MATH 4080 Introduction to Statistical Computations (3 credits) This class gives the students the opportunity to learn writing codes for performing statistical analysis and data manipulation including writing their own functions or macros in one of the high level programming languages. Students will have a better hand on one/more statistical programming language(s) so as to carry out statistical analysis. Students will be prepared to handle and manipulate different types of data files and write their own functions (macros) to perform specific procedures. Prerequisites: MATH 3030 and MATH 3300. MATH 4100 Introduction to Topology (3 credits) This course is an introduction to topology and elements of algebraic topology, including metric spaces, continuity, compactness, topological spaces, separation axioms, product spaces, subspaces, quotient spaces, connectedness, and the fundamental group. Prerequisite: MATH 2200. MATH 4200 Complex Variables (3 credits) This is a first course in complex variables. Topics covered in this course include the origin, algebra, topology and geometry of complex numbers, the mappings, continuity, branches, and transformations of analytic and harmonic functions, and the computation of contour integrals. Prerequisite: MATH 3200. MATH 4300 Numerical Methods (3 credits) This is an introductory survey course to standard numerical methods, the mathematical ideas behind them and their use in obtaining numerical solutions. Topics include polynomial interpolation, numerical integration and differentiation, numerical solution of nonlinear equations and ordinary differential equations. Prerequisite: MATH 2200. MATH 4350 Abstract Algebra I (3 credits) This course is an introduction to the concepts of groups and rings from modern abstract algebra. Group theoretic topics include: modular arithmetic, groups, cyclic groups, permutation groups, normal groups, factor groups, group homomorphism and isomorphism, cosets, Lagrane’s theorem, and external (internal) direct products. Ring theoretic topics include: rings, integral domain, ideals, factor rings, ring homomorphism and isomorphism, factorizations, divisibility, and fields. Prerequisites: MATH 3300 and either MATH 2500 or CSIS 2050. MATH 4360 Abstract Algebra II (3 credits) This course, which is a continuation of Math 4350, further develops the theory of groups and rings and introduces the concept of field theory. Group theoretic topics include: group theory, Sylow’s theorem, symmetric groups, Burnsie’s theorem. Ring theoretic topics include: ring theory, polynomial rings, factorizations, and divisibility. Field theoretic topics include: extension fields, algebraic extension, finite fields, and Galois theory. Prerequisite: MATH 4350. MATH 4400 Partial Differential Equations (3 credits) Introduction to second-order linear partial differential equations (heat, wave and Laplace equations), separation of variables, Sturm-Liouville eigenvalue problems, method of eigenfunction expansions (Fourier analysis), and Green’s functions. Possible introduction to first-order PDEs, the method of characteristics, and non-linear PDE as time permits. Prerequisites: MATH 3200 and MATH 3400. MATH 4450 Basic Probability (3 credits) Probability spaces, discrete and continuous distributions, conditional probability space, effect on distributions by linear, and non-linear functions of one and two random variables, moments, characteristic functions, vectors and sequences of one and two random variables, laws of large numbers, central limit theorem, special probability laws. Prerequisite: MATH 2200. MATH 4500 Probability and Statistics (3 credits) Probability functions, random events, expectation, conditional probability distribution functions, and foundations of statistics. Prerequisite: MATH 2200. MATH 4600 Introduction to Applied Mathematics (3 credits) This course provides an introduction to the methods of applied Mathematics. Topics include the spectral theory of vector and function spaces, orthogonal functions, series expansion, differential operators, Green’s functions, complex variables including derivatives and integrals, laurent series, special functions, and transforms. Prerequisites: MATH 3200 and MATH 3300. MATH 4700 Applied Cryptography (3 credits) This is an introductory course to applied cryptography. Symmetric-key cryptography topics include stream ciphers, block-ciphers, permutations, groups and Galois fields. Public-key cryptography topics include factorization, discrete logarithm problem, and elliptic curves. Prerequisite: MATH 4350 MATH 4900 Special Topics in Mathematics (3 credits) The Special Topics in Mathematics course presents mathematical topics that are not covered in any of our current courses. Course contents and schedule are announced in the course syllabus. Prerequisites: Junior standing. Specific course content and prerequisites are announced in the course schedule for the given term.