NSU 2014-2015 Undergraduate Catalog

402 Nova Southeastern University • Undergraduate Student Catalog • 2014–2015 COURSE DESCRIPTIONS including generating functions, the principle of inclusion and exclusion, as well as graph theory. Prerequisite: MATH 2200. MATH 3270 Logic (3 credits) Topics covered are syntax and semantics of formal languages; sentential logic, proofs in first order logic; Godel’s completeness theorem; compactness theorem and applications; cardinals and ordinals; the Lowenheim- Skolem-Tarski theorem; Beth’s definability theorem; effectively computable functions; Godel’s incompleteness theorem; undecidable theories. Prerequisite: MATH 2500 MATH 3300 Introductory Linear Algebra (3 credits) This is an elementary linear algebra course. The focus of the course is on the methods in matrix computations and the basic theory of vector spaces. Prerequisite: MATH 2100 or MATH 2100H. MATH 3340 Linear Algebra II (3 credits) This advanced linear algebra (mainly matrix theory) course covers linear vector spaces, inner product spaces, minimal and characteristic polynomials, eigenvalues and eigenvectors, canonical forms of matrices, tensor and Hadamard products, and properties of positive defininte matrices, Hermitian matrices and normal matrices. Prerequisites: MATH 3300 and MATH 2200. MATH 3350 Number Theory (3 credits) This introductory course to Number Theory is open to students with interests in mathematics, science or secondary math education. Topics covered include divisibility, Division (Euclidean) Algorithm, greatest common divisor and least common multiple, prime numbers, Fundamental Theorem of Arithmetic, multiplicative functions, and Chinese Remainder Theorem. Additional topics may be included at the discretion of the instructor. Prerequisite: MATH 2200 or permission of instructor. MATH 3400 Ordinary Differential Equations (3 credits) Topics covered in this course include first-order separable, linear, and nonlinear differential equations, first-order systems, forced second order linear equations, qualitative techniques, bifurcations, numerical methods, linearization, and applications to numerous areas such as biology, chemistry, economics, physics, and social sciences. This course has been exempted from the requirements of the Writing Across the Curriculum policy. Prerequisite: MATH 2200. MATH 3450 Elementary Differential Geometry (3 credits) This course is an introduction to differential geometry which studies the local and global geometric properties of curves, surfaces and higher dimensional mathematical objects. This course will introduce the concept of the curvature for both curves and surfaces in three dimensions. Along with the global properties such as Gauss-Bonnet theorem and fundamental forms, this course will also cover Gauss map, parallel transport and their applications. Prerequisite: MATH 3200. MATH 3900 History of Mathematics (3 credits) Designed primarily for secondary math education majors. Includes from the early development in mathematics to current thinking. Students will gain the perspective that mathematics is the cumulative creation of many people over time. Prerequisite: MATH 2200. MATH 4020 Applied Regression Analysis (3 credits) An applied course in regression analysis discussing simple, multiple regression; exponential and logistic regression; resolution of fit of a model, including, residual analysis; precision of estimate; ANOVA and tests of general hypotheses; model building; step-wise regression; use of indicator variables, and multi co-linearity. Prerequisite: MATH 3030. MATH 4040 Applied Multivariate Statistical Analysis (3 credits) An applied course in multivariate statistical analysis. This includes the study of the multivariate normal distribution and inference about one and several multivariate means. Also, students will study principal components and factor analysis and apply such techniques to real multivariate data. Also, the study of classification and cluster analysis will enable the students to better apply such techniques in marketing research, biological models, and social studies. Prerequisites: MATH 3030 and MATH 3300. MATH 4050 Advanced Calculus I (3 credits) The course is an introduction to the theoretical treatment of the real numbers, sets, functions, sequences, limits and calculus. The course places an emphasis on reading and writing formal mathematical proofs. Topics include: the real number system, convergence of sequence and series, continuity, limits, functions of one real variable, and the theoretical foundations of differentiation and integration of functions of a single variable. Pre-requisite: MATH 3200 MATH 4060 Advanced Calculus II (3 credits) This course is a continuation of Advanced Calculus I providing an introduction to metric spaces and their topology. The course places an emphasis on extending results for real functions to multivariable functions. Topics include: metric spaces and topology, integration, differentiation, optimization and analysis in several variables. Pre-requisite: MATH 4050