Catalog 73 - National University

Course Descriptionscomputer science prerequisites. Graphing calculatoris required.MTH 216A: College Algebra I (3 quarter units)(Prerequisite: Placement Evaluation)The first part of a comprehensive two-month treatmentof algebra and trigonometry preliminary tomore specialized study in mathematics. The courseis a continuation of intermediate algebra and covershigher degree polynomials, rational functions, transformationsand the algebra of function, matrix algebraand basic arithmetic of complex numbers.MTH 216B: College Algebra II (3 quarter units)(Prerequisite: Placement Evaluation)The second month of a comprehensive two-monthtreatment of algebra and trigonometry; this course isa continuation of MTH 216A. Topics include trigonometricfunctions, analytic trigonometry and application,parametric equations, matrix algebra,sequences and series; and applied problems.Graphing calculator is required.MTH 220: Calculus I(Cross listed and equivalent to CSC208)(Prerequisite: MTH 215, or placement evaluation)An introduction to limits and continuity. Examinesdifferentiation and integration concepts with applicationsto related rates, curve sketching, engineeringoptimization problems, and business applications.Students may not receive credit for both MTH220and CSC208.MTH 221: Calculus II(Prerequisite: MTH 220)A discussion of differentiation and integration conceptsof the natural logarithm, exponential andinverse trigonometric functions and applications tovolumes of revolution, work and arc length. Coversimproper integrals and highlights ideas and contributionsof Natpier, Huygens and Pascal. Graphingcalculator is required.MTH 222: Calculus III(Prerequisite: MTH 221)A study of sequences, Taylor Polynomials, infiniteseries, and tests for convergence, and the powerseries. An overview of ordinary differential equations;the initial-value Problem; exactness and integratingfactors; and Bernoulli and higher-orderequations with forcing functions.MTH 223: Calculus IV(Prerequisite: MTH 222)A study of functions of several variables: extremaand Lagrange Multipliers, with application totoday’s optimization-problems in engineering, business,and ecology. Vector algebra and space geometry;Kepler's Laws with application to satelliteorbital velocity problems and the rendezvous phenomenon,iterated integrals and applications, theJacobian transformation will be studied.MTH 301: Fundamentals of Mathematics II(Prerequisite: MTH 209A)This continuation of MTH 209A includes concepts ofmeasurement, geometry, probability and statistics,elementary synthetic and Euclidean Geometry.Methods are incorporated whenever possible.However, both MTH 209A and MTH 301 are content/conceptcourses as prescribed by State regulations,not methods courses.MTH 304: Math Practicum and Portfolio(Prerequisites: MTH 215 or MTH 216 A and B orPlacement Evaluation)*Should be taken as early as possible in the student’sprogram. Students observe and reflect on the actualwork of public secondary school mathematics teachers(at least 28 hours in pubic middle or secondaryschool mathematics classrooms and at least 3.5hours of student activities and administrative meetings).Grading is by S or U only.MTH 311: Topics from Geometry(Prerequisites: MTH 215, MTH 216A/B or placementevaluation)A survey of main concepts of Euclidean geometrywith the emphasis on the axiomatic approach, constructions,logic of proof, and some ideas from non-Euclidean geometry including historical aspects. Astudy of axioms of Euclidean Geometry, inferencerule, some basic theorems of Euclidean Geometry,and rigorous proofs will be offered.MTH 317: Mathematical Modeling(Prerequisites: MTH 215 or MTH 216A/B and MTH210)An introductory to mathematical modeling, utilizinga variety of diverse applications from physical, biological,business, social, and computer sciences.Discuss the limitations, as well as the capabilities, ofmathematics as applied to understanding of ourworld. Teaches problem identification, models ofsolutions and model implementation.MTH 325: Discrete Mathematics(Cross listed and equivalent to CSC331)(Prerequisites: MTH 215 or MTH 216A/B or placementevaluation)This course studies combinatory and graph theoryas the theoretical foundation for today’s advancedtechnology. It analyzes algorithms, logic, circuits,number bases, and proofs. Ample applications(graphs, counting problems, Turing Machines,codes) examine the ideas of Euler, Boole, Floyd,Warshall, Dijkstra, Church and Turing, Shannon,Bernoulli. Students may not receive credit for bothMTH325 and CSC331.MTH 410: Technology in Math Education(Prerequisite: MTH 215 or MTH 216A/B or MTH 301)An overview of the computer-based technology inthe mathematics classroom. Evaluates graphing calculators,and computer software such as Maple,Scientific Workplace, Geometer’s Sketchpad,MiniTab, SPSS, and others to determine their valuein illuminating concepts in the curriculum.MTH 411: Number Theory(Prerequisite: MTH 215 or MTH 216A/B or MTH 209Aor placement evaluation)An examination of fundamental concepts of numbers,including divisibility, congruencies, the distributionof Primes, Pythagorean triples, the EuclideanAlgorithm, the Fundamental Theorem of Arithmetic,Diophantine equations and Goldbach's conjecture.Emphasis active student involvement in posing andtesting conjectures, formulating counter examples,logical arguments, and proofs.MTH 412: History of Mathematics(Prerequisites: MTH 215, MTH 216A/B, or MTH 301)Examines currents in the development of mathematicsand throughout ancient Egypt, Babylon, China,and the Middle East. It studies math's influence onsociety through the major events of Europe, contemporarydevelopments, and some projections into thefuture, including the women and men who playedkey roles in evolution of mathematics.MTH 416: Algebraic Structures(Prerequisite: MTH 325 and MTH 435)A look at groups, rings and fields, as well as applicationsof these systems. Discusses equivalence relations,Lagrange’s Theorem, homomorphisms, isomorphisms,Cayley’s Theorem and quaternions.Also examines error correcting codes and issues ofcryptography. Graphing calculator may be required.MTH 417: Foundations of Geometry(Prerequisites: MTH 215 or MTH 216A/B and MTH311)A discussion of fundamental ideas and processescommon to Euclidean and Non-Euclidean geometries:projective, affine and metric geometry.Examines the interplay between inductive anddeductive reasoning, and formal and informal proof.Addresses uses in science (transformations, scaling),art (Escher-type tessellations, projections), architecture(three-dimensional figures), and computer science(fractals, computer-aided design).MTH 418: Statistical Analysis(Prerequisites: MTH 210 and MTH 220)An examination of statistical applications to business,computer science, psychology, education, socialsciences, and mathematics with fundamental conceptsof probability distribution, mathematical modelsrelating independent and dependent randomvariables, hypothesis testing and experimentaldesign. Includes fundamental analysis of variance,various distributions and methods of regression,analysis and scaling.MTH 432: Advanced Calculus(Prerequisite: MTH 223)A look at sets, functions, and the real numbers.Topics include the Completeness axiom, cardinality,and Cantor's theorem, Limsup, and Liminf; thetopology of R1 and R2, open sets, limit points, compactnessand the Heine-Borel theorem, continuousfunctions properties, uniform continuity, the Mean-Value theorem; the Riemann integral, and Lebesguemeasure.MTH 433: Differential Equations(Prerequisite: MTH 223 and MTH 435)Examines systems of linear equations and matrices,elementary vector-space concepts, and geometricinterpretations. Discusses finite dimensional vectorspaces, linear functions and their matrix representations,determinants, similarity of matrices, innerproduct, rank, eigenvalues and eigenvectors, canonicalform, and Gram-Schmidt process.MTH 435: Linear Algebra(Prerequisites: MTH 325 and MTH 220)Examination of systems of linear equations andmatrices, elementary vector-space concepts, and geometricinterpretations. Discusses finite dimensionalvector spaces, linear functions and their matrix representations,determinants, similarity of matrices,inner product, rank, eigenvalues and eigenvectors,canonical form, and Gram-Schmidt process.Computer software will demonstrate computationaltechniques with larger matrices.MTH 438: Applied Mathematical Modeling(Prerequisites: MTH 433, MTH 416, and MTH 418)A capstone course intended to culminate the coremathematics major studies and should be taken at ornear the end of the program. Discusses principlesand methods of constructing, analyzing, interpreting,evaluating, and refining mathematical models.Compares analytic and simulation, discrete and continuous,deterministic and stochastic models.MTH 440: Numerical Analysis(Prerequisite: MTH 223)An introduction to numerical computation.Discusses errors in numerical computation, truncationand discretization, and machine storage restrictionsas well as function approximation, roots ofnonlinear equations, systems of linear equations,algebraic eigenvalue problems, polynomial interpolation,and cubic spline interpolations, quadratures,numerical differentiation, initial and boundary-valueproblems.CourseDescriptions405