Course Catalog 2008-2009 - Concordia University

MTH 3103 Problem Solving: Combinatorics 1,0General problem solving techniques and specificproblem solving strategies will be used in solvingcombinatorics problems.MTH 3104 Problem Solving: Misc Problems 1,0General problem solving techniques and specificproblem solving strategies will be used inmiscellaneous problems including recreationalproblems.MTH 3301 Mathematics for Elem Teachers I 2,2Logic, sets, relations, functions, operations,numeration systems, and elementary number theory.Field experience required. Prerequisites: Admission toProfessional Education Program; MTH 1323Quantitative Literacy or higher.MTH 3302 Mathematics for Elem Teachers II 2,2Rational numbers, real numbers, informal geometry,measurement, computers, probability, and statistics.Field experience required. Prerequisite: MTH 3301.MTH 3303 Mathematics for Secondary Teachers I 2,2Concepts from 7th and 8th grade mathematics, mathematicsof finance, algebra, and geometry are examined usingmanipulatives. Use of mathematics in modeling our worldand techniques for teaching mathematics are emphasized.MTH 3304 Mathematics for Secondary Teachers II 2,2Concepts from geometry, probability, statistics,trigonometry, analytical geometry, discrete mathematics,and calculus. Use of mathematics in modeling our worldand techniques for teaching mathematics are emphasized.MTH 3309 Numerical Analysis 3,0Algorithms of numerical analysis are covered. Topicsinclude floating point arithmetic, approximation,numerical integration and differentiation, solution ofnonlinear equations, and solution of ordinarydifferential equations. Programming assignments willgive experience in applying selected algorithms.Prerequisites: CSC 1302 and MTH 2402 or consent ofinstructor. Cross-listed with CSC 3309.MTH 3311 Linear Algebra 3,0Systems of linear equations, vector spaces, lineartransformations, representation of lineartransformations by matrices, matrix algebra, anddeterminates. Prerequisite: MTH 2401.MTH 3313 Number Theory 3,0Divisibility, primes, congruencies, quadric reciprocity,Diophantine equations and simple continued fractions.Prerequisite: Six academic hours of mathematics at orabove the level of MTH 1341, excluding MTH 2301.MTH 3315 Abstract Algebra 3,0The basic concepts of groups, rings, integral domains,fields, isomorphism's, and group homomorphism.Prerequisite: Three academic hours of upper levelmathematics.MTH 3316 Geometry 3,0The extension of geometry concepts including thestudy of tessellations, transformations, isometrics,topology, and non-Euclidean geometries. Prerequisite:Six academic hours of mathematics at or above thelevel of MTH 1341, excluding MTH 2301.MTH 3317 Differential Equations 3,0Methods of solution to ordinary differential equations,including exponential, complex exponential, Laurentseries solutions and Laplace transforms. Applicationsto simple harmonic motion, mixing problems andlogistic problems. Phase portrait analysis andapplication to predator-prey and soft-spring problems.Prerequisite: MTH 3410 Calculus III.MTH 3318 Topics in Secondary SchoolMathematics 3,0Topics discussed include applications of mathematicsto business statistics (basic concepts), history ofmathematics, problem solving using a graphiccalculator and a computer, and discrete mathematics(introduction). Prerequisite: MTH 2402 Calculus II.MTH 3325 Real Analysis 3,0Construction of the real numbers and rigorous study oftheir properties, including topological considerations,limits of sequences, continuity and differentiation offunctions, the Riemann and Lebesgue integrals, andthe topologies of function spaces. Prerequisite: MTH3410 Calculus III and one other 3000-levelmathematics course.MTH 3410 Calculus III 4,0Convergence properties of infinite series and powerseries, the calculus and geometry of vector-valuedfunctions, the calculus and geometry of multi-variablefunctions, Divergence Theorem, Green's Theorem andStokes' Theorem. Prerequisite MTH 2402 Calculus II.MTH 3412 Advanced Calculus for Applications 4,0Infinite series, ordinary differential equations,practical differential equations, partial differentialequations, and Fourier series. Prerequisite: MTH 2402.MTH 4310 Cryptology 3,0Applications to abstract algebraic and numbertheoretic concepts to the science of securecryptography. Topics include historical ciphers,public-key cryptography, signed messages, secureprotocols, and cryptanalysis, especially as these dealwith electronic communications. Prerequisite: MTH2008-2009 Catalog Page 124