Academic Calendar 2012/2013

MATH-222Introduction to Discrete Mathematics3 Credits (45:0:0 hours)This course is an introduction to discrete mathematics, covering coding,cryptography, induction and recursion, and graph theory. Secret codes,error-detecting and error-correcting codes are introduced. Induction andrecursive definitions are described. The Eulerian tour is used to illustrategraph definitions and properties.Prerequisites: Minimum grade of C- in any 100-level Mathematics course.MATH-225Linear Algebra II3 Credits (45:0:0 hours)This course introduces the theory of vector spaces, inner product spaces,linear transformations and diagonalization. Specific topics of studyinclude Euclidean n-space, spaces of continuous functions, matrixspaces, Gram-Schmidt process, QR-factorization, least squares method,change of basis, eigenspaces, orthogonal diagonalization, quadraticforms, matrices of transformations and similarity. Various applicationsare presented.Prerequisites: Mathematics 31 or a minimum grade of C- in MATH 113,and a minimum grade of C- in MATH 120 or MATH 125.MATH-228Algebra: Introduction to Ring Theory3 Credits (45:0:0 hours)This course is an introduction to the theory of rings includingintegral domains, division rings, ring homomorphisms, ideals,quotient rings, fields of quotients, rings of polynomials, irreduciblepolynomials, Euclidean domains and fields. Specific topics includethe well-ordering axiom, the Binomial Theorem, the Euclideanalgorithm, the Fundamental Theorem of Arithmetic, and the ChineseRemainder Theorem.Prerequisites: Minimum grade of C- in MATH 120 or MATH 125.MATH-241Geometry3 Credits (45:0:0 hours)Basic Euclidean geometry, congruence, parallelism, area, and similarity.Sound axiomatic development with emphasis on problem solving.Constructions and loci, inequalities, maxima and minima, circles,isometries, and additional topics.Prerequisites: Minimum grade of C- in any 100- levelmathematics course.MATH-310Real Analysis3 Credits (45:0:0 hours)In this course a rigorous treatment of limit processes in one variable ispresented. Topics includes real numbers, sequences, limits, continuousfunctions, differentiation, the Riemann integral and the topology of thereal number system. .Prerequisites: Minimum grade of C- in MATH 214 and in either MATH200 or MATH 241.MATH-311Theory of Functions of a Complex Variable3 Credits (45:0:0 hours)This course provides an introduction to the fundamental conceptsof single variable complex analysis. The main topics include analyticfunctions, complex power series, Cauchy’s Integral Theorem, Cauchy’sIntegral Formula, the residue theorem and applications to improperreal integrals and Fourier transforms.Prerequisites: Minimum grade of C- in MATH 215.MATH-312Probability Theory3 Credits (45:0:0 hours)This course offers a rigorous approach to probability theory. Topicscovered include basic concepts of probability theory, univariate andmultivariate probability distributions, discrete and continuous randomvariables, expectation, moment generating and characteristic functions,different types of convergence and relationships between them, andbasic limit theorems. Note: This course may not be taken for credit ifcredit has been obtained in STAT 312.Prerequisites: Minimum grade of C- in MATH 215, STAT 265, and in oneof MATH 120 or MATH 125.MATH-320Elementary Number Theory3 Credits (45:0:0 hours)Elementary methods in number theory are presented. The followingtopics are included: divisibility, linear Diophantine equations, primenumbers, the fundamental theorem of arithmetic, congruences,the Chinese remainder theorem, Fermat’s little theorem, arithmeticfunctions, Euler’s theorem, applications of number theory.Prerequisites: Minimum grade of C- in MATH 200.MATH-321Fields and Modules3 Credits (45:0:0 hours)This course builds on the knowledge of rings and fields obtained inMATH 228, and introduces the student to basic module theory. Topicsstudied include finite fields, quadratic number fields and algebraicfield extensions, the Fundamental Theorem of Algebra, modules, andNoetherian rings.Prerequisites: Minimum grade of C- in MATH 200 and MATH 228 .MATH-330Ordinary Differential Equations3 Credits (45:13:0 hours)This course provides techniques for solving ordinary differentialequations and systems of first order equations and investigates thequalitative nature of solutions of dynamical systems. Topics coveredinclude first order equations, linear equations of higher order andlinear dynamical systems with constant coefficients.Prerequisites: Minimum grade of C- in MATH 120 or MATH 125 and inMATH 214.course Descriptions • course Descriptions • course Descriptions • course Descriptions • course Descriptions • course DescriptionsGrant MacEwan University • A C A D E m I CRefer to the Online Alberta Transfer Guide at www.transferalberta.ca for transfer opportunitiesC A L E N D A R 2012/2013 • www.MacEwan.ca319