## Mathematics

## Mathematics 0500

Essential MathematicsCredit hours: 3.0Contact hours per week: 3-0-1Polynomials and rational functions, trigonometry, exponential and logarithmic functions, inequalities, rudiments of probability and counting.Prerequisite(s): Applied Mathematics 30 or equivalentNote: This course may not be taken for credit by students with Pure Mathematics 30 or equivalent.This course may not be included among the mathematics courses required for Computer Science or Mathematics majors in Arts and Science.## Mathematics 1410

Elementary Linear AlgebraCredit hours: 3.0Contact hours per week: 3-0-1Linear systems and matrices. Matrix algebra. Determinants. Vector geometry. Complex numbers. Markov chains and other applications.Prerequisite(s): One of Pure Mathematics 30, Mathematics 30, Mathematics 0500, or [Applied Mathematics 30 and at least 75 percent standing in Athabasca University's Mathematics 101]## Mathematics 1510

Calculus for Management and Social SciencesCredit hours: 3.0Contact hours per week: 3-0-1Differentiation of elementary functions, the chain and product rules, extrema problems, integration. Applications from management, humanities and the social sciences.Prerequisite(s): One of Pure Mathematics 30, Mathematics 30, Mathematics 0500, or [Applied Mathematics 30 and at least 75 percent standing in Athabasca University's Mathematics 101]Substantially Similar: Mathematics 1560Note: Mathematics 1510 may not be counted toward the requirements for a major in Mathematics and is not suitable for students requiring more than one semester of Calculus.## Mathematics 1560

Calculus ICredit hours: 3.0Contact hours per week: 3-0-1Functions. Limits. Continuity. Differentiation and integration of polynomial, rational, root, trigonometric, exponential, and logarithmic functions. Applications of derivatives. Curve sketching and optimization. Anti-derivatives. Change of variable. Definite integrals. Fundamental Theorem of Calculus.Prerequisite(s): One of Pure Mathematics 30, Mathematics 30, Mathematics 0500, or [Applied Mathematics 30 and at least 75 percent standing in Athabasca University's Mathematics 101]Recommended Background: Mathematics 31 and a blended grade of at least 75 percent in Pure Mathematics 30 or Mathematics 30Substantially Similar: Mathematics 1510## Mathematics 2000

Mathematical ConceptsCredit hours: 3.0Contact hours per week: 3-0-1Logic, proofs. Set theory. Relations and functions. Finite and countable sets. Induction. Examples of axiomatic mathematical theories.Prerequisite(s): Four courses (12.0 credit hours) in Arts and Science;

One of Mathematics 31,

or a blended grade of at least 80% in Pure Mathematics 30,

or Logic 2003,

or a 1000-level course in Mathematics, Computer Science, Statistics, or Physics## Mathematics 2090

Number SystemsCredit hours: 3.0Contact hours per week: 3-0-1Principles of Logic. Number Systems and Bases. Sets of real numbers: Integers, Rationals, Irrationals. Modular Arithmetic and applications. Divisibility, primes and elementary number theory.Prerequisite(s): Eight university-level courses (24.0 credit hours)Note: Students should not take Mathematics 2090 if they have received credit for Mathematics 2000 prior to enrolling in Mathematics 2090.Mathematics 2090 may not be counted toward the requirements for a major in Mathematics or Computer Science.Mathematics 2090 is primarily intended for prospective elementary school teachers who would not ordinarily take university mathematics courses.## Mathematics 2560

Calculus IICredit hours: 3.0Contact hours per week: 3-0-1Applications of integration; logarithmic, exponential and hyperbolic functions; inverse functions; inverse trigonometric and hyperbolic functions; indeterminate forms; improper integrals; techniques of integration.Prerequisite(s): Mathematics 1560## Mathematics 2570

Calculus IIICredit hours: 3.0Contact hours per week: 3-0-0Sequences and series, convergence tests, Taylor's series, vector-valued functions of a real variable, polar coordinates, applications to analytic geometry.Prerequisite(s): Mathematics 1410;

Mathematics 2560## Mathematics 2580

Calculus IVCredit hours: 3.0Contact hours per week: 3-0-0Calculus of functions of several variables: partial differentiation, chain rule, applications, multiple integration, change of variables, theorems from vector analysis, including Stokes' Theorem.Prerequisite(s): Mathematics 2570## Mathematics 2865

Combinatorial MathematicsCredit hours: 3.0Contact hours per week: 3-0-1Graphs, trees and digraphs. Network flows. Scheduling. Enumeration, including the principle of Inclusion-Exclusion and generating functions.Prerequisite(s): Mathematics 1410## Mathematics 3100

Introduction to Mathematical LogicCredit hours: 3.0Contact hours per week: 3-0-0First Order Logic. Validity, provability, completeness, consistency, independence, categoricity, decidability, Gödel's Theorem.Prerequisite(s): Mathematics 2000Substantially Similar: Logic 3003## Mathematics 3200

GeometryCredit hours: 3.0Contact hours per week: 3-0-0Introduction to classical geometry from the axiomatic point of view. Lines and affine planes. Separation, order, similarity, congruence. Isometries and their classification. Groups of symmetries. Projective, hyperbolic and inversive geometries.Prerequisite(s): Mathematics 2000## Mathematics 3400

Group and Ring TheoryCredit hours: 3.0Contact hours per week: 3-0-0Groups, abelian groups, subgroups, quotient groups. Homomorphism. Isomorphism theorems. Lagrange's theorem. Permutation groups. Sylow theorems. Commutative rings, subrings, ideals. Quotient rings and ideals. Polynomial rings.Prerequisite(s): Mathematics 2000Recommended Background: At least one 3000-level course in Mathematics## Mathematics 3410

Linear AlgebraCredit hours: 3.0Contact hours per week: 3-0-0Vector spaces over the real and complex numbers. Basis and dimension. Linear transformations. Change of basis. Gram-Schmidt orthogonalization. Eigenvectors and diagonalization. Canonical forms. Cayley-Hamilton Theorem.Prerequisite(s): Mathematics 1410;

Mathematics 2000## Mathematics 3461

Elementary Number TheoryCredit hours: 3.0Contact hours per week: 3-0-0Division algorithm. Fundamental Theorem of Arithmetic. Euclidean Algorithm. Linear Diophantine equations. Congruences. Chinese Remainder Theorem. Quadratic reciprocity. Additional topics such as Pythagorean triples, Gaussian integers, sums of squares, continued fractions, arithmetic functions, or cryptography.Prerequisite(s): Mathematics 2000## Mathematics 3500

Analysis ICredit hours: 3.0Contact hours per week: 3-0-0Rigorous treatment of the notions of calculus of a single variable, emphasizing epsilon-delta proofs. Completeness of the real numbers. Upper and lower limits. Continuity. Differentiability. Riemann integrability.Prerequisite(s): Mathematics 2000;

Mathematics 2570Recommended Background: At least one 3000-level course in Mathematics## Mathematics 3560

Functions of a Complex VariableCredit hours: 3.0Contact hours per week: 3-0-0Complex number system and complex plane. Analytic functions. Complex integration. Power series. Calculus of residues.Prerequisite(s): Mathematics 2580;

One of Mathematics 2000 or Physics 2150Equivalent: Mathematics 4560 (prior to 2007/2008)## Mathematics 3600

Differential Equations ICredit hours: 3.0Contact hours per week: 3-0-0First order ordinary differential equations. Second and higher order ordinary differential equations. Linear systems of ordinary differential equations. Qualitative theory of ordinary differential equations. Applications. Series solutions. Singular point expansions. Elementary linear difference equations.Prerequisite(s): Mathematics 1410;

Mathematics 2560Corequisite(s): Mathematics 2570## Mathematics 3850

Topics in MathematicsCredit hours: 3.0Contact hours per week: 3-0-0## Mathematics 3860

CombinatoricsCredit hours: 3.0Contact hours per week: 3-0-0Burnside's theorem, Polya's theorem. Finite fields and combinatorial design. Coding theory. Ramsey Theory.Prerequisite(s): Mathematics 2865## Mathematics 4310

TopologyCredit hours: 3.0Contact hours per week: 3-0-0Topological spaces. Topology of metric spaces. Continuity. Open covers and compactness. Separation. Connectedness.Prerequisite(s): Mathematics 3500Equivalent: Mathematics 3310 (prior to 2007/2008)## Mathematics 4400

Field TheoryCredit hours: 3.0Contact hours per week: 3-0-0Polynomial rings. Fields and field extensions, construction problems. Finite fields. Galois Theory. Fundamental Theorem of Algebra.Prerequisite(s): Mathematics 3400## Mathematics 4500

Analysis IICredit hours: 3.0Contact hours per week: 3-0-0This follow-up course to Mathematics 3500 (Analysis I) presents concepts that are crucial for an understanding of both pure and applied mathematics at an advanced level. Sequences and series of functions. Uniform continuity. Uniform convergence. The Stone-Weierstrass Theorem. The Lebesgue (or Riemann-Stieltjes) integral. Fourier series. Other topics.Prerequisite(s): Mathematics 3500## Mathematics 4600

Differential Equations IICredit hours: 3.0Contact hours per week: 3-0-0Adjoints. Oscillation theory. Matrix methods. Matrix exponential functions. Sturm-Liouville theory. Orthonormal systems and Fourier series. Eigenfunction expansions. Laplace, Fourier and Mellin transforms. Convolutions. Convergence theory. Plancherel and Parseval formulae. Distributions. Solving PDEs using integral transforms. Fundamental solutions. Separation of variables. Heat, wave and Poisson equations. Harmonic functions.Prerequisite(s): Mathematics 2570;

Mathematics 3600Recommended Background:

Mathematics 3500## Mathematics 4850

Topics in MathematicsCredit hours: 3.0Contact hours per week: 3-0-0