Mathematics   (MATH)

Faculty of Arts and Science

Mathematics 0100

Preparation for Essential Mathematics

Credit hours: 0.00

Contact hours per week: 3-0-1

Preparation for university-level mathematics. Review of fractions, exponents and percentages; equations, functions and applications for linear and quadratic polynomials; systems of equations and their applications; and right triangle and oblique triangle trigonometry.

Prerequisite(s):Admission to the Indigenous Student Success Cohort AND
One of Mathematics 20-1, or Mathematics 20-2

Grading:Pass/Fail

Note:Mathematics 0100 is a non-credit course designed for the Indigenous Student Success Cohort. The course is for students who lack the prerequisite mathematics background to complete Mathematics 0520 successfully or who have been out of school for some years and require upgrading in mathematics.

Mathematics 0500

Essential Mathematics

Credit hours: 3.00

Contact hours per week: 3-0-1

Polynomials and rational functions, trigonometry, exponential and logarithmic functions, inequalities, rudiments of probability and counting.

Prerequisite(s):Mathematics 30-2 or Applied Mathematics 30

Equivalent:Mathematics 0520

Lib Ed Req:Science

Note:This course may not be taken for credit by students with Mathematics 30-1 or Pure Mathematics 30 This course may not be included among the mathematics courses required for Computer Science or Mathematics majors in Arts and Science.

Mathematics 0520

Essential Mathematics

Credit hours: 3.00

Contact hours per week: 3-0-1

Polynomials and rational functions, trigonometry, exponential and logarithmic functions, inequalities, rudiments of probability and counting.

Prerequisite(s):Admission to the Indigenous Student Success Cohort AND
One of Mathematics 0100, Mathematics 30-2, or Applied Mathematics 30

Equivalent:Mathematics 0500

Lib Ed Req:Science

Note:This course may not be taken for credit by students with Mathematics 30-1 or Pure Mathematics 30. This course may not be included among the mathematics courses required for Computer Science or Mathematics majors in Arts and Science.

Mathematics 1010

Introduction to Calculus

Credit hours: 3.00

Contact hours per week: 3-0-1

Review of algebra. Properties and graphs of polynomial, rational, exponential, logarithmic, and trigonometric functions. Algebra of functions, including composition and inverses. Elementary calculus, including limits, continuity, derivatives, and antiderivatives. Applications of derivatives to curve sketching.

Prerequisite(s):One of Mathematics 30-1, Pure Mathematics 30, Mathematics 0500, or Mathematics 0520

Substantially Similar:
Mathematics 1510

Lib Ed Req:Science

Note:Credit is not allowed for Mathematics 1010 subsequent to the completion of Mathematics 1560.

Mathematics 1410

Elementary Linear Algebra

Credit hours: 3.00

Contact hours per week: 3-0-1

Linear systems. Vectors and matrices. Determinants. Orthogonality and applications. Vector geometry. Eigenvalues, eigenvectors, and applications. Complex numbers.

Prerequisite(s):One of Mathematics 30-1, Mathematics 30-2, Pure Mathematics 30, Mathematics 0500, or Mathematics 0520

Lib Ed Req:Science

Mathematics 1510

Calculus for Management and Social Sciences

Credit hours: 3.00

Contact hours per week: 3-0-1

Differentiation of elementary functions, the chain and product rules, extrema problems, integration. Applications from management, humanities and the social sciences.

Prerequisite(s):One of Mathematics 30-1, Pure Mathematics 30, Mathematics 0500, or Mathematics 0520

Mutually Exclusive:
Mathematics 1560

Substantially Similar:
Mathematics 1010;
Mathematics 1560

Lib Ed Req:Science

Note:Mathematics 1510 may not be counted toward the requirements for a major in Mathematics and is not suitable for students requiring more than one term of Calculus.

Mathematics 1560

Calculus I

Credit hours: 3.00

Contact hours per week: 3-0-1

Functions. Limits. Continuity. Differentiation and integration of polynomial, rational, root, trigonometric, exponential, and logarithmic functions. Inverse functions, including inverse trigonometric functions. Applications of derivatives, including linear approximations and Taylor polynomials. Curve sketching, optimization, and related rates. Anti-derivatives. Definite integrals and Fundamental Theorem of Calculus. Change of variables.

Prerequisite(s):One of Mathematics 30-1, Mathematics 0500, or Mathematics 0520

Mutually Exclusive:
Mathematics 1510;
Mathematics 1565

Substantially Similar:
Mathematics 1510;
Mathematics 1565

Lib Ed Req:Science

Mathematics 1565

Accelerated Calculus I

Credit hours: 3.00

Contact hours per week: 3-0-1.5

Elementary functions: polynomial, rational, root, trigonometric, exponential, logarithmic, hyperbolic. Inverse functions, including inverse trigonometric functions. Limits and continuity. Differentiation of elementary and inverse functions. Applications of derivatives, including linear approximations, Taylor polynomials, and l'Hospital's rule. Curve sketching and optimization. Anti-derivatives. Definite integrals and the Fundamental Theorem of Calculus. Integration by substitution. Area between curves. Numerical integration.

Prerequisite(s):One of Mathematics 1010 or Mathematics 31

Mutually Exclusive:
Mathematics 1560

Substantially Similar:
Mathematics 1560

Lib Ed Req:Science

Mathematics 2000

Mathematical Concepts

Credit hours: 3.00

Contact hours per week: 3-0-1

Logic, 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 AND
One of Logic 2003, or a 1000-level course in Mathematics, Computer Science, Statistics, or Physics, or Mathematics 31, or a blended grade of at least 80 percent in either Mathematics 30-1 or Pure Mathematics 30

Lib Ed Req:Science

Mathematics 2090

Number Systems

Credit hours: 3.00

Contact hours per week: 3-0-1

Principles 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)

Lib Ed Req:Science

Note:Mathematics 2090 is primarily intended for prospective teachers who would not ordinarily take university mathematics courses. This course cannot be counted as a 2000 level mathematics course towards the major requirements for the B.Sc. (Mathematics), B.Sc./B.Ed (Mathematics/Mathematics Education), or B.Sc/B.Mgt. (Mathematics) programs. Credit is not allowed for Mathematics 2090 subsequent to the successful completion of Mathematics 2000.

Mathematics 2560

Calculus II

Credit hours: 3.00

Contact hours per week: 3-0-1

Review of inverse trigonometric functions. Techniques of integration; applications of integration; improper integrals/indeterminate forms and l'Hospital's rule; parametric curves in the plane; polar coordinates; introduction to differential equations.

Prerequisite(s):One of Mathematics 1560 or Mathematics 1565

Mutually Exclusive:
Mathematics 2565

Substantially Similar:
Mathematics 2565

Lib Ed Req:Science

Mathematics 2565

Accelerated Calculus II

Credit hours: 3.00

Contact hours per week: 3-0-1.5

Techniques of integration. Improper integrals. Applications of integration, including volume, arc length, and surface area. Separable and linear first-order Ordinary Differential Equations. Sequences and series, power series. Parametric curves in the plane and space. Polar coordinates. Partial derivatives. Tangent planes to graphs of functions of two variables.

Prerequisite(s):One of Mathematics 1565 or a minimum 'B' grade in Mathematics 1560

Mutually Exclusive:
Mathematics 2560

Substantially Similar:
Mathematics 2560

Lib Ed Req:Science

Mathematics 2570

Calculus III

Credit hours: 3.00

Contact hours per week: 3-0-0

Sequences and series, convergence tests, power series, and Taylor series. Calculus of vector-valued functions of a real variable; velocity, acceleration, arc length, curvature. Limits and continuity for real-valued functions of several variables. Partial derivatives and tangent planes to graphs of functions of two variables.

Prerequisite(s):Mathematics 1410 AND
One of Mathematics 2560 or Mathematics 2565

Lib Ed Req:Science

Note:Credit is not allowed for Mathematics 2570 subsequent to the completion of Mathematics 2575.

Mathematics 2575

Accelerated Calculus III

Credit hours: 3.00

Contact hours per week: 3-0-1.5

Calculus of Vector valued functions; Differential calculus of multivariable functions, with applications including optimization. Integral calculus of functions of multiple variables including changes of variables in multiple integrals and different coordinate systems. Calculus of Vector fields; including Greens Theorem, Stokes Theorem, and the Divergence Theorem.

Prerequisite(s):Mathematics 1410 AND
One of Mathematics 2565 or Mathematics 2570

Substantially Similar:
Mathematics 2580

Lib Ed Req:Science

Mathematics 2580

Calculus IV

Credit hours: 3.00

Contact hours per week: 3-0-0

Review of partial differentiation. Chain rule and implicit differentiation. Gradients and directional derivatives. Maxima, minima, and optimization. Double and triple integrals and applications. Changes of variables in multiple integrals, including polar, cylindrical, and spherical coordinates. Divergence and curl of a vector field. Line and surface integrals. Green's Theorem, Stokes' Theorem, and Divergence Theorem.

Prerequisite(s):Mathematics 2570

Substantially Similar:
Mathematics 2575

Lib Ed Req:Science

Mathematics 3100

Introduction to Mathematical Logic

Credit hours: 3.00

Contact hours per week: 3-0-0

First Order Logic. Validity, provability, completeness, consistency, independence, categoricity, decidability, Gödel's Theorem.

Prerequisite(s):Mathematics 2000

Lib Ed Req:Science

Mathematics 3200

Geometry

Credit hours: 3.00

Contact hours per week: 3-0-0

Introduction 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

Lib Ed Req:Science

Mathematics 3400

Group and Ring Theory

Credit hours: 3.00

Contact hours per week: 3-0-0

Groups, 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 2000

Recommended Background:
At least one 3000-level course (3.0 credit hours) in Mathematics

Lib Ed Req:Science

Mathematics 3410

Linear Algebra

Credit hours: 3.00

Contact hours per week: 3-0-0

Vector 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 AND
Mathematics 2000

Lib Ed Req:Science

Mathematics 3461

Elementary Number Theory

Credit hours: 3.00

Contact hours per week: 3-0-0

Division 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

Lib Ed Req:Science

Mathematics 3500

Analysis I

Credit hours: 3.00

Contact hours per week: 3-0-0

Rigorous 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 AND
One of Mathematics 2565 or Mathematics 2570

Recommended Background:
At least one 3000-level course (3.0 credit hours) in Mathematics

Lib Ed Req:Science

Mathematics 3560

Functions of a Complex Variable

Credit hours: 3.00

Contact hours per week: 3-0-0

Complex number system and complex plane. Analytic functions. Complex integration. Power series. Calculus of residues.

Prerequisite(s):One of Mathematics 2575 or Mathematics 2580 AND
One of Mathematics 2000 or Physics 2150

Lib Ed Req:Science

Mathematics 3600

Differential Equations I

Credit hours: 3.00

Contact hours per week: 3-0-0

First 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

Corequisite(s):One of Mathematics 2565 or Mathematics 2570

Lib Ed Req:Science

Mathematics 3650

Differential Equations II

Credit hours: 3.00

Contact hours per week: 3-0-0

Adjoints. 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 3600

Corequisite(s):One of Mathematics 2575 or Mathematics 2580

Lib Ed Req:Science

Mathematics 3860

Combinatorics

Credit hours: 3.00

Contact hours per week: 3-0-0

Graph theory. Combinatorial designs. Enumerative Combinatorics or other topics.

Prerequisite(s):Mathematics 2000

Lib Ed Req:Science

Mathematics 4310

Topology

Credit hours: 3.00

Contact hours per week: 3-0-0

Topological spaces. Topology of metric spaces. Continuity. Open covers and compactness. Separation. Connectedness.

Prerequisite(s):Mathematics 3500

Lib Ed Req:Science

Mathematics 4400

Field Theory

Credit hours: 3.00

Contact hours per week: 3-0-0

Polynomial rings. Fields and field extensions, construction problems. Finite fields. Galois Theory. Fundamental Theorem of Algebra.

Prerequisite(s):Mathematics 3400

Lib Ed Req:Science

Mathematics 4405

Algebra (Series)

Credit hours: 3.00

Contact hours per week: 3-0-0

Topics in group and ring theory, modules, commutative and non-commutative algebras.

Prerequisite(s):Mathematics 3400 AND
Mathematics 3410

Lib Ed Req:Science

Mathematics 4460

Advanced Number Theory (Series)

Credit hours: 3.00

Contact hours per week: 3-0-0

Topics in analytic and algebraic number theory, elliptic curves, and modular forms.

Prerequisite(s):Mathematics 3461

Lib Ed Req:Science

Mathematics 4500

Analysis II

Credit hours: 3.00

Contact hours per week: 3-0-0

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

Lib Ed Req:Science

Mathematics 4505

Analysis (Series)

Credit hours: 3.00

Contact hours per week: 3-0-0

Topics in measure theory, Banach spaces, Lp-spaces, Fourier and Complex analysis.

Prerequisite(s):Mathematics 4500

Lib Ed Req:Science

Mathematics 4995

Undergraduate Thesis

Credit hours: 6.00

Contact hours per week: Variable

This is a challenging, work-intensive, research-oriented course in which students will conduct fieldwork, text, library-based or empirical research, submit a report in the form of an Undergraduate Thesis which will be made publicly available, and report orally on the work. In consultation with their Thesis Supervisor, students will define a research problem and formulate a research plan.

Prerequisite(s):Fourth-year standing (a minimum of 90.0 credit hours) AND
A cumulative GPA of 3.30 or higher

Note:Contact hours will vary. Students should be aware that this course involves regular contact with the Thesis Supervisor as well as considerable independent work.