Faculty of Arts and Science
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 Undergraduate Certificate in Indigenous Student Success AND
One of Mathematics 20-1 or Mathematics 20-2
Grading:Pass/Fail
Note:Mathematics 0100 is a non-credit course designed for the Undergraduate Certificate in Indigenous Student Success. 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.
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.
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 Undergraduate Certificate in Indigenous Student Success AND
One of Mathematics 0100 or Mathematics 30-2
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.
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.
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
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.
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
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
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
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.
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 AND
Additional prerequisites may be specified, including any recommended background, for individual offerings
Lib Ed Req:Science
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
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
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 minimum GPA of 3.30 calculated on all completed University of Lethbridge courses or calculated on all University of Lethbridge and transferable courses taken within the terms containing the last 20 courses (60.0 credit hours), whichever is 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.