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 University of Calgary Calendar 2013-2014 COURSES OF INSTRUCTION Course Descriptions M Mathematics MATH
Mathematics MATH
MATH 113 114 117 205 211 213 249 251 253 271 273 281 283 311 313 321 331 335 349 353 355 381 401 403 411 423 445 447 501 521 545 601 621
 

Instruction offered by members of the Department of Mathematics and Statistics in the Faculty of Science.

Department Head – M. Lamoureux

Note: For listings of related courses, see Actuarial Science, Applied Mathematics, Pure Mathematics, and Statistics.
 
Mathematics 113       Eigenvalues and Eigenvectors
A review of these particular topics for students who have completed Mathematics 211 or equivalent.
Course Hours: E(8 hours)
Antirequisite(s): Credit for both Mathematics 113 and 013 will not be allowed.
Notes: Open to students with credit in Mathematics 211 or equivalent.
NOT INCLUDED IN GPA
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Mathematics 114       Multivariate Topics from Applied Mathematics 219
Multiple Integration and applications.
Course Hours: E(16 hours)
Prerequisite(s): Mathematics 253 or 283 or Applied Mathematics 219 or consent of the Department.
Antirequisite(s): Credit for both Mathematics 114 and 014 will not be allowed.
Notes: Designed to rectify a deficiency for those students whose Calculus I and II courses did not cover the multivariate topics from Applied Mathematics 219.
NOT INCLUDED IN GPA
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Mathematics 117       Topics from Applied Mathematics 217
Inverse functions and inverse trigonometric functions. Hyperbolic and inverse hyperbolic functions. Indeterminate forms. Applications of integration.
Course Hours: E(8 hours)
Prerequisite(s): Mathematics 249 or 251 or 281 or Applied Mathematics 217 or consent of the Department.
Antirequisite(s): Credit for both Mathematics 117 and 017 will not be allowed.
Notes: Designed to rectify a deficiency for those students whose first Calculus course did not cover some of the topics from Applied Mathematics 217.
NOT INCLUDED IN GPA
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Junior Courses

Note: Students who have not studied mathematics for some time are strongly advised to review high school material thoroughly prior to registering in any junior level mathematics course.
 
Mathematics 205       Mathematical Explorations
A mathematics appreciation course. Topics selected by the instructor to provide a contemporary mathematical perspective and experiences in mathematical thinking. May include historical material on the development of classical mathematical ideas as well as the evolution of recent mathematics.
Course Hours: H(3-1)
Prerequisite(s): Mathematics 30-1, Mathematics 30-2, Pure Mathematics 30, Applied Mathematics 30, or Mathematics II (offered by Continuing Education).
Notes: For students whose major interests lie outside the sciences. Highly recommended for students pursuing an Elementary School Education degree.  It is not a prerequisite for any other course offered by the Department of Mathematics and Statistics, and cannot be used for credit towards any Major or Minor program in the Faculty of Science except for a major in General Mathematics.
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Mathematics 211       Linear Methods I
Systems of equations and matrices, vectors, matrix representations and determinants. Complex numbers, polar form, eigenvalues, eigenvectors. Applications.
Course Hours: H(3-1T-1)
Prerequisite(s): A grade of 70 per cent or higher in Mathematics 30-1 or Pure Mathematics 30. (Alternatives are presented in C.1 Mathematics Diagnostic Test in the Academic Regulations section of this Calendar).
Antirequisite(s): Credit for Mathematics 211 and either 213 or 221 will not be allowed.
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Mathematics 213       Honours Linear Algebra I
Systems of equations and matrices, vectors, linear transformations, determinants, eigenvalues and eigenvectors.
Course Hours: H(3-1T-1)
Prerequisite(s): A grade of 70 per cent or higher in Mathematics 30-1 or Pure Mathematics 30.
Antirequisite(s): Credit for Mathematics 213 and either 211 or 221 will not be allowed.
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Mathematics 249       Introductory Calculus
Algebraic operations. Functions and graphs. Limits, derivatives, and integrals of exponential, logarithmic and trigonometric functions. Fundamental theorem of calculus. Applications.
Course Hours: H(4-1T-1)
Prerequisite(s): A grade of 70 per cent or higher in Mathematics 30-1 or Pure Mathematics 30. (Alternatives are presented in C.1 Mathematics Diagnostic Test in the Academic Regulations section of this Calendar).
Antirequisite(s): Not open to students with 60 per cent or higher in Mathematics 31, except with special departmental permission. Credit for more than one of Mathematics 249, 251, 281, or Applied Mathematics 217 will not be allowed.
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Mathematics 251       Calculus I
Functions and graphs, transcendental functions. Limits, derivatives, and integrals of exponential, logarithmic and trigonometric functions. Fundamental theorem of calculus. Applications.
Course Hours: H(3-1T-1)
Prerequisite(s): A grade of 70 per cent or higher in Mathematics 30-1 or Pure Mathematics 30 and a grade of 50 per cent or higher in Mathematics 31. (Alternatives to Pure Mathematics 30 are presented in C.1 Mathematics Diagnostic Test in the Academic Regulations section of this Calendar).
Antirequisite(s): Credit for more than one of Mathematics 249, 251, 281, or Applied Mathematics 217 will not be allowed.
Notes: This course provides the basic techniques of differential calculus as motivated by various applications. Students performing sufficiently well in a placement test may be advised to transfer directly to Mathematics 253.
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Mathematics 253       Calculus II
Inverses of trigonometric functions. Methods of integration, improper integrals. Separable differential equations, first and second order linear differential equations, applications.
Course Hours: H(3-1T-1)
Prerequisite(s): Mathematics 249 or 251 or 281 or Applied Mathematics 217.
Antirequisite(s): Credit for more than one of Mathematics 253, 263, 283, or Applied Mathematics 219 will not be allowed.
Notes: Mathematics 253 or 283 is a prerequisite for many 300-level courses in Pure Mathematics, Applied Mathematics, Statistics and Actuarial Science. Students in programs offered by the Department of Mathematics and Statistics are strongly recommended to take Mathematics 283.
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Mathematics 271       Discrete Mathematics
Proof techniques. Sets and relations. Induction. Counting and probability. Graphs and trees.
Course Hours: H(3-1T-1)
Prerequisite(s): Mathematics 30-1 or Pure Mathematics 30.
Antirequisite(s): Credit for both Mathematics 271 and 273 will not be allowed.
Notes: Philosophy 279 or 377 is highly recommended to complement this course.
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Mathematics 273       Honours Mathematics: Numbers and Proofs
Introduction to proofs. Functions, sets and relations. The integers: Euclidean division algorithm and prime factorization; induction and recursion; integers mod n. Real numbers: sequences of real numbers; completeness of the real numbers; open and closed sets. Complex numbers.
Course Hours: H(3-1T-1)
Prerequisite(s): A grade of 80 per cent or higher in Mathematics 30-1 or Pure Mathematics 30. (Alternatives are presented in C.1 Mathematics Diagnostic Test in the Academic Regulations section of this Calendar).
Antirequisite(s): Credit for both Mathematics 273 and 271 will not be allowed.
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Mathematics 281       Honours Calculus I
Limits and continuity; Differentiation of functions of one real variable; the Mean Value Theorem and its consequences; Riemann integration; fundamental theorem of calculus; applications.
Course Hours: H(3-1T-1)
Prerequisite(s): A grade of 80 per cent or higher in Pure Mathematics 30 or Mathematics 30-1 and a grade of 50 per cent or higher in Mathematics 31. (Alternatives to Pure Mathematics 30 are presented in C.1 Mathematics Diagnostic Test in the Academic Regulations section of this Calendar).
Antirequisite(s): Credit for more than one of Mathematics 249 or 251 or 281 or Applied Mathematics 217 will not be allowed.
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Mathematics 283       Honours Calculus II
Methods of integration, improper integrals. Sequence and series, Taylor series, functions defined by series. Ordinary differential equations. Partial derivatives.
Course Hours: H(3-1T-1)
Prerequisite(s): Mathematics 281 or a grade of "B+" or better in Mathematics 249 or 251 or Applied Mathematics 217 or equivalent.
Antirequisite(s): Credit for more than one of Mathematics 253 or 263 or 283 or Applied Mathematics 219 will not be allowed.
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Senior Courses
 
Mathematics 311       Linear Methods II
Vector spaces and subspaces. Linear independence. Matrix representations of linear transformations. Gram-Schmidt orthogonalization. Students will complete a project using a computer algebra system.
Course Hours: H(3-1T)
Prerequisite(s): One of Mathematics 211 or 213.
Antirequisite(s): Credit for both Mathematics 311 and 313 will not be allowed.
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Mathematics 313       Honours Linear Algebra II
Diagonalization. Canonical forms. Inner products, orthogonalization. Spectral theory. Students will be required to complete a project using a computer algebra system.
Course Hours: H(3-1T)
Prerequisite(s): Mathematics 213 or a grade of "B+" or better in Mathematics 211.
Antirequisite(s): Credit for both Mathematics 311 and 313 will not be allowed.
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Mathematics 321       Mathematical Probability
Sample spaces. Discrete probability. Discrete and continuous random variables. Standard distributions. Mathematical expectation and variance. Moments and moment generating functions. Central limit theorem. Functions of random variables. Introduction to statistical inference.
Course Hours: H(3-1T)
Prerequisite(s): Mathematics 253 or 283 or Applied Mathematics 219.
Notes: Statistics 205 is strongly recommended as preparation for this course for Statistics majors.
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Mathematics 331       Multivariate Calculus
Systems of ordinary differential equations. Calculus of functions of several variables. Introduction to vector analysis, theorems of Green, Gauss and Stokes.
Course Hours: H(3-1T)
Prerequisite(s): Mathematics 253 or 283 or Applied Mathematics 219 and Mathematics 211 or 213.
Antirequisite(s): Credit for both Mathematics 331 and either 353 or 381 or Applied Mathematics 309 will not be allowed.
Notes: This course is not a member of the list of courses constituting the fields of Actuarial Science, Applied Mathematics, Pure Mathematics, or Statistics and cannot normally be substituted for Mathematics 353 or 381 in degree programs in any of those fields.
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Mathematics 335       Analysis I
The real numbers, sequences, series, functions, continuity and uniform continuity, differentiation, intermediate and mean value theorems, the Riemann integral, integrability of continuous functions on closed intervals.
Course Hours: H(3-1T)
Prerequisite(s): Mathematics 253 or 263 or 283 or Applied Mathematics 219, or consent of the Department.
Antirequisite(s): Credit for more than one of Mathematics 335, 355, Pure Mathematics 435 and 455 will not be allowed.
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Mathematics 349       Calculus III
Infinite sequences and series. Polar co-ordinates, parametric equations, arc length. Vector geometry, differentiation of vector-valued functions. Partial differentiation. Students will complete a project using a computer algebra system.
Course Hours: H(3-1T)
Prerequisite(s): Mathematics 253 or 283 or Applied Mathematics 219 and Mathematics 211 or 213.
Antirequisite(s): Credit for both Mathematics 349 and 381 will not be allowed.
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Mathematics 353       Calculus IV
Applications of partial differentiation, multiple integrals, vector calculus including Stokes' and the Divergence Theorems.
Course Hours: H(3-1T)
Prerequisite(s): Mathematics 349.
Antirequisite(s): Credit for more than one of Mathematics 353, 331, 381 or Applied Mathematics 309 will not be allowed.
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Mathematics 355       Honours Analysis I
The real numbers, sequences, series, functions, continuity and uniform continuity, differentiation, intermediate and mean value theorems, the Riemann integral, integrability of continuous functions on closed intervals.
Course Hours: H(3-1T)
Prerequisite(s): Mathematics 283 or 263;  or a grade of "B+" or better in Mathematics 253 or Applied Mathematics 219.
Antirequisite(s): Credit for more than one of Mathematics 335, 355, Pure Mathematics 435 and 455 will not be allowed.
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Mathematics 381       Honours Calculus III
Functions of several variables; differentiability, extrema. Implicit and inverse function theorems. Integration of functions of several variables; line integrals; surface integrals. Students will complete a project using a computer algebra system.
Course Hours: H(3-1T)
Prerequisite(s): Mathematics 283 or a grade of "B+" or better in Mathematics 253 or Applied Mathematics 219; and Mathematics 211 or 213.
Antirequisite(s): Credit for Mathematics 381 and any one of Mathematics 331, 349, 353, and Applied Mathematics 309 will not be allowed.
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Mathematics 401       Special Topics
Higher level topics which can be repeated for credit.
Course Hours: H(3-0)
Prerequisite(s): Consent of the Department.
Notes: This course is designed to add flexibility to completion of an undergraduate pure mathematics or general mathematics program.
MAY BE REPEATED FOR CREDIT
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Mathematics 403       Topics in Mathematics for Economics
Techniques of integration. Multiple integrals. Analysis of functions. Continuity. Compact sets. Convex sets. Separating hyperplanes. Lower and upper hemi-continuous correspondences. Fixed point theorems, Optimal control.
Course Hours: H(3-0)
Prerequisite(s): Mathematics 211 or 213 and Mathematics 253 or 283 or Applied Mathematics 219; or both Economics 387 and 389.
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Mathematics 411       Linear Spaces with Applications
Canonical forms. Inner product spaces, invariant subspaces and spectral theory. Quadratic forms.
Course Hours: H(3-1T)
Prerequisite(s): Mathematics 311 and one of 331, 353, 381, or Applied Mathematics 309.
Antirequisite(s): Credit for Mathematics 411 and 313 or Applied Mathematics 441 will not be allowed.
Notes: May not be offered every year. Consult the Department for listings.
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Mathematics 421       Complex Analysis I
Basic complex analysis – complex numbers and functions, differentiation, Cauchy-Riemann equations, line integration, Cauchy’s theorem and Cauchy’s integral formula, Taylor’s theorem, the residue theorem, applications to computation of definite integrals.
Course Hours: H(3-1T)
Prerequisite(s): Both Mathematics 349 and 353; or both Mathematics 283 and 381.
Antirequisite(s): Credit for more than one of Mathematics 421, 423, Pure Mathematics 421 or 521 will not be allowed.
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Mathematics 423       Honours Complex Analysis
Basic complex analysis – complex numbers and functions, differentiation, Cauchy-Riemann equations, line integration, Cauchy’s theorem and Cauchy’s integral formula, Taylor’s theorem, the residue theorem, applications to computation of definite integrals.
Course Hours: H(3-1T)
Prerequisite(s): Both Mathematics 349 and 353; or both Mathematics 283 and 381.
Antirequisite(s): Credit for more than one of Mathematics 421, 423, Pure Mathematics 421 or 521 will not be allowed.
Notes: Open only to Honours Applied Mathematics and Honours Pure Mathematics students.
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Mathematics 445       Analysis II
Basic topology of Euclidean space, Fubini’s theorem, the total derivative, change of variable in multiple integrals, inverse and implicit function theorems, submanifolds of Euclidean spaces, differential forms, Stokes’ theorem in arbitrary dimension.
Course Hours: H(3-0)
Prerequisite(s): Mathematics 353 or 381; and Mathematics 311 or 313; and Mathematics 335 or 355 or Pure Mathematics 435 or 455, or consent of the Department.
Antirequisite(s): Credit for more than one of Mathematics 445, 447 or Pure Mathematics 545 will not be allowed.  
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Mathematics 447       Honours Analysis II
Basic topology of Euclidean space, Fubini’s theorem, the total derivative, change of variable in multiple integrals, inverse and implicit function theorems, submanifolds of Euclidean spaces, differential forms, Stokes’ theorem in arbitrary dimension.
Course Hours: H(3-0)
Prerequisite(s): Mathematics 381 or "B+" or higher in Mathematics 353; and Mathematics 313 or "B+" or higher in Mathematics 311; and Mathematics 355 or "B+" or higher in Mathematics 335 or Pure Mathematics 435 or 455, or consent of the Department.
Antirequisite(s): Credit for more than one of Mathematics 445, 447 or Pure Mathematics 545 will not be allowed.
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Mathematics 501       Measure and Integration
Abstract measure theory, basic integration theorems, Fubini's theorem, Radon-Nikodym theorem, Lp Spaces, Riesz representation theorems.
Course Hours: H(3-0)
Prerequisite(s): Mathematics 545 or Pure Mathematics 545 or consent of the Division.
Antirequisite(s): Credit for more than one of Mathematics 501, 601, Pure Mathematics 501 or 601 will not be allowed.
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Mathematics 521       Complex Analysis II
Analytic functions as mappings, local properties of analytic functions, Schwarz lemma, Casorati-Weierstrass and Picard theorems, analytic continuation, harmonic and subharmonic functions, approximation theorems, conformal mappings, Riemann surfaces.
Course Hours: H(3-0)
Prerequisite(s): Mathematics 335 or 355 or Pure Mathematics 435 or 455; and Mathematics 421 or 423 or Pure Mathematics 421; or consent of the Department.
Antirequisite(s): Not open to students with credit in Pure Mathematics 521.
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Mathematics 545       Analysis III
Sequences and series of functions; Lebesgue integration on the line, Fourier series and the Fourier transform, pointwise convergence theorems, distributions and generalized functions.
Course Hours: H(3-0)
Prerequisite(s): Mathematics 447 or a grade of "B+" or better in Pure Mathematics 445 or Mathematics 445.
Antirequisite(s): Not open to students with credit in Pure Mathematics 545.
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Graduate Courses Note: In addition to the prerequisites listed below, consent of the Applied Mathematics Division or the Pure Mathematics Division is a prerequisite for these graduate courses.
 
Mathematics 601       Measure and Integration
Abstract measure theory, basic integration theorems, Fubini's theorem, Radon-Nikodym theorem, Lp spaces, Riesz representation theorem.
Course Hours: H(3-0)
Prerequisite(s): Mathematics 545 or Pure Mathematics 545 or consent of the Division.
Antirequisite(s): Credit for more than one of Mathematics 501, 601, Pure Mathematics 501 or 601 will not be allowed.
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Mathematics 621       Complex Analysis
Analytic functions as mappings, local properties of analytic functions, Schwarz lemma, Casorati-Weierstrass and Picard theorems, analytic continuation, harmonic and subharmonic functions, approximation theorems, conformal mappings, Riemann surfaces.
Course Hours: H(3-0)
Prerequisite(s): Mathematics 335 or 355 or Pure Mathematics 435 or 455 or consent of the Department.
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