Not all courses described in the Course and Program Catalogue are offered each year. For a list of course offerings in 2021-2022, please consult the class search website.

The following conventions are used for course numbering:

- 010-099 represent non-degree level courses
- 100-699 represent undergraduate degree level courses
- 700-999 represent graduate degree level courses

## Course search

### 72 Results

#### MATH 101.3: Quantitative Reasoning

This course will expose students to various aspects of quantitative reasoning, including the use of quantitative arguments to analyze problems, critique arguments, and draw and justify conclusions; the recognition and evaluation of quantitative assumptions; and the detection and interpretation of trends and patterns in quantitative data drawn from real-world sources and case studies. The course will nurture basic skills in numeracy, arithmetic, and estimation. In the process, students will learn to use algebraic and statistical methods to solve problems and understand changing quantities. They will also use visual and technological tools to assist with calculations and analysis. The format of the course involves 1 hour of lecture and 3 hours of lab-based active learning activity per week, emphasizing inquiry and practice.

**Weekly hours:**
1 Lecture hours and 3 Practicum/Lab hours**Note:** This course may not be taken for credit concurrently with or after any other 100-level MATH course or any course in statistics. Students may only have credit for one of MATH 101 and MATH 150. In Arts & Science programs, this course may be used only in the Quantitative Requirement (if listed for that program) or the Electives Requirement.

#### MATH 102.3: Precalculus Mathematics

Discusses mathematical ideas essential for the study of calculus. Topics include: the fundamentals of algebra; functions, their properties and graphs; polynomial and rational functions; exponential and logarithmic functions; trigonometric and inverse trigonometric functions; trigonometric properties.

**Weekly hours:**
3 Lecture hours and 1.5 Practicum/Lab hours**Prerequisite(s):** Workplace & Apprenticeship Mathematics 30, Foundations of Mathematics 30, or Pre-Calculus 20, or equivalent background in mathematics.

**Note:** This course may not be taken for credit concurrently with or after MATH 104, MATH 110, MATH 121, MATH 125, or MATH 176. MATH 102 may not be included in the courses required in C4 or C6 for Applied Mathematics, Mathematical Physics, Mathematics or Statistics. In Arts & Science programs, this course may be used only in the Quantitative Requirement (if listed for that program) or Electives Requirement.

#### MATH 104.3: Elementary Calculus

An elementary introduction to calculus including functions, limits, derivatives, techniques of differentiation, curve sketching and maximum and minimum problems, antiderivatives and the integral.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** Foundations of Mathematics 30, Pre-Calculus 30, or MATH 102

**Note(s):** As of 2020-2021 students can have credit for only one of MATH 104, MATH 110, MATH 121, MATH 123, MATH 125 or MATH 176. Students who attempted MATH 104 in 2019-2020 or earlier may have credit for both MATH 104 and one of MATH 110, MATH 121, MATH 123, MATH 125, or MATH 176. This course may not be included in the courses required in C4 or C6 for Applied Mathematics, Mathematical Physics, Mathematics or Statistics.

#### MATH 110.3: Calculus I

Introduction to derivatives, limits, techniques of differentiation, maximum and minimum problems and other applications, implicit differentiation, anti-derivatives.

**Weekly hours:**
3 Lecture hours and 1.5 Practicum/Lab hours** Prerequisite(s):** Pre-Calculus 30 or MATH 102.3

** Note(s):** Students can have credit for only one of MATH 104, MATH 110, MATH 121, MATH 123, MATH 125, MATH 133 or MATH 176. The Math Readiness Assessment helps students assess their readiness for MATH 110. It is especially valuable for students without credit for MATH 102. More information is available at http://math.usask.ca/placement.

#### MATH 116.3: Calculus II

A continuation of MATH 110. Topics include definite and indefinite integrals, the Fundamental Theorem of Calculus, techniques of integration, approximate integration, indeterminate forms & L'Hospital's rule, improper integrals, applications of integration, and introduction to differential equations.

**Weekly hours:**
3 Lecture hours and 1.5 Practicum/Lab hours**Prerequisite(s):** MATH 110.3

**Note:** Students may have credit for only one of MATH 112, MATH 116, MATH 124, MATH 134 or MATH 177. Students with credit for MATH 123 may take this course for credit.

#### MATH 121.3: Mathematical Analysis for Business and Economics

An introduction to mathematics for business and economics students using examples from business to motivate mathematical techniques. Necessary mathematical terms and concepts are developed, but emphasis is on applications to business with sufficient theory to support applications. Topics: algebraic functions, mathematics of finance, analysis of functions, differential and integral calculus.

**Weekly hours:**
3 Lecture hours and 1.5 Practicum/Lab hours** Prerequisite(s):** Foundations of Mathematics 30 or Pre-Calculus 30 (Pre-Calculus 30 preferred); or MATH 102.3

** Note(s):** Students can have credit for only one of MATH 104, MATH 110, MATH 121, MATH 123, MATH 125, MATH 133 or MATH 176. The Math Readiness Assessment helps students assess their readiness for MATH 121. It is especially valuable for students without credit for MATH 102. More information is available at http://math.usask.ca/placement.

#### MATH 125.3: Mathematics for the Life Sciences

An introduction to mathematical modelling with a focus on applications to the life sciences. Topics include: algebraic functions and their graphs, limits and rates of change, differentiation techniques and applications, exponential and logarithmic functions, integration and the area under a curve, introduction to differential equations. The main feature of this course is the use of structured examples from life sciences to establish a need for mathematical techniques. Necessary mathematical terms and concepts will be developed. The emphasis throughout this course is on applications of mathematics to life sciences with enough theory to support applications. Extensive examples from Biology, Health Sciences, Chemistry and Physics will be used.

**Weekly hours:**
3 Lecture hours and 1.5 Practicum/Lab hours** Prerequisite(s):** Pre-Calculus 30 or MATH 102.3

** Note(s):** This course is restricted to students majoring in, or intending to major in, Biochemistry, Microbiology and Immunology; Biology; Biomedical Foundations; Biomedical Neuroscience; Cellular, Physiological, and Pharmacological Sciences; Environment & Society; Environmental Biology; Health Studies; Toxicology; or Pharmacy. Students can have credit for only one of MATH 104, MATH 110, MATH 121, MATH 123, MATH 125, MATH 133 or MATH 176.

#### MATH 133.4: Engineering Mathematics I

An introduction to foundational concepts and tools in calculus, linear algebra, and statistics that are essential to engineering. Topics include basic integration techniques, limits and continuity, derivatives and their applications, matrix operations and linear transformations, linear regression, and graphing data on various scales.

**Weekly hours:**
1.5 Lecture hours and 1.5 Practicum/Lab hours**Restriction(s):** Restricted to students in the College of Engineering.

**Prerequisite(s):** Pre-Calculus 30, or MATH 102.3

#### MATH 134.3: Engineering Mathematics II

This course is a continuation of Engineering Mathematics I. Topics include integration techniques and applications, dot products and cross products for vectors, polar coordinates, and complex numbers.

**Weekly hours:**
1.5 Lecture hours and 1.5 Practicum/Lab hours**Restriction(s):** Restricted to students in the College of Engineering.

**Prerequisite(s):** ): MATH 133.4; or [(MATH 110.3 or MATH 123.3 or MATH 176.3) and (MATH 164.3 or MATH 264.3 or MATH 266.3)].

#### MATH 150.3: Mathematics for Early and Middle Years Teachers

An introductory course in mathematics specifically designed for students enrolled in the Early/Middle Years route of the Bachelor of Education program. A broad survey of mathematical topics aligned with the Saskatchewan mathematics curriculum, including logical and set-theoretic reasoning, number theory and numerical operations, algebraic expressions and modelling, functions and their graphs, planar and solid geometry, probability and statistics. Collaborative group work in labs and reflective journaling ensure that mathematical communication and appreciation are emphasized alongside quantitative proficiency throughout the course.

**Weekly hours:**
3 Lecture hours and 1.5 Practicum/Lab hours**Restriction(s):** Restricted to students in the College of Education

**Prerequisite(s):** Precalculus 30; or Foundations of Mathematics 30

**Note:** Intended for students enrolled in the Early/Middle Years route of the Bachelor of Education program. Students who excel at mathematics and/or have chosen mathematics as one of their teaching areas should speak to an advisor about alternate mathematics and statistics course recommendations. Does not fulfill requirements of a major or honours in either mathematics or statistics, or any other Arts & Science degree program. This course may not be taken for credit concurrently with or after any other 100-level MATH course or any course in statistics. Students may have credit for only one of MATH 100, MATH 101 or MATH 150.

#### MATH 163.3: Introduction to Mathematical Reasoning

A broad introduction to the language of Mathematics through the study of logic and proof techniques, sets, functions and relations, integers and counting, complex numbers, and graphs.

**Weekly hours:**
3 Lecture hours and 1 Practicum/Lab hours**Prerequisite(s):** Pre-Calculus 30; or Foundations of Mathematics 30.

#### MATH 164.3: Introduction to Linear Algebra

Systems of linear equations over the real numbers. Vector algebra on ordered n-tuples (Euclidean n-space). Representation of linear systems as rectangular matrices. Elementary row operations; the row canonical form of a matrix. Basic matrix algebra (addition, subtraction, scalar multiplication). Matrix-vector multiplication; linear maps between Euclidean spaces. Matrix multiplication, square matrices, algorithms for matrix inverses. Introduction to determinants, eigenvalues, eigenvectors, and applications. Numerical linear algebra with computer algebra systems. Applications of linear algebra to other disciplines.

**Weekly hours:**
3 Lecture hours and 1.5 Practicum/Lab hours**Prerequisite(s):** Pre-Calculus 30; or Foundations of Mathematics 30; or 3 credit units of MATH or STAT

**Note:**Students with credit for MATH 264 or MATH 266 (taken prior to 2019-20) will not receive credit for this course.

#### MATH 176.3: Advanced Calculus I

An introduction to calculus and analytical reasoning. Topics include sequences and series; completeness of real numbers; limits and continuity in a single variable; differentiation and its basic properties; implicit differentiation; L'Hôspital's rule; Newton's method; optimization; and introduction to Taylor series. This course introduces a number of fundamental concepts that will be useful in future courses in mathematics, statistics and other sciences.

**Weekly hours:**
3 Lecture hours and 1.5 Practicum/Lab hours** Prerequisite(s):** Calculus 30

** Note(s):** This course is recommended for students intending to major in mathematics and related disciplines. Students can have credit for only one of MATH 104, MATH 110, MATH 121, MATH 123, MATH 125, MATH 133 or MATH 176.

#### MATH 177.3: Advanced Calculus II

A continuation of MATH 176, with an emphasis on integral calculus and analytical reasoning. Topics include the Riemann integral and its basic properties; the Fundamental Theorem of Calculus; techniques and applications of integration; numerical integration; power series and applications. This course introduces a number of fundamental concepts that will be useful in future courses in mathematics, statistics and other sciences.

**Weekly hours:**
3 Lecture hours and 1.5 Practicum/Lab hours**Prerequisite(s):** MATH 110.3, or MATH 123.3, or MATH 176.3

**Note:** This course is recommended for students intending to major in mathematics and related disciplines. MATH 176 is the recommended prerequisite for this class. Students entering with MATH 110 or MATH 123 with a grade of less than 85% should consult a departmental adviser before registering in this course. Students may have credit for only one of MATH 116, MATH 124, MATH 134 or MATH 177.

#### MATH 211.3: Numerical Analysis I

An introductory course. Topics include errors, solutions of linear and non-linear equations, interpolation, numerical integration, solutions of ordinary differential equations.

**Weekly hours:**
3 Lecture hours and 1 Practicum/Lab hours**Prerequisite(s):** MATH 116 or MATH 124 or MATH 177; and MATH 164.

#### MATH 223.3: Calculus III for Engineers

Vectors and coordinate geometry in 3- space; vector functions and curves; partial differentiation; applications of partial derivatives; multiple integration.

**Weekly hours:**
3 Lecture hours and 1 Practicum/Lab hours**Restriction(s):** Enrollment in the College of Engineering.

**Prerequisite(s):** MATH 123 and 124.

**Note:** Engineering students may take this course with prerequisite of MATH 110 and 116 if they seek permission of the Engineering Students' Centre. Arts & Science students majoring in Physics may receive permission to take this course by contacting the Department of Mathematics and Statistics. Students with credit for MATH 225 or 276 may not take this course for credit.

#### MATH 224.3: Calculus IV for Engineers

Vector fields; vector calculus; ordinary differential equations; sequences, series, and power series.

**Weekly hours:**
3 Lecture hours and 1 Practicum/Lab hours**Restriction(s):** Enrollment in the College of Engineering.

**Prerequisite(s):** MATH 123, 124 and 223 (all taken).

**Note:** Arts & Science students majoring in Physics may receive permission to take this course by contacting the Department of Mathematics and Statistics. Students with credit for MATH 226 may not take this course for credit.

#### MATH 225.3: Intermediate Calculus I

Analytic geometry, vectors, vector functions, partial differentiation, multiple integration, line integrals and Green's theorem.

**Weekly hours:**
3 Lecture hours and 1 Practicum/Lab hours**Prerequisite(s):** MATH 116.3 or MATH 177.3.**Note:** Students with credit for MATH 223 or MATH 276 may not take this course for credit.

#### MATH 226.3: Intermediate Calculus II

Infinite sequences and series, complex numbers, first order and linear differential equations.

**Weekly hours:**
3 Lecture hours and 1 Practicum/Lab hours**Prerequisite(s):** MATH 116.3 or MATH 177.3.

**Note:** Students with credit for MATH 224 may not take this course for credit.

#### MATH 238.3: Introduction to Differential Equations

This course introduces students to ordinary differential equations, including elementary existence results, power series solutions, and techniques of solution involving matrix computations. Examples will be drawn from the physical and biological sciences.

**Weekly hours:**
3 Lecture hours and 1.5 Practicum/Lab hours**Prerequisite(s):** MATH 116 or MATH 124 or MATH 177; and MATH 164.

#### MATH 258.3: Euclidean Geometry

A course in plane Euclidean geometry. Particularly recommended for teachers of mathematics.

**Weekly hours:**
3 Lecture hours and 1 Practicum/Lab hours** Prerequisite(s):** MATH 163

** Note(s):** May not be included in the courses required in C4 or C6 for Honours programs in Applied Mathematics, Mathematical Physics, Mathematics or Statistics.

#### MATH 266.3: Linear Algebra II

This course follows MATH 164 (Introduction to Linear Algebra). Topics include: abstract vector spaces, linear transformations, polynomials, trace and determinant, eigenvectors and invariant subspaces, canonical forms, and inner products.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** MATH 164

#### MATH 276.3: Vector Calculus I

This course is an introduction to calculus in higher dimensions, including linear transformations between real vector spaces, limits and continuity in Rn using epsilon-delta, the derivative as a linear transformation (including the Jacobian matrix), Newton's method for functions from Rn to Rn, and the inverse function theorem.

**Weekly hours:**
3 Lecture hours and 1.5 Practicum/Lab hours**Prerequisite(s):** MATH 116 or MATH 124 or MATH 177; and MATH 164

#### MATH 277.3: Vector Calculus II

A continuation of MATH 276, this course introduces students to Taylor series for functions from Rn to Rm and higher derivatives of functions from Rn to Rm; inner products, critical points and their classification; constrained optimization through Lagrange multipliers; and integration via differential forms leading to Stokes' Theorem.

**Weekly hours:**
3 Lecture hours and 1.5 Practicum/Lab hours**Prerequisite(s):** MATH 276.3

#### MATH 298.3: Special Topics

Offered occasionally by visiting faculty and in other special situations to cover, in depth, topics that are not thoroughly covered in regularly offered courses.

**Weekly hours:**
3 Lecture hours

#### MATH 299.6: Special Topics

Offered occasionally by visiting faculty and in other special situations to cover, in depth, topics that are not thoroughly covered in regularly offered courses.

**Weekly hours:**
3 Lecture hours

#### MATH 313.3: Numerical Linear Algebra

Numerical methods in linear algebra. Topics covered include approximation theory, least squares, direct methods for linear equations, iterative methods in matrix algebra, eigenvalues, systems of non-linear equations.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** MATH 164 or MATH 266; and MATH 211.

#### MATH 314.3: Numerical Solution of Ordinary Differential Equations

Numerical differentiation and integration, initial-value, and boundary-value problems for ordinary differential equations, introduction to numerical solutions to partial-differential equations.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** MATH 211.3 and MATH 238.3

#### MATH 325.3: Introduction to Optimization

This course introduces the fundamentals of mathematical optimization methods, centering around linear programming. Topics include formulating real-life problems (such as production planning, inventory, shortest path and assignment problems) as linear programs, the simplex algorithm, geometry of feasible regions and optimal solutions, duality theory and complementary slackness conditions. Tools relating linear and integer programs such as Gomory cuts and branch-and-bound methods, as well as applications in game theory, will also be discussed.

**Weekly hours:**
3 Lecture hours and 1 Practicum/Lab hours**Prerequisite(s):** MATH 163.3; and MATH 164.3 or MATH 266.3.

#### MATH 327.3: Graph Theory

Graph Theory and its contemporary applications including the nomenclature, special types of paths, matchings and coverings, and optimization problems soluble with graphs.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** MATH 164.3 or MATH 266.3; and CMPT 260.3 or 6 credit units 200-level MATH.

#### MATH 328.3: Combinatorics and Enumeration

The theory of Combinatorics and Enumeration and its contemporary applications, including generating functions and recurrence relations, and the Polya and Ramsey Theories. A wide variety of practical applications will be presented.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** ): MATH 164.3 or MATH 266.3; and CMPT 260.3 or 6 credit units 200-level MATH.

#### MATH 331.3: Applied Differential Equations

General theory of ordinary differential equations with constant coefficients, series solutions of ordinary differential equations, special functions, Fourier series, introduction to Sturm-Liouville theory, physical origin of heat, wave and Laplace equations, solution by separation of variables.

**Weekly hours:**
3 Lecture hours and 1.5 Practicum/Lab hours**Prerequisite(s):** MATH 224.3 or MATH 226.3 or MATH 238.3 (or approval of instructor)

**Note:** Students with credit for MATH 338 may not take this course for credit.

#### MATH 336.3: Mathematical Modelling I

The course is designed to teach students how to apply Mathematics by formulating, analyzing and criticizing models arising in real-world situations. An important aspect in modelling a problem is to choose an appropriate set of mathematical methods - 'tools' - in which to formulate the problem mathematically. In most cases a problem can be categorized into one of three types, namely: continuous, discrete, and probabilistic. The course will consist of an introduction to mathematical modelling through examples of these three basic modelling types.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** MATH 164.3 or MATH 266.3; and MATH 211.3, and STAT 241.3, and (MATH 224.3) or (MATH 225.3 and MATH 226.3) or (MATH 277.3).

#### MATH 339.3: Differential Equations and Special Functions

Basic Sturm-Liouville theory, Green's functions, hypergeometric equation, special functions of Mathematical Physics, Fourier transform, introduction to distributions/generalized functions, applications to linear differential equations.

**Weekly hours:**
3 Lecture hours and 1.5 Practicum/Lab hours**Prerequisite(s):** MATH 223 and MATH 224; or MATH 225 and MATH 226; or MATH 238 and MATH 276; or approval of the instructor.

**Note:** Students with credit for MATH 338 may not take this course for credit.

#### MATH 352.3: Elementary Differential Geometry

Introduction to differential geometry of curves, surfaces, hypersurfaces, curvature and geodesics.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** MATH 266; and (MATH 238 and MATH 277) or (MATH 223 and MATH 224) or (MATH 225 and MATH 226 - with grades of at least 80% and permission of the instructor).

**Note:** Students may receive credit for only one of MATH 350 or MATH 352.

#### MATH 361.3: Group Theory

Introduction to group theory, including: cyclic groups, symmetric groups, subgroups and normal subgroups, Lagrange's theorem, quotient groups and homomorphisms, isomorphism theorems, group actions, Sylow's theorem, simple groups, direct and semidirect products, fundamental theorem on finitely generated Abelian groups.

**Weekly hours:**
3 Lecture hours and 1 Practicum/Lab hours**Prerequisite(s):** MATH 163 and MATH 164; or MATH 266

#### MATH 362.3: Rings and Fields

Introduction to ring and field theory, including: polynomial rings, matrix rings, ideals and homomorphisms, quotient rings, Chinese remainder theorem, Euclidean domains, principal ideal domains, unique factorization domains, introduction to module theory, basic theory of field extensions, splitting fields and algebraic closures, finite fields, introduction to Galois theory.

**Weekly hours:**
3 Lecture hours and 1 Practicum/Lab hours**Prerequisite(s):** MATH 163 and MATH 164; or MATH 266

#### MATH 364.3: Number Theory

A course in elementary number theory with emphasis upon the interrelation of number theory and algebraic structures: review of unique factorization and congruences, the ring of integers modulo n and its units, Fermat's little theorem, Euler's function, Wilson's theorem, Chinese remainder theorem, and quadratic reciprocity.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** MATH 163

#### MATH 371.3: Real Analysis I

An introduction to concepts and principles of mathematical analysis in Rn, including Cauchy sequences, compactness, the theory of continuous functions, and uniform convergence.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** MATH 163 and MATH 277; or MATH 277 and permission of the instructor.

**Note:** Students majoring in Applied Mathematics who have completed MATH 223 and 224; or MATH 225 and 226 will be granted a prerequisite waiver to register in MATH 371.

#### MATH 373.3: Real Analysis II

A continuation of MATH 371, centering around Lebesgue integration theory, Lp spaces, and applications.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** MATH 371.

#### MATH 379.3: Complex Analysis

Fundamental concepts, analytic functions, infinite series, integral theorems, calculus of residues, conformal mappings and applications.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** MATH 225 and 226; or MATH 238 and 277.

#### MATH 398.3: Special Topics

Offered occasionally by visiting faculty and in other special situations to cover, in depth, topics that are not thoroughly covered in regularly offered courses.

**Weekly hours:**
3 Seminar/Discussion hours

#### MATH 399.6: Special Topics

**Weekly hours:**
3 Seminar/Discussion hours

#### MATH 402.0: Honours Thesis in Mathematics

Students taking an Honours program in Mathematics or a Double Honours program in Mathematics and a second subject are required to submit a written presentation of a topic in mathematics under the supervision of a faculty advisor and deliver a subsequent oral presentation on the topic. Students in Mathematical Physics must enroll in either MATH 402 or PHYS 491 or PHYS 493.

**Prerequisite(s):** Students must be registered in an Honours or Double Honours program in Mathematical Physics, Mathematics, or Statistics.

**Note:** Students enrolled in this course are expected to find a faculty advisor for the thesis work from Mathematics & Statistics (or from another unit, with the approval of the Undergraduate Chair for Mathematics & Statistics). The Undergraduate Chair will assist with finding an advisor as necessary.

#### MATH 420.3: Topics in Combinatorics

This course will cover topics in combinatorics not discussed in other courses. Possible subjects include: algebraic approaches to combinatorics, coding theory, combinatorial optimization, finite geometries, and topics in graph theory.

**Weekly hours:**
3 Lecture hours**Permission of the instructor is required.**

**Note:** Students may take this course more than once for credit, provided the topic covered in each offering differs substantially. Students must consult the Department to ensure that the topics covered are different.

#### MATH 425.3: Numerical Optimization

An introductory course on numerical optimization. Topics include unconstrained optimization, descent methods, constrained optimization, penalty, barrier, and augmented Lagrangian methods, and applications to inverse problems and deep learning.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** MATH 224.3 or MATH 226.3 or MATH 277.3; and MATH 211.3 and MATH 313.3.

#### MATH 433.3: Applied Group Theory

Treats the following topics from group theory: permutation groups, crystallographic groups, kinematic groups, abstract groups, matrix Lie groups, group representations. Specific topics include the rotation group (spinors and quantum mechanical applications), the Lorentz group (representations and wave equations), SU (3) (its Lie algebra and physical relevance).

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** (MATH 238 and MATH 277) or (MATH 223 and MATH 224) or (MATH 225 and MATH 226 - with grades of at least 80% and permission of the instructor); and MATH 266.

#### MATH 436.3: Mathematical Modelling II

This course is a continuation of MATH 336. The course is designed to further develop students' capacity to formulate, analyze and criticize mathematical models arising in real-world situations. The present course will put emphasis on student activities rather than on lectures. Students will be expected to work in small groups on problems chosen by the instructor and to develop their independent skills at the formulation, analysis and critique of specific problems, and ultimately come to a greater understanding of the modelling process.

**Weekly hours:**
3 Practicum/Lab hours**Prerequisite(s):** MATH 336.3 or permission of the instructor.

#### MATH 438.3: Methods of Applied Mathematics

Calculus of variations, integral equations and applications.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** MATH 238.3, and MATH 277.3.

**Note:** Students cannot receive credit for MATH 438 and MATH 838.

#### MATH 439.3: Partial Differential Equations

Classification of second order partial differential equations, some properties of elliptic, parabolic, and hyperbolic equations, applications.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** MATH 238, 276 and 277.

#### MATH 450.3: Topics in Geometry

This course introduces students to topics in modern geometry drawn from algebraic, differential, and/or symplectic geometry. The course may focus on major themes and emerging phenomena such as the minimal model program, noncommutative geometry, and mirror symmetry; or upon individual classes of interesting geometric spaces, such as algebraic curves and Riemann surfaces, Calabi-Yau manifolds, minimal surfaces, and moduli spaces.

**Weekly hours:**
3 Lecture hours**Permission of the instructor is required.**

**Note:** This course is highly recommended as an elective for students in Honours Mathematical Physics. Students may take this course more than once for credit, provided the topic covered in each offering differs substantially. Students must consult the Department to ensure that the topics covered are different.

#### MATH 452.3: Introduction to Modern Differential Geometry

Submanifolds of Rn; Riemannian manifolds; tensors and differential forms; curvature and geodesics; selected applications.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):**MATH 266; and MATH 352 or MATH 371

**Note:** Students may receive credit for only one of MATH 350 or 452.

#### MATH 460.3: Topics in Algebra

Covers important topics in algebra not discussed in other courses. Possible subjects include: algebraic geometry, commutative algebra, Lie theory, number theory, representation theory.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** MATH 361 and MATH 362; or permission of the instructor.

**Note:** Students may take this course more than once for credit, provided the topic covered in each offering differs substantially. Students must consult the Department to ensure that the topics covered are different.

#### MATH 465.3: Introduction to Cryptography

Presents a thorough introduction to the mathematical foundations of cryptography. Results from number theory and algebra and how they are used for the safe transmission of information are studied. Various security protocols, the mathematical principles needed for them, and the mathematical principles used in possible attacks are examined.

**Weekly hours:**
3 Lecture hours and 1.5 Tutorial hours**Prerequisite(s):** MATH 364 or permission of the instructor.

#### MATH 470.3: Topics in Analysis

This course introduces students to topics of current interest in analysis. The list of possible topics include: distribution theory, random matrix theory, spectral theory, free probability, free Euler hydrodynamics, quantum groups, and recent advances in operator algebras.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** MATH 371 and MATH 379; or permission of the instructor.

**Note:** This course is highly recommended as an elective for students in Honours Mathematics, Honours Mathematical Physics and other Honours streams. Students may take this course more than once for credit, provided the topic covered in each offering differs substantially. Students must consult the Department to ensure that the topics covered are different.

#### MATH 480.3: Topics in Mathematical Physics

This course is intended for students interested in recent developments in mathematical physics. The list of possible topics include: special functions in mathematical physics, representation theory of Lie algebras in the context of the Standard Model; random matrix theory and its applications; topological and quantum materials; and quantum field theory and/or string theory.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** MATH 379 and PHYS 383; or permission of the instructor.

**Note:** Taking at least one iteration of this course is highly recommended for students in Mathematical Physics. Interested Honours students in Mathematics or Physics are encouraged to take this course with permission of the instructor. Students may take this course more than once for credit, provided the topic covered in each offering differs substantially. Students must consult the Department to ensure that the topics covered are different.

#### MATH 485.3: Elements of General Topology

Topological spaces, separation axioms, products, quotients, convergence, connectedness, extension theorems, and metric spaces.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** MATH 371.

#### MATH 498.3: Special Topics

**Weekly hours:**
3 Seminar/Discussion hours

#### MATH 499.6: Special Topics

**Weekly hours:**
3 Seminar/Discussion hours

#### MATH 818.3: Special Topics in Applied Mathematics

The topics to be discussed will be related to recent developments in applied mathematics (numerical analysis, differential equations, mechanics, applied analysis, etc.) of interest to the instructor and students.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** A graduate course in applied mathematics, or permission of the department.**Note:** Students may take this course more than once for credit, provided the topic covered in each offering differs substantially. Students must consult the Department to ensure that the topics covered are different.

#### MATH 838.3: Methods of Applied Mathematics II

The course is devoted to classical topics in Applied Mathematics, including Integral equations, Theory of Distributions, Fourier Transforms, and Calculus of Variations. By the end of the course, students will be able to analyze modern mathematical models involving ordinary and partial differential equations and integral equations, and approach the solution from different points of view, building on knowledge of classical mathematical methods and hands-on practical experience gained in this course.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** (MATH 331.3, MATH 339.3, MATH 371.3, and MATH 373.3), or equivalents as determined by the colllege, or permission of the instructor.

**Note:** Cannot receive credit for MATH 438.3 and MATH 838.3. Cannot receive credit for MATH 838.6 and MATH 838.3.

#### MATH 839.3: Methods of Applied Mathematics I

This course covers methods pertaining to the formulation and solution of problems involving linear and nonlinear Partial and Ordinary Differential Equations (PDE, ODE). Topics include: Linear equations of mathematical physics; Initial/boundary value problems; Bases of functions; Fourier series; Operators in function spaces; Separation of variables; Method of characteristics; Green’s functions; Traveling wave solutions. At the end of the term, students will be able to formulate complex mathematical models, and approach their solution from different points of view, building on knowledge of classical mathematical methods and hands-on practical experience gained in this course.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** (MATH 331.3, MATH 339.3, MATH 371.3, MATH 373.3, and MATH 379.3), or equivalents as determined by the colllege, or permission of the instructor.

**Note:** Cannot receive credit for MATH 439.3 and MATH 839.3.

#### MATH 872.3: Special Topics in Pure Mathematics

The topics to be discussed will be related to recent developments in an area of pure mathematics (analysis, topology, algebra, etc.) of interest to the students and instructor.

**Weekly hours:**
3 Lecture hours**Note:** Students may take this course more than once for credit, provided the topic covered in each offering differs substantially. Students must consult the Department to ensure that the topics covered are different.

#### MATH 875.3: Functional Analysis

An introduction to functional analysis at the graduate level. Topics will include Normed and Banach spaces, Bounded linear operators, The Hahn-Banach Theorem, The Principle of Uniform Boundedness, The Open Mapping and Closed Graph Theorem, Weak and Weak topologies, Adjoint operators, Compact operators on Banach space, Hilbert spaces, Bounded linear operators on Hilbert spaces, Spectrum of operators on Hilbert spaces, Compact Normal operators.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** MATH 371, MATH 373, and MATH 379 or equivalent.

#### MATH 876.3: Operator Theory

An introduction to operator theory at the graduate level. Topics will include Banach algebras, Specturm of an element in Banach algebras, Spectral radius, Analytic functional calculus, C-algebras of operators, Continuous and Borel functional calculus, Spectral measures.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** MATH 371, MATH 373, and MATH 379 or equivalent.

#### MATH 882.3: Algebraic Topology I

Two-dimensional Manifolds, the Fundamental Group including the Seifert-Van Kampen Theorem, Applications to Knot Theory and Group Theory.

**Weekly hours:**
3 Lecture hours**Prerequisite(s):** MATH 485.

#### MATH 898.3: Special Topics

Offered occasionally in special situations. Students interested in these courses should contact the department for more information.

#### MATH 899.6: Special Topics

Offered occasionally in special situations. Students interested in these courses should contact the department for more information.

#### MATH 990.N/A: Seminar

All graduate students in the department enroll each year. Students attend the regular department colloquia. After the first year in their program, they are expected to join the regular seminar series in their area of specialization.

#### MATH 992.0: Project

Students undertaking the project Master's degree (M.Math.) must register for this course.

#### MATH 994.N/A: Research

Students writing a Master's thesis must register for this course.

#### MATH 996.N/A: Research

Students writing a Ph.D. thesis must register for this course.