Course Descriptions

Each student in the course is required to prepare and submit a written document treating a topic in the mathematical and/or statistical sciences. The topic should be one that is not typically taught in the standard course offerings of the Department of Mathematics and Statistics. Each student will work under the guidance of a faculty advisor. After submitting the thesis, the student will deliver an oral presentation on their topic for their peers in the course, the faculty advisors, and the course coordinator(s).

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 course coordinator(s) will assist with finding an advisor as necessary. Mathematical Physics students taking PHYS 491 or PHYS 493 in addition to MATH 402 may be able to coordinate their research project in PHYS 491 or PHYS 493 with their thesis work in MATH 402, subject to the approval of both the MATH 402 course coordinator(s) and the PHYS 491 or PHYS 493 supervisor(s).

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.

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.

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.

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.

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.

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.

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.

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.

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

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