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Pure Mathematics


Mathematics is both an art and a science, and Pure Mathematics lies at its heart. Many study Pure Mathematics for the pursuit of knowledge for its own sake and because of its beauty, while others want a strong foundation for graduate work or with a view to applying their knowledge. Pure Mathematics courses explore the boundary of Mathematics and pure reason; they stimulate the mind, promise intellectual growth, and are an asset to any program. We hope to impart in our students a love for learning, and to develop their abilities to work independently and to think critically and creatively. This is achieved with small classes and a supportive atmosphere in which all students are challenged to fulfill their academic potential.

Pure Mathematics graduates have been successful in a wide variety of careers. Many go into industry as the skills they have acquired are recognized by employers as being valuable and transferable. Others go into education at all levels or continue their studies at graduate school in either Mathematics or some other discipline.

Pure Mathematics comprises a broad spectrum of Mathematics. Interests of the Department include algebra, number theory, analysis, geometry, topology, logic and functional equations, and range from the very classical to the most modern. The Department offers several programs. All are available to both co-op and regular students. Many students have found it rewarding to combine Pure Mathematics with another mathematical discipline, and for such students joint programs are available. Students from other departments, especially those considering pursuing graduate work (in any area of Mathematics), are encouraged to speak with a Pure Mathematics advisor about which Pure Mathematics courses would be particularly important, interesting and beneficial for them. A more detailed description of the Department and its programs may be found in the Pure Mathematics Undergraduate Handbook, available upon request.

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Honours Pure Mathematics

In conjunction with the common degree requirements in Table I in "Degree Requirements", this program requires at least 26 math half-credits. These overall requirements must include the Faculty core courses outlined in Table II in "Degree Requirements" and the following courses:

All of
PMATH 343 Abstract Algebra 1
PMATH 344 Abstract Algebra 2
PMATH 351 Real Analysis
PMATH 352 Complex Analysis
PMATH 353 Fourier Analysis
PMATH 367 Set Theory and General Topology

One of
PMATH 441 Algebraic Number Theory
PMATH 444 Non-Commutative Algebra
PMATH 446 Group Theory
PMATH 448 Commutative Algebra

One of
PMATH 451/AM 431 Measure and Integration
PMATH 452 Topics in Complex Analysis
PMATH 453/AM 432 Functional Analysis
Three additional 400-level PMATH half-credits

All of
C&O 230 Introduction to Combinatorics
Two additional 400-level math half-credits

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Joint Honours Pure Mathematics
See "Academic Programs" for a complete description of Joint program requirements.

All of
PMATH 343 Abstract Algebra 1
PMATH 344 Abstract Algebra 2
PMATH 351 Real Analysis
PMATH 352 Complex Analysis

One of
PMATH 353 Fourier Analysis
PMATH 367 Set Theory and General Topology

Three additional 400-level PMATH half-credits

One additional 300- or 400-level Group 2 PMATH half-credit

Notes
The following requirements and recommendations also apply for the Joint Honours partners indicated:

  1. AM: PMATH 353 required; PMATH 451, 453 strongly recommended
  2. C&O: PMATH 444, 446, 448 at least one is strongly recommended
  3. CS: one of PMATH 432 , 444, 446, and 448 is required
  4. STAT: PMATH 451 required

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Honours 'X' with Pure Mathematics Minor

See "Academic Programs" for a complete description of Minor program requirements.

All of
PMATH 344 Abstract Algebra 2
PMATH 351 Real Analysis
PMATH 352 Complex Analysis

Three additional 300- or 400-level Group 2 PMATH half-credits.

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