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Introduction toGRADUATE STUDIES inPURE MATHEMATICS
Spiro Karigiannis
Associate Chair of Graduate Studies
September 17, 2014
S. Karigiannis (Grad Chair) Intro to Pure Math Grad Studies September 17, 2014 1 / 12
Why be a Pure Math Graduate Student?
Pure mathematics trains your mind to think logically and analytically
• Excellent preparation for professional careers
Computing industry
Financial industry
Government
Teaching
To obtain a solid foundation for further studies in more applied areas(for example: theoretical physics, computer science)
To become a professional mathematician
For personal interest
S. Karigiannis (Grad Chair) Intro to Pure Math Grad Studies September 17, 2014 2 / 12
Being a Pure Math Graduate Student
What is it like?
A new kind of educational experience.Learn mostly on your own or from your advisor; courses are secondary.Questions not well-defined. Research doesn’t proceed as expected.Collegial atmosphere – learn from your fellow graduate students.Students come from across Canada and around the world
Financial support
Minimum support ≥ $26 300/year.Funding from a combination of TAs, GRSs, and Scholarships.NSERC/OGS holders could earn $31,000 – $48,000/year.Non-major award holders should expect to be assigned 1 or 2 TAunits per term, equivalent to 5 or 10 hours of work per week.
S. Karigiannis (Grad Chair) Intro to Pure Math Grad Studies September 17, 2014 3 / 12
Aspects of the Pure Math Graduate Program
Courses
We offer a variety of intellectually stimulating and challenging courses:functional analysis, measure theory, algebraic topology, Lie groups,representation theory, commutative algebra, algebraic geometry,differential geometry, computability theory, model theory, more . . .We also have 3–4 advanced topics graduate courses per term.
Project / Thesis
work one-on-one with a supervisor, or multiple advisors.learn how to do mathematical research.explore a topic in depth; maybe discover new mathematical results.
S. Karigiannis (Grad Chair) Intro to Pure Math Grad Studies September 17, 2014 4 / 12
Specifics of our Graduate Programs
MMath (Master of Mathematics) – a one year (3 terms) program
Requires 6 courses, with average ≥ 70%. {≤ 2 can be held withundergrad courses; ≥ 2 must be advanced topics (900-level) courses.}MMath Research Paper requirement: typically 25–35 typeset pages.Usually completed in the spring term.∃ MMath THESIS OPTION for most qualified students. [Ask me!]
PhD (Doctor of Philosophy) – typically 4–5 years in duration
Admission usually requires equivalent of Master’s degree in pure math.Requires 4 courses, with average ≥ 70%. {None can be held withundergrad courses; ≥ 3 must be advanced topics (900-level) courses.}Y1: Comprehensive written exams: Algebra; Analysis & TopologyY2: Oral exam: tests readiness for independent specialized research.Thesis: the PhD thesis must contain original results that are ofpublishable value. This is the most important requirement!
S. Karigiannis (Grad Chair) Intro to Pure Math Grad Studies September 17, 2014 5 / 12
Research area: Analysis
Ken Davidson Brian Forrest Kathryn HareLaurent Marcoux Andu Nica Nico Spronk
• harmonic analysis • operator theory– abstract – single operators– commutative / real line – operator algebras / C*-algebras– Lie groups – operator spaces
• free probability • topological quantum groups• fractal analysis
S. Karigiannis (Grad Chair) Intro to Pure Math Grad Studies September 17, 2014 6 / 12
Research area: Algebra and Logic
Jason Bell Barbara Csima Wentang Kuo David McKinnonRahim Moosa Ross Willard Frank Zorzitto
• model theory • computatibilty theory• universal algebra • logical limit laws• ring theory • representation theory
– dimension theory – Lie groups– Grobner bases • algebraic geometry
– Langlands program
S. Karigiannis (Grad Chair) Intro to Pure Math Grad Studies September 17, 2014 7 / 12
Research area: Number Theory
Kevin Hare Wentang Kuo Yu-Ru LiuDavid McKinnon Mike Rubinstein Cam Stewart
• analytic number theory • algebraic number theory– Diophantine equations – algebraic geometry– modular forms / L-functions – arithmetic geometry– p-adic analysis – elliptic curves– circle methods • computational number theory– probabilistic number theory – fractal analysis
S. Karigiannis (Grad Chair) Intro to Pure Math Grad Studies September 17, 2014 8 / 12
Research area: Geometry and Topology
Benoit Charbonneau Spiro Karigiannis David McKinnonRahim Moosa Ruxandra Moraru Doug Park
• Differential / algebraic geometry • low dimensional topology– complex geometry – 4-manifolds– geometric analysis – exotic smooth structures– PDEs on manifolds • algebraic topology– gauge theory • differential fields– connections to physics – Galois theory of Lie groups
S. Karigiannis (Grad Chair) Intro to Pure Math Grad Studies September 17, 2014 9 / 12
Next steps – thinking about Pure Math
Course preparation
Take advanced sections of math courses [145–148, 245, 247]Take a broad selection of the 300-level and 400-level PMATH courses.
Undergraduate research
Apply for an NSERC USRA. To learn more, see here:http://math.uwaterloo.ca/pure-mathematics/
Faculty mentorship
Engage a PMATH faculty member to advise you on a possibleacademic plan, based on your interests.
S. Karigiannis (Grad Chair) Intro to Pure Math Grad Studies September 17, 2014 10 / 12
Practicalities of applying
Applying for admission
The application deadline is January 15. Some offers of admissionwill be made as early as mid-December, so apply early toensure full consideration! For more info, see here:http://math.uwaterloo.ca/pure-mathematics/graduate-studies/application-procedure-admissionsStart thinking now about suitable people to write letters of reference.
Scholarships
Apply for NSERC and OGS scholarships through Pure Math Dept.These application deadlines have now passed.
S. Karigiannis (Grad Chair) Intro to Pure Math Grad Studies September 17, 2014 11 / 12
Contact information
Spiro Karigiannis – Associate Chair of Graduate StudiesMC5082, karigiannis@uwaterloo.ca
Nancy Maloney – Graduate Studies Administrative AssistantMC5064, nfmaloney@uwaterloo.ca
S. Karigiannis (Grad Chair) Intro to Pure Math Grad Studies September 17, 2014 12 / 12
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