# Teaching

## Recent Courses

• MAT 347 (Groups, Rings, and Fields), Fall 2018
• MAT 1200/415 (Algebraic Number Theory), Fall 2018
• MAT 1110 (Linear Algebraic Groups), Winter 2017
• MAT 247 (Algebra II), Winter 2017
• MAT 1100 (Algebra I), Fall 2016
• MAT 224 (Linear Algebra II), Winter 2016
• MAT 1100 (Algebra I), Fall 2015
• MAT 1210 (Arithmetic of Elliptic Curves), Winter 2015
Main reference: Silverman, The Arithmetic of Elliptic Curves
• Homework 1 (due Feb 25):
• Problems 1.10, 2.3, 2.4, 3.3(d) + show this is an elliptic curve + find a Weierstrass equation (hint: recall how we found Weierstrass coordinates for a general elliptic curves), 3.5, 3.8
• Consider E: y^2 = x^3 - 43x + 166 over the rationals and P = (3,8). Show by hand that P has finite order. (Hint: it may be more efficient to compute some 2^i P first.)
• Homework 2 (due Mar 27):
• Homework 3 (due Apr 30):
• Problems 7.3, 7.4, 7.5(c), 8.1, 8.2, 8.3, 8.12(e)
• MAT 1200/415 (Algebraic Number Theory), Winter 2014
Main reference: Milne's notes
• Homework 1 (due Feb 27): Marcus chapter 2, exercises 11, 28, 30, 40, 41, 42(ab).
• Homework 2 (due Apr 4):
• Determine the class groups of Q(root(d)) for d equal to 6, 10, -19, -23, -14, -21.
• Show that the class number of Q(a) is 1, where a^3-a+1 = 0.
• Marcus chapter 5, exercises 33, 47. Determine the unit group of O_K where K = Q(root(d)) for d equal to 5, 14.
• Marcus chapter 3, exercises 16, 17, 30. Marcus chapter 4, exercises 5, 6, 7.
• Homework 3 (due Apr 18):
• Let K be the 527-th cyclotomic field. Determine all quadratic and all cubic subextensions of K. Give a description of the primes that split completely in the cubic subextensions.
• Cassels chapter 4, exercises 3, 5, 6. Also, answer the following question: for the cubic field K = Q(a), where a has minimal polynomial F(X) given in Cassels exercise 6, find all e_i and f_i for p = 2, 3, 5, 7.
• Cassels chapter 7, exercises 5 (only (i)-(iii)), 10, 13, 18.
• Milne, appendix B, problem 6.
• MAT 135 (Calculus I(A)), Fall 2013
• MAT 1110 (Linear Algebraic Groups), Winter 2013
• Homework 1 (due Feb 25): Springer 2.1.5(3,5), 2.2.2(4), 2.3.4(2,3), 2.4.10(3), 3.2.10(2,3,4,5)
Homework 2 (due Apr 5): Springer 4.4.11(1,3,4), 4.4.15(6), 5.3.5(2), 5.5.9(1,3), 5.5.11(2), additional problems
(for 4.4.11(4) try to generalise to all diagonalisable groups)
Homework 3 (due Apr 30): Springer 6.2.11(4), 6.3.7(2,3,4,5), 6.4.15(1,2,4), 7.2.5(3), 7.4.7(2,3,4)
please do at least three of these problems
• Course Notes (typed by Joshua Seaton)
• MAT 327 (Introduction to Topology), Fall 2012
• MAT 1104, (The Mod p Representation Theory of p-adic Groups), Winter 2012
• MAT 327 (Introduction to Topology), Fall 2011
• Math 230 (Differential Calculus of Multivariable Functions), Spring 2010
• Math 470-3 (Graduate Algebra), Spring 2010
• Math 220 (Differential Calculus of One Variable), Fall 2009
• Math 470-1 (Graduate Algebra), Fall 2009
• Math 224 (Integral Calculus of One Variable), Winter 2009
• Math 330-2 (Abstract Algebra: Ring Theory), Winter 2009
• Math 220 (Differential Calculus of One Variable), Fall 2008
• Math 330-1 (Abstract Algebra: Group Theory), Fall 2008
• Math 224 (Integral Calculus of One Variable), Winter 2008
• Math 224 (Integral Calculus of One Variable), Winter 2008
• Math 220 (Differential Calculus of One Variable), Fall 2007
• Math 220 (Differential Calculus of One Variable), Fall 2007