I enjoy teaching in an interactive environment, with an emphasis on active learning.
Jump to:
 Current courses
 Past courses
 Course evaluations
 Awards and certificates
 Publications (on pedagogy)
 Resources for Teachers (course materials)
 Resources for Students
Current Courses: Spring 2021
 Mathematics 6180. Algebraic Number Theory. Spring 2021.
Introduces number fields and completions, norms, discriminants and differents, finiteness of the ideal class group, Dirichlet’s unit theorem, decomposition of prime ideals in extension fields, decomposition, and ramification groups. Prereqs., MATH 6110 and 6140. Undergraduates must have approval of the instructor. Monday, Wednesday and Friday, 11:30 – 12:20 am, Remotely.
 Homework List
 Course Info/Announcement
 Required CU Syllabus Statements
 Algebraic Number Theory (by Matthew Baker) — these are the notes we base the course on.
 My own corrections to Baker’s notes — based on my reading last time I taught it.
 Number Theory Motivating Questions/Answers
Past Courses at CU Boulder
 Mathematics 4440/5440. Cryptography and Coding Theory. Fall 2020.
Gives an introduction, with proofs, to the algebra and number theory used in coding and cryptography. Basic problems of coding and cryptography are discussed; prepares students for the more advanced ECEN 5032 and 5682. Prereq., MATH 3130. Recommended prereqs., MATH 3110 and 3140.
 Monday, Wednesday and Friday, 1:50 – 2:40 pm, Remotely.
 Course website

 Mathematics 2001. Introduction to Discrete Mathematics. Fall 2020.
Introduces the ideas of rigor and proof through an examination of basic set theory, quantification theory, elementary counting, discrete probability, and additional topics. Prereq., MATH 1300 or APPM 1350.
 Section 5: Monday, Wednesday and Friday, 3:00 – 3:50 pm, Remote.
 Course website

 Mathematics 8114. Topics in Number Theory. Spring 2020.
(a.k.a. Elliptic Curves)
May include the theory of automorphic forms, elliptic curves, or any of a variety of advanced topics in analytic and algebraic number theory. Department enforced prerequisite: MATH 6110. Instructor consent required for undergraduates. [Edit: I will cover the arithmetic of elliptic curves.]
 Monday, Wednesday and Friday, 1:00 – 1:50 pm, MATH 220.
 Course announcement.
 Homework listing.

 Mathematics 3110. Introduction to Theory of Numbers. Spring 2019.
(a.k.a. Number Theory)
Studies the set of integers, focusing on divisibility, congruencies, arithmetic functions, sums of squares, quadratic residues and reciprocity, and elementary results on distributions of primes. Prerequisite: MATH 2001. Monday, Wednesday and Friday, 2:00 – 2:50 am, ECCR 105.
 Course Website
 Mathematics 6180. Algebraic Number Theory. Spring 2019.
Introduces number fields and completions, norms, discriminants and differents, finiteness of the ideal class group, Dirichlet’s unit theorem, decomposition of prime ideals in extension fields, decomposition, and ramification groups. Prereqs., MATH 6110 and 6140. Undergraduates must have approval of the instructor. Monday, Wednesday and Friday, 3:00 – 3:50 am, ECCR 118.
 Algebraic Number Theory (by Matthew Baker) — these are the notes we base the course on.
 My own corrections to Baker’s notes — based on my reading last time I taught it.
 Some Motivational Question in Number Theory (the onepage version without answers is here).
 Mathematics 2001. Introduction to Discrete Mathematics. Spring 2018.
Introduces the ideas of rigor and proof through an examination of basic set theory, quantification theory, elementary counting, discrete probability, and additional topics. Prereq., MATH 1300 or APPM 1350. Section 1: Monday, Wednesday and Friday, 9:00 – 9:50 pm, ECCR 108.
 Section 1: Monday, Wednesday and Friday, 10:00 – 10:50 pm, ECCR 108.
 Course website
 Mathematics 6180. Algebraic Number Theory. Spring 2017.
Introduces number fields and completions, norms, discriminants and differents, finiteness of the ideal class group, Dirichlet’s unit theorem, decomposition of prime ideals in extension fields, decomposition, and ramification groups. Prereqs., MATH 6110 and 6140. Undergraduates must have approval of the instructor. Monday, Wednesday and Friday, 11:00 – 11:50 am, ECCR 139.
 Course Announcement.
 Algebraic Number Theory (by Matthew Baker) — these are the notes we base the course on.
 My own corrections to Baker’s notes — based on my reading this semester.
 Some Motivational Question in Number Theory (the onepage version without answers is here).
 Mathematics 4440/5440. Cryptography and Coding Theory. Fall 2016.
Gives an introduction, with proofs, to the algebra and number theory used in coding and cryptography. Basic problems of coding and cryptography are discussed; prepares students for the more advanced ECEN 5032 and 5682. Prereq., MATH 3130. Recommended prereqs., MATH 3110 and 3140. Monday, Wednesday and Friday, 1:00 – 1:50 pm, ECCR 139.
 Course website
 Mathematics 2001. Introduction to Discrete Mathematics. Fall 2016.
Introduces the ideas of rigor and proof through an examination of basic set theory, quantification theory, elementary counting, discrete probability, and additional topics. Prereq., MATH 1300 or APPM 1350. Monday, Wednesday and Friday, 2:00 – 2:50 pm, ECCR 139.
 Course website
 Mathematics 8114. Topics in Number Theory: The Arithmetic of Kleinian Groups. Spring 2016.
Please see the Course Announcement. Monday, Wednesday and Friday, 9:00 – 9:50 am, ECCR 118.
 Course Announcement.
 Course Notes (ongoing).
 Moebius Transformations Revealed (video).
 Hopf fibration (video).
 Hyperbolic Spaces (notes by John Parker).
 Indra’s Pearls website (to accompany the book; pictures/code).
 Computational tools for hyperbolic 3manifolds and Kleinian groups.
 Curtis T. McMullen, The evolution of geometric structures on 3manifolds; also video.
 A Crash Course on Kleinian Groups (notes by Caroline Series).
 Hyperbolic Geometry (notes by Caroline Series).
 Mathematics 3170. Introduction to Combinatorics, Fall 2015.
Covers basic methods and results in combinatorial theory. Includes numeration methods, elementary properties of functions and relations, and graph theory. Emphasizes applications. Prerequisites: Requires prerequisite course of MATH 2001 (minimum grade C). Monday, Wednesday and Friday, 11:00 – 11:50 am, ECCR 118.
 Mathematics 2001. Introduction to Discrete Mathematics, Fall 2015.
Introduces the ideas of rigor and proof through an examination of basic set theory, quantification theory, elementary counting, discrete probability, and additional topics. Prereq., MATH 1300 or APPM 1350. Monday, Wednesday and Friday, 1:00 – 1:50 pm, ECCR 108.
 Course website
 Syllabus
 Proof Grading Sheet
 Day One: Exploration
 Worksheet on Counting with Independent Choices
 Worksheet on Truth Tables
 Worksheet on Quantifiers and Negation
 Worksheet on Negating for Contradiction
 Second Counting Worksheet
 An Example Combinatorial Proof
 Worksheet on Combinatorial Proof
 More Example Combinatorial Proofs
 Worksheet on the game SET
 Worksheet on Relations and their Properties
 Worksheet on Relations and Equivalence Classes
 Worksheet on Functions
 Worksheet on Inverse Functions
 A function is bijective if and only if it has an inverse
 Take One or Two: Game Theory Worksheet
 Take One or Two: Solution by Induction
 Worksheet on Induction Format
 FCQ Results: numerical and comments
 Mathematics 2001. Introduction to Discrete Mathematics, Spring 2015.
Introduces the ideas of rigor and proof through an examination of basic set theory, quantification theory, elementary counting, discrete probability, and additional topics. Prereq., MATH 1300 or APPM 1350.

 Monday, Wednesday and Friday, 9:00 – 9:50 am, ECCR 108.
 D2L course website
 Course syllabus
 FCQ Results
 Mathematics 6130. Algebra 1, Fall 2014.
Studies group theory and ring theory. Prerequisite, Math 3140. Undergraduates need instructor consent. Prerequisites: Restricted to graduate students only. Monday, Wednesday and Friday, 9:00 – 9:50 am, KOBL 330.
 Course website
 FCQ Results
 Mathematics 4440/5440. Coding and Cryptography, Spring 2014.
Gives an introduction, with proofs, to the algebra and number theory used in coding and cryptography. Basic problems of coding and cryptography are discussed; prepares students for the more advanced ECEN 5032 and 5682. Prereq., MATH 3130. Recommended prereqs., MATH 3110 and 3140.

 Monday, Wednesday and Friday, 2:00 – 2:50 pm, FLMG 156 (changed to ECCR 118).
 Course website
 Mathematics 3130. Linear Algebra, Fall 2013.
Examines basic properties of systems of linear equations, vector spaces, linear independence, dimension, linear transformations, matrices, determinants, eigenvalues, and eigenvectors. Prereq., MATH 2300 or APPM 1360. Credit not granted for this course and APPM 3310. Monday, Wednesday and Friday, 1:00 – 1:50 pm, KOBL 220.
 Course website
 FCQ Results
 Mathematics 6110. Introduction to Number Theory, Fall 2013
Examines divisibility properties of integers, congruencies [sic], diophantine equations, arithmetic functions, quadratic residues, distribution of primes, and algebraic number fields. Prereq., MATH 3140. Undergraduates must have approval of the instructor. Monday, Wednesday, and Friday, 3:00 – 3:50 pm, ECST 1B21 (part of the Engineering Center).
 Course website
 Course Notes
 FCQ Results
 Mathematics 2300. Calculus 2, Honours Section, Fall 2012
Continuation of MATH 1300. Topics include transcendental functions, methods of integration, polar coordinates, conic sections, improper integrals, and infinite series. Prereq., MATH 1300. Credit not granted for this course and MATH 1320 or APPM 1360. Monday, Tuesday, Wednesday, Thursday and Friday, 9:00 – 9:50 am, ECCR 118.
 Course website
 FCQ Results
 Mathematics 6110. Introduction to Number Theory, Fall 2012
Examines divisibility properties of integers, congruencies, diophantine equations, arithmetic functions, quadratic residues, distribution of primes, and algebraic number fields. Prereq., MATH 3140. Undergraduates must have approval of the instructor. Monday, Wednesday and Friday, 3:00 – 3:50 pm, ECST 1B21.
 Course website
 FCQ Results
Courses Taught at the University of British Columbia
 Mathematics 317. Vector calculus, Fall 2010 Parametrizations, inverse and implicit functions, integrals with respect to length and area; grad, div, and curl, theorems of Green, Gauss, and Stokes.
 Course website
 Virtual office hours (course blog)
 Midterm I • Midterm II
 Pencast: An Example Computing Flux (online video)
 Lastday gameshow questions (answers in the course website)
 The Big Theorems (handout for end of term)
 Example homework problems (line integrals in vector fields)
 Sage plotting commands
Courses Taught at Harvard University
 Mathematics 129. Number Fields, Spring 2009 Algebraic number theory: number fields, unique factorization of ideals,
finiteness of class group, structure of unit group, Frobenius elements,
local fields, ramification, weak approximation, adeles, and ideles. Course website was internal to Harvard
 Course lecture notes (incomplete)
 Mathematics 152. Discrete Mathematics, Fall 2008
An introduction to finite groups, finite fields, finite geometry,
discrete probability, and graph theory. A unifying theme of the course
is the symmetry group of the regular icosahedron, whose elements can be
realized as permutations, as linear transformations of vector spaces
over finite fields, as collineations of a finite plane, or as vertices
of a graph. Taught in a seminar format, and students will gain
experience in presenting proofs at the blackboard. Course website was internal to Harvard
 Course weblog (by the students and myself)
 Course syllabus (the course has a very unusual structure driven by student seminars)
 Tips for proofs and presenting (my advice to students)
 Proofs (example outline I wrote for student preparation of presentations)
 Change ringing field trip (student account of the trip)
 RSA encryption (exploratory homework project I designed)
 Homeworks, quizzes, outlines available upon request.
Courses Taught at Brown University
 Mathematics 52. Linear Algebra, Spring 2006 Vector spaces, linear transformations, matrices, systems of linear equations, bases, projections, rotations, determinants, and inner products. Applications may include differential equations, difference equations, least squares approximations, and models in economics and in biological and physical sciences.
 Mathematics 18. Multivariable Calculus, Fall 2004 Threedimensional analytic geometry. Differential and integral calculus of functions of two or three variables: partial derivatives, multiple integrals, Green’s Theorem.
 Course website
 Green’s Theorem lecture (video taped as part of Sheridan Centre Teaching Certificate program)
 Worksheet on surfaces (for inclass use)
 Lecture notes on Lagrange multipliers (for inclass use)
 Mathematics 9. Introductory Calculus, Fall 2003 An intensive course in the calculus of one variable including limits; differentiation; maxima and minima, and the chain rule for polynomials, rational functions, trigonometric functions, and exponential functions. Introduction of integration with applications to area and volumes of revolution.
 Teaching Assistant, Mathematics 9 (Introductory Calculus) in Fall 2002, Spring 2003 An intensive course in the calculus of one variable including limits; differentiation; maxima and minima, and the chain rule for polynomials, rational functions, trigonometric functions, and exponential functions. Introduction of integration with applications to area and volumes of revolution.
Other Teaching
 A Taste of Pi: Clocks, Set, Elliptic Curves and the Secret Math of Spies, Fall 2010 A presentation and workshop for interested high school students, as part of A Taste of Pi. I recommend to interested high school students Joe Silverman’s book A Friendly Introduction to Number Theory and also the summer program, PROMYS.
 Lecture component
 Worksheet
 News brief (sidebar page 7)
Course Evaluations
 The University of Colorado conducts the Faculty Course Questionnaire. Numerical Summary accessible via CU’s FCQ website: [ web ] See individual courses above for full comments
 The University of British Columbia Mathematics Department conducts departmental evaluations by email questionnaire. Report for Math 317 – Fall 2010 [ pdf ]
 The Harvard University Mathematics Department conducts departmental evaluations by email questionnaire. Math 129 had too few students to qualify for evaluation.Numerical Breakdown for Math 152 – Fall 2008 [ pdf ] Complete Record of Reviews for Math 152 – Fall 2008 [ pdf ]
 The Harvard Q is a student organisation that conducts evaluations by email questionnaire.Harvard Q Review for Math 152 – Fall 2008 [ numerical  comments ]
 The Brown University Mathematics Department conducts reviews by paper questionnaire. Although I have a record of the whole stack of reviews, I’ve only entered the breakdown and a selection of comments into the computer. Full reviews are available upon request.Selected Quotes and Student Reviews (Math 52) [ html ]Numerical Breakdown of Departmental Evaluations (Math 9, 18, 52) [ html ]
 The Brown University Critical Review is a studentrun publication which
independently evaluates courses and instructors. Evaluations
include a numerical breakdown and a summary of student comments.
Critical Review for Math 9 – Introductory Calculus – Fall 2003 [ pdf ] Critical Review for Math 18 – Multivariable Calculus – Fall 2004 [ pending ] Critical Review for Math 52 – Linear Algebra – Spring 2006 [ pdf ]
Awards and Certificates
 University of Colorado ASSETT Development Award [blog post] – 2015
 University of British Columbia Mathematics Department Postdoctoral Teaching Award – May 2011
 Brown University Mathematics Department Outstanding Teaching Award – May 2008
 Twice Mathematics Department Nominee for Brown University’s Presidential Award for Excellence in Teaching (2005, 2007).
 Sheridan Centre Teaching Certificate – May 2005