Teaching

I enjoy teaching in an interactive environment, with an emphasis on active learning.

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Current Courses

  • Mathematics 4440/5440. Cryptography and Coding Theory. Fall 2024.
    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.

  • Mathematics 6110. Introduction to Number Theory, Fall 2024
    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.

Summer Schools

  • The two summer schools below led to Course Notes, a current draft of which is available here.
  • Graduate Summer School, NUS IMS, June 3-7, 2024.
    Integral packings and number theory.

  • Graduate Summer School, CIRM, July 2023.
    Number theory as a door to geometry, dynamics and illustration.

Past Courses at CU Boulder

  • Mathematics 2001.  Introduction to Discrete Mathematics.  Spring 2023.
    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.

  • Mathematics 4440/5440. Cryptography and Coding Theory. Fall 2022.
    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.

  • 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 2001.  Introduction to Discrete Mathematics.  Spring 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, 2:00 – 2:50 pm, ECCR 131.
      • 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.]

  • 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.

  • 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.

  • 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.

  • 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.

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  • 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.

 
 

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

Courses Taught at the University of British Columbia

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.

  • 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.

Courses Taught at Brown University

Other Teaching

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 student-run 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