Current Courses: Spring 2017

  • Mathematics 6180. Algebraic Number Theory.

            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.

Past Courses at CU Boulder

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).
  • 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

 

Resources for Teachers

If you use or adapt any of my resources, I would appreciate you letting me know. It makes me feel useful.


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