Department of Mathematics

University of Wisconsin-Madison

Office: Van Vleck B127

Phone: (608) 263-1541

Email: edhanson at math dot wisc dot edu

- Monday 1:00 to 2:00 p.m.
- Monday 3:45 to 4:45 p.m.
- Wednesday 9:30 to 10:30 a.m.
- By appointment.

- How to recognize a Leonard pair.
*Linear and Multilinear Algebra*; arXiv:1901.10659v1. - A characterization of bipartite Leonard pairs using the notion of a tail.
*Linear Algebra Appl.*452 (2014) 46-67; arXiv:1308.3826v1. - A characterization of Leonard pairs using the parameters {a
_{i}}_{0≤i≤d}.*Linear Algebra Appl.*438 (2013) 2289-2305; arXiv:1205.4368v1. - A characterization of Leonard pairs using the notion of a tail.
*Linear Algebra Appl.*435 (2011) 2961-2970; arXiv:0911.0098v1.

- Math 435, Introduction to Cryptography

In the past, I taught the following courses:

- Math 435, Introduction to Cryptography (Summer 2019)
- Math 461, College Geometry I (Spring 2019)
- CS/Math/Stat 475, Combinatorics (Spring 2019)
- Math 461, College Geometry I (Fall 2018)
- CS/Math/Stat 475, Combinatorics (Fall 2018)
- CS/ECE/Math 435, Introduction to Cryptography (Summer 2018)
- CS/ECE/Math 435, Introduction to Cryptography (Spring 2018)
- Math 521, Analysis I (Spring 2018)

In the past, I taught the following courses at SUNY New Paltz:

- MAT 303, Foundations of Analysis, Fall 2017
- MAT 362, Linear Algebra, Fall 2017 (two sections)
- MAT 251, Calculus I, Spring 2017 (two sections)
- MAT 331, Axiomatic Geometry, Fall 2016
- MAT 362, Linear Algebra, Fall 2016
- MAT 363, Combinatorics, Fall 2016
- MAT 362, Linear Algebra, Spring 2016
- MAT 363, Combinatorics, Spring 2016
- MAT 364, Introduction to Abstract Algebra I, Spring 2016
- MAT 304, Foundations of Algebra, Fall 2015
- MAT 362, Linear Algebra, Fall 2015
- MAT 364, Introduction to Abstract Algebra I, Fall 2015
- MAT 252, Calculus II, Spring 2015
- MAT 304, Foundations of Algebra, Spring 2015
- MAT 362, Linear Algebra, Fall 2014 (two sections)

I also taught the following courses at Williams College:

- Math 432, Lie Algebras, Spring 2014
- Math 250, Linear Algebra, Fall 2013 (three sections)

As a graduate student, I was instructor for the following courses at the University of Wisconsin-Madison:

- Math 138, Mathematics for Teaching: Conjecture, Generalization, and Proof, Spring 2013
- Math 136, Pre-calculus and Calculus for Middle School Teachers, Fall 2012
- Math 138, Mathematics for Teaching: Conjecture, Generalization, and Proof, Spring 2012
- Math 136, Pre-calculus and Calculus for Middle School Teachers, Fall 2011
- Math 138, Mathematics for Teaching: Conjecture, Generalization, and Proof, Spring 2011
- Math 136, Pre-calculus and Calculus for Middle School Teachers, Fall 2010

*Krawtchouk matrices: new interpretations*, University of Wisconsin-Madison Combinatorics Seminar, Madison, WI, March 26, 2019*How to recognize a Leonard pair*, University of Wisconsin-Madison Combinatorics Seminar, Madison, WI, October 1, 2018*New characterizations of Leonard pairs*, University of Wisconsin-Madison Combinatorics Seminar, Madison, WI, February 26, 2018*Motivating examples for teaching discrete mathematics*, MAA Session on Discrete Mathematics in the Undergraduate Curriculum—Ideas and Innovations in Teaching, 2018 Joint Mathematics Meetings, San Diego, CA, January 10, 2018*Maxima and minima without calculus*, SUNY New Paltz Math and Cookies Seminar, New Paltz, NY, November 8, 2017*New characterizations of Leonard pairs*, AMS Special Session on Algebraic Combinatorics, 2016 Fall Central Section Meeting, University of Denver, Denver, CO, October 8, 2016*The tail condition for Leonard pairs*, Maseeh Mathematics & Statistics Colloquium, Portland State University, Portland, OR, June 3, 2016*sl*, Portland State University Discrete Mathematics Seminar, Portland, OR, June 2, 2016_{2}(ℂ)-modules and orthogonal polynomials*Computing finite sums*, 11^{th}annual Spuyten Duyvil Undergraduate Mathematics Conference, New Paltz, NY, April 23, 2016*Solving calculus problems without calculus*, SUNY New Paltz Math and Cookies Seminar, New Paltz, NY, March 9, 2016*New characterizations of Leonard pairs*, Association Schemes Minisymposium, 8^{th}Slovenian International Conference on Graph Theory, Kranjska Gora, Slovenia, June 23, 2015*New characterizations of Leonard pairs*, 13^{th}International Symposium on Orthogonal Polynomials, Special Functions and Applications, National Institute of Standards and Technology, Gaithersburg, MD, June 5, 2015*New characterizations of Leonard pairs*, SUNY New Paltz Mathematics Department Seminar, New Paltz, NY, March 11, 2015*Vectors, complex numbers, and hypercomplex numbers*, SUNY New Paltz Math and Cookies Seminar, New Paltz, NY, October 29, 2014*Generalizations of the cross product*, Hudson River Undergraduate Mathematics Conference, Marist College, Poughkeepsie, NY, April 27, 2014*Introduction to Leonard pairs*, Five College Number Theory Seminar, Amherst, MA, March 11, 2014*Characterizations of Leonard pairs*, SUNY New Paltz Mathematics Department Seminar, New Paltz, NY, January 22, 2014*Graphs and matrices*, University of Massachusetts Undergraduate Mathematics Seminar, Amherst, MA, October 30, 2013*Introduction to Leonard pairs*, Williams College Faculty Seminar, Williamstown, MA, October 25, 2013*The tail condition for Leonard pairs*, ILAS Session on Matrices and Orthogonal Polynomials, International Linear Algebra Society 2013 Meeting, Providence, RI, June 5, 2013*The tail condition for Leonard pairs*, AMS Special Session on Algebraic and Geometric Combinatorics, 2013 Spring Central Section Meeting, Iowa State University, Ames, IA, April 28, 2013*Characterizations of Leonard pairs*, University of Wisconsin-Madison Combinatorics Seminar, Madison, WI, February 4, 2013*Characterizations of Leonard pairs*, AMS Contributed Paper Session on Linear Algebra and Applications, 2013 Joint Mathematics Meetings, San Diego, CA, January 12, 2013*The tail condition for Leonard pairs*, Mathematics, Statistics and Computer Science Research Seminar, St. Olaf College, Northfield, MN, November 9, 2012*Characterizations of Leonard pairs*, 2012 Shanghai Conference on Algebraic Combinatorics, Shanghai Jiao Tong University, Shanghai, China, August 21, 2012*Fiedler's characterization of tridiagonal matrices*, University of Wisconsin-Madison Combinatorics Seminar, Madison, WI, February 6, 2012*A characterization of Leonard pairs using the parameters {a*, AMS Special Session on Association Schemes and Related Topics, 2011 Fall Central Section Meeting, University of Nebraska-Lincoln, Lincoln, NE, October 15, 2011_{i}}_{0≤i≤d}*A characterization of Leonard pairs using the parameters {a*, Representations of Graphs Minisymposium, 7_{i}}_{0≤i≤d}^{th}Slovenian International Conference on Graph Theory, Bled, Slovenia, June 24, 2011*Leaves, tails, and Leonard pairs*, University of Wisconsin-Madison Combinatorics Seminar, Madison, WI, December 6, 2010*Graphs and matrices*, Bi-State Undergraduate Math Colloquium, Loras College, Dubuque, IA, November 19, 2010*A characterization of Leonard pairs using the notion of a tail*, 2^{nd}Second International Workshop on Symmetries of Graphs and Networks, Rogla, Slovenia, August 6, 2010*A characterization of Leonard pairs using the notion of a tail*, 6^{th}Graduate Student Combinatorics Conference, Auburn University, Auburn, AL, April 3, 2010*Orthogonal polynomials and tridiagonal matrices*, University of Wisconsin-Madison Combinatorics Seminar, Madison, WI, March 15, 2010*A characterization of Leonard pairs in terms of tails*, University of Wisconsin-Madison Combinatorics Seminar, Madison, WI, August 31, 2009

*Using Transformations, Computer Coding, and 3D Printing to Investigate Solids in the Mathematics Classroom*, ANYthing Expo and Poster Session, SUNY New Paltz, November 5, 2015