Craig Larson Assistant Professor Department of Mathematics and Applied Mathematics Virginia Commonwealth University teaching my papers and notes miscellany VCU Discrete Math Seminar My Favorite Graph Theory Conjectures @ JMM 2012
email: clarson@vcu.edu

My office is 4106 Harris Hall. In Fall 2011 I will be teaching Linear Algebra (MATH 310) Precalculus (MATH 151), an Honors module (HONR 399), and team-teaching Graph Theory (MATH 591).

• Resources for Linear Algebra (Math 310)
  • Our Course
    • Here is the 310 Syllabus (pdf).
    • The text is Introduction to Linear Algebra, 4th ed. by Gilbert Strang. The ISBN is 0980232716.
    • Here is the Assigned Homework list and the Recommended Homework list. Math requires lots of practice. While the Recommended homework is not collected, it is certainly necessary (and you may see questions like these on the tests).
    • Here are copies of the Classroom Worksheets: c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23.

    • Here are Prof Strang's own videos of the text content.
    • We will be using MATLAB (or Octave, a free open source program that has the same command syntax as MATLAB for everything we'll do) to supplement the course. Our book refers to MATLAB commands.
    • Here's the MIT MATLAB - OCTAVE Cheatsheet.

  • Other Linear Algebra Resources
    • Don Spickler's (free) Linear is a very easy-to-use linear algebra program.
    • Here are some great free Linear Algebra videos from the Khan Academy.
    • Here is an interesting brief history of matrices and determinants.

• Resources for Precalculus (Math 151):
  • Syllabus for Larson's Section 012.
  • Everything else!

• Resources for Think Like a Mathematician (HONR 399):
  • Grinvin is a free computer program that can be used to calculate invariants, generate graphs, and otherwise explore.
  • Richard Hammack's Book of Proof is a good reference for the proof methods that will be discussed in our class.
  • Adrian Bondy and U.S.R. Murty's Graph Theory with Applications is a classic introductory text for students who wish to go further.

  • Classroom Worksheets:
    • What is Mathematics?
    • Some Graph Invariants.
    • Finding Counterexamples.
    • Seeing Patterns.
    • Starting an Investigation.
    • Investigating the diameter of a graph.

  • Homework Worksheets:
    • Finding Counterexamples.
    • Seeing Patterns.
    • Starting an Investigation.
    • My Investigation.
    • Mid-Term Review.
    • My Investigation - Progress Report 2.
    • Final Presentation Guide.

  • Grinvin tutorial videos:
    • Making a Graph in Grinvin.

  • Other Stuff
    • Syllabus.
    • Bibliography.
    • Investigating the Independence Number investigation example
    • Class Notes 1.
    • Grinvin 1.2 for Windows (with comparator option)
    • Independence Number Investigation - Progress Report 2.

• Resources for Graph Theory:
  • Grinvin is a free computer program that can be used to calculate invariants, generate graphs, and otherwise explore.
  • Groups & Graphs is another free computer program for graph theory exploration.
  • Good free books online
    • Diestel's Graph Theory (grad).
    • Bondy and Murty's Graph Theory with Applications (undergrad).
    • Wilf's Algorithms and Complexity (undergrad).

• Other Stuff for Current Students:
  • When will I use math?
  • Why do math?
  • The American Mathematical Society (AMS) has a web page for news for student math majors. You can also sign up for a very useful (free) email bulletin there.

• VCU Math Texts Project

• Resources for Master's students:
  • VCU Stuff & Forms:
    • Application to Graduate. Do this at the beginning of your last semester.
    • Application to Defend Thesis. Must be done prior to defending your thesis.
    • Thesis Approval Signature Form. Bring this with you to your thesis defense.
    • VCU Digital Archive. After your thesis is approved it must be uploaded to this archive.

  • Useful LaTeX links:
    • A VCU Math thesis template and required files (the "cls" file must be in the directory where you compile your "tex" file).
    • TeXshop. A very good (free) TeX editor and compiler for Mac.
    • TeXnicCenter. A very good (free) TeX editor for Windows. (You still need MikTeX as the compiling "engine").
    • MikTeX. The TeX compiler for Windows users (free).
    • The Not So Short Introduction to LaTeX. A guide to LaTeX basics.
    • Tikz Manual. A guide for making pictures directly in your TeX code.
    • DeTeXify. Draw a math symbol and get the LaTeX code. You can also find Iphone and Android apps.
    • LyX A freeware WYSIWYG LaTeX editor.

• Thesis Students
  • Michelle Grigsby, M.S., ``Independence and Horizontal Edges'', December 2011.
  • Andrew Bristow, M.S., ``Independence Number is NP-Complete'', August 2011.
  • William Willis, M.S., ``Bounds for the Independence Number of a Graph'', August 2011.
  • Taylor Short, M.S., ``KE Theory and the Number of Vertices Belonging to all Maximum Independent Sets of a Graph'', February 2011.
  • Nisreen Bukhary, M.S., ``Domination in Benzenoids'', May 2010.

14. E. DeLaVina and C. E. Larson, A Parallel Algorithm for Computing the Critical Independence Number and Related Sets, submitted.

13. L. Eroh, R. Gera, C. Kang, C. E. Larson, and E. Yi, Domination in Functigraphs, to appear in Discussiones Mathematicae Graph Theory.

12. C. E. Larson and R. Pepper, Graphs with Equal Independence and Annihilation Numbers, Electronic Journal of Combinatorics, 18(1) 2011.

11. E. DeLaVina, C. E. Larson, R. Pepper, and B. Waller, A Characterization of Graphs where the Independence Number Equals the Radius, to appear in Graphs and Combinatorics.

10. C. E. Larson, The Critical Independence Number and an Independence Decomposition, European Journal of Combinatorics 32(2), 2011, 294--300.

9. G. Abay-Asmeron, R. Hammack, C. E. Larson, D. T. Taylor, Notes on the independence number in the Cartesian product of graphs, Disquisitiones Mathematica Graph Theory 31(1), 2011, 25--35.

8. E. DeLaVina, C. Larson, R. Pepper and B. Waller, On total domination and support vertices of a tree, AKCE International Journal of Graphs and Combinatorics, 7 (1), 2010, 85--95.

7. E. DeLaVina, C. E. Larson, R. Pepper, and B. Waller, Graffiti.pc on the 2-domination number of a graph, Congressus Numerantium 203, 2010, 15--32.

6. G. Abay-Asmerom, R. Hammack, C. E. Larson, and D. Taylor, Direct Product Factorization of Bipartite Graphs with Bipartite-Switching Involutions, SIAM Journal on Discrete Mathematics 20(4), 2010, 2042--2052.

5. E. DeLaVina, C. E. Larson, R. Pepper, and B. Waller, Graffiti.pc on the total domination number of a tree, Congressus Numerantium 195, 2009, 5--18.

4. C. E. Larson, A Note on Critical Independence Reductions, Bulletin of the Institute of Combinatorics and its Applications 5, 2007, 34--46.

3. C. E. Larson, A Survey of Research in Automated Mathematical Conjecture-making, in Graphs and Discovery, ed. by S. Fajtlowicz, P. W. Fowler, P. Hansen, M. F. Janowitz and F. S. Roberts, DIMACS, 2005, 297--318.

2. S. Fajtlowicz and C. E. Larson, Graph-theoretic Independence as a Predictor of Fullerene Stability, Chemical-Physics Letters, 377/5-6, 2003, 485--490.

1. C. E. Larson, Intelligent Machinery and Mathematical Discovery, Graph Theory Notes of the New York Academy of Science XLII, 2002, 8--17.

Other

1. C. E. Larson, Technology, Education and the Single-Salary Schedule, Notices of the American Mathematical Society, May 2006, 525.

• Biographical: I am originally from California. My mom is German and my dad is Chicagoan. I have a younger brother Kevin (he's a researcher at Microsoft now). Dad was an aerospace engineer (he worked on Skylab, Shuttle, and the Space Station, among other things) and taught us a lot of math when we were kids. We grew up in Huntington Beach , where I still have a lot of buddies. I grew up a huge fan of the Los Angeles Dodgers, the Boston Celtics (which was a little awkward), and UCLA Bruins basketball. I'm still a fan. Of course, now I'm a big VCU fan too.

  In high school I was a Congressional Page, ran cross country and track (I ran a 4:50 mile as a sophomore), and was pretty geeky. I went to the University of Houston on a National Merit scholarship. In college I studied philosophy as well as math, and have advanced degrees in both. I taught for many years in the math department at the University of Houston, where I won a teaching award, and met my beautiful wife Jeanine.

  We're both big music fans and cat lovers. We like to run, bike, travel, read, eat, see bands, movies and the ballet. We just added a little guy, Linus Carl Larson, to join us in our adventures. And now I'm at VCU. My research currently involves graph theory, fullerenes and artificial intelligence; but I'm interested in many many many things.

• My heroes and people I admire include my parents and my wife, Alan Turing, Thomas Paine, Jackie Robinson, John Wooden, Charlie Chaplin, Julian Simon, Jaime Escalante, John Coltrane, Woody Allen, Bill Russell, Laszlo Lovasz, Linus Pauling, James Randi, Ludwig Wittgenstein, Bertrand Russell, Paul Erdos, Milton Friedman, Noam Chomsky, Nels Cline, Louis Armstrong, and Krzysztof Kieslowski. Be a punk, question authorities, think for yourself, work hard, create yourself, your own art, your own values, and the world you want to live in. ("Start your own band. Write your own book. Paint your own picture!")

• Bertrand Russell's Ten Commandments of teaching.
• A Richmond Rental Nightmare.
• Best and Worst of Richmond, 2008-2010.