Our main objective is to discuss issues of teaching and learning in the context of combinatorial and algebraic problems – especially those that connect the two- taking particular note of the need for proof.
To that end here are some resources that may help:
- Bogart, K. P. (2004). Combinatorics through guided discovery.
- Catalan Number. Wikipedia.
- Combinatorics: High School Math. Art of Problem Solving.
- Gessel, I. M. (2013). Rook polynomials. University of Washington Combinatorics Seminar
- Hilton, P., & Pedersen, J. (1991). Catalan numbers, their generalization, and their uses. The Mathematical Intelligencer, 13(2), 64-75.
- Hodkinson, J. (2016) Proof by storytelling. Chalkdust, October 3
- Nelsen, R. B. (1993). Proofs without words: Exercises in visual thinking (No. 1). MAA.
- Nelsen, R. B. (1994). Proof without words: Geometric series. Mathematics magazine, 67(3), 230.
- Richards, I. (1984). Proof without words: Sum of integers. Mathematics Magazine, 57(2), 104-104.
- Rook Polymomials. Wikipedia.
- Siu, M. K. (1984). Proof without words: Sum of squares. Mathematics Magazine, 57(2), 92-92.