This paper introduces a new matrix tool for the sowing game Tchoukaillon, which establishes a relationship between board vectors and move vectors that does not depend on actually playing the game. This allows for simpler proofs than currently appear in the literature for two key theorems, as well as a new method for constructing move vectors.We…

In this paper, we review the rules and game board for "Chutes and Ladders", define a Markov chain to model the game regardless of the spinner range, and describe how properties of Markov chains are used to determine that an optimal spinner range of 15 minimizes the expected number of turns for a player to complete the game. Because the Markov…

Dodgson's method of computing determinants is attractive, but fails if an interior entry of an intermediate matrix is zero. This paper reviews Dodgson's method and introduces a generalization, the double-crossing method, that provides a workaround for many interesting cases.

Proposes methods to teach the more difficult concepts of linear algebra. Examines features of the Linear Algebra Curriculum Study Group Core Syllabus, and presents problems from the core syllabus that utilize the mathematical process skills of making conjectures, proving the results, and communicating the results to colleagues. Presents five…