# Learning Goals, Math 340-101, Fall 2015

Materials here may contain errors; some corrections might only be announced in class.

 Recent News Brief solutions for most of the problems of the 2014 Final Exam have been added to this webpage; these were mostly covered in the last two days of class. Matrix Games and Poker, Sections 1--9 except Section 7. This year we defined the "duality gap" to mean the difference between the values of the pure game strategies (Section 7 gives a more general view of this). Simplex Method (Chvatal, Chapter 2), Two-Phase Method, Unbounded Linear Programs, and the Perturbation Method (Chvatal, Chapter 3). Applications of the Simplex Method to Game Theory and Curve Fitting. (See class notes and homework problems.) Duality Theory, Complementary Slackness (Chvatal, Chapter 5). Revised Simplex Method (Chvatal, Chapter 7); this year studied only the term c_B^T A_B^(-1) A_N of the revised simplex method. The topic of Sensitivity Analysis (Chvatal, Chapter 10) will not be examined this year. Solution to the "big poker game" (described in Section 8 of the handout on game theory); matrix games where the columns are concave or convex functions of the row number. See class notes and this writeup of the analysis. [The only functions you will see on the final are quadratic functions.] Here is a list of representative problems. Perturbation Method: Homework 4, (1); Fin 14: 5(d); Mid 08: 4; Mid 01: 3; Applications to Curve Fitting: Homework 4, (2); Fin 14: 5(h); Fin 10: 6; Complmentary Slackness: Homework 5, (2); Fin 14: 3; Fin 10: 9; Mid 10: 3; Mid 08: 3; Mid 01: 2; Revised Simplex: [This year, as in recent years, we did not focus on the entire revised simplex procedure, rather focused on the $c_B^{\rm T}A_B^{-1} A_N$ computation, which is the main issue.] Homework 6, (1,2); Fin 10: 5; Fin 09: 1; Big Poker Game and Convexity/Concavity: Problems in this writeup of the analysis. Fin 14: 5(g); Game Theory: Learning Goals and Sample Exam Problems given in Section 9 of the article Matrix Games and Poker. Other sample exam problems: Mid 07: 4; Mid 08: 1; Fin 08: 1; Mid 09: 2,6; Fin 09: 3; Mid 10: 1; Fin 10: 10; Mid 14: 2; Fin 14: 1. Topic 2: The Simplex Method (Ch. 2) and Two-Phase Method (Ch. 3): Mid 97: 1; Fin 97 1; Mid 99: 1; Fin 99 2; Mid 00: 1,2; Fin 00 1; Mid 01: 1; Mid 07: 1; Mid 08: 2; Mid 09: 1,3; Fin 09: 4; Mid 10: 2; Mid 14: 1; Fin 14: 2. Note that material and emphasis changes from year to year; look at "Learning Goals" above to see which problems on which exams are relevant to our course. Exams available (some with brief solutions): midterm 1997 (solutions) [Anstee's rule is explained in Problem 1], final 1997, midterm 1999 (solutions), final 1999 (solutions), midterm 2000 (solutions), final 2000 (solutions). midterm 2001 (solutions), midterm 2007 (solutions) [The equilibrium strategry for each player is the same as the optimum "announce a mixed strategry"], midterm 2008 (solutions) [Here "Announce" means "announces a pure strategry" and "Scream" means "announces a mixed strategy"], final 2008, midterm 2009 (solutions) [Same remark as Midterm 08 regarding "Annouce" and "Scream"], final 2009, and midterm 2010 (solutions) [Same remark as Midterm 08 regarding "Annouce" and "Scream"], final 2010, and midterm 2014 (solutions), final 2014, brief solutions.

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