Math 210

Math 210 Class Notes

Last update: 12/9/15

TSP example form 12/9 class - Google map link - weighted graph and cost matrix
Intro to the Traveling Salesman Problem (TSP)
Santa Claus and the TSP: image - text
Spanning Tree Algorithm PowerPoint (from 12/8 class)
Euler Cycle Algorithm Flowchart (from 11/30 class)
Test #3 Solutions & Comments (Test #3 blank copy)
Solutions & Comments: Homework #7 - Homework #8 (induction proofs)
Test #2 Solutions & Comments (Test #2 blank copy)
Test #1 Solutions & Comments (Test #1 blank copy)
Homework #2 solutions (scans from student work): #1 #2 #3
Course Prerequisite Hasse Diagram (from 10/16 class)

LINKS (to several web-based activities and other optional reading material)

* Links with an asterisk are from Doug Ensley's Discrete Math Resources web page at Shippensburg University

Section of textbook	Corresponding links
1.0	Set notation- practice with set-builder notation Set operations - input two sets, shows union and intersection
1.1	Venn Diagrams* - find the region of a 3-set Venn diagram corresponding to a given set Element chasing* - "fill in the blank" practice for element chasing proofs. (These are subset proofs, not set equality proofs - note the difference.)
1.2	Proofs using set identities* - "scrambled proofs," using set identity laws to prove ne set identities Note terminology differences between our text and this web page: Our book's "weak absorption" laws are called "universal bound" laws on this page Our book's "complementarity" laws are called "negation" laws on this page Our book's "involution" law is called "double negation" on this page
5.1	Truth Tables: Truth tables - practice* - with "and," "or" and "not" Truth tables - equivalence* - to prove logical equivalence between two propositions Truth tables - implications* - propositions with the "implies" connective Truth tables in three variables* - and more here Truth tables - applications* - truth tables used to solve word problems Syllogisms: http://www.math.hawaii.edu/~hile/math100/logice.htm http://branemrys.blogspot.com/2006/07/lewis-carroll-logic-puzzles.html http://www.cut-the-knot.org/LewisCarroll/soriteses.shtml
5.2	Boolean algebra* properties - "scrambled proofs" (similar to the Section 1.2 link below) Boolean algebra truth tables* (Note: in these applets, the notation x' is used for "inversion")
1.3	Two-set arrow diagrams for functions* Two-set arrow diagrams for relations* Function composition* Proofs about injective and surjective functions*
1.4 - 1.5	One-set arrow diagrams for relations * Proofs about properties of relations on a set * Counterexamples *
2.0	Geometric Proof of the Irrationality of Square Roots (from cut-the-knot.org) Find counterexamples * - Find more counterexamples * "Fill in the blank" proofs * "Proof Reader" * - practice proofreading proofs and looking for possible errors More "Proof Reader" * proofreading exercises Scrambled Proofs * - More Scrambled Proofs *
Chapter 4	Seven Bridges of Konigsberg (Wikipedia) Euler cycles & paths * Hamiltonian cycles * (vocabulary note: in the applets, "trail" = "path," and "circuit" = "cycle")