MAT 118: Mathematical Thinking
Spring 2019

## Welcome to MAT 118

The syllabus of this course can be found here

## Schedule

Day Content Homework Notes
01/28/19 (Week 1) Basic facts and the plurality method. 1.2 Ex 14
1.3 Ex 25
1.4 Ex 36 (due 02/04/19)
Notes for the first week
01/30/19 Borda count and plurality with elimination voting counts
02/01/19 Plurality with elimination and method of pairwise comparisons.
02/04/19 (Week 2) Fairness criteria, weighted voting and Banzhaf Power 2.1 Ex 7
2.2 Ex 13
2.3 Ex 31 (due 02/11/19)
Notes for the second week
02/06/19 Shapley-Shubik Power, Fair division games principles
02/08/19 Divider chooser method, lone divider method
02/11/19 (Week 3) Divider chooser, lone divider methods 3.3 Ex 25
3.4 Ex 36,38 (due 02/18/19)
Notes for the third week
02/13/19 Lone chooser, sealed bids
02/15/19 Marker methods, Street routing problems
02/18/19 (Week 4) Introduction to graphs, Euler's theorem 5.2 Ex 1, 7
5.3 Ex 30(due 02/25/19)
Notes for the fourth week
02/20/19 Fleury's algorithm
02/22/19 Eulerization and Semi-Eulerizations, Hamilton paths and circuits
02/25/19 (Week 5) Optimal Hamilton paths: the brute force method 6.2 Ex 2,14
6.3 Ex 27(due 03/06/19)
Notes for the fifth week
02/27/19 Review for mid term
03/01/19 Midterm 1
03/04/19 (Week 6) (Canceled) 6.4 Ex 36, 37
6.5 Ex 52(due 03/11/19)
03/06/19 Nearest Neighbor Algorithm Notes I
03/08/19 Cheapest link algorithm Notes II
03/11/19 (Week 7) Spanning trees : Introduction 7.2 Ex 22, 23
(due 03/25/19)
Notes I
03/13/19 How to find a spanning tree Notes II
03/15/19 Minimal spanning trees Notes III
03/18 to 03/24 Spring Break
03/25/19 (Week 8) End of Kruskal algorithm, Probability theory 16.1 Ex 1, 2,3, 7 , 8 , 9
(due 04/01/19)
Notes I
03/27/19 Probability II: Events Notes II
03/29/19 Probability III: Multiplication law Notes II
04/01/19 (Week 9) Expectations 16.2 Ex 18,22,27
16.3: 33,43
16.4 58,62
(due 04/08/19)
Notes IV
04/03/19 Gambler's ruins
04/05/19 Expectations continued
04/08/19 (Week 10) Review for midterm II
04/10/19 Midterm II
04/12/19 Correction of the midterm
04/15/19 (Week 11) On linear growth and sequences 9.1 Ex 9,18
9.2: 19,34
(due 04/22/19)
Sequences
Sequences II
04/17/19 Arithmetic sequences
04/19/19 Arithmetic sum formula
04/22/19 (Week 12) Geometric sequences
04/24/19 Geometric sequences (continued)
04/26/19 Geometric sums
04/29/19 (Week 13) Logistic growth model 9.2 Ex 31,32,
9.3 Ex 50,
9.4 Ex 62,65, 66 (due 05/06/19)
05/01/19 Logistic growth model (continued)
05/03/19 Von Koch snowflake: length and areas
05/06/19 (Week 14) Area of Sierpinski Gasket
05/08/19 Review on probability
05/10/19 Review on sequences