# MAT 118: Mathematical Thinking

Stony Brook University, Spring 2017

Lectures: MWF 10:00am-10:53am, Engineering 143
Email: c s c a d u t o @ s c g p . s t o n y b r o o k . e d u
Office: Simons Center for Geometry and Physics 309
Office hours: MW 11:00am-12:00pm

The course syllabus can be found here. This contains basic logistical information about the course.

The scanned notes below were written before each lecture and may slightly differ from what we did in class.

## Course Schedule

Date Lecture Content Files
1/23/17 Syllabus overview; Ch.1 The Mathematics of Elections: preference schedules, plurality method Scanned notes
1/25/17 Ch.1: Borda count method, plurality-with-elimination method Scanned notes
1/27/17 Ch.1: Method of pairwise comparisons, Arrow's Impossibility Theorem Scanned notes
1/30/17 Finished up Ch.1; started Ch.2: The Mathematics of Power: weighted voting systems Scanned notes
2/1/17 Ch.2: weighted voting systems (continued), dictators and veto power Scanned notes
2/3/17 Ch.2: Banzhaf power: wining coalitions, critical counts, BPI's Scanned notes
2/6/17 Ch.2: Shapley-Shubik power: sequential coalitions, factorials Scanned notes
2/8/17 Ch.2: Shapley-Shubik power: pivotal players, SSPI's; Example 2.16 from text (not in scans) Scanned notes
2/10/17 Ch.3: The Mathematics of Sharing: divider-chooser method, fair division games Scanned notes
2/13/17 Ch.3: the lone-divider method (by example) Scanned notes
2/15/17 Ch.3: the lone-divider method, continued (formal steps) Scanned notes
2/17/17 Ch.3: Finished lone-divider method, started lone-chooser method Scanned notes
2/20/17 Ch.3: Finished lone-chooser method, began method of sealed bids Scanned notes
2/22/17 Ch.3: The method of sealed bids, continued Scanned notes
2/24/17 Ch.3: The end of the method of sealed bids; the method of markers Scanned notes
2/27/17 Review of the practice exam for Midterm #1 practice exam
3/1/17 Midterm #1 midterm
3/3/17 Discussion of grades; review of Midterm #1 midterm solutions
3/6/17 Ch.5: The Mathematics of Getting Around: street routing problems, intro to graphs Scanned notes
3/8/17 Ch.5: Graph theory rudiments continued Scanned notes
3/8/17 Ch.5: Graph theory rudiments continued Scanned notes
3/10/17 Ch. 5: Euler's theorems Scanned notes
3/13-3/17 Spring Break week!
3/20/17 Ch.5: Review of Euler's theorems, and intro to Fleury's algorithm Scanned notes
3/22/17 Ch.5: More of Fleury's algorithm Scanned notes
3/24/17 Ch.5: Eulerizing a graph Scanned notes
3/27/17 Ch.6: The Mathematics of Touring: Travelling salesman problems, Hamilton circuits/paths Scanned notes
3/29/17 Ch.6: The Brute Force Algorithm Scanned notes
3/31/17 Ch.6: The Nearest Neighbor Algorithm (NNA) Scanned notes
4/3/17 Ch.6: Repetitive Nearest Neighbor Algorithm (RNNA), Cheapest Link Algorithm Scanned notes
4/5/17 Ch.7: The Mathematics of Networks Scanned notes
4/7/17 Ch.7: Kruskal's algorithm Scanned notes
4/10/17 Class cancelled
4/12/17 Ch. 7: More examples and exercises
4/14/17 Ch. 9: Population Growth Models Scanned notes
4/17/17 Review of the practice exam for Midterm #2 practice exam
4/19/17 Midterm #2 midterm
4/21/17 Discussion of grades; review of Midterm #1
4/24/17 Ch. 9: Linear growth Scanned notes
4/26/17 Ch. 9: More linear growth; started exponential growth Scanned notes
4/28/17 Ch. 9: More exponential growth; the geometric sum formula Scanned notes
4/28/17 Ch. 9: Finished exponential growth; started logistic growth Scanned notes
5/1/17 Ch. 9: More logistic growth
5/3/17 Ch. 9: More logistic growth, Ch. 9 overview
5/5/17 Last class! Review of practice final practice final

## Homework Assignments

Assignment Due Date
Homework #1 Friday, 2/3/17
Homework #2 Friday, 2/10/17 (snow storm) Monday, 2/13/17
Homework #3 Friday, 2/17/17
Homework #4 Friday, 2/24/17
Homework #5 Friday, 3/10/17
Homework #6 Friday, 3/24/17
Homework #7 Friday, 3/31/17
Homework #8 Friday, 4/7/17
Homework #9 Friday, 4/14/17
Homework #10 Friday, 4/28/17

## Exams

Exam File
Practice Exam for Midterm #1, without solutions (reviewed in class 2/27/17) pdf
Practice Exam for Midterm #1, with solutions pdf
Midterm #1, without solutions (given in class 3/1/17) pdf
Midterm #1, with solutions pdf
Practice Exam for Midterm #2, without solutions (reviewed in class 4/17/17) pdf
Practice Exam for Midterm #2, with solutions pdf
Midterm #2, without solutions (given in class 4/19/17) pdf
Midterm #2, with solutions pdf
Practice Final Exam, without solutions (reviewed in class 5/5/17) pdf
Practice Final Exam, with solutions pdf