MAT 118

Syllabus

At a glance	Week	dates	Topics covered	Homework
Voting methods: Chapter 1, 2.1-2.3. 2/6: last day to drop without W	Week 1	Jan/27	Admin. stuff. Voting: ballots, plurality method (1.1 - 1.2 (started))	HW1: p.30-41: 2, 6, 11, 16, 18, 24, 28, 61, 66, 67. Due in recitation in Week 2. Voting methods calculator
	Week 1	Jan/29	Finished 1.2. Borda method (1.3)
	Week 2	Feb/3	Plurality with elimination (1.4), Pairwise comparisons (1.5)	HW2: pp. 34-41: 30, 34, 38 (problem 38 to be done using all 4 methods we had discussed, not just one), 44, 62, 72, 76. Due in recitation in Week 3.
	Week 2	Feb/5	Rankings. Arrow's Impossibility Theorem (1.6)
	Week 3	Feb/10	Weighted Voting. Banzhaf Power Index (2.1-2.3)	HW3: pp.72-79: 3, 8, 12, 19, 20, 28, 33, 35, 62, 67
	Week 3	Feb/12	Example: Israel Knesset 2009. Shapley-Shubik Power Index (2.4 - 2.5)	HW3: pp.72-79: 3, 8, 12, 19, 20, 28, 33, 35, 62, 67
Euler circuits and traveling salesman problem: Chapters 5, 6	Week 4	Feb/17	Graphs; Euler circuits and paths. Euler's Theorem. (5.1-5.5)	HW4: pp. 185-195: 6, 18 (in addition to drawing the graph, also find whether it is possible to have a marathon route as described in the problem. If yes, show it; if not, explain why), 27, 34, 40 ab, 42, 48, 58
	Week 4	Feb/19	Eulerizing a graph. Fleury's algorithm for finding an Euler circuit/path (5.6, 5.7)
	Week 5	Feb/24	Hamiltonian circuits and traveling salesman problem (6.1 - 6.5). Brute force and nearest neighbor algorithms.	HW5: p. 222-227: 12, 30, 36, 42, 48 (using cheapest link method!), 52
	Week 5	Feb/26	Repetitive nearest neighbor and cheapest link algorithms for TSP.
	Week 6	Mar/3	Midterm 1
Networks: Chapter 7	Week 6	Mar/5	MST and Kruskal algorithm (7.1 - 7.3)
	Week 7	Mar/10	Steiner points and shortest network (7.4 - 7.5)	HW6: pp. 259-267: 2, 12, 20, 24, 28, 42 (Hint: this graph does not have to be connected), 64, 74*( extra credit problem)
	Week 7	Mar/12	Population growth: linear and exponential growth (10.1 - 10.3)
Population growth: chapter 10. 3/27: last day to P/NC.	Week 8	Mar/17	Exponential function: properties.	HW7
	Week 8	Mar/19	Compound interest. Number "e".	HW7
	Week 9	Mar/24	Sum of geometric progression; monthly investment.	HW 8: p. 364--371, problem 26, 38,42, 44, 46, 75,
	Week 9	Mar/26	Logistic model	HW 8: p. 364--371, problem 26, 38,42, 44, 46, 75,
	Week 10	Mar/31	Review for Midterm 2
	Week 10	Apr/2	Midterm 2
Spring Recess
Symmetries: Chapter 11	Week 11	Apr/14	Rigid motions. Rotations, reflections, translations. Proper and improper motions. Product of rigid motions.	HW 9: p.395-405:2, 8, 12, 16, 24, 28, 58, 66
	Week 11	Apr/16	More on rigid motions. Glide reflections.	HW 9: p.395-405:2, 8, 12, 16, 24, 28, 58, 66
	Week 12	Apr/21	Symmetries of finite figures. Symmetries of border patterns.	HW 10: p.395-405: 30, 36, 40, 38, 42, 44, 50, 70
	Week 12	Apr/23	Symmetries of wallpaper patterns.	HW 10: p.395-405: 30, 36, 40, 38, 42, 44, 50, 70
Probabilities: Chapter 15	Week 13	Apr/28	Basic probabilites. Addition and product rule for probabilities.	HW 11: p. 531-537: 10, 14, 32, 34, 50, 58, 71, 74, 79
	Week 13	Apr/30	Combinations: _nP_k, _nC_k	HW 11: p. 531-537: 10, 14, 32, 34, 50, 58, 71, 74, 79
	Week 14	May/5
	Week 14	May/7
		May/19	Final Exam (5-7:30 pm)