Updated August 7. All remaining readings and homework have been filled in.

Please read the sections associated with each class date before that class, and do the problems after.

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Week 1	Date	HW to be collected	Topics	Reading	Problems
	M 6/23		Propositional logic Propositional equivalences	1.1 1.3	1.1 #14, 16, 28, 31 1.3 #22, 30, 32, 40
	Tu 6/24		Predicates and quantifiers	1.4	1.4 #8, 50, 60
	W 6/25		Nested quantifiers Rules of inference	1.5 1.6	1.5 #8, 28 1.6 #10, 35 (show your work)
	Th 6/26	Assigned problems from 1.1 to 1.6	Introduction to proofs	1.7	1.7 #8, 16, 26, 34
	F 6/27		Proof methods and strategy Sets	1.8 2.1	1.8 #4, 18, 26, 34 2.1 #7, 18, 22, 30, 38, 41, 46
Week 2	Date	HW to be collected	Topics	Reading	Problems
	M 6/30	1.7 to 2.1 except 2.1 #30, 38	Set operations	2.2	2.2 #2, 16, 40
	Tu 7/1		Functions Sequences and summations	2.3 2.4	2.3 #6, 20, 22, 24, 40, 70, 72 2.4 #12, 14, 34, 36
	W 7/2		Cardinality of sets	2.5	2.5 #4, 20
	Th 7/3	2.1 #30, 38 2.2 to 2.4	Divisibility and modular arithmetic	4.1	4.1 #6, 8, 14, 16, 20, 36, 40, 46
	F 7/4		No class (Independence Day)
Week 3	Date	HW to be collected	Topics	Reading	Problems
	M 7/7	2.5, 4.1 and Supplement to HW 4	Integer representations Primes	4.2 4.3 (to p. 264)	4.2 #2, 4, 8, 22(d), 32
	Tu 7/8		Primes and GCDs	4.3 (the rest)	4.3 #6, 12, 15, 28, 32(c,d), 40(c,d), 49, 50
	W 7/9		Solving congruences	4.4	4.4 #6, 8, 12, 20, 22, 26
	Th 7/10	4.2 to 4.4	Applications of congruences Midterm review	4.5
	F 7/11		Midterm 1, 2:00-3:00pm (to cover material through 4.4)
Week 4	Date	HW to be collected	Topics	Reading	Problems
	M 7/14	None	Fermat’s Little Theorem Cryptography (RSA)	4.4 4.6	4.4 #17, 34, 35, 38 4.6 #26 (use Wolfram Alpha for computation)
	Tu 7/15		Mathematical induction	5.1	5.1 #3, 6, 10, 20, 22, 32, 50
	W 7/16		Strong induction and well-ordering	5.2	5.2 #4, 12, 14
	Th 7/17	4.4 to 5.1 (starting with M 7/14 problems)	Recursive definitions The basics of counting	5.3 6.1	5.3 #12, 48-52 6.1 #16, 22, 32, 35, 50
	F 7/18		The pigeonhole principle Permutations and combinations	6.2 6.3	6.2 #8, 9, 16, 44 6.3 #16, 18, 24, 30, 36, 41
Week 5	Date	HW to be collected	Topics	Reading	Problems
	M 7/21	5.2 to 6.2	Binomial coefficients and identities	6.4	6.4 #8, 10, 20, 22, 28, 33
	Tu 7/22		Generalized permutations and combinations	6.5	6.5 #4, 9, 14, 22, 30, 38, 64
	W 7/23		Integer partitions	Not in book. Notes	Supplement to HW 9
	Th 7/24	6.3 to 6.5	Intro to discrete probability Probability theory	7.1 7.2	7.1 #10, 14, 36, 38 7.2 #10, 16, 18, 28, 38
	F 7/25		Bayes’ Theorem Expected value and variance	7.3 7.4	7.3 #4, 6, 16(b) 7.4 #5, 6, 10, 37
Week 6	Date	HW to be collected	Topics	Reading	Problems
	M 7/28	Supplement to HW 9 and 7.1 to 7.3	Expected value and variance (continued)		7.4 #12, 16, 21, 28, 29, 32, 38 Ch. 7 Supplementary Exercise #22
	Tu 7/29		Applications of recurrence relations Solving linear recurrence relations	8.1 8.2	8.1 #12, 28 8.2 #4(a,b,d,e), 7, 17
	W 7/30		Inclusion-exclusion Applications of inclusion-exclusion	8.5 8.6	8.5 #6, 14 8.6 #3, 6, 10, 18
	Th 7/31	7.4 to 8.2	Midterm review
	F 8/1		Midterm 1, 2:00pm (to cover 4.4 through 8.2)
Week 7	Date	HW to be collected	Topics	Reading	Problems
	M 8/4	None	Expected value, revisited Generating functions	8.4	7.4 #7, 25, 47-49 8.4 #4, 6, 9, 11
	Tu 8/5		Generating functions (continued)		8.4 cont’d: #18, 22, 24, 33, 34, 42
	W 8/6		Relations and their properties Equivalence relations	9.1 9.5	9.1 #6, 49 9.5 #2, 8, 16, 40, 62
	Th 8/7	Problems assigned from W 7/30 through Tu 8/5	Graphs and graph models Graph terminology	10.1 10.2	10.1 #28—make a graph model of BART 10.2 #5, 18, 24, 26, 60, 64
	F 8/8		Graph representations; isomorphism	10.3	10.3 #28, 38, 40, 42, 44
Week 8	Date	HW to be collected	Topics	Reading	Problems
	M 8/11		Connectivity Euler and Hamilton paths	10.4 10.5	10.4 #21, 24, 28, 30 10.5 #28, 34 (recommended—see below)
	Tu 8/12	9.1 to 10.4	Planar graphs	10.7	10.7 #6, 8, 16, 18 (recommended)
	W 8/13		TBA
	Th 8/14		Final exam review
	F 8/15		Final exam, 2:00 to 4:00pm

The last homework will be collected on Tuesday, August 12. Problems from 10.5 and 10.7 will not be collected, but they are recommended as practice; solutions will be posted as usual.