Assignments Page

Math 17
An Introduction to Mathematics Beyond Calculus
Last updated June 27, 2016 13:25:43 EDT

Announcements:

The student presentations are scheduled as follows: March 4 (Nick, Mike B., Henry), March 6 (Patricia and Shawn), March 8 (Madi and Mike L.). Feel free to ask me about references or how much material is reasonable to present in the time you have.

Homework Assigments

Date	Covered in class	Written homework assignment	Due date	Problems to discuss in next class (not to be turned in)
1/7	Introduction, basic counting	Problem 4	1/16	Problem 5 (to be discussed in class on 1/16)
1/9	Fibonnaci numbers, tilings (taught by Natasha Komarov)	Prove using a direct combinatorial argument: a) f₁+f₃+...+f_2n-1=f_2n-1, b) f_n²+f_n+1²=f_2n+2.	1/16
1/11	More Fibonnaci identities, Lucas numbers (taught by Natasha Komarov)	Prove using a direct combinatorial argument: c) L_n=f_n-1+2f_n-2.	1/16
1/15 (x-hour)	Compositions, subsets	Problem 5	1/23	Problem 10
1/16	Binomial coefficients	Problems 8,12	1/23	Problem 13
1/18	Binomial coefficient identities	Problem d)	1/23	Problem 20
1/22 (x-hour)	Lattice paths, sequences	Problem e)	1/30	Problem 21
1/23	Divisibility, multisets	Problem 26	1/30	Problem 31
1/25	Fibonnaci numbers revisited	Problems 32, 33	1/30	Problems 34, 35
1/28	Permutations, basics	Problem 41	2/6	Problem 47
1/30	Fixed points and inversions in permutations	Problem 46	2/6
2/1	Derangements, the Principle of Inclusion-Exclusion	Problem 48	2/6	Problem 50
2/4	More derangements, cycle decomposition	Problem 55	2/13	Problem 53
2/5 (x-hour)	Involutions, cycles			Problem 56
2/6	Stirling numbers of the first kind	Problems f) and g)	2/13	Problem 61
2/11	Records, Foata's fundamental transformation	Problem 63	2/20	Problem 72
2/13	Alternating permutations, Integer partitions	Problems 87	2/20	Problems 94, 98
2/15	Partition bijections	Problems 89, 93	2/20	Problems 96, 98, 103
2/18	More partition bijections	Problem h)	2/27
2/20	Harmonic number indentities (taught by Natasha Komarov)
2/22	Stirling number indentities (taught by Natasha Komarov)	Problems i) and j)	2/27
2/25	Euler's pentagonal number formula			Problem 119
2/27	Parking functions	Problems k) and l)	3/6	Problem 164
3/1	Catalan numbers	Problem 161	3/6
3/4	Student presentation 1. Mike B., Henry and Nick: Domino tilings of Aztec diamonds.
3/6	Student presentation 2. Patricia and Shawn. Derangements and the sum of the largest fixed points.
3/8	Student presentation 3. Madi and Mike L.: The inversion number and the major index of permutations.

Last updated June 27, 2016 13:25:43 EDT