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+...+f2n-1=f2n-1,   b) fn2+fn+12=f2n+2. 1/16
1/11 More Fibonnaci identities, Lucas numbers (taught by Natasha Komarov) Prove using a direct combinatorial argument:   c) Ln=fn-1+2fn-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