## MATH 525 Calendar for Spring 2016

 Note: This calendar is subject to change; check frequently for updates. Disclaimer: Lecture notes are written in advance and may not always reflect exactly what was done in class on that day. (For example, a student's question could lead to a discussion of examples not included in the notes. Also, lecture notes may contain a few extra examples not done in class, in interest of time.)

Tuesday
Thursday
Jan. 19
Today: §2.1, §2.2: Pigeonhole Principle
21
§2.3: A Theorem of Ramsey
§3.1: Two Basic Counting Principles: (Addition and Multiplication Principles)
26
§3.2, §3.4: Permutations of Sets and Multisets
28
§3.3: Combinations of Sets
Homework #1 due:
§2.4: 5, 14, 16
§3.6: 1, 4, 6
Feb. 2
§3.5: Combinations of Multisets
4
§5.1, §5.2, §5.3: Pascal's Formula, the Binomial Theorem and Identities.
Homework #2 due:
§3.6: 8, 12, 17, 25, 31, 36
9
§5.5, §5.6: Multinomial Theorem and Newton's Binomial Theorem

11
§6.1: Inclusion-Exclusion Principle
Homework #3 due:

§5.8: 9, 13, 16, 18, 21, 36
You can find the §5.8 problems here.
16
§6.2: Combinations with Repetition
18
§6.3: Derangements
§6.4: Permutations with Forbidden Positions
23
§6.5: Another Forbidden Position Problem
Homework #4 due:
§6.6: 1, 5, 8, 11, 14, 21
You can find the §6.6 problems here.
25
TEST #1 [ Blank | Solved ]
§2.1, §2.2,  §3.1– §3.5,  §5.1–§5.6,  §6.1–§6.4
March 1
§7.1: Some Number Sequences

3
§7.2: Linear Homogeneous Recurrence Relations

8
SPRING BREAK

10
SPRING BREAK

15
§7.2: Linear Homogeneous Recurrence Relations (continued)
17
§7.3: Non-homogeneous Recurrence Relations
Homework #5 due:

§7.8: 6, 7, 11, 12
Here is a link to the §7.8 exercises
22
§7.4: Generating Functions
24
§7.4: Generating Functions (continued)
§7.5: Recurrences and Generating Functions
Homework #6 due:
§7.8: 16, 18, 19, 20, 23, 24
Here is a link to the §7.8 exercises
March 25:
Last day to withdraw with a grade of "W"
29
§7.6: A Geometry Example
31
§7.7: Exponential Generating Functions
April 5
Test discussion
§8.1: Catalan Numbers
Homework #7 due:
§7.8: 25d, 30, 31, 33, 35, 37c, 39, 41
7
TEST #2 [ Blank | Solved ]
§7.2, §7.3, §7.4, §7.5, §7.7
12
§8.1: Catalan Numbers (continued)
§8.2: Difference Sequences and Stirling Numbers
14
§8.2: Difference Sequences and Stirling Numbers (Continued)
19
§8.2: Difference Sequences and Stirling Numbers (Continued)
21
§8.3: Partition Numbers
Here is a link to the truncated generating function for the partition numbers.
Here is a link to Rashad's improved version of the truncated generating function.
Homework #8 due:
§8.5:
2, 4, 6, 8, 12, 15
26
§8.4: A Geometric Problem
28
§8.4 Continued: An introduction to the fourth dimension
Homework #9 due:
§8.5:
13, 19, 20, 25, 27, 29
May 3
Final Exam Discussion
Homework #10 due:
(but no penalty for turning it in any time before noon May 6.)
 §2.4: 20 §5.8: 25 §7.8: 40 §3.6: 9 §6.6: 17 §8.5: 26
Note: The text has a typo in §3.6: 9, above. It should read "a committee of 5" (not 4).
Also note that §8.5: 26(e) is a partition of 29 (not 30).
5
10
12
FINAL EXAM 8:00–10:50 am
[ Blank | Solved ]