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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.) |
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| Jan. | 19 Read Chapter 1 for background. Today: §2.1, §2.2: Pigeonhole Principle |
21 §2.3: A Theorem of Ramsey §3.1: Two Basic Counting Principles: (Addition and Multiplication Principles) |
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| 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 |
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| 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 |
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| 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. |
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| 16 §6.2: Combinations with Repetition |
18 §6.3: Derangements §6.4: Permutations with Forbidden Positions |
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| 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 |
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| March | 1 §7.1: Some Number Sequences |
3 §7.2: Linear Homogeneous Recurrence Relations |
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| 8 SPRING BREAK |
10 SPRING BREAK |
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| 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 |
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| 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" |
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| 29 §7.6: A Geometry Example |
31 §7.7: Exponential Generating Functions |
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| 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 |
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| 12 §8.1: Catalan Numbers (continued) §8.2: Difference Sequences and Stirling Numbers |
14 §8.2: Difference Sequences and Stirling Numbers (Continued) |
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| 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 |
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| 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 |
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| May | 3 Final Exam Discussion Homework #10 due: (but no penalty for turning it in any time before noon May 6.)
Also note that §8.5: 26(e) is a partition of 29 (not 30). |
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| 10 |
12 FINAL EXAM 8:00–10:50 am [ Blank | Solved ] |
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