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KSU Main page |
Office
Hours: MWF 1:30pm--2:20pm or by
appointment.
Office Location: Cardwell Hall 210.
Tel.: 532-0573
Course Webpage: http://www.math.ksu.edu/~zlin/m510
Text Book: Introductory Combinatorics Fourth
Edition (2004, by Richard A. Brualdi Published by Prentice Hall.
The book should be available in K-State Union Book Store.
Ch 2. The Pigeonhole Principle-------- 3 Lectures
2.1. Pigeonhole Principle: the simple form
2.2. Pigeonhole Principle: The strong form.
2.3. A theorem of Ramsey
Ch 3. Permutations and Combinations---5 Lectures
3.1. Two Basic counting Principles
3.2. Permutations of sets
3.3. Combinations of sets
3.4. Permuations of multisets
3.5. Combinations of multisets
Ch 5. The Binomial Coefficients-----------5 Lectures
5.1. Pascal's formula
5.2. The binomial theorem
5.3. Indentities
5.5. The multinomial Theorem
5.6. Newton's binomial theorem
EX I : and Review ------- 2 classes
Ch 6. The Inclusion-Exclusion Principle---5 Lectures
6.1. The inclusion-exclusion principle
6.2. Combinations with repetition
6.3. Derangements
6.4.Permutations with forbidden positions
6.5. Another forbidden position problem
Ch 7 -Recurrence Relations and Generating Functions---4
Lectures
7.1.Some number sequences
7.2. Linear homogeneous recurrence relations
7.4. Generating Functions,
7.5. Recurrences and generating functions
Ch 9. Matchings in Bipartite Graphs-------6 Lectures
9.1. General problem formulation
9.2. Matchings
9.3. System s of distinct representatives
9.4. Stabel marriages
Ch 11. Introduction to Graph Theory---5 Lectures
11.1. Basic properties
11.2. Eulerian trails
11.3 Hamilton chains and cycles
11.5. Trees
EXII: and Review ------- 2
classes
Ch 12. Digraphs and Networks -------3 Lectures
12.1. Digraphs
12.2. Networks
Ch 13. More on Graph Theory-----4 Lectures
13.2. Plane and planner graphs
13.4. Independence number and clique number
Reciew for the Final: 2-classes
Advance Math Help Session Schedule
| HW No. | Sections | Homework Problems | Practice Problems (hint) |
Due Day | solutions (pdf) |
| #1 | 2.4 |
1, 4, 8, 11, 14 |
3, 5, 7, 9, 10, 15 |
W.1/24 |
Solution |
| #2 | 2.4 3.6 |
16,18,23 2,4, 6,7 |
17,19 1,5, 8 |
W. 1/31 |
solution |
| #3 | 3.6 |
10, 12, 13, 17, 20, 25 30, 34, 41 | 9, 11, 14, 15, 18, 23, 27, 35, 42 | W.2/7 |
solution |
| #4 | 5.8 |
3, 5, 8, 12, 16, 22 | 6, 7, 9, 11, 16, 21 | F.2/16 |
solution |
| #5 | 6.7 |
2, 4, 6, 9, 11, 13, 15 | 1, 3, 5, 8, 10, 12, 14 | M.3/5 |
solution |
| #6 | 6.7 |
21, 24(c), 25, 28, 29 | 20, 24(b), 26, 27, 30 | F. 3/9 |
solution |
| #7 | 7.8 |
12, 14, 28(a,c), 30(b), 35 |
16, 28(b,d), 36 |
F. 3/16 |
solution |
| #8 | 9.5 |
2,3,6,8,11 |
1,4,7, 9, 10 |
F. 3/30 |
solution |
| #9 | 9.5 |
13, 15, 20, 22, 26 | 12, 14, 16, 19, 21 | F. 4/6 |
solution |
| #10 | 11.8 |
2,5, 9, 12, 14 | 1,4,6,11,13,15 | M. 4/16 |
solution |
| #11 | 11.8 |
18, 26, 30, 41, 44, 51(b), 62 | 19, 27, 31, 47, 51(c), 64 | W. 4/25 |
solution |
| #12 |
12.3 |
4, 6, 8 |
7, 9, 10 |
W.5/2 |
solution |
Solutions to Exam 1
Solutions to Exam 2
hw=(sum(hw1:hw12)-small(hw1:hw12,1)-small(hw1:hw12,2))/10
Overall
Score=.2*hw+.2*ex1+.2*ex2+.4*fe+.2*max(0; fe-ex1; fe-ex2)
Final Exam is on a 100 pt scale
Then computer will do the work!
Why do I have to do reasoning?
Can you convince Pa and Ma that you are right and they wrong?
What happens if Pa and Ma are your working boss?
Although it is not a prerequisite for this course, CIS
students should have taken
CIS 301.
Knowledge of the contents of CIS
301 will be very helpful to
students. Computer engineering students
may not have
taken CIS 301. It is strongely recommended that students
should at least take a look
at the text book of
CIS
301 to get familier with
proofs, reasoning, and mathematical induction
as
well as basic logic.
Related Computer Science
courses that take this course as a requirement.