2009 Summer : Math 454
A different kind of mathematics.
A different kind of class.
Welcome to the web page for Math 454 at Rutgers University, Summer of 2009. This will be your one-stop source for everything related to the brisk 6-week course. I am using this course as a chance to experiment with a few new methods of teaching, so I will list these new things first:
- As little paper as possible – I will not be handing out any paper syllabus, as all of the information necessary is on this website.
- Twitter feed – I’m still under the belief that Twitter is a flash in the pan, but for now it has the potential to be useful. I will be tweeting the range from banal class information (like if I’m running late to class for whatever reason) to thoughts on discrete math and combinatorics that pass by during the day. The twitter feed is shown to the right, but if you subscribe to Twitter you can follow me at
Math454. - Chat “office hours” - I will still have normal office hours, but I will also make myself available on certain evenings, as I will be around working on my thesis. The downside is I will only be available via Google Chat under the username
math454@gmail.com. The downside of this is you’ll have to create a gmail account to get started, in case you don’t have one already.
Syllabus
Instructor Name: Paul Raff
Instructor Email: praff@math.rutgers.edu
Class Location: Hill 423
Class Time: Mondays through Thursdays, 10am to noon
Class Website: http://www.myraff.com/teaching/454 (redirected from http://www.math.rutgers.edu/~praff/454)
Book: Applied Combinatorics (2nd Edition) by Fred Roberts and Barry Tesman. Click here for answers to selected exercises.
Class Calendar:
Day-by-day Schedule:
| Class Number | Date | Title | Book Sections | Homework |
|---|---|---|---|---|
| 1 | June 22 | Instant Insanity and the Fundamentals | 2.1, 2.2, 2.3 | 2.1: 1, 6, 8, 9, 10 2.2: 1, 2, 3, 5, 6, 8 2.3: 1, 3, 6, 7, 9 |
| 2 | June 23 | Combinations, Permutations, and Subsets | 2.4, 2.5, 2.6, 2.7 | 2.5: 1, 3, 4, 5 2.6: 3, 4, 5 2.7: 8, 13, 14, 16, 19, 23 |
| 3 | June 24 | Probability | 2.8, 2.9 | 2.8: 3, 8, 9, 14, 15 2.9: 3, 5, 7, 8 |
| 4 | June 25 | Quiz; The Twelvefold Way | 2.10, 2.11 | 2.10: 1, 10, 11, 12 2.11: 6, 8, 11, 15 |
| 5 | June 29 | Permutations with Classes of Indistinguishable Objects | 2.11 (continued), 2.13 | 2.13: 3, 6, 9, 11 |
| 6 | June 30 | The Binomial Expansion, generating combinations and permutations | 2.14, 2.16 | 2.14: 3, 13, 14, 16a 2.16: 2, 5, 6 |
| 7 | July 1 | The Pigeonhole Principle, recap of Chapter 2 | 2.19 | 2.19: 1, 2, 6, 23, 24, 32abc Additional Exercises for Chapter 2: 2, 3, 4, 8, 9, 11, 12, 18, 21, 24 |
| 8 | July 2 | Quiz; Fundamental Concepts of Graph Theory | 3.1 | 3.1: 15, 16, 18, 23, 24, 25, 26, 27 |
| 9 | July 6 | Connectedness, Graph Coloring | 3.2, 3.3 | 3.2: 1, 2, 5, 6, 7, 8, 11 3.3: 3, 4, 12, 20, 21, 22 (use whichever method you wish), 23, 24 |
| 10 | July 7 | More Graph Coloring, Chromatic Polynomials | 3.4 | 3.4: 1, 5, 6, 14 |
| 11 | July 8 | Trees | 3.5, 3.7 | 3.5: 6, 9, 11, 16, 18, 19, 26 3.7: 1a, 3, 18 |
| 12 | July 9 | Exam 1 | ||
| 13 | July 13 | Introduction to generating functions | 5.1, 5.2 | 5.1: 2 (turn in 2f), 3, 4, 5, 6 5.2: 2, 3, 4, 11, 12, 15 |
| 14 | July 14 | How to count with generating functions | 5.3 | 5.3: 1, 2, 3, 4, 6, 7, 17 |
| 15 | July 15 | The binomial theorem, exponential generating functions | 5.4, 5.5 | 5.4: 2, 6, 7, 8, 9, 10, 13, 21 5.5: 1, 2, 5, 6, 12, 13, 14, 15, 18 |
| 16 | July 16 | Quiz; recap of generating functions | ||
| 17 | July 20 | Introduction to recurrence relations; the method of characteristic roots | 6.1, 6.2 | 6.1: 1, 15, 16, 21, 27, 28, 34 6.2: 1, 2, 5, 9, 10, 11, 12abde, 17 |
| 18 | July 21 | Using generating functions to solve recurrences; recurrences involving convolutions | 6.3, 6.4 | 6.3: 1, 2 (turn in 2b), 3, 4, 9, 11 6.4: 1-6, 12, 17 |
| 19 | July 22 | The Principle of Inclusion-Exclusion | 7.1 | 7.1: 2, 3, 4, 8, 9, 13, 30 |
| 20 | July 23 | Quiz; more Inclusion-Exclusion | 7.2 | 7.2: 8, 12, 17, 20 |
| 21 | July 27 | Introduction to coding theory; error-correcting codes | 10.1, 10.2, 10.3 | 10.2: 1-3 10.3: 5, 6, 11, 14, 23 |
| 22 | July 28 | Linear codes; Eulerian chains and paths | 10.4, 11.3, 11.4 | 10.4: 1, 2, 7 11.3: 10, 14, 16 11.4: 1, 5, 8, 10 |
| 23 | July 29 | Hamiltonian chains and paths; exam review | 11.5 | 11.5: 1, 2, 7, 8, 15 |
| 24 | July 30 | Final Exam |
#1 by Katy at June 29th, 2009
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I’m still 90% sure that your Raffsanity is not solvable.
#2 by Anoop at July 2nd, 2009
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I just want to say in general that what we learn on a Wednesday should be on the quiz of the next week as new material just doesn’t sink in right away and we don’t discuss HW questions before the quiz.
Just a thought : )