Department of Mathematical Sciences
Binghamton University

Math 386: Combinatorics Announcements
Fall 2010

Index

• Tests and Quizzes
• Mathspeak
• Additions to Textbook
• Corrections to Textbook
• Solutions to Selected Problems

Tests

• Test I (Tues., Oct. 12)

  Covering all of Homework Sets I-VI (except the infinite series in Sect. 5.5). Grading guidelines:

   	A       B       C       D       F
  	85-100	68-74	50-67	45-49	0-44
  

• Test II (Tues., Nov. 23)

  Covering all of Homework Sets VII-XII. Grading guidelines:

  	A       B       C       D       F
  	90-100	75-89	55-74	48-54	0-47
  

• Final Exam (Mon., Dec. 13)

  The final exam will cover the whole course, i.e., everything we've done.
  The exam will be in room S2-145. The time is 2:00 p.m - 4:00 p.m. I will allow an extra 15 minutes. Grading guidelines:

  	A       B       C       D       F
  	130-150	105-129	75-104	70-74	0-69
  

• Quizzes

  • Quiz 1 (11/2).

Mathspeak

Here are some tips on using English correctly and clearly in mathematics.

• To write "a divides b" or "a is a factor of b" as a formula, use a vertical bar: a|b .
• "Unique" has one and only one meaning in mathematics: "unique" = "only one". If you can't replace "unique" by "only one" in your writing, you're using it incorrectly.
  "There is a unique" also has one and only one meaning: "there is one and only one". If you can't replace "there is a unique" by "there is one and only one" in your writing, it's incorrect usage.
  N.B. In correct standard English, "unique" means "of which there is only one" or a closely related meaning -- see Oxford English Dictionary. It does not mean "different"; if you mean that, say "different" or, in mathematics, "distinct".
• "Distinct" means "different from each other".
• A definition is what tells you the meaning of a word or phrase. In math, you should be able to replace the word by its definition. If you can't, you are probably using it incorrectly. A definition is not in any way like a theorem, which is something that has to be proved.

Additions to Textbook

• Here is a summary sheet (PDF) (or in PostScript) of basic counting problems and formulas.


• And here is an informative note (PDF) on magic squares of all orders, odd or even. (Just 5 pages.)


• This is a well illustrated article about the order-3 magic hexagon.


• Stirling's approximation to n! is very useful to get an idea of how big D_n is. The Wikipedia article has a good treatment but too much technical detail. I wrote a summary which you can read on this page (PDF).


• Non-attacking crook placements: Read all about them.

Corrections to Textbook

• In Exercise 2.16, the theorem is Theorem 2.3.1, not 3.3.1.
• In Exercise 2.28, a "block" is the part of a street between one corner and the next.
• In Exercise 3.16, assume that acquaintance is a symmetric relation. I.e., if X is acquainted with Y, Y is also acquainted with X (even though occasionally that's not so in real life).
• Don't forget that Exercise 6.33 has two parts. One part is to show that a(n,k) has the formula given. The other part is to show that a(n,k) counts the number of ways to choose k children, as specified in the exercise. I'm not sure which part should be done first, but I incline towards doing the second part first and using it to find the formula.
• In Chapter 7 there are references to "Newton's binomial theorem (see Section 5.6)"; the correct section is 5.5. (Pages 216, 256.)
• In Exercise 7.51, the section should be 7.5, not 7.6.
• In Theorem 8.1.1 "always positive" should be "always non-negative" (or "never negative", if you prefer).
• In the hint for Problem 7.6 (page 587), "induction on m" should read "induction on b".
• In the hint for Problem 7.7 (page 587), the "standard algorithm" is what is known as the Euclidean algorithm.
• In the middle of page 276, where it says "The nbumber of sequences of (n+1) +1s and (n+1) -1s", it should read "(n-1) -1s".
• Equation (8.7) has an extra C₁ in the second term of the written-out sum. Instead of C₁C_n-2C₁ it should be C₁C_n-2.

Solutions to Selected Problems

• Solution of Problem 7.7.
• Solution of Problem F3 (still partial, awaiting further ideas).