Binghamton University

Fall 2010

Go to homework | course information | syllabus.

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

### 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)

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

### Quizzes

- Quiz 1 (11/2).

- 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.

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

- 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.

- 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 C_{1}in the second term of the written-out sum. Instead of C_{1}C_{n-2}C_{1}it should be C_{1}C_{n-2}.

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