Archimedes did combinatorics 2200 years ago! Read all about it!

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**FINAL EXAM (date change)**

**FINALS WEEK**

### Test I (Oct. 2)

Covering the parts we've done so far in Chapters 1, 3, and 5 (that is, HW Sets I-V). Grading guidelines:

A B C D F 80-100 65-79 45-64 36-44 0-35

### Test II (Oct. 30)

Covering Sections 5.3-5 and all of Chapter 6 (approximately, that's HW Sets VI-IX). Grading guidelines:

A B C D F 86-100 67-85 48-66 38-47 0-37

### Test III (Dec. 4)

Covering the parts assigned in Sections 2.1-3 (excluding the Chinese Remainder Theorem), 5.6, 7.1, 7.2, 7.4, 7.5. Grading guidelines:

A B C D F 80-100 65-79 50-64 41-59 0-40

### Final Exam (Thurs., Dec. 18)

On Thursday, December 18, at 11:00 a.m. - 1:00 p.m. in S2-144. I will allow an extra 15 minutes if possible. The exam will cover everything in the course, with some emphasis on the part since Test III (that is, on Homework XIV), but excluding the Chinese Remainder Theorem.

- 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'' = ``one and only one''. If you can't replace ``unique'' by ``one and only one'' in your writing, you're using it incorrectly.

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 (mathematically) ``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.

- In the discussion of subsequences in
**Ch. 2, Application 9**, the term "not decreasing" is the wrong technical term. A correct technical term for this property is "weakly increasing" or "nondecreasing" (both are used). **Ch. 2, #16.**It should also be assumed that acquaintanceship is symmetrical: i.e., if A is acquainted with B, then B is acquainted with A. (This isn't always so in real life!)**Ch. 3, #9:**The committee should consist of*5 (five)*members.**Ch. 3, #16:**``no two rooks can attack*one*another.''**Sect. 5.7:**- In Theorem 5.7.2, first paragraph of proof, the s's should be m's.
- In properties 1 and 2 at the top of p. 152, each of the first two A's should be X. (The A
^{+}and A^{-}and the last A are correct.)

- In
**Section 6.3, p. 174, line 15**, the expression (n-2)!D should be just (n-2)!. - In the
**answers to Ch. 6**, the last 3 problem numbers are 1 greater than they should be. - In
**Section 8.4, Equation (8.23)**, the definition of h_{n}^{(k)}is valid for all k, n >= 0. - In
**Ch. 8, #4(b)**, the parenthesization is incomplete and there are extra parentheses. Use the following expression instead:- ( ( (a
_{1}× a_{2}) × (a_{3}× (a_{4}× a_{5})) ) × ((a_{6}× a_{7}) × a_{8}) )- In
**Ch. 10, page 341**, the term ``GCD'' is introduced. It is an abbreviation for ``greatest common divisor,'' as mentioned in Theorem 10.1.2 on p. 343.- In
**Ch. 10, page 343**, in the table at the top, the entries in Cols. A and B are sometimes interchanged from what the algorithm would give. - ( ( (a

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