Instructor: |
Monty (or William)
McGovern
Office: Padelford C-450 Phone: 206-543-1149 Email: mcgovern@math.washington.edu Office Hours: MW 2:30 or by appointment, Padelford C-450 |
Lectures: |
Monday, Wednesday & Friday, 1:30-2:20 p.m., Smith Hall 304 |
Prerequisites: |
Math 125 or the equivalent. |
Exams: |
1st Midterm: Friday, January 30, in
class. |
Grading: |
Your grade will be based equally on weekly homework (300 points) and tests (two midterms and final, 300 points total). The homework will require a great deal of writing, but no essays or papers. I will give you the opportunity to work on the homework in groups in class, but it will be submitted individually. The final exam will be comprehensive. If you must miss an exam because of illness or emergency, I would very much appreciate advance notice. If you cannot complete a homework assignment on time, you can always turn it in by 3:00 on the day it is due to my mailbox. PLEASE turn in WHATEVER YOU CAN rather than nothing. In all tests you may use two letter-sized pages (one sheet front and back of notes in your own handwriting). |
Incompletes and Drops: |
The grade of Incomplete will be given ONLY if a student has been doing satisfactory work until the end of the quarter and then misses the final exam for a documented illness, religious reason, or family emergency. |
What to Expect: |
The first half of the course will be devoted to the language of mathematical proofs, introducing some basic ideas of mathematical logic and the basic templates of most proofs: direct proofs, proofs by contradiction, and proofs by induction. In the second half you will see these techniques in action as we prove some results in number theory (the theory of integers). You will see the techniques mentioned above used in more and more complicated and powerful ways. |
Due: | Problems: |
Jan 9 |
Exercises 1.1,4 (pp. 8,9), Problems I.1,4,5 (p. 53): read
Chapters 1 to 3 |
Jan 16 |
Problems I.11,13,14, board problems: A certain island is
inhabited by two tribes, one consisting of people who always tell
the truth, the other consisting of people who always lie. You
can't tell the tribes apart by looking (but the natives know who
belongs to each tribe). If you meet someone on the
island, how can you ask him just one question that will reveal
which tribe he belongs to? If you meet three people A,B, and C,
and if A says that B is a liar while B says that if A is a liar,
then so is C, then which tribe does each belong to? Also read Chapters 4
and 5. |
Jan 23 |
Problems I.22,25; II.4,11(i-v),14: read Chapters 6-9 |
Jan 30
|
study problems, first midterm: make up your own problems with
liars and truth-tellers; Problems I.19,21, Exercise 8.5 (p. 99);
Problem II.16: read Chapters 10,11 |
Feb 6 |
Problems III.3,4,5,8: read Chapters 12,13
|
Feb 13 |
Exer. 12.5,6 (p. 155); Probs. III.14,16,20: read Chapter 14 |
Feb 20 |
Probs. IV.1,2,3,6,7: read 15 and 16 |
Feb 27
|
study problems, second midterm: Ex. 19.4,5; Probs. VI.16,17;
given 5 points inside a square of side 1, show that some two of them
are at most \sqrt(2)/2 apart. |
Mar 6
|
Probs. V.2,4; Probs. VI.1,2,6: read Chaps. 19,20,23,24 |
Mar 13
|
study problems, final: Probs. I.19, III.28, V.5, VI.13, Exer. 20.1 |