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Due date if any
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Fuchsia means graded homework.
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December
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Page 3 on
Proofs
is due in December.
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November
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Section 4.5 on pages 321-323. 2, 4, 10, 14, 15a.
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Section 4.4 on pages 310-313. 2, 3a, 4a, (22, 23 (both a bit hard)).
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Section 4.3 on pages 298-301. 1ac, 2a, 3a, 10e, 16, 26 (a bit hard).
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Section 4.2 on pages 277-283. 1, 19, 29 (a bit hard).
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Section 4.1 on pages 264-268. 2, 17bc, 25bd.
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Section 3.4 on pages 227-229. 8.
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Section 3.3 on pages 219-221. 2a, 11a.
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Section 3.2 on pages 208-209. 1c, 17, 24 (a bit hard).
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Section 3.1 on pages 193-197. 1, 18a, 32, and a problem about
sets.
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November
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October
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Modular arithmetic.
n is always a non-negative integer.
- Show that if n is odd and divisible by 3, then n^2-1 is divisible by 8
(not easy).
- Page 149 32a, show that given seven integers, there are two that have a
difference divisible by 6.
- Show that there is no n such that n^2 = 3 modulo 4.
- Show that if n is odd, then 3^n+1 is divisible by 4.
- Show that if n is odd, then 2^n-1 is not divisible by 3.
- Show that 4^n-1 is divisible by 3.
- Compute 2^502 modulo 31 (try 2^1, then 2^2, then 2^3, etc).
- Compute 98^4 modulo 101.
- Compute 3^4 modulo 101.
- Compute 9998 * 9997 modulo 10000.
- Compute 2 * 3 modulo 10000.
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Pages 146-149, problems 1, 2, 6, 12, 22, 8d, 15, 19b, 39 (very hard, until you
see the easy proof).
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Pages 130-132, problems 1bc, 8d, 15, 19b.
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Pages 121-122, problems 1abd, 2, 3e, 4b, 13.
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Pages 107-110, problems 1abcd, 2abcdf, 3fg, 6ab, 14a (a bit long), 23.
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Pages 96-98, problems 1bcehi, 2acd (2g is true but not easy to prove), 4ad
(4 is a proof writing exercise), 10bc (proof writing), 13c (ignore the hint).
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October
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September
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Pages 65-68, problems 4, 17, 22, 28, 30.
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Pages 51-53, problems 1, 2ab, 9a, 10ad, 11, 14, 15.
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Pages 37-40, problems 1, 3, 9, 21, 23ab (just simplify).
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11-13 September
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Pages 37-40, problems 5, 8, 11abc, 21bd.
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8 September
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Pages 20-23, problems 2ad, 4c, 8c, 9b, 18, 24, 29ab.
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6 September
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Page 9, problem 7.
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For the book's original version of the grid problem on page 6, but on a 2 by 2
grid rather than 4 by 4, show that there is a winning strategy for the 2nd
player.
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Page 7
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In class we found a winning strategy for the game between 2 players A and B
for the simplified game of page 6-7.
We are given a generalized chess board of size m rows by n columns.
Beginning with player A, the players alternatingly must pick an empty field,
and then either fill the entire row or the entire column with X's.
The player who fills the last unused squares wins.
Task:
Describe the winning strategy.
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