 Text:
How to Prove It, a structured approach
by Daniel Velleman, Cambridge University Press 2nd
ed..
Exam
Schedule:
Midterm : Friday, Feb. 8, in class
Final: Wednesday, March 20, 8-11am, in class
Grading:
Homework 10%; Quiz 10%; Midterms 30%; Final 50%.
HW #1 (due 1/11)
Batch 1:
p13: 2, 3, 4, 6, 7.
Batch 2:
p24: 2, 4, 5, 6, 8.
Solutions
HW #2 (due 1/18)
Batch 1:
p25: 10, 12, 13, 18; p33: 3, 4; p42: 2.
Batch 2:
p42: 4, 5, 8, 9; p53: 2, 4, 6.
Batch 3:
p54: 5, 10; p63: 2, 3, 5, 7.
Solutions
HW #3 (due 1/25)
Batch 1: p72, 2, 3, 4, 5, 6, 8, 9, 10, 12.
Batch 2: p81: 2, 3, 5, 6, 7, 9, 10.
Solutions
HW #4 (due 2/1)
Batch 1:
p93: 1, 2, 3, 4, 5, 6, 7.
Batch 2:
p94: 8, 10, 11, 12, 15, 16.
Batch 3:
p106: 3, 4, 5, 6, 9.
Solutions
HW #5 (due 2/8)
Batch 1:
p122: 2, 4, 8, And
4.) Suppose n is an integer. Prove that if n^2 is
divisible by 3, then n is also divisible by 3.
5.) Prove that \sqrt{3} is irrational.
Batch 2:
p122: 18, 20, 21, 23.
Solutions
HW #6 (due 2/15)
Batch 1:
p143: 2, 7, 8, 10, 14. And
6). Suppose n is an integer. Prove that if n^2 is
divisible by 5, so is n.
7). Suppose m and n are integers. Prove that if
m^2+n^2 is even, then either both m,n are even or both
are odd.
Batch 2:
p133: 6, 7, 10, 22; p161: 9. And
6). Prove that there is a unique set of three
consecutive odd positive integers that are all primes.
(Hint: recall that any integer can be written as 3k,
3k+1, or 3k+2 for some integer k.)
Batch 3:
p170: 4, 5, 6, 9.
Solutions
HW #7 (due 2/22)
Batch 1:
p178: 2, 3, 6, 8; p186: 2, 6, 7, 8, 12, 13, 22.
Batch 2:
p188: 16, 18; p222: 2, 3.
Solutions
Solutions
to Midterm
HW #8 (due 2/29 i.e. 3/1
;-> )
Batch 1:
p223: 4, 5, 7, 8, 10, 11, 13, 16
Batch 2:
p233: 2, 3, 4, 7, 8, 9.
Batch 3:
p236: 17, 18, 19; p243: 4, 6.
Solutions
HW #9 (due 3/8)
Batch 1:
p243: 8, 9, 12, 15, 16; p253: 8, 9, 11.
Batch 2:
p254: 13; p265: 2, 4, 5, 9.
Batch 3:
p266: 8, 12, 16, 17.
Solutions
HW #10 (Due 3/15)
Batch 1:
p296: 3, 4, 5, 6, 8, 9.
Batch 2:
p298: 11, 16; p277: 12.
Solutions I
Solutions
II
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