MA 315 Introduction to Abstract Mathematics Spring 2011 Instructor: Peter Turbek Oce: CLO 329 Telephone: 989-2277 Class Webpage: http:/ems.calumet.purdue.edu/mcss/psturbek/index.html e-mail: [email protected] Oce Hours: MW: 2:00-3:30, 5:00-6:30, a
MA 315, Spring 2011
Proofs To Critique
Critique the following proofs line by line. For each line, you should state whether the line is correct or not. In addition, state whether the line is needed or not. Can any of the lines be improved?
Theorem: If a,b
MA 315, Spring 2011 Handout 2 1. Assume a, b, and c are integers. Prove or disprove: if b + c is not divisible by a, then b is not divisible by a and c is not divisible by a.
2. Assume a, b, and c are integers. Prove or disprove: if a | b + c and a does n
MA 315, Spring 2011 Handout 1 For each problem below, let n be an integer. (1) Why cant we divide by n by 0?
(2) Prove that if n is even, then n2 is even.
1
2
(3) Prove that if n2 is odd, then n is odd.
(4) Prove that if n is odd, then n2 is odd.
(5) Prov
MA 315, Spring 2011 Homework 4 Due Tuesday, February 16, 2011 Your paper must be typed and you must write in complete sentences with correct spelling, punctuation and grammar. (1) Assume n is an integer. Prove that n2 + 2 is not divisible by 5. (2) Assume
MA 315, Spring 2011 Homework 3 Answers Due Wednesday, February 9, 2011 For this homework assignment you are allowed to use the following fact about integers: If n is an in integer, then n leaves a remainder of either 0, 1, or 2 when n is divided by 3. For
MA 315, Spring 2011 Homework 3 Due Wednesday, February 9, 2011 For this homework assignment you are allowed to use the following fact about integers: If n is an in integer, then n leaves a remainder of either 0, 1, or 2 when n is divided by 3. For example
MA 315, Spring 2011 Homework 2 Due Wednesday, February 2, 2011 Your paper must be typed. Each proof must be written in complete sentences with correct spelling, punctuation and grammar.
(1) Prove the following: If n is an odd number then n2 1 is divisible
MA 315, Spring 2011 Homework 2 Due Wednesday, February 2, 2011 Your paper must be typed. Each proof must be written in complete sentences with correct spelling, punctuation and grammar. (1) Prove the following: If n is an odd number then n2 1 is divisible
MA 315, Spring 2011 Homework 1 Answers Due Wednesday, January 26, 2011 Prove the following two statements. Your paper must be typed. Each proof must be written in complete sentences with correct spelling, punctuation and grammar. (1) Let a, b, and c be in
MA 315, Spring 2011 Homework 1 Due Wednesday, January 26, 2011 Prove the following two statements. Your paper must be typed. Each proof must be written in complete sentences with correct spelling, punctuation and grammar. (1) Let a, b, and c be integers.