Homework 3
MA 2312 Due Tuesday at the beginning of your recitation
1. Prove that if n is a positive integer, n is even if and only if 7n + 4 is even. 2. Prove that 5 divides n if and only if 5 divides n2 . 3. Prove or disprove that 2n 1 is prime for all i
Homework 1
You must hand it your homework on paper. It can be either typed or hand-written; I type it using the A L TEXsystem, which is used by many mathematicians and scientists because of its ability to typeset math A quickly and with high-quality resul
Sample nal This is the subset of the union of two actual nals I have given in the past. I have deleted many questions that we did not cover the material on. You should make sure you can solve easy problems! you can practice by trying the problems in the b
MA2312 Spring 2010 Homework 2
John Iacono January 28, 2010
Read sections 1.1-1.7. 1. For each of these expressions, tell me in the simplest way possible what they evaluate to. For example, if the question is 2 + 2, you should respond 4, and not 1 + 3, 2 +
Homework 4
MA 2312 Due Tuesday at the beginning of your recitation
1. Precisely dene (a) A relation on the reals where two numbers relate if they are relatively prime. (b) A function that takes a set of integers and returns the sum of all elements in the
MA2312 Homework 5
John Iacono February 24, 2010
1. Prove by induction, that for all integer n where n > 1
n
i=1
1 1 <2 i2 n
2. Prove by induction, that for all integer n where n 1
n
i(i + 1)(i + 2) =
i=1
n(n + 1)(n + 2)(n + 3) 4
3. Prove by induction, tha