MAT 345 Assignment #1 Due 1/25/12 Please write up your solutions on a separate sheet of paper. 1. Show that 131 / 4 is an algebraic number. 2. Show that (2 + 2 )1 / 2 is an algebraic number 3. Show that (3 + 2 ) 2 / 3 is an algebraic number.
MAT 345 Assignment #10 Due 3/7/12 Please write up your solutions on a separate sheet of paper. 1. Exercise 2(e) on page 42 of the text. Hint: Since the sine function only takes on values between -1 and 1, we can say 1 1 1 sin n = sin n n n n 2. Prove that
MAT 345 Assignment #9 Due 3/5/12 Please write up your solutions on a separate sheet of paper. (-1) n which converges to 0. n
1. Consider the sequence s n =
a.
1 , find a value of N that satisfies the definition of convergence. In addition, 10 graph your r
MAT 345 Assignment #8 Due 2/29/12 Please write up your solutions on a separate sheet of paper. 1. Exercise 1 on page 36 of the text. 2. Exercise 2 on page 36 of the text. (You only need to complete (a) and (d).) 3. Exercise 3 on page 36 of the text. (You
MAT 345 Assignment #7 Due 2/15/12 Please write up your solutions on a separate sheet of paper.
1. Exercise 10 on page 26 of the text. Hint: Use the Archimedean Property and its corollaries.
MAT 345 Assignment #6 Due 2/13/12 Please write up your solutions on a separate sheet of paper. We want to developed two "corollaries" to the Archimedean Property:
i.
Given any real number x there exists a natural number n where n > x. 1 < y. n
ii. Given a
MAT 345 Assignment #5 Due 2/8/12 Please write up your solutions on a separate sheet of paper. 1. Without worrying about formal proofs, decide of the statements are true or false. For any that are false, supply an example where the claim in question does n
MAT 345 Assignment #4 Due 2/6/12 Please write up your solutions on a separate sheet of paper. 1. Exercise 1 on page 25 of the text. 2. Exercise 2 on page 25 of the text. 3. Exercise 3 on page 25 of the text. 4. Exercise 4 on page 25 of the text.
MAT 345 Assignment #3 Due 2/1/12 Please write up your solutions on a separate sheet of paper. 1. Exercise 1 on page 18 of the text.
2. As we discussed in class, the algebraic properties that we use regarding equalities and inequalities all stem from the a
1. I found the following on a math-help website as a response to the question "How do you prove the Rational Roots Theorem?":
The theorem states that if a polynomial has a rational root, then the denominator of the root must divide the coefficient of the
MAT 345 Assignment #11 Due 3/19/12 Please write up your solutions on a separate sheet of paper. 1. Today in class, we assumed that lim 1 = 1 in our solution to the final problem. We don't n want to just assume this though; we want to prove this! Prove the