Math 380a, Fall 2013
HOMEWORK #1
due Tue, October 1
Homework consists of four parts: the written assignment W1-W4 which counts towards
the nal grade for the course, the extra credit problems which are for those who are interested
in taking the Putnam comp
Math 380a
HOMEWORK #3
due Tue, October 15, 2013
This homework has no reading assignment.
Written assignment (4 problems).
W1. Prove that the formula V E + F = 2 is true for convex polyhedrons with V vertices,
F faces, and E edges.
W2.
1. We say that x cfw
Math 380a
HOMEWORK #9
Written assignment (4 problems).
due Tue, November 26, 2013
W1. From where he stands, one step toward the cli would send a drunken man over the
edge. He takes random steps on a line, either toward or away from the cli. At any step
hi
MATH 380
Practice Final
Autumn 2013
Due December 3, 2013
NAME:
SIGNATURE:
Instructions: there are 6 problems on the nal. You need to solve (completely and impeccably)
four of them to get 100%. Partial credit will be given on all 6 but sparringly. One comp
Math 380a
HOMEWORK #8
due Tue, November 19, 2013
Reading assignment: Sections 5.1-5.4 in the book.
Written assignment (4 problems).
W1. Let a, b, c be distinct integers. Can the polynomial (x a)(x b)(x c) 1 be factored
into the product of two polynomials
Math 380a
HOMEWORK #7
due Tue, November 12, 2013
Written assignment (4 problems).
W1. Let x be a real number such that |x| < 1. Compute limn
W2. Dene the sequence cfw_xn by x0 = , and xn+1 =
n=1
divergence of the sequence for = 0.5 and = 2.
xn
W3. Let x0
Math 380
HOMEWORK #5
due Tue, October 29, 2013
Written assignment (4 problems).
1
W1. Show that 1 + 2 + 1 + +
3
1
n
can never be an integer.
W2. Prove that consecutive Fibonacci numbers are always relatively prime.
W3. Let A = 55553333 .
1. Let A1 be the
Math 380
HOMEWORK #4
due Tue, October 22, 2013
We strongly recommend that you read Chapter 8 (you may know all or some of it depending
on your background in geometry).
Written assignment (4 problems).
W1. Let ABC be a triangle, and A , B and C be points o
Math 380a, Fall 2013
HOMEWORK #2
due Tue, October 8
This homework consists of four parts: the written assignment, the bonus problem, the
presentation assignment, and a reading assignment.
Written assignment.
W1.
1. Prove the following combinatorial identi
Math 380a
HOMEWORK #6
due Tue, November 5, 2013
Reading: Section 5.5 in [Zeitz].
Written assignment (4 problems).
W1. Let a1 , . . . , an be positive numbers. Show that
(a1 + + an )(
1
1
+ + ) n2
a1
an
W2. Prove AM-GM for four numbers.
W3. Let a1 , . . .