Math 245 An Introduction to Proof
Fall 2010
Department of Mathematical Sciences
University of Delaware
Instructor: Sebastian Cioab
a
Lecture Time and Place: MonWedFri, 10.10am-11am, Colburn Lab 104.
Oce Hours: MonWedFri 11-noon, Ewing 506 or by appointmen
Arithmetic and Geometric Sequences
Felix Lazebnik
This collection of problems1 is for those who wish to learn about arithmetic
and geometric sequences, or to those who wish to improve their understanding
of these topics, and practice with related problems
Homework 6, Math 245, Fall 2010
Due Wednesday, December 1 in class.
The solution of each exercise should be at most one page long. If you can, try to write
your solutions in LaTex. Each question is worth 2 points.
1. Find all integers x that satisfy the f
Homework 5, Math 245, Fall 2010
Due Monday, November 1 in class.
The solution of each exercise should be at most one page long. If you can, try to write
your solutions in LaTex. Each question is worth 2 points.
1. Show that among any 20 distinct numbers f
Homework 5, Math 245, Fall 2010
Due Monday, November 1 in class.
The solution of each exercise should be at most one page long. If you can, try to write
your solutions in LaTex. Each question is worth 2 points.
1. Show that among any 20 distinct numbers f
Homework 4, Math 245, Fall 2010
Due Wednesday, October 20 in class.
The solution of each exercise should be at most one page long. If you can, try to write
your solutions in LaTex. Each question is worth 2 points.
1. A club of 8 men and 10 women has to se
Homework 4, Math 245, Fall 2010
Due Wednesday, October 20 in class.
The solution of each exercise should be at most one page long. If you can, try to write
your solutions in LaTex. Each question is worth 2 points.
1. A club of 8 men and 10 women has to se
Homework 3, Math 245, Fall 2010
Due Friday, October 1 in class.
The solution of each exercise should be at most one page long. If you can, try to write
your solutions in LaTex. Each question is worth 2 points.
1. The Fibonacci numbers (Fn )n1 are dened as
Homework 3, Math 245, Fall 2010
Due Friday, October 1 in class.
The solution of each exercise should be at most one page long. If you can, try to write
your solutions in LaTex. Each question is worth 2 points.
1. The Fibonacci numbers (Fn )n1 are dened as
Homework 2, Math 245, Fall 2010
Due Wednesday, September 22 in class.
The solution of each exercise should be at most one page long. If you can, try to write
your solutions in LaTex. Each question is worth 2 points.
1. In a tournament with n 2 teams, ever
Homework 2, Math 245, Fall 2010
Due Wednesday, September 22 in class.
The solution of each exercise should be at most one page long. If you can, try to write
your solutions in LaTex. Each question is worth 2 points.
1. In a tournament with n 2 teams, ever
Homework 1, Math 245, Fall 2010
Due Wednesday, September 15 in class.
The solution of each exercise should be at most one page long. If you can, try to write
your solutions in LaTex. Each question is worth 2 points.
1. Let A, B, C be sets. Prove that A (B
Homework 1, Math 245, Fall 2010
Due Wednesday, September 15 in class.
The solution of each exercise should be at most one page long. If you can, try to write
your solutions in LaTex. Each question is worth 2 points.
1. Let A, B, C be sets. Prove that A (B
NOTES ON INEQUALITIES
FELIX LAZEBNIK
Order and inequalities are fundamental notions of modern mathematics. Calculus and Analysis depend heavily on them, and properties of inequalities provide the
main tool for developing these subjects. Often students are
MATH 245, Fall 2010
University of Delaware
This le contains some suggested problems from the textbook that may help your understanding and your writting skills.
Please do NOT hand in solutions for these problems.
Chapter 1: 1.3, 1.7, 1.9, 1.15, 1.30, 1.3
Name:
Midterm 2, Math 245 - Fall 2010
Duration: 50 minutes
To get full credit you should explain your answers.
Each of the rst three questions is worth 5 points.
The bonus questions is worth 3 points.
1. Find all the integer solutions (x, y ) of the equat
Name:
Midterm 1, Math 245 - Fall 2010
Duration: 50 minutes
To get full credit you should explain your answers.
1. Prove that
1
1
+ + > 2 n + 1 2
n
1
for every natural number n 1.
#
Score
1
2
3
Total
2. Let A, B, C be sets. Prove that (A B ) \ C must be a