Spring 2009
MATH 302: Introduction to proofs via number theory
Branko Ćurgus
 Monday, June 8, 2009


This is what I wrote during the exam.
 Friday, June 5, 2009


Here is my proof that among any sixteen consecutive integers there is always at least one integer relatively prime to the other fifteen.
 The usual update of the
list of done and todo problems.
 Monday, June 1, 2009

 Friday, May 29, 2009


This is what I wrote during the exam.
 Thursday, May 28, 2009

 The usual update of the
list of done and todo problems.
 Tuesday, May 26, 2009

 The usual update of the
list of done and todo problems.

Here I finish the proof that I started in class today.
 Thursday, May 21, 2009

 The usual update of the
list of done and todo problems.
 Here is the second
Assignment.
 Monday, May 18, 2009

 The usual update of the
list of done and todo problems.

Solutions for Assignment 1.
 Thursday, May 14, 2009


Chapter 3 of the class notes.
 The usual update of the
list of done and todo problems.
 Monday, May 11, 2009

 The usual update of the
list of done and todo problems.
 The following statement we used often: Let u and v be positive integers. If uv = 1, then u = 1 and v = 1. Here is a proof. It is easier to prove the contrapositive: Let u and v be positive integers. If u > 1 or v > 1, then uv > 1. A proof of the contrapositive follows. Let u and v be positive integers such that u > 1 or v > 1. There are two cases. Case 1: u > 1 and v > 0, and Case 2: v > 1 and u > 0. In Case 1, Axioms 13 and 9 we have uv > v. Since v >= 1, we conclude uv > 1. In Case 2 Axioms 13 and 9 imply uv > u, and since u >=1, we again conclude uv > 1. The contrapositive is proved.
 Thursday, May 7, 2009

 The usual update of the
list of done and todo problems.
 Here is the first
Assignment.
 Tuesday, May 5, 2009

 I am posting Grayce's proof of
Proposition 1.4.1.
 The usual update of the
list of done and todo problems.

Here are few statements (Lemmas, Propositions and Theorems, with proofs) related to Section 2.3.
 Thursday, April 30, 2009

 The usual update of the
list of done and todo problems.

Here are colored and dramatized proofs of Propositions 2.1.5, 2.1.7 and 2.1.10. I don't recall that we did 2.1.7 in class. The proof of 2.1.10 here is different from the proof that was done in class.
 Today I assigned a homework due on Monday. The homework is to write a complete proof of Proposition 1.4.1 in your own words and in your own style. You should study the proof given in class and the proof in the notes until you internalize the basic ideas. Then you can write a proof in your own words. I will grade these proofs by an integer between 1 and 10. These points will be added to your score on the exam. On Monday, please hand in your exam together with the homework.
 Wednesday, April 29, 2009

 Dan gave a perfect solution for
Problem 4 on Exam 1.
 Tuesday, April 28, 2009


This is what I wrote during the exam.
 Monday, April 27, 2009

 Britt asked an interesting question today.
This is a summary of my answer.
 The current
list of done and todo problems.
 Friday, April 17, 2009

 The
list of done and todo problems.

Chapter 2 of the class notes.
 Thursday, April 16, 2009

 The
list of done and todo problems.
 Tuesday, April 14, 2009

 The
list of done and todo problems.
 Monday, April 13, 2009

 The
list of done and todo problems.
 A few thoughts about
proofs.

Here I collected 12 different ways to say: If p, then q.
 Friday, April 10, 2009

 The list of done and todo
problems.
 Some useful Wikipedia links:
 Tuesday, March 31, 2009
