MATH 266

Principles of Mathematics

News

On the solutions for Homework #5, section 3.2 problem #9 - I seem to have stopped writing the solution about halfway through. The proof of reflexivity should continue with "so xTx for all x in A", and then there should be proofs of symmetry and transitivity after that. Sorry!

Practice your Euclidean algorithm skills, and check your work at: The Euclidean Algorithm page.

Handouts

The modular arithmetic handout in class is two sections from Bruce Ikenaga's number theory notes. He also has a section on the RSA public key algorithm. The sections are:

• Congruences and modular arithmetic.
• Wilson's Theorem and Fermat's Theorem.
• Exponentiation Ciphers and Public Key Cryptography

A handout on divisibility problems. Note that in class #5 and #8 were questioned. #5 did need the extra hypothesis that c is nonzero, but #8 was ok as stated. The online version of the handout is correct.

A handout on propositional calculus. Note that the handout in class had an error in the "Addition" tautology. Addition should read: P => (P v Q). It's fixed in this online version.

General Information

• Course: Math 266-02 Principles of Mathematics
• Meets: MWF 10:00-10:50 in Ritter 200.
• Instructor: Dr. Bryan Clair
• Syllabus: syllabus.pdf
• Textbook: D. Smith, M. Eggen, R. St. Andre, A Transition to Advanced Mathematics (6ed).

Homework Assignments

1. Due Friday, 9/4:

Ch 1.1 # 5, 7, 8d, 12
Ch 1.2 # 8bcfi, 9, 10, 11
Problem A & B
(PDF Version)

2*. Due Wednesday, 9/9

Do problems 1.4 # 7g, 7j. Each on a separate sheet. You'll be giving these to a classmate for critique.

2. Due Friday, 9/18

Ch 1.4 # 7dhi, 6b, 8, 9a
Ch 1.5 # 3dh, 7a, 11
Ch 1.3 # 7, 10
Ch 1.6 # 1dh, 2a, 4, 5bde
Ch 1.7 # 3
Problem A.
Also, attach your critique of your classmate's work on 1.4#7gj.
(PDF Version)

3. Due Friday, 10/2

Ch 2.1 # 5, 8, 11, 14
Ch 2.2 # 10af, 11abc, 12c, 13b, 14bc, 15
Ch 2.3 # 5b, 9, 11c, 13
Problems A, B, C.
(PDF Version)

4. Due Friday, 10/16

Ch 2.4 # 8cdikstu, 9bf, 13
Ch 2.5 # 3a, 4, 9, 12, 14b

5. Due Friday, 10/30

Ch 1.7 # 9ab, 11af. Note: #8 in this chapter is not due, but is an important exercise.
Ch 2.5 # 5b
Ch 3.1 # 11abce
Ch 3.2 # 2, 4cfj, 8, 9, 13, 15

6. Due Friday, 11/13

Modular arithmetic problems on a handout.