MAS3301 -- Modern Algebra -- Spring 2006

Click here for the syllabus

Schedule:

Week 1
- Day 1: Introduction, integers, greatest common divisor.
- Day 2: Bezout's identity which is used to prove the unique factorization theorem.
- Day 3: Rational numbers, Irrational numbers, irrationality proof for the square root of 2.
Week 2
- Day 4: Algebraic numbers and Transcendental numbers, Fields, Field Axioms, Homework Set 1
- Day 5: Complex Numbers: Definitions and Basics
Week 3
- Day 6: Euler's Formula, Unimodular Numbers, de Moivre's Formula .
- Day 7: Work through Homework Set 2.
- Day 8: More on homework set 2.
Week 4
- Day 9: Rings, Split-complex Numbers.
- Day 10: Dual Numbers, Zero Divisors.
- Day 11: Work through Homework Set 3.
Week 5
- Day 12: Quaternions: Motivation, Definitions, Basics
- Day 13: Quaternions. Some questions on quaternions (we skipped some of these questions).
- Day 14: Reviewing the sample questions for test 1.
Week 6
- Day 15: Test 1.
- Day 16: Review of test 1.
- Day 17: More on quaternions. Sums of squares and Euler's four-square identity.
Week 7
- Day 18: No class on Monday Feb 20.
- Day 19: Redid test 1, questions can now be dowloaded here.
- Day 20: The Integers modulo n: Definitions and Basics.
Week 8
- Day 21: More on the integers modulo n. Exponentiation modulo n.
- Day 22: RSA.
- Day 23: Fermat's little theorem and primality testing.
Week 9
- Day 24: RSA example.
- Day 25: Questions on the integers modulo n.
- Day 26: More on the integers modulo n
Week 10
- Day 27: More on finite fields.
- Day 28, 29: Reviewing sample questions for the test next week.
Week 11
- Day 30: Test 2.
- Day 31: Group theory.
- Day 32: More on groups.
Week 12
- Day 33: More on groups
- ...
Week 14
- Diffie-Hellman key exchange
- Lagrange's theorem
...