Math 211

List of Overheads

List of all handouts     For further reading
01. Algebraic Methods (2 pages)
02. Number Systems
03. Divisibility
03a. The Principle of Induction
04. The Euclidean Algorithm
05. The greatest common divisor
06. The division algorithm
07. The Euclidean Algorithm: 1st/2nd Version (2 pages)
08. The Euclidean Algorithm: 2nd Version
09. The extended Euclidean Algorithm - Examples (2pp)
10. The extended Euclidean Algorithm
11. Diophantine equations (2 pages)
11a. The Plimpton 322 Clay Tablet
12. The GCD-criterion and its consequences
13. The general solution of the diophantine equation mx+ny=c
14. How to solve mx+ny=c
15. Proof of the Formula (2pp.)
16. How to solve mx+ny+kz=c
16a. Prime numbers
17. Unsolved conjectures about primes
18. The Fundamental Theorem of Arithmetic
19. The GCD-formula
20. The GCD-formula vs. Euclidean algorithm
21. The Calculus of Remainders
22. Computing a^n efficiently
23. The Cancellation Law
24. Solving the congruence ax=b (mod m)
25. The Ring Z/mZ and the Field F_p
26. The Wheels Problem
27. The Chinese Remainder Theorem
28. Fermat's Theorem
29. Mersenne numbers
29a. The Binomial Theorem (2pp.)
30. Public Key Cryptography (2pp.)
31. The dancing men
32. The RSA method (2pp.)
32a. The RSA-155 Challenge (3pp.)
32b. The History of Algebra
33. Complex Numbers (History)
33a. Complex Numbers (3pp.)
34. Arctan and Argument
35. Solutions of z^n=a
36. Solutions of z^6=1+sqrt(-3)
36a. The sixth roots of a = 1+i
37. Polynomials
37a. The Degree of a Polynomial
38. The Division Algorithm (for polynomials)
39. The Remainder Theorem (2pp.)
40. The Euclidean Algorithm (for polynomials)
41. The GCD-criterion for polynomials
42. Irreducible polynomials
43. The Quadratic Formula
43a. Irreducible Quadratic Polynomials over Fp for p le 5
44. Unique Factorization for polynomials
45. The Multiplicity of a root
46. Rules for factoring over Q (2pp.)
47. The Method of Comparing Coefficients (2pp.) (not presented)
48. The Fundamental Theorem of Algebra
49. The Factorization Theorem in R[x]