http://www.math.tamu.edu/~map/courses/470-sp06/

Homework

• HW #1: Due Tues. 1/24
  Read Trappe and Washington, Appendix C, pp. 527-533.
  Download pdf supplement matlab.pdf
  Download the zip archive MATH470.zip
  Do Problem #1 in the supplement.

• HW #2: Due Thurs. 2/2
  Read Trappe and Washington, 3.1-3.2, pp. 63-70.
  Problems: p. 104: 1a, 4ab, 6abc
  A. Use the Euclidean Algorithm to find gcd(11160,16492) and to find integers s and t so that 11160*s + 16492*t = gcd(11160,16492).
  B. Let a and b be non-zero integers, and let r_0, r_1, r_2, ... be the remainders obtained from the Euclidean algorithm to find gcd(a,b). Show for i=0, 1, 2, ..., that r_{i+2} < 1/2*r_i. Conclude that the maximum number of steps for the Euclidean algorithm is 2*log_2(b), where log_2(b) is the logarithm of b in base 2. Show that the maximum number of steps is at most 7 times the number of decimal digits in b.

• HW #3: Due Tues. 2/14
  Read Trappe and Washington, 3.3, pp. 70-75.
  Problems: p. 104: 1b, 2a, 3, 7, 8
  A. Find all solutions in the integers to the equation 12345*x + 2347*y = gcd(12345,2347).

• HW #4: Due Tues. 2/21
  Read Trappe and Washington, 2.1-2.2, pp. 12-16.
  Problems: p. 55: 1, 3, 4, 5, 7
  

• HW #5: Due Thurs. 3/2
  Read Trappe and Washington, 2.7, pp. 34-38; 3.4-3.5, pp. 76-79.
  Problems: p. 59: 10; Do also 5 problems from p. 54: 13, 14; p. 59: 3; p. 104: 10, 12, 13, 14, 18, 19
  

• HW #6: Due Thurs. 3/9
  Read Trappe and Washington, 3.5-3.6, pp. 76-83
  Problems: p. 104: 15, 16, 20; p. 111: 3 (Use Euler's Thm.), 6

• HW #7: Due Tues. 3/28
  Read Trappe and Washington, 3.7, pp. 84-8; 6.1, pp. 164-168
  Problems: p. 107: 21-22; p. 112: 9; p. 192-195: 1, 7, 23; p. 197-199: 3, 9, 10, 11

• HW #8: Due Thurs. 4/6
  Read Trappe and Washington, 6.3, pp. 176-181; 7.1, pp. 201-202; 7.4-7.5, pp. 210-212
  Problems: p. 192: 15; p. 197: 9; p. 214: 6, 10, 11

• HW #9: Due Thurs. 4/20
  Read Trappe and Washington, 2.3, pp. 16-24; 6.4-6.5, pp. 181-189
  Problems: p. 59: 8; p. 104: 37; p. 192: 26, 27; p. 197: 14

• HW #10: Due Tues. 4/25
  Problems: 1. Use the Quadratic Sieve to factor n=629287 using 29-smooth numbers.
  2. Use continued fractions to factor n=629287. That is, if p_i/q_i are the convergents of the continued fraction expansion of sqrt(n), let a_i=p_i^2-q_i^2*n. Find x and y so that x^2=y^2 (mod n) but that x is not y or -y (mod n), by letting x be the product of some collection of p_i's and letting y be the square root of the corresponding product of a_i's.

• HW #11: Not to be turned in.
  Read Trappe and Washington, 4.1-4.4, pp. 113-131; 7.2-7.3, pp. 202-210
  Problems: p. 146: 1, 4, 5; p. 214: 9; p. 216: 4