Homework Assignments
Math 402       Fall 2015

• HW 1 due Tuesday September 8.
  Ch. 0: 2,5,9,11,16,27 (use induction on n), 28, 31,59
  Problem A. Use the iterated Division algorithm to find integers s,t such that 94s + 73t = 1. Show your work, neatly.
  Problem B. Find the prime power factorizations of 4900 and 2420. Use these to find gcd(2420,4900).
  Ch. 1: 1,2,3de,10,11,21,24(just for the first two designs in the top row)
  
  
• HW 2 due Tuesday September 15.
  Ch. 2: 8,11,13a,20,36,37,47,52,53
  Ch. 3: 2,8,18,28,30,55,73
  
  
• HW 3 due Tuesday September 22.
  Ch. 4: 2,4,9,15,17,27,46,64,69,82,85
  Ch. 5: 1ab, 2a (just for alpha), 5abc, 8, 9 (just S_6 and A_6), 11cd, 17,24,28,31,32,35,54,65,72(hint: table 5.1)
  
  
• HW 4 due Tuesday September 29.
  Ch. 6: 1,2,7,8,10,17,21,27,28,35,52,56,57,58,61(Hint: square roots),62
  
  
• HW 5 due Tuesday October 6.
  Ch. 7: 1,3,6,7,9,10,12,14,16,17,19,21,22,25,26,28,29,41,43,45,52
  Hint on 25: You are asked to prove something about a general finite abelian group with an odd number of elements. When you don't see an answer to a problem, look for an easier special case to start with -- here, start (on scratch paper) with the case of a cyclic group.
  
  
• HW 6 due Tuesday October 13.
  Ch. 8: 3,8,9,14,20,25,26,35,37
  Ch. 9: 1,5,6,7,8,9,13,16,31,34,46
  
  
• HW 7 due Tuesday October 20.
  Ch. 10: 5,9,14,17,19,26
  Ch. 11: 2,4,5,9,10,19,32
  (click here for solved sample problems about Ch. 11)
  
  
• HW 8 due Tuesday November 3.
  Ch. 12: 1,2,3,9,14,22,31,34 (prove by induction)
  Ch. 13: 6,11,13,18,21,47,48,49,51
  
  
• HW 9 due Tuesday November 10.
  Ch. 14: 5, 10, 11c, 17, 24(Hint: R=2Z), 35,56
  Ch. 15: 1,13,16,30 (Hint: consider a^2 + (a+1)^2 + (a+2)^2 mod 8), 46
  
  
• HW 10 due Tuesday November 17.
  Ch. 16: 2, 3, 15,61
  Ch. 17: 2,3,5,6,8,10,12ab,14,29,27,32,36
  
  
• HW 11 due Tuesday November 24.
  Ch. 18: 1*, 3, 6, 10, 14, 15**, 17, 20***, 24, 28, 32, 34, 39, 40, 46
  *This will be among the graded problems.
  **See the hint, page A30. (Use the norm here -- also in some other questions.)
  ***(Hint: 4=(2)(2)= (1+sqrt{-3})(1-sqrt{-3}).
  
  
• HW 12 due Tuesday Dec. 8.
  Ch.20: 23;    
  Ch. 21: 7,11,41;    
  Ch. 22: 3, 10(Hint: Theorem 22.1)    
  Problem X: Prove the fields Q[x]/(x^2 +1) and Q[x]/(x^2 -3) are not isomorphic