Math 453 material, Fall 2005


Course information sheet (PDF format)

Homework assignments (from the 4th edition of the text)

  1. Homework #1. Practice : 1.4 # 5,7,11,35,41,45; 3.2 # 1,5
    Problems due Fri. Sept. 2 : 1.4 # 8, 36, 40, 42; 3.2 # 6, 14

  2. Homework #2. Practice : 3.1 # 1, 3, 5, 7, 13; 3.2 # 21; 3.3 # 1,3; 3.4 # 1, 5, 11
    Problems due Fri. Sept. 9 : 3.1 # 6, 16; 3.2 # 22; 3.3 # 4(c); 3.4 # 14

  3. Homework #3. Practice : 3.4 # 6, 31, 33, 41, 43, 44, 47
    Problems due Friday, Sept. 16 : 3.4 # 38, 60; Prove that if a/b is a reduced fraction with a>1 and b>1, and m is an integer >1,
    then logm(a/b) is irrational.
    Extra Credit: 3.4 #48 (may be turned in until Friday, Sept. 30)

  4. Homework #4. Practice : 4.1 # 3, 5, 7, 8, 14, 17, 23
    Problems due Friday, Sept. 23 : 4.1 # 10, 16, 22

  5. Homework #5. Practice : 4.2 # 1, 7, 11; 4.3 # 3, 5, 11, 17
    Problems due Friday, Sept. 30 : 4.2 # 12; 4.3 # 10, 20(b), 30

  6. Homework #6. Practice : 6.1 # 3, 5, 11, 17, 19, 31, 39; 6.3 # 1, 7, 9, 17
    Problems due Friday, Oct. 7 : 6.1 # 22, 30; 6.3 #10

    Extra credit (due Oct. 21) : 4.2 # 16; 4.3 #32; 6.1 #42 (use 4.3 #32, not #30)

  7. Homework #7. Practice : 6.2 # 1, 5, 7, 11(a), 16 (a-f)
    Problems due Monday, Oct. 17 : 6.2 # 8, 18

  8. Homework #8. Practice : 9.1 # 1, 3, 7, 9, 15
    Problems due Friday, Oct. 21 : 9.1 # 6, 14

  9. Homework #9. Practice : 9.2 # 1, 3, 7, 9; 9.5 # 5
    Problems due Friday, Oct. 28 : 9.2 # 8, 16; 9.5 # 6
    Extra credit (due Nov. 11) : (A) 9.2 #14; (B) Use the method from 9.4 #10 to prove that for every positive integer m, there are infinitely many primes of the form 2mk+1; (C) 7.1 # 22

  10. Homework #10. Practice : 9.3 # 1, 3, 5, 9; 9.4 # 19
    Problems due Friday, Nov. 4 : 9.3 # 6 (a,b); 9.4 # 9, 10. On 9.4 # 9, ignore the solution in the back of the textbook and use Theorem 6.13 from class notes.

  11. Homework #11. Practice : 9.6 # 1, 3, 9; 7.1 # 1, 2, 4, 5; 7.2 # 1, 7
    Problems due Friday, Nov. 11 : 9.6 # 4 (e,f), 6; 7.1 # 6; 7.2 # 4

  12. Homework #12. Practice : 7.1 # 13, 15; 7.2 # 7, 11, 21; 7.3 # 3, 7, 9; 7.4 # 1, 2
    Problems due Friday, Nov. 18 : 7.2 # 12, 22; 7.3 # 8; 7.4 # 30

  13. Homework #13. Practice : 11.1 # 1-5, 7, 11, 17, 27; 11.2 # 1, 2, 3
    Problems due Wednesday, Dec. 7 : 11.1 # 6, 28(a) (Hint: uses #7. Also, show that N=(p1 p2 ... pn)2 +2 cannot be only the product of primes of the form 8k+1); 11.2 # 4, 6

Homework assignments (from the 5th edition of the text)

  1. Homework #1. Practice : 1.5 # 5,7,11,23,29,33; 3.3 # 1,5
    Problems due Fri. Sept. 2 : 1.5 # 8, 24, 28, 30; 3.3 # 6, 14

  2. Homework #2. Practice : 3.1 # 1, 3, 5, 7; 3.2 # 3; 3.3 #21; 3.4 # 1, 3; 3.5 # 1, 5, 11
    Problems due Fri. Sept. 9 : 3.1 # 6; 3.2 # 12; 3.3 # 22; 3.4 # 4(c); 3.5 # 14

  3. Homework #3. Practice : 3.5 # 6, 31, 33, 41, 43, 44, 47
    Problems due Friday, Sept. 16 : 3.5 # 38, 60; Prove that if a/b is a reduced fraction with a>1 and b>1, and m is an integer >1,
    then logm (a/b) is irrational.
    Extra credit: 3.5 # 48 (may be turned in until Friday, Sept. 30)

  4. Homework #4. Practice : 4.1 # 3, 5, 7, 8, 14, 17, 23
    Problems due Friday, Sept. 23 : 4.1 # 10, 16, 22

  5. Homework #5. Practice : 4.2 # 1, 7, 11; 4.3 # 3, 5, 11, 17
    Problems due Friday, Sept. 30 : 4.2 # 12; 4.3 # 10, 20(b), 30

  6. Homework #6. Practice : 6.1 # 3, 5, 11, 17, 19, 31, 39; 6.3 # 1, 7, 9, 17
    Problems due Friday, Oct. 7 : 6.1 # 22, 30; 6.3 #10

    Extra credit (due Oct. 21) : 4.2 # 16; 4.3 #32; 6.1 #42 (use 4.3 #32, not #30)

  7. Homework #7. Practice : 6.2 # 1, 5, 7, 11(a), 16 (a-f)
    Problems due Monday, Oct. 17 : 6.2 # 8, 18

  8. Homework #8. Practice : 9.1 # 1, 3, 7, 9, 15
    Problems due Friday, Oct. 21 : 9.1 # 6, 14

  9. Homework #9. Practice : 9.2 # 1, 3, 7, 9; 9.5 # 5
    Problems due Friday, Oct. 28 : 9.2 # 8, 16; 9.5 # 6
    Extra credit (due Nov. 11) : (A) 9.2 #14; (B) Use the method from 9.4 #10 to prove that for every positive integer m, there are infinitely many primes of the form 2mk+1; (C) 7.1 # 26.

  10. Homework #10. Practice : 9.3 # 1, 3, 5, 9; 9.4 # 19
    Problems due Friday, Nov. 4 : 9.3 # 6 (a,b); 9.4 # 9, 10. On 9.4 # 9, ignore the solution in the back of the textbook and use Theorem 6.13 from class notes.

  11. Homework #11. Practice : 9.6 # 1, 3, 9; 7.1 # 1, 2, 4, 5; 7.2 # 1, 7
    Problems due Friday, Nov. 11 : 9.6 # 4 (e,f), 6; 7.1 # 6; 7.2 # 4

  12. Homework #12. Practice : 7.1 # 13, 15; 7.2 # 7, 11, 21; 7.3 # 3, 7, 9; 7.4 # 1, 2
    Problems due Friday, Nov. 18 : 7.2 # 12, 22; 7.3 # 8; 7.4 # 30

  13. Homework #13. Practice : 11.1 # 1-5, 7, 11, 17, 27; 11.2 # 1, 2, 3
    Problems due Wednesday, Dec. 7 : 11.1 # 6, 28(a) (Hint: uses #7. Also, show that N=(p1 p2 ... pn)2+2 cannot be only the product of primes of the form 8k+1); 11.2 # 4, 6


Homework Solutions


Exam #1.

Wednesday, October 12. Covers the material from the first 6 homework sets. Practice test (given in 2002)


Exam #2.

Friday, December 2. Covers material from homework sets 7-12 (orders, primitive roots, multiplicative functions, etc.). Practice test (given in 2002)

Final Exam.

Wednesday, Dec. 14, 1:30--4:30.

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