# Math 326 Assignments

## Spring Semester, 2001

Assignments are listed by the date due.

Most of these assignments are simply exercises designed to prepare you for the quizzes and the written assignments. Those which are to be submitted as written assignments are so labeled. While you may find it helpful to discuss the exercises with others, no collaboration is permitted on the written assignments.

• Wed., May 16: Final Examination 1:00 - 3:00

• Mon., May 7: Written Assignment 5 (DVI)
Bring review questions.

• Fri., May 4
1. What integers in the interval [1, 48] are primitive mod 7? Which of those are primitive mod 49?
2. If p is an odd prime and c is an integer that is primitive mod p, what is the "probability" that c is also primitive mod p^2?
3. Find the smallest odd prime p for which the smallest positive primitive root mod p is not also primitive mod p^2.

• Wed., May 2:  Read Ch 24 A, B Exercises: 23A 11, 12 28C 15, 16, 21 28D 5 24B 5, 10 - 12

• Mon., Apr 30:  Read Ch 23 A Exercises: 28C 10 - 14 28D 3, 4 23A 2, 3, 8, 9

• Fri., Apr 27:  Read Ch 28 D Exercises: 28B 10 28C 6 - 9 28D 2

• Wed., Apr 25: Written Assignment 4 (DVI)

• Mon., Apr 23: Quiz

• Fri., Apr 20:  Read Ch 28 C Exercises: 28B 7, 8 28C 1 - 5

• Wed., Apr 18:  Read Ch 28 B Exercises: 28A 4 - 8 28B 1, 2, 4, 5

• Mon., Apr 16:  Read Ch 15 D and Ch 28 A Exercises: 15D 4, 6, 8 28A 1 - 3

• Fri., Apr 6: Written Assignment 3 (DVI)

• Wed., Apr 4:  Read Ch 15 C Exercises: 15C 1, 2, 6, 8 - 10

• Mon., Apr 2:  Read Ch 15 B Exercises: 15A 6 - 8, 11 15B 1 For each odd prime p < 20 find the smallest positive integer a that is primitive mod p.

• Fri., Mar 30:  Read Ch 14 and Ch 15 A Exercises: 14 1, 4, 5 15A 1

• Wed., Mar 28:  Read Ch 10 D and Ch 12 B Exercises: 10C 6, 7 10D 2 12B 5, 8

• Fri., Mar 23:  Read Ch 10 C Exercises: 12A 3, 6, 11 10C 1 - 3

• Wed., Mar 21:  Read Ch 12 A Exercises: 10B 6 12A 1, 10, 12

• Mon., Mar 19: Written Assignment 2

Write and submit (typeset on paper) an essay explaining the relation between, on the one hand, the repetition pattern in the ``decimal'' expansion of a given rational number relative to a given base and, on the other hand, the repetition pattern in the powers of a given integer relative to a given modulus.

• Fri., Mar 16: Midterm Test, in class

• Wed., Mar 14: Review Session: Bring questions.

• Mon., Mar 12:  Read Ch 10 B Exercises: 10A 7, 10, 13, 14 10B 2 with r = 1 and then with r = 2 10B 5 with r = 2 Also: Find an RSA decoding exponent for the encoding exponent 3 and the modulus m = 4369 .

• Fri., Mar 9:  Read Ch 10 A Exercises: 9A 18 9B 19 9C 13 10A 1 - 4

• Wed., Mar 7:  Short Quiz Covering assignments due before the recess Read Ch 9 C, D Exercises: 9A 9 - 11, 15 9B 16, 17 9C 7 - 9 9D 1 - 3

• Mon., Mar 5: Class cancelled due to snow storm.
Please take notice of the assignment due Wed., Mar 7.

• Mon., Feb 26 -- Fri., Mar 2: Recess

• Fri., Feb 23:  Read Ch 9 A, B Exercises: 6E 11, 12 8B 8, 9 9A 2, 3, 7 9B 3 - 5, 9, 11

• Wed., Feb 21:  Read Ch 8 Exercises: 6E 3, 5, 8, 9 8B 4, 6, 7

• Fri., Feb 16: Written Assignment 1 (DVI) -- Solutions

• Wed., Feb 14: Quiz

• Copy of the Maple program written in class on Mon., Feb. 12.

• Mon., Feb 12:  Read 6 C, E; Exercises: 2E 1, 2 2F 2 5E 2, 5-7 6C 2, 3, 4 6E 2, 6, 7
In Monday's class there will be a demonstration of writing a Maple program.

• Fri., Feb 9:  Read 5 E; 6 A, B Exercises: 4B 30 5B 3, 4, 5, 6 5E 1

• Wed., Feb 7:  Read 5 A, B, D Exercises: 4B 2, 3, 4, 12, 25 5A 3, 5, 6
Also: Find the length of the period in the decimal expansion of the rational number 3/19.

• Mon., Feb 5:  Read 4 A, B Exercises: 4A 2, 3, 4 4B 8, 9
Also: Find the length of the period of the continued fraction expansion of the square root of 19.

• Fri., Feb 2:  Read 3 E Exercises: 3C: 2, 3, 7, 8, 11 3E: 2

• Wed., Jan 31: First quiz.

• Mon., Jan 29 (DVI)

• Fri., Jan 26:  Scan Chs. 1, 2 Read 3 A, B, C Exercises: 3A: 1, 4; 3B: 1, 2, 5, 6

DVI files for printing (if you are equipped to print them) are available parallel to the HTML files. Simply substitute .dvi for .html in the URL for any assignment.

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