Classical Algebra (Math 326)
Assignments
Fall Semester, 2002
Assignments are listed by the date due.
PDF and DVI (requires
TeX software) versions of this
page are available for printing.
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., Dec. 18:

Final Exam 3:30  5:30
 Wed., Dec. 11:

Review Session: bring questions.
Expect a short quiz.
 Mon., Dec. 9:

Written assignment No. 5 (also available as PDF or DVI) is due.
 Fri., Dec. 6:

Read § 28C
Exercises:
 417: 8, 10, 12
 421: 9
 424: 1, 5, 6, 9, 12
 Wed., Dec. 4:

Read §§ 24B, 28B
Exercises:
 350: 10
 356: 6, 10
 361: 5
 416: 3, 5, 7
 421: 1, 3, 7
 Mon., Dec. 2:

Read §§ 24A, 28A
Exercises:
 307: 9, 12  14
 309: 2(ii, iii), 3
 350: 2, 4, 6  8
 356: 2, 5
 416: 2
 Wed, Fri., Nov. 27, 29:

Recess
 Mon., Nov. 25:

Written assignment No. 4 (also available as PDF or DVI) is due.
 Fri., Nov. 22:

Read § 23A
Exercises:
 263: 7, 10
 304: 4  6
 309: 2(i)
Expect a pop quiz.
 Wed., Nov. 20:

Read § 20B
Exercises:
 258: 6
 262: 5, 6
 303: 1  3
 Mon., Nov. 18:

Read § 20A
Exercises:
 249: 14
 251: 8, 9
 257: 1  3
 262: 1  4
 Fri., Nov. 15:

Read §§ 16C, 16D
Exercises:
 249: 8  10, 12
 250: 2
 251: 4, 5
 Wed., Nov. 13:

Read §§ 16A, 16B
Exercises:
 246: 2, 4
 248: 6, 7
 251: 7
 • Find the smallest positive primitive root modulo
the prime 503.
 • What is the pattern of repetition in the base 8
“decimal” expansion of each of the rational numbers 17/60
and 13369/32704 ? In each case notice that the base is not
coprime to the denominator. Compare these patterns of repetition with
the patterns of repetition for the powers of 8 modulo each of the
denominators of the two given rational numbers.
 Mon., Nov. 11:

Written assignment No. 3 (also available as PDF or DVI) is due. In regard to
the fourth problem, an ASCII Chart (also available as PDF or DVI) will be
helpful to those who are previously unfamiliar with ASCII codes.
 Fri., Nov. 8:

Read §§ 15C, 15D
Exercises:
 243: 5, 8
 246: 1
 163: 18
 • What is the pattern of repetition in the decimal
expansion of the rational number 11/91 ?
 • Find the smallest positive primitive root modulo
the prime 89.
 Wed., Nov. 6:

Read §§ 15A, 15B
Exercises:
 234: 3
 236: 5
 238: 7, 9
 241: 1
 243: 6, 7
 Mon., Nov. 4:

Read Ch 14
Exercises:
 169: 6
 200: 7, 9, 10, 11
 233: 1, 2
 Fri., Nov. 1:

Read § 12 A
Exercises:
 163: 14, 16, 17
 169: 5
 196: 3
 Wed., Oct. 30:

Read § 10B
Exercises:
 158: 3, 4
 163: 10, 12, 13
 166: 2
 169: 4
 Mon., Oct. 28:

Read §§ 9F, 10A
Exercises:
 141: 16
 145: 12, 13
 147: 4
 154: 3
 158: 1, 2
 Fri., Oct. 25:

Read §§ 9D, 9E
Exercises:
 138: 10, 13, 14
 141: 3  7
 144: 8, 9
 147: 2
 Wed., Oct. 23:

Read §§ 9A, 9B, 9C
Exercises:
 123: 13, 15, 17
 125: 5, 6
 136: 2, 3, 8, 9
 Mon., Oct. 21:

Read §§ 8A, 8B
Exercises:
 89: 5  7
 121: 1  3, 5, 7
 125: 3
 Fri., Oct. 18:

Midterm Test
 Wed., Oct. 16:

Review Session: Bring questions.
 Mon., Oct. 14:

Written Assignment No. 2:
Find all solutions that are incongruent (mod 10) of each of
the following congruences:
17 x EQUIV 1 (mod 10).
47 x EQUIV 25 (mod 10).
14 x EQUIV 43 (mod 10).
53 x EQUIV 74 (mod 10).
15 x EQUIV 55 (mod 10).
Let a, b, and c be integers with not both a, b zero.
Prove that if there is an integer point (r, s) on the line
then there is one and only one integer point (x, y) on the line for
which
0 <= x < {b}/{gcd(a, b)} .

Please remember that written assignments must be typed.
 Fri., Oct. 11:

Read §§ 6D, 6E
Exercises:
 73: 2
 84: 5
 86: 1, 3, 4
 89: 1  3
 Wed., Oct. 9:

Read §§ 6A, 6B, 6C
Exercises:
 70: 6
 72: 3, 5, 6
 74: 5  7
 84: 1, 3, 4
 Mon., Oct. 7:

Read §§ 5D, 5E
Exercises:
 67: 8
 70: 1  3
 72: 1
 73: 1
 Fri., Oct. 4:

Read §§ 2E, 2F, 5C
Exercises:
 23: 1  3
 24: 1, 2
 54: 30
 65: 6
 67: 5, 6, 9
 Wed., Oct. 2:

Revised office hours:
 Mon & Thurs. 3:30  4:30
or by appointment.
Read §§ 5A, 5B
Exercises:
 54: 25, 26, 29
 65: 2, 3, 5
 Mon., Sep. 30:

Written assignment No. 1 (also available as PDF or DVI) is due.
 Fri., Sep. 27:

Prepare for a short quiz.
Begin working on the written assignment that is due Monday.
 Wed., Sep. 25:

Read § 4C
Exercises:
 35: 11
 52: 9, 13
 53: 19, 20, 21
 55: 1
 Mon., Sep. 23:

Read § 4B
Exercises:
 35: 8, 21
 45: 2
 50: 4
 51: 3
 Fri., Sep. 20:

Read §§ 3E, 4A
Exercises:
 35: 7
 45: 1
 50: 3
 Wed., Sep. 18:

Prepare for a 5 point quiz covering material through the last
assignment.
Exercises:
 29: 6(v)
 33: 4(iv)
 35: 5
 Mon., Sep. 16:

Recess: no class
 Fri., Sep. 13:

Do the ff. exercises:
 27: 6
 27: 7
 29: 3
 29: 6(iii)
 33: 4(ii)
 Wed., Sep. 11:

Scan: Chs 1, 2
Read: §§ 3 A, B, C
Do the ff. exercises:
 Evaluate the continued fraction [3, 7, 15, 1, 292]
= 3 + 1/(7 + 1/(15 + 1/(1 + 1/292))) .
 Find the continued fraction of the rational number 355/113 .
 26: 4
 28: 1
Note regarding 9/11 observance: Professor David Janower of the
Music Department will conduct the Mozart Requiem with Albany Pro
Musica as part of a worldwide “Rolling Requiem” at 8:30
a.m. in the Amphitheater at the Hudson Riverfront. For more
information, see http://www.rollingrequiem.org/.
Our class will meet at the normal time.
 Mon., Sep. 9:

Recess: no class
 Fri., Sep. 6:

Read the first four sections of the supplementary material on
continued fractions (also available as PDF or DVI).
If you wish to enter the writing intensive division of the course
(Math 326Z), please be sure to submit the
required essay (also available as PDF or DVI) at this class (or earlier).
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