Classical Algebra (Math 326)
Assignments
Fall Semester, 2006
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.
 Mon., Dec. 18:
 Final Examination: 3:30  5:30
 Exam Period Office Hours

Thurs., Dec. 14  2:30  3:30 
Fri., Dec. 15  3:00  4:00 
Mon., Dec. 18  12:00  1:00 
 Tue., Dec. 12:
 Last regular class meeting.
Expect a quiz.
Written Assignment No. 5 (also available as PDF) is due.
Bring questions for review.
 Thu., Dec. 7:
 Read: §§ 28B, 28C
Exercises:
 351: 13, 15
 356: 6, 7, 10
 418: 8, 11, 12
 421: 1, 2, 5  7
 425: 4  6, 9  12
 Tue., Dec. 5:
 Read: §§ 24A, 28A
Exercises:
 252: 14, 15
 263: 11
 307: 8  10, 12, 14
 350: 9, 10, 12
 356: 2  5
 416: 2, 3, 5, 6
 Thu., Nov. 30:
 Expect a quiz.
Read: §§ 20A, 20B, 23A
Exercises:
251: 10  13
257: 3, 5, 6
262: 7, 9, 10
303: 1  5
309: 1  3
350: 2  4, 11
Find primitive elements for Z/17Z and Z/34Z.
Show that there is no primitive element in Z/32Z.
 Tue., Nov. 28:
 Read: §§ 15D, 16A, 16B, 16C, 16D
Exercises:
205: 7, 8
243: 5, 7, 8
246: 1  4, 6
248: 6  10
251: 7  9
257: 1, 2
262: 1  3, 6
 Thu., Nov. 23:
 Thanksgiving Recess: no class
 Tue., Nov. 21:
 Written Assignment No. 4 (also available as PDF) is due
 Thu., Nov. 16:
 Read: §§ 15A, 15B
Exercises:
 163: 18, 21, 22
 200: 13, 15
 205: 5, 6
 236: 4, 5
 238: 7  9
 241: 1
 243: 4, 6
 245: 1
 Tue., Nov. 14:
 Expect a quiz.
Read: §§ 12B, 14
Exercises:
 141: 18
 163: 15  17
 200: 5  7, 11, 12
 202: 1, 3
 233: 1  3
 Thu., Nov. 9:
 Written Assignment No. 3 (also available as PDF) is due.
 Tue., Nov. 7:
 Read: §§ 10B, 12A
Exercises:
 141: 16, 17, 19
 145: 16, 17
 153: 3, 8
 163: 10, 11, 13, 14
 166: 1, 2
 169: 3, 4
 196: 1  3
 Thu., Nov. 2:
 Read: §§ 9E, 9F, 10A
Exercises:
 141: 9  11, 13  15
 144: 7, 11(iiii), 12, 13, 15
 147: 3, 5, 6(ii)
 153: 1, 2
 158: 1  4, 7
 Tue., Oct. 31:
 Read: §§ 9B, 9C, 9D
Exercises:
 123: 14, 15
 126: 7  9
 133: 7, 8, 10
 137: 3, 5, 7  9
 141: 3  5, 7
 142: 1, 4
 144: 8
 147: 2, 4, 6(i)
 Thu., Oct. 26:
 Expect a quiz.
Read: §§ 8B, 8C, 9A
Exercises:
 90: 12, 13
 110: 4(e, f), 5(a) with x_{0} = 15, 5(b) with x_{0} = 36
 122: 8, 9, 12, 13
 125: 2  6
 133: 5, 6, 9
 136: 1, 2, 4
 Tue., Oct. 24:
 University classes suspended, no assigment.
 Thu., Oct. 19:
 Midterm Test, in class
 Tue., Oct. 17:
 Read: § 8A
Exercises:
 89: 6, 7, 9  11
 102: 3
 105: 2
 110: 4(c, d)
 121: 1  5
Review the course, and bring your questions.
 Thu., Oct. 12:
 Written Assignment No. 2 (also available as PDF) is due
 Tue., Oct. 10:
 Read: §§ 6E, 7C, 7D, 7E
Exercises:
 74: 9
 86: 5, 7  9
 89: 1  5
 100: 1 (i  iv), 2
 105: 1, 3
 110: 4(a, b)
 Thu., Oct. 5:
 Read: §§ 6A, 6B, 6C, 6D
Exercises:
 54: 32  34
 67: 9
 70: 6
 72: 4, 5
 73: 2  8
 80: 3
 84: 1  5
 86: 1  4
 Tue., Oct. 3:
 Read: §§ 5C, 5D, 5E
Exercises:
 52: 10, 11, 13, 15
 54: 28, 30, 31
 65: 6  8
 67: 2, 3, 5  8
 70: 1  5
 72: 1  3
 73: 1
 Thu., Sep. 28:
 Read: §§ 4C, 5A, 5B
Exercises:
 35: 18
 50: 3, 4
 51: 3  5, 7  9
 53: 19  21, 25
 55: 1
 64: 1, 3, 4, 5
 Tue., Sep. 26:
 Written Assignment No. 1 (also available as PDF) is due
 Thu., Sep. 21:
 Read: §§ 3E, 4A, 4B
Exercises:
35: 8, 9, 13, 20
45: 1, 3
49: 1, 2
51: 1, 2
Find the continued fraction expansion of:
40487/257.
{1 + SQRT{5}}/{2}.
SQRT{17}.
 Tue., Sep. 19:
 Read: Read the notes on Continued
Fractions
Exercises:
29: 4, 6(ii, v)
33: 2, 3, 4(iii, iv, v)
35: 5, 6, 7(i, ii)
And these:
Find the continued fraction expansions of the rational numbers
{61}/{67}.
{44}/{37}.
Find the continued fraction expansion of SQRT{2}.
Find the first three integers in the continued fraction expansion
of SQRT[3]{5}. (Feel free to use a calculator for this one.)
Evaluate the finite continued fraction represented by the
sequence [3,2,7,2] .
 Thu., Sep. 14:
 Read: §§ 3B, 3C
Exercises:
 23: 5
 24: 5
 27: 6, 9, 10, 11
 29: 2, 5, 6(iii, iv)
 33: 4(i)
 And this: Recall that 20314_{5} was found to be 1334_{10}.
Cipher in base 5 to convert this number from base 5 to base 7,
and then check that result by converting it from base 7 to base 10.
 Tue., Sep. 12:
 Read: §§ 2D  2F, 3A, 3B
Exercises:
 6: 4
 11: 6, 8
 18: 2
 19: 1
 23: 1  4
 24: 1  3
 27: 5
 Thu., Sep. 7:
 Read: §§ 1, 2A  2C
Exercises:
 6: 2
 11: 2, 4, 5, 10, 14
 15: 2, 4
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) at this class (or earlier).
 Tue., Sep. 5:
 First meeting: no assignment.
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