Classical Algebra (Math 326)
Assignments
Fall Semester, 2003
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.
Final Exam: Friday, December 12, at 10:30
 Wed., Dec. 10:

Bring review questions.
Expect a short quiz.
 Mon., Dec. 8:

Written Assignment No. 5 (also available as PDF or DVI) is due.
Bring review questions.
 Fri., Dec. 5:

Read: §§ 28B, 28C
Exercises:
 351: 12, 13, 15
 356: 6, 7, 10
 418: 8, 11, 12
 421: 1, 2, 5  7
 425: 4  6, 9  12
 Wed., Dec. 3:

Read: §§ 24A, 28A
Exercises:
 305: 6, 7
 307: 9, 10, 14
 350: 9  11
 356: 2  5
 416: 2, 3, 5, 6
 Mon., Dec. 1:

Read: § 23A
Exercises:
252: 14, 15
263: 11
304: 4, 5
307: 8  10, 12
309: 1  3
350: 2  4
The field F_{9} of 9 elements is defined as a ring of
congruence classes:
F_{9} = F_{3}[t]/(t^{2} + 1)F_{3}[t] .

Find the order of t in F_{9}.
Find a primitive element of F_{9}.
How many primitive elements does F_{9} have?
 Wed, Fri., Nov. 26, 28:

University Recess
 Mon., Nov. 24:

Read: §§ 20A, 20B
Exercises:
 249: 15
 251: 10  13
 257: 4  6
 262: 7, 9, 10
 303: 1  3
 Fri., Nov. 21:

Written Assignment No. 4 (also available as PDF or DVI) is due.
 Wed., Nov. 19:

Read: §§ 16A, 16B, 16C, 16D
Exercises:
 249: 10, 11
 251: 8, 9
 257: 1, 3
 262: 1  3, 6
 Mon., Nov. 17:

Read: § 15D
Exercises:
248: 7  9, 12
251: 4, 5, 7
Why should 3 and 31 have the same order mod 7 ?
Show that 3 is primitive in Z/49Z.
Show that 31 is not primitive in Z/49Z.
Find the smallest prime p > 2 for which the smallest positive
integer c that is primitive in Z/pZ is not also primitive
in Z/p^{2}Z.
 Fri., Nov. 14:

Read: § 15C
Exercises:
243: 10, 11
246: 1, 2, 4, 6
Show that 2 is a primitive element in Z/mZ for
m = 11 and 19 but not for m = 11 * 19 = 209.
Find all roots of the polynomial x^{3}  1 in (Z/mZ)[t] for
m = 11, 19, and 209.
What is the largest order of any element in Z/209Z ?
 Wed., Nov. 12:

Read: § 15B
Exercises:
243: 4, 5, 7, 8
245: 1
Find primitive elements for Z/17Z,
Z/23Z, and Z/34Z.
Show that there is no primitive element in Z/32Z.
 Mon., Nov. 10:

Read: § 15A
Exercises:
 163: 22
 200: 13, 15
 205: 6, 8
 236: 5
 238: 7  9
 241: 1
 243: 6
 Fri., Nov. 7:

Read: Ch. 14
Exercises:
 163: 18, 21
 200: 11, 12
 205: 5, 7
 233: 1, 2
 234: 3
 236: 4
 Wed., Nov. 5:

Written Assignment No. 3 (also available as PDF or DVI) is due.
 Mon., Nov. 3:

Read: § 12B
Exercises:
 163: 15  17
 169: 5, 6
 196: 5  7, 10
 203: 1, 3
 Fri., Oct. 31:

Read: § 12A
Exercises:
 141: 18
 163: 10, 11, 13, 14
 169: 3, 4
 196: 1  3
 Wed., Oct. 29:

Read: § 10B
Exercises:
 141: 17, 19
 145: 16, 17
 147: 6
 153: 3, 8
 158: 3, 4, 7
 166: 1, 2
 Mon., Oct. 27:

Read: §§ 9F, 10A
Exercises:
 138: 14  18
 141: 13, 15, 16
 145: 12, 13, 15
 147: 3, 5
 153: 1, 2
 158: 1, 2
 Fri., Oct. 24:

Read: §§ 9D, 9E
Exercises:
 122: 16, 17
 137: 10  13
 141: 6, 9  11, 14
 144: 8, 11(iiii)
 147: 2, 4
 Wed., Oct. 22:

Read: §§ 9B, 9C
Exercises:
 122: 14, 15
 127: 8, 9
 133: 7, 10
 137: 3, 5, 7  9
 141: 3  5, 7
 142: 1
 Mon., Oct. 20:

Read: §§ 8C, 9A
Exercises:
 90: 12, 13
 122: 9, 12, 13
 125: 5  7
 133: 5, 6, 9
 136: 1, 2, 4
 Fri., Oct. 17:

Midterm Test
 Wed., Oct. 15:

Review Session: Bring questions.
 Mon., Oct. 13:

Read: §§ 8A, 8B
Exercises:
 74: 9
 86: 8, 9
 89: 4  7, 9  11
 121: 1, 3, 5, 8
 125: 2  4
 Fri., Oct. 10:

Written Assignment No. 2 (also available as PDF or DVI) is due.
 Wed., Oct. 8:

Read: §§ 6D, 6E
Exercises:
 73: 6  8
 84: 2  5
 86: 1  3, 5, 7
 89: 1  3
 Mon., Oct. 6:

University in recess.
 Fri., Oct. 3:

Read: §§ 6A, 6B, 6C
Exercises:
 54: 32  34
 62: 1, 2
 67: 9
 70: 6
 72: 2, 4, 5
 73: 2  5
 80: 3
 84: 1
 Wed., Oct. 1:

Read: §§ 5D, 5E
Exercises:
 52: 15, 16
 54: 28, 30, 31
 59: 5
 65: 7, 8
 67: 7, 8
 70: 4, 5
 72: 1, 3
 73: 1
 Mon., Sep. 29:

No class. University recess ends at 12:20 on this date.
 Fri., Sep. 26:

Note: This class will meet. (A University recess begins at
12:10 on this date.)
Read: §§ 5B, 5C
Exercises:
 35: 20
 51: 10, 11, 13
 53: 19  21, 25
 65: 5, 6
 67: 2, 3, 5, 6
 70: 1, 3
 Wed., Sep. 24:

Written Assignment No. 1 (also available as PDF or DVI) is due.
 Mon., Sep. 22:

Read: §§ 4C, 5A
Exercises:
 35: 11, 14, 18
 50: 3, 4
 51: 3, 4, 7  9
 64: 1, 3, 4
 Fri., Sep. 19:

Read: §§ 4A, 4B
Exercises:
 35: 8, 9, 13, 20
 45: 3
 49: 1, 2
 51: 1, 2
 Wed., Sep. 17:

Read: § 3 E
Exercises:
33: 4(iv, v)
35: 6, 7(i, ii)
Find the continued fraction expansion of:
40487/257
(1 + SQRT{5})/2
SQRT{17}
45: 1
 Mon., Sep. 15:

Read: the course notes on Continued
Fractions (also available as PDF or DVI)
Exercises:
29: 4, 6(ii, iv)
33: 2, 3, 4(iii)
35: 5
Find the continued fraction expansions of
61/67.
44/37.
Evaluate the continued fraction represented by the sequence
[3,2,7,2] .
 Fri., Sep. 12:

Read: § 3C
Exercises:
 23: 5
 24: 5
 27: 9, 11
 29: 6(iii, v)
 33: 4(i)
 Wed., Sep. 10:

Read: §§ 3A, 3B
Exercises:
 23: 3, 4
 24: 1, 3
 27: 5, 6, 10
 29: 2, 5
 Mon., Sep. 8:

Read: §§ 2D, 2E, 2F
Exercises:
 6: 4
 11: 6, 8
 18: 2
 19: 1
 23: 1, 2
 24: 2
 Fri., Sep. 5:

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 or DVI) at this class (or earlier).
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