Bianca Viray
Padelford C-525 | Department of Mathematics | 206.543.7986

Introduction to Modern Algebra
Math 402 B; Autumn 2016


e-mail: Include [Math 402] in the subject of all emails, send to bviray+402 AT uw.edu
Office Hours: Mon. 4:00-4:50pm, Fri. 10:30-11:20am, or by appointment
Syllabus: pdf

Resourses
An advanced level math class requires different strategies than ones that you likely used in your lower level classes. Here are some tips on how to approach the class.

  1. How to read a math textbook by Prof. Katherine E. Stange
  2. Why studying math is like studying a language by Prof. Katherine E. Stange
  3. Homework strategies by Prof. Katherine E. Stange
  4. Problem solving by Prof. Terence Tao
  5. For what not to do, see Common errors in undergraduate mathematics, particularly the section on errors in reasoning, by Prof. Eric Schechter
  6. The value of "stupid" questions by Prof. Terence Tao



Announcements

  1. Dec. 8: My office hours during finals week will be Monday, Dec. 12 at 11 - 12:30pm and Tuesday, Dec. 13 at 10-11am.
  2. Dec. 8: Solutions to problems on finite abelian groups
  3. Nov. 23: I will have extra office hours on Tuesday, Nov. 29 at 4 - 4:50pm.
  4. Nov. 22: The second midterm, which is on November 30, will cover Sections 8–12 from the textbook and pages 121 – 125 from Section 13 as well as all of the material we have covered in class, including the substitute lecture on finite matrix groups.

    Suggested practice problems from sections 12 and 13: 12.2, 12.4abcgi, 12.14, 12.16, 12.17, 12.20, 12.23, 12.24, 12.27, 12.28, 12.31, 12.33, 12.34, 13.1, 13.2, 13.3, 13.6, 13.7, 13.8, 13.9, 13.13
  5. Nov. 2: Since UW is closed on Friday Nov. 11, my office hours that day are cancelled. I will instead have office hours on Thursday, Nov. 10 from 2:25 - 3:15pm.
  6. Oct. 19: I will have extra office hours Thursday, October 20 10:30 - 11:20am, Friday, October 21 10:30 - 11:20am and 4:00 - 4:50pm
  7. Oct. 19: Suggested practice problems from Sections 4 and 5: 4.1, 4.3, 4.5, 4.16, 4.17, 4.22, 4.23, 5.1, 5.9, 5.10, 5.15, 5.22, 5.27
  8. Oct. 14: The first midterm, which is on October 24, will cover Sections 1–5 from the textbook as well as all of the material we have covered in class, particularly symmetries of an equilateral triangle. You should be comfortable with the material in Section 0 and 7 from Math 300; this material will not be tested directly, but may be tested with other material.
    You should do problems from Sections 4 and 5 even though there are none on the homework assignments that are due before the midterm.
  9. Oct. 14: Office hours on Monday, Oct. 17 will be from 3:40 - 4:30 (instead of 4:00 - 4:50)



Reading assignments or exercises from class
All assignments are from Abstract Algebra by Saracino unless otherwise stated.

  1. Due Oct. 1: Sections 0 and 7
  2. Due Oct. 4: Section 1
  3. Due Oct. 5: Complete multiplication table for symmetries of an equilateral triangle.
  4. Due Oct. 10: Prove that in each row, each symmetry appears at least once. For either the symmetries of a non-square rectangle or the rotational symmetries of a square, determine how many symmetries there are, label them, write out the multiplication table of symmetries, and list what rules you used to compute the table and what properties the table has.
  5. Due Oct. 12: Section 2
  6. Due Oct. 14: Section 3
  7. Due Oct. 17: pp. 33 and 34 and Section 5 up to Theorem 5.5, skip Thm. 5.2 ; for any element x of a group, the notation <x> denotes the subset {x^n : n any integer}
  8. Due Oct. 19: Section 4 and the rest of Section 5
  9. Due Oct. 21: Section 8
  10. Due Nov. 5: Section 9
  11. Due Nov. 9: Section 11, not including page 105
  12. Due Nov. 16: Section 10 and p. 105, excluding paragraph after Thm. 11.7
  13. Due Nov. 18: Section 12



Homework assignments
All homework assignments are due at the beginning of class on the specified day. All problems are from Abstract Algebra by Saracino unless otherwise stated. Warm-up problems do not need to be turned in.

  1. Due Oct. 5: 0.4, 0.7, 0.14, 0.16, 7.2, 7.4, 7.6 (refer to section 1 for the definition of the operation), 1.3, 1.5, 1.9; Warm-up problems: 0.1, 0.2, 7.1
  2. Due Oct. 12: These problems
  3. Due Oct. 19: 2.1, 2.3, 2.5, 2.7, 2.8, 2.10, 3.3, 3.4, 3.7 (without the finiteness assumption), 3.11, 3.14, 3.15, 3.16; Warm-up problems: 2.2, 2.4, 3.1
  4. Due Nov. 2: 4.9, 4.10, 4.14, 4.24, 4.32, 4.33, 5.6, 5.7, 5.17, 5.18, 8.7, 8.10, 8.11
  5. Due Nov. 9: 9.1, 9.3, 9.5, 9.6, 9.10, 9.11, 9.14, 9.16, 9.18, 9.19
  6. Due Nov. 16: 10.11, 11.1, 11.2, 11.3, 11.11, 11.16, 11.17, 11.18, 11.26; The only information from section 10 that you need is the definition of the index of a subgroup.
  7. Due Nov. 23: 10.2, 10.5, 10.6, 10.14, 10.15, 10.16, 12.1, 12.9, 12.12, 12.13
  8. Due Dec. 5 at 4:50pm, in my mailbox : 12.17, 12.20, 12.23, 12.31, 12.34, 13.2, 13.6, 13.8, 13.9
  9. Due Dec. 8 at 4:50pm, in my mailbox : 6.3, 6.5, 6.10, 6.12, 13.10, 13.11, 13.16, 13.20, 13.25; Warm-up problems: 6.1, 6.2