MATH 320: Abstract Algebra I

TEXT: Dan Saracino, Abstract Algebra, A First Course, Waveland Press, 1992.

INSTRUCTOR: David Lantz

• Email: dlantz@mail.colgate.edu
• Office : McGregory 202B ----- Extension : 7737
• Formal Office Hours : MTWRF 11:20-12:10 p.m.
• Effective Office Hours: Weekdays, 9:00-5:00, except when I am teaching or in a meeting
• Home: 146 Lebanon Street, Hamilton
• Phone : 824-0965 (Please do not call after 10 p.m.)

WEB ADDRESS: This page has the web address:

HOMEWORK: Due dates will be specified.

• Section 1: 1.2, 1.3, 1.5, 1.6, 1.9. (Solutions)
• Section 2: 2.1, 2.2, 2.3, 2.4, 2.5, 2.6 (Consider c*b*c.), 2.10. (Read 2.8.) (Solutions)
• Section 3: 3.1, 3.2, 3.3, 3.4, 3.6, 3.9, 3.11, 3.12 and supplementary questions. (Solutions)
• Section 4: 4.1, 4.2, 4.4, 4.7, 4.8, 4.13, 4.18, 4.20, 4.22, 4.24. (Solutions)
• Section 5: 5.1, 5.4a, 5.7, 5.11, 5.12, 5.13, 5.17, 5.18, 5.21, 5.22, 5.26. (Solutions)
• Section 6: 6.1a, 6.2, 6.7, 6.8; and Section 7: 7.1, 7.3, 7.4, 7.7, 7.11. (Solutions)
• Section 8: 8.1, 8.2, 8.3, 8.7, 8.11, 8.12, 8.16, 8.17, 8.19 (For part a), just use trial and error). (Solutions)
• Section 9: 9.1, 9.2, 9.3, 9.4, 9.7, 9.9, 9.11, 9.12. (Solutions)
• Section 10: 10.1, 10.2ab, 10.5, 10.6, 10.7, 10.8, 10.9, 10.13, 10.16, 10.23. (If we cover the class equation, also 22.) (Hint for 23: If a is in a group G but not in Z(G), why is Z(a) strictly between Z(G) and G? And what does that mean about [G:Z(a)], [G:Z(G)] and 1?) (Solutions)
• Section 11: 11.2, 11.5, 11.7, 11.9, 11.17, 11.19, 11.23bc. (Solutions)
• Section 12: 12.1, 12.3, 12.4, 12.11, 12.14, 12.19, 12.21, 12.22, 12.27, 12.30. (Solutions)
• Section 13: 13.2, 13.3, 13.5, 13.7, 13.11, 13.13, 13.17, 13.19, 13.20, 13.23, 13.26. (Solutions)
• Section 16: 16.1, 16.2, 16.3, 16.9, 16.11, 16.14, 16.15, 16.16, 16.17 (In a), distributivity is a mess. Use a Venn diagram.), 16.24 (Part a) is like parts of Exercise 16.3.). (Solutions)
• Section 17: 17.1, 17.2, 17.10a, 17.12, 17.20, 17.21, 17.22ab, 17.25, 17.33, 17.34. (Solutions)
• Section 18: 18.1, 18.2, 18.5, 18.9, 18.10, 18.12, 18.13ab, 18.16 (the hard part is "onto"; given (I+a,J+b), write both a and b in terms of elements of I and J), 18.21. (Solutions)

TESTS: There will be three mid-term exams, on Tuesday evenings, 7:30-9:30 p.m., on February 19, March 11 and April 15, in McGregory 215 (our usual classroom). A cumulative final exam will be given during the officially scheduled final exam period for this course, Thursday, May 8, at 3:00, in McGregory 214. If it is impossible for you to take one of the exams during the scheduled period, please see me to set a time to take it early, ahead of the scheduled period. The date and time for the final cannot be altered; please consult the final exam schedule before making travel plans.

GRADING: Homework will be worth one-fifth of the course grade, and each exam (including the final) will be worth one-fifth of the grade. The grading will likely be based on a 90-80-70-60 scale, but I will feel free to shade results near the boundaries. In particular, I am more impressed by mastery than by industry: If Student A has exam grades average 85 and homework brings the average to an 87, while Student B has exam grades average 89 and homework brings it down to an 87, I am more likely to give a B+ to Student B.

GRAPHICS AND SUPPLEMENTS:

• Practice first exam, from the distant past, with solutions
• First exam, with solutions
• Practice second exam, from the distant past, with solutions
• Second exam, with solutions
• Practice third exam, from the distant past, with solutions
• Third exam, with solutions
• Practice final exam, from the distant past, with solutions
• Full class notes from Section 1
• Class graphics from Section 1
• Full class notes from Section 2
• Full class notes from Section 3
• Full class notes from Section 4
• The Platonic solids
• Full class notes from Section 5
• Full class notes from Sections 6 and 7
• Full class notes from Section 8
• An example of how multiplying an element of S_n by a transposition changes the parity of the number of backward pairs.
• Full class notes from Section 9
• Full class notes from Section 10
• Full class notes from Sections 11, 12 and 13
• Venn diagram of subgroups of S(G)
• Sketch and example of the proof of Cayley's Theorem
• Proof of Wedderburn's Theorem on division rings. (He also has his name on a theorem about "semisimple" rings.)
• Full class notes from Section 16
• Full class notes from Section 17
• Index of LaTeX lesson files
• Full class notes from Section 18
• Full class notes from Sections 14 and 15
• Photos of Emmy Noether, Max Noether, Edmund Landau and Emil Artin

SIGNIFICANT DATES:

• Mon Jan 21: First class (short session. 11:30 a.m.)
• Wed Jan 30: Drop/Add ends
• Tue Feb 19: First midterm exam (7:30 p.m., McGregory 215)
• Tue Mar 11: Second midterm exam (7:30 p.m., McGregory 215)
• Sat-Sun Mar 15-23: Mid-term recess
• Wed Mar 26: W-day
• Tue Apr 15: Third midterm exam (7:30 p.m., McGregory 215)
• Fri May 2: Last class
• Thur May 8: Final exam (3:00 p.m., McGregory 214)

SUGGESTIONS:

1. If you see an error at the board, or if you do not understand something, stop me and ask (even if everyone else seems to understand).
2. Doing the homework, regularly and thoughtfully, is absolutely essential to your success in the course.