MATH 320: Abstract Algebra I

TEXT: Dan Saracino, Abstract Algebra, A First Course, Second edition, Waveland Press, 2008.

INSTRUCTOR: David Lantz

• Email: dlantz@mail.colgate.edu
• Office : McGregory 202B ----- Extension : 7737
• Formal Office Hours : MWF 1:20-2:10 p.m., TR 11:20-12:05
• Effective Office Hours: Weekdays, 9:00-5:00, except when I am teaching or in a meeting
• 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. To get to the index page for the solutions, type the code word in the box, then click the button:

• Section 1: 1.2, 1.3, 1.5, 1.6, 1.9. (Due Mon 24 Jan.)
• Section 2: 2.1, 2.2, 2.3, 2.4, 2.5, 2.6 (Consider c*b*c.), 2.10. (Read 2.8.) (Due Mon 31 Jan.)
• Section 3: 3.1, 3.2, 3.3, 3.4, 3.6, 3.9, 3.11, 3.12 and supplementary questions. (Due Fri 4 Feb.)
• Section 4: 4.1, 4.2, 4.4, 4.7, 4.8, 4.13, 4.18, 4.20, 4.22, 4.24. (Due Wed 9 Feb.)
• Section 5: 5.1, 5.4a, 5.7, 5.11, 5.12, 5.13, 5.17, 5.18, 5.21, 5.22, 5.26. (Due Fri 18 Feb.)
• Section 6: 6.1a, 6.2, 6.7, 6.8; and Section 7: 7.1, 7.3, 7.4, 7.7, 7.11. (Due Mon 28 Feb.)
• Section 8 (and following): 8.1, 8.2, 8.3, 8.7, 8.11, 8.14, 8.15, 8.18, 8.19, 8.21 (For part a), just use trial and error), 8.22, 8.24. (Due Fri 4 Mar.)
• Section 9: 9.1, 9.2, 9.4, 9.5, 9.8, 9.10, 9.12, 9.14. (Due Mon 7 Mar.)
• Section 10: 10.1, 10.2ab, 10.5, 10.6, 10.7, 10.8, 10.13, 10.16, 10.21, 10.27. (If we cover the class equation, also 10.26.) (Hint for 27: 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?) (Due Fri 11 Mar, not including 10.26.)
• Section 11: 11.2, 11.5, 11.7, 11.8, 11.10, 11.12a, 11.14, 11.19, 11.23, 11.27, 11.29. (Due Mon 4 Apr.)
• Section 12: 12.1, 12.3, 12.4, 12.11, 12.14, 12.19, 12.21, 12.22, 12.27, 12.30, 12.34, 12.36. (Due Fri 8 Apr.)
• Section 13: 13.2, 13.3, 13.5, 13.7, 13.14, 13.16, 13.19, 13.21, 13.22, 13.25, 13.27. (Due Fri 15 Apr.)
• Section 16: 16.1, 16.2, 16.3, 16.9, 16.14, 16.15, 16.16, 16.24 (Part (a) is like parts of Exercise 16.3.). (Think about how you might answer 16.11 -- but first, suppose (a,b) is an element in a direct sum of rings. What must be true about a and/or b to make the pair a unit, or a zero-divisor, or a nilpotent? Also, read 16.17. If you were to actually write out part (a), distributivity would be a mess -- a Venn diagram would help.). (Due Fri 22 Apr.)
• Section 17: 17.1abc, 17.2, 17.10a, 17.20, 17.21, 17.22ab, 17.25, 17.33. (Read, and think about how you would answer, 17.12 and 17.34.)(Due Mon 25 Apr.)
• Section 18: 18.1, 18.2, 18.5, 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. (Read, and think about how you would answer, 18.9 and 18.10.) (Due Fri 29 Apr.)

TESTS: There will be three mid-term exams, on Tuesday evenings, 7:30-9:30 p.m., on the dates and in the place specified in the calendar. A cumulative final exam will be given during the officially scheduled final exam periods for this course (see the calendar -- no matter which section you are in, you may take the final during either period). If it is impossible for you to take any of the exams during the scheduled period(s), 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:

• Index of LaTeX lesson files
• Blank LaTeX file for you to use for submitting homework assignments
• 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
• Operation tables related to forming factor groups
• 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
• Full class notes from Section 18
• Answers to a couple of last-minute questions on rings
• Full class notes from Sections 14 and 15
• Presentation on the structure theorem for finite abelian groups
• Photos of Emmy Noether, Max Noether, Edmund Landau and Emil Artin

Course calendar: Click here.

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.