Welcome to the Math 647/8/9 web page!
Here are the course notes chapter by chapter. Please let me know of mistakes -- I will correct them on-line when you do!
No starred sections will be on the qualifying examination.
Title page: title.pdf.
Table of contents: contents.pdf.
Chapter 0 - Categories: ch0.pdf.
Chapter 1 - Groups: ch1.pdf.
Chapter 2 - Rings: ch2.pdf.
Chapter 3 - Modules: ch3.pdf.
Chapter 4 - Algebras: ch4.pdf.
Chapter 5 - Fields: ch5.pdf.
Chapter 6 - Commutative algebra: ch6.pdf.
Here are exercise sets for each chapter.
Exercises from chapter 0: ch0ex.pdf
and with solutions ch0exs.pdf.
Exercises from chapter 1: ch1ex.pdf
and with solutions ch1exs.pdf.
Exercises from chapter 2: ch2ex.pdf
and with solutions ch2exs.pdf.
Exercises from chapter 3: ch3ex.pdf
and with solutions ch3exs.pdf.
Exercises from chapter 4: ch4ex.pdf
and with solutions ch4exs.pdf.
Exercises from chapters 5 and 6: ch5ex.pdf
and with solutions ch5exs.pdf.
Here are the solutions for the midterms and finals.
Fall midterm: midterm1.pdf
and with solutions midterm1s.pdf.
Fall final: final1.pdf
and with solutions final1s.pdf.
Winter midterm: midterm2.pdf
and with solutions midterm2s.pdf.
Winter final: final2.pdf
and with solutions final2s.pdf.
Spring midfinal: midfinal.pdf
and with solutions midfinals.pdf.
Here are is an old qualifying exam from when I taught the course in 1999.
Qualifying exam from Fall 2000: qual.pdf.
CORRECTIONS. If people find mistakes, I'll post them here (and correct the on-line version of the notes).
Page 26, example (5). This is a correction to the previous correction!!!
Its definitely right this time.
The penultimate sentence should have the semidirect products of $C_3$ (normal) by $V_4$ (on top) being isomorphic to $D_3 \times C_2 \cong D_6$,
$V_4$ (normal) by $C_3$ (on top) being isomorphic to $A_4$,
and $C_3$ (normal) by C_4 being the new group $T$.
I seem to keep messing this one up, so make sure you do not!
Page 22, 4 lines from the bottom. The equation 2n = ... should read
3n= ... on the left hand side.