Math 25500, Winter 2008
"Basic Algebra 2"
Instructor: Yon-Seo Kim,
Class homepage: http://www.math.uchicago.edu/~yskim/w08M255.html
Class Hours: Sec 11] MWF 8:30am - 9:20am at Eckhart 207,
Sec 31] MWF 10:30am - 11:20am at Eckhart 308
email: yskim@math.uchicago.edu
(please start the message title with Math255-)
Office: E306, Office Hours
MWF 9:25am - 10:25am or by
appointments.
College Fellow: Francis Chung, email:
fjchung@math.uchicago.edu
OH R 2:30pm - 5:30pm
Office:
Basement of 5720
Woodlawn,
Discussion session: Tuesdays 6pm-7pm at Eckhart 312
Textbook: A first course in Abstract Algebra by John B. Fraleigh, 7th
ed. , Abstract Linear Algebra by Morton Curtis.
Course
Outline
This course will cover Ideals, Factor Rings, Extension Fields,
Factorization, Vector spaces, Matrices, and Polynomial rings. We will
first use Fraleigh's book and then change to Curtis' book when we start
discussing Vector spaces.
Homework will be assigned every week and will be collected one-week
after the homework is assigned.
There will be one midterm and the final exam. Midterm is scheduled
on a regular class hour during 5th week.
Grading basis: Homework -30%, Midterm -30%, Final Exam -40%
Notes
and Comments on Past/Future Lectures
Jan 7th : Ideals and Factor Rings. Note for the next 3 classes.
Jan 9th : Fundamental Homomorphism Theorem. Examples.
Jan 11th: Prime/Maximal Ideal. Prime Fields.
Jan 14th: Polynomial Ring.
Jan 16th: Extension Fields. Note
Jan 18th: Extension Fields contd.
Jan 23rd: Simple Extension. Note
Jan 25th: Vector Spaces. Note
Jan 28th: Factorization. Note
Jan 30th: Factorization contd.
Feb 1st : Euclidean domains. Note
Feb 4th : Review.
Feb 6th : Midterm exam. Will cover from the beginning to Euclidean
domain. Solution
Feb 8th : Fermat's Theorem. Note
Feb 11th: Vector space and Linear maps. Note
Feb 13th: Rank Theorem and Direct Sums. Note
Feb 15th: College break.
Feb 18th: Eigenvalue and Dual space. Note
Feb 20th: Associated Matrix. Note
Feb 22nd: Exterior Algebra. Note
Feb 25th: Determinant. Note
Feb 27th: Characteristic Polynomial. Note
Feb 29th: Cayley-Hamilton Theorem. Note
Homework
Assignments
Prefix 'F' stands for Fraleigh's book and 'C' stands for Curtis'
book.
HW#1 (due Jan 18th): F26-1,3,4,8,12,13,15,17,22,23,32,36.
F27-2,4,5,18.
HW#2 (due Jan 25th): F27-24,25,26,29,33,37. F29-17,18,25,30,32,33,36.
HW#3 (due Feb 1st ): F30-1,6,10,16,17,18,20,22,24.
HW#4 (due Feb 11th): F45-10,14,22,25,26,29,31,33. F46-1,2,3,9,10,16,19.
HW#5 (due Feb 18th): F47-5,6,7,10,13,15,16.
HW#6 (due Feb 22nd): C I-A-1,3,5,9. C I-B-2,4,6. C I-C-2,5,6,7,11.
HW#7 (due Feb 29th): C I-D-1,3,4. C I-E-8,9. C I-F-3,6-10.
HW#8 (due Mar 12th): C II-A-1,3,5,7. C II-C-(p65)3,5 (p69-)10,11. C
II-D-2,3,8. C II-E-4. C III-C-1. C III-D-3,4. C III-E-1,2,4.