Frederick M. Goodman, Algebra: Abstract and Concrete, 2nd edition, Prentice Hall, 2002.
This text is required.
I. N. Herstein, Topics in Algebra, 2nd edition
This text is recommended.
Review sheet on fields for the final.
Errata sheet for Goodman, Algebra
Correct link to purchase Herstein, Topics in Algebra at discount: Abebooks .
Reserve list in Math Library:
Herstein, Topics in Algebra (2 copies)
Vinberg, A Course in Algebra.
Jacobson, Basic Algebra I (1985)
Jacobson, Lectures in Abstract Algebra, Vol II (Linear Algebra)
Improved text for section 2.7.
Revised section 3.4 and new section 3.5. (revised Saturday, March 19; added some comments on similar matrices and similar transformations)
Improved text for sections 6.1 through 6.3.
Improved text for section 6.6.
New sections M.1-M.2 (modules, version of Monday Feb. 21)
New section M3 (determinants, version of Monday Feb 28, needs proofreading.)
New sections M4-M5 (version of Saturday, March 19. complete, but needs exercises. Removed superfluous section M6 with a second proof of structure theorem for finitely generated torsion modules over a PID).
New section M6 (Version of Saturday, March 26, with subsection on characteristic and minimal polynomials)
Program for diagonalizing integer or polynomial matrices, and examples of canonical form computations.
Office:325G Maclean Hall |
Email:goodman at math dot uiowa dot edu |
Phone:Office: 319-335-0791 |
Paper Mail:Fred Goodman Department of Mathematics MLH The University of Iowa Iowa City, IA 52242-1419 USA |
Office Hours:MW 1:30-2:20 |
Teaching Assistant:Oscar VegaOffice hours: TBA |
12:30P - 1:20P T 116 MH
Frederick M. Goodman, Algebra: Abstract and Concrete, 2nd edition, Prentice Hall, 2002.
|
|
I. N. Herstein, Topics in Algebra, 2nd edition This text is recommended. |
|
There will be 8 to 12 written assignments. Details will appear here as the assignments are made.Please see the remarks on the syllabus about the standard of explanation expected on the homework.
First assignment, Due Friday, Jan. 28:
Section 6.1, Exercises: 8, 15.
Section 6.2, Exercises from the revised text: 2, 10-15, 22.
2nd assignment, Due Friday, Feb. 4:
Section 6.3, Exercises from the revised text: 2, 3, 8, 9, 11
Section 6.4, Exercises 1, 2
Section 6.5, Exercises 5, 7, 10, 11, 12, 23, 24.
Section 6.6, Exercises 3, 4, 5. Note: for exercise 5, the correct statement is that R does not satisfy the ACC for principal ideals, but every irreducible is prime.
Section 6.8, Exercises 4, 5, 6.
Section 3.5, Exercises 3, 4, 11, 12.
Let B and C be two ordered bases of a finite dimensional vector space V. Let T be an element of End_K(V). Show that there is an invertible matrix S such that (the matrix of T with respect to C) = S (matrix of T with respect to B) S^{-1}.
Section M1, Exercises 3, 5, 8, 9,10.
7th assignment, Due Friday, March 11:
Section M2, Exercises 4 and 7
Section M3, Exercises 1, 2, 3, 4, 6
8th assignment, Due Friday, March 25:
Characteristic polynomials and triangular form.
9th assignment, Due Friday, April 1 (ha!):
10th assignment, Due Friday, April 8 :
11th assignment, Due Monday, April 25 :
Section 7.3 Exercises 5, 6, 7, 10.
Section 8.1 Exercises 1-3.
Section 8.2 1, 3.
There will be two midterm exams, dates to be negotiated; the dates will appear here when they are known. There will be a comprehensive final exam. The text of the exams will appear here after the exams have been done by all students.