Gary Brookfield

brookfield photo
College of Natural & Social Sciences
Department of Mathematics
Office Location: ST F206
Phone: 3-2150 Email: gbrookf@calstatela.edu

 

Publications


  • Translation: Analysis I, by H. Amann and J. Escher, Birkhäuser, 2004
Monoids and Categories of Noetherian Modules - Ph.D. Dissertation - 186 pages! - 1997
Direct Sum Cancellation of Noetherian Modules - J. Algebra 200, 207-224, (1998)
The Grothendieck Group and the Extensional Structure of Noetherian Module Categories - Proceedings of the International Conference of Algebra and its Applications, March 1999, 111-131, (2000)
Cancellation in Primely Generated Refinement Monoids - Algebra Universalis, 46 No. 3, 343-371, (2001)
Extensional Structure of Commutative Noetherian Rings - Comm. Algebra 31(6), 2543-2571 (2003)
The Length of Noetherian Modules - Comm. Algebra 30(7), 3177-3204 (2002)
A Krull-Schmidt Theorem for Noetherian Modules - J. Algebra, 251, 70-79 (2002)
The Length of Noetherian Polynomial Rings - Comm. Algebra 31(11), 5591-5607, (2003)
Commutative Noetherian Semigroups are Finitely Generated - Semigroup Forum, 66, 323-327 (2003)
Noetherian Generalized Power Series Rings - Comm. Algebra 32(3), 919-926 (2004)
A Triangle Problem - Math Horizons - September 2003
When Graded Domains are Schreier or pre-Schreier with David E. Rush - J. Pure and Appl. Algebra, 195, 225-230 (2005)
Convex Polytopes and Factorization Properties in Generalized Power Series Domains with David E. Rush - Rocky Mountain Journal of Mathematics, 38, (6), 1909-1919 (2008)
Factoring Quartic Polynomials: A Lost Art - Mathematics Magazine, 80(1), 67-70, (2007)
Yet Another Elementary Solution of the Brachistochrone Problem - Mathematics Magazine, 83(1), 59-63, (2010)
Mini-Sudokus and Groups with Carlos Arcos and Michael Krebs - Mathematics Magazine, 83(2), 111-122, (2010)
Factoring Forms - MAA Monthly, 123(4), 347-362, (April 2016)
The Coefficients of Cyclotomic Polynomials - Mathematics Magazine, 89(3), 179-188, (2016)

 

Algebra Comprehensive Exam Solutions


Click on the links for solutions to some recent comprehensive exams in algebra. The occasional references are to

  • Fraleigh, A First Course in Abstract Algebra, 7th ed.
  • Dummit and Foote, Abstract Algebra, 3rd ed.

Some exams have only partial solutions so far. But otherwise, I think that the solutions are mostly complete and correct. Please send corrections, suggestions to gbrookf@calstatela.edu

 

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Spring 13 Fall 13
Spring 14 Fall 14
Spring 15 Fall 15
Spring 16 Fall 16
Spring 17 Fall 17

Here is a collection of miscellaneous older exam questions: Old stuff