Robert W. Fitzgerald

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Reprints and preprints

Robert W. Fitzgerald

Department of Mathematics

Southern Illinois University

Carbondale, IL 62901-4408

The more recent papers are available as DVI files.
 

  1. Norm principles for forms of higher degree permitting composition (with S. Pumplün). Preprint. download this paper
  2. Invariants of trace forms over finite fields of characteristic 2. Preprint. download this paper
  3. Highly degenerate quadratic forms over F_2. Finite Fields and Their Applications 13 (2007) 778--792.  download this paper
  4. Explicit factorizations of cyclotomic and Dickson polynomials over finite fields (with J. Yucas). Arithmetic of Finite Fields 2007, Lecture Notes in Computer Science, vol. 4547, Springer, Berlin, 2007, pages 1--10. download this paper
  5. Represented value sets for integral binary quadratic forms and lattices (with A. G. Earnest). Proceedings of the American Math. Society 135 (2007) 3765--3770. download this paper
  6. Generalized reciprocals, factors of Dickson polynomials and generalized cyclotomic polynomials over finite fields. (with J. Yucas).  Finite Fields and Their Applications 13 (2007) 492--515. download this paper
  7. A generalization of Dickson polynomials via linear fractional transformations. (with J. Yucas).  International Journal of Mathematics and Computer Science 1  (2006) 391--416. download this paper
  8. Bass series for small Witt rings. Communications in Algebra 34 (2006) 1753-1762. Download this paper
  9. Factors of Dickson polynomials over finite fields. (with J. Yucas).  Finite Fields and Their Applications 11 (2005) 724--737. Download this paper
  10. Highly degenerate quadratic forms over finite fields of characteristic 2.  Finite Fields and Their Applications 11 (2005) 165--181. Download this paper
  11. Sums of Gauss sums and weights of irreducible codes. (with J. Yucas).  Finite Fields and Their Applications 11 (2005) 89--110. download this paper
  12. Pencils of quadratic forms over finite fields. (with J. Yucas). Discrete Math. 283 (2004) 71--79.       download this paper
  13. Irreducible polynomials over GF(2) with three prescribed coefficients. (with J. Yucas). Finite Fields and Their Applications 9 (2003) 286--299.                                 Download the dvi file
  14. A characterization of primitive polynomials over finite fields. Finite Fields and Their Applications 9 (2003) 117--121.  Download the dvi file
  15. Isotropy and factorization in reduced Witt rings. Documenta Math. (Quadratic Forms LSU) (2001) 141--163.       Download the dvi file
  16. Norms of sums of squares. Linear Algebra and Its Applications 325 (2001) 1--6. Download the file NORMS.dvi
  17. Torsion-free modules over reduced Witt rings.  Journal of Algebra 231 (2000) 786--804.         Download the file lociso.dvi
  18. Small extensions of Witt rings. Pacific Journal of Math. 189 (1999) 31--53.     Download the file wrext.dvi.
  19. Orderings of finite fields and balanced tournaments. (with M. Beintema, J. Bonn, J. Yucas) Ars Combinatoria 49 (1998) 41--48.
  20. Gorenstein Witt rings II. Canadian Journal of Math. 49 (1997) 499--519.         Download the file gorgor.dvi.
  21. K-regular Witt rings. Proceedings Amer. Math. Soc. 125 (1997) 1309--1313.          Download the file kreg.dvi.
  22. Local Artinian rings and the Fröberg relation. Rocky Mountain Journal of Math. 26 (1996) 1351--1369.
  23. Projective modules over Witt rings. Journal of Algebra 183 (1996) 286--305.
  24. The spectrum of symmetric Krawtchouk matrices. (with P. Feinsilver) Linear Algebra and Its Applications 235 (1996) 121--139.
  25. Characteristic polynomials of symmetric matrices. Linear and Multilinear Algebra 36 (1994) 233--237.
  26. Half factorial Witt rings. Journal of Algebra 155 (1993) 127--136.
  27. Witt rings under odd degree extensions. Pacific Journal of Math.158 (1993) 121--143.
  28. Picard groups of Witt rings. Math. Zeitschrift 206 (1991) 303--319.
  29. Combinatorial techniques and abstract Witt rings III. Pacific Journal of Math. 148 (1991) 39--58.
  30. Linked quaternionic quotients and homomorphisms. Communications in Algebra 18 (1990) 4171- - 4224.
  31. Ideal class groups of Witt rings. Journal of Algebra124 (1989) 506 -520.
  32. Combinatorial techniques and abstract Witt rings II. (with J. Yucas) Rocky Mountain Journal of Math. 19 (1989) 687--708.
  33. On generating linear spans over GF(p). (with J. Yucas) Congressus Numerantium 69 (1989) 55--60.
  34. Gorenstein Witt rings. Canadian Journal of Math. 60 (1988) 1186--1202.
  35. Combinatorial techniques and abstract Witt rings I. (with J. Yucas) Journal of Algebra 114 (1988) 40--52.
  36. Derivation algebras of finitely generated Witt rings. Pacific Journal of Math. 128 (1987) 265--297.
  37. Local factors of finitely generated Witt rings. (with J. Yucas) Rocky Mountain Journal of Math. 16 (1986) 619--627.
  38. Primary ideals in Witt rings. Journal of Algebra 96 (1985) 368--385.
  39. Quadratic forms of height two. Transaction of Amer. Math. Soc.283 (1984) 339--351.
  40. Rotations and Linkage of 2-fold Pfister forms. Proceedings of Amer. Math. Soc. 89 (1983) 19--23.
  41. Witt kernels of function field extensions. Pacific Journal of Math. 109 (1983) 89--106.
  42. Function fields of quadratic forms. Math Zeitschrift 178 (1981) 63--76. 

Math 319: Introduction to Abstract Algebra
 

Days

Time

 Room   

Section

M W F

11

Wham 317

1

 


 
 

 
   


  

 

Syllabus

Office: Neckers 379

Hours:  M W F 12 - 2

WORK: 1.Weekly homework, assigned on Mondays and due the following Monday. There will be 11 homework assignments, worth 10 points each. I will take the 10 best scores for a total of 100 points possible.

    2. Three exams, each worth 100 points.
First exam (covers Chapter 1 ):                                   Wednesday, September 29
Second exam (covers Chapter 2):                                 Wednesday, October 24

    3. Final exam, worth 200 points. It is comprehensive.

Grades:
    Grades are curved with a scale that depends on the performance of the class, but not stricter than A 90 -100, B 80 -89, C 70 -70, D 65 - 70.

Text:   Algebra: Abstract and Concrete (Stressing Symmetry) (2nd edition) by Frederick Goodman

Topics: Chapters 1, 2, and 6. We also do sections 4.1 and 4.3. We omit sections 1.4, 1.8, 1.9, 1.12 and 6.7.        


Final Exam :  

 Back to the top of the Math 319 page

Homework

1


 
 
 

Math 520

Section 

Day

Time

Room

1

MWF

12

AG 152 


 

Syllabus

Office: 379 Neckers

Hours:  MWF 1 - 3

Work: 1. Weekly homework, assigned on Mondays and due the following Monday. There will be 11 assignments, worth 10 points each. I count the ten best scores for a total of 100 points possible.

 2. One mid-term, March 5, covering Chapter 13 and Chapter 14, sections 1 and 2. It is worth 100 points.

        3. Final exam, worth 200 points. It is comprehensive.

Grading: Standard graduate grading scale.

Text:   Abstract Algebra (3rd edition) by D.S. Dummit and R.M. Foote
 

Topics: Chapter 13, omitting section 3

            Chapter 14, omitting sections 3, 5, 8, and 9

            Chapter 15, omitting sections 2 and 5

            Chapter 16


 Final Exam:  
 

Homework

  1.  

Exam solutions