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. PDF versions can be found at http://opensiuc.lib.siu.edu/math_articles/
 

  1. The number of quadratic forms of fixed codimension (with P. Feinsilver and A. Klapper). Preprint.
  2. Norm Euclidean quaternionic orders. Integers 11 (2011) A58, 12pp. Download this paper
  3. Sun’s conjectures on fourth powers in the class group of binary quadratic forms. Journal of Number Theory 130 (2010) 192--197. Download this paper
  4. Multiplicative properties of integral binary quadratic forms (with A. Earnest). Contemporary Mathematics 493 (2009) 107--115. Download this paper
  5. Trace forms over finite fields of characteristic 2 with prescribed invariants. Finite Fields and Their Applications 15 (2009) 69--81. download this paper
  6. Norm principles for forms of higher degree permitting composition (with S. Pumplün). Communications in Algebra 37 (2009) 3851--3860. download this paper (PDF file)
  7. Invariants of trace forms over finite fields of characteristic 2. Finite Fields and Their Applications 15 (2009) 261--275.  download this paper
  8. Highly degenerate quadratic forms over F_2. Finite Fields and Their Applications 13 (2007) 778--792.  download this paper
  9. 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
  10. 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
  11. 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
  12. 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
  13. Bass series for small Witt rings. Communications in Algebra 34 (2006) 1753-1762. Download this paper
  14. Factors of Dickson polynomials over finite fields. (with J. Yucas).  Finite Fields and Their Applications 11 (2005) 724--737. Download this paper
  15. Highly degenerate quadratic forms over finite fields of characteristic 2.  Finite Fields and Their Applications 11 (2005) 165--181. Download this paper
  16. Sums of Gauss sums and weights of irreducible codes. (with J. Yucas).  Finite Fields and Their Applications 11 (2005) 89--110. download this paper
  17. Pencils of quadratic forms over finite fields. (with J. Yucas). Discrete Math. 283 (2004) 71--79.       download this paper
  18. 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
  19. A characterization of primitive polynomials over finite fields. Finite Fields and Their Applications 9 (2003) 117--121.  Download the dvi file
  20. Isotropy and factorization in reduced Witt rings. Documenta Math. (Quadratic Forms LSU) (2001) 141--163.       Download the dvi file
  21. Norms of sums of squares. Linear Algebra and Its Applications 325 (2001) 1--6. Download the file NORMS.dvi
  22. Torsion-free modules over reduced Witt rings.  Journal of Algebra 231 (2000) 786--804.         Download the file lociso.dvi
  23. Small extensions of Witt rings. Pacific Journal of Math. 189 (1999) 31--53.     Download the file wrext.dvi.
  24. Orderings of finite fields and balanced tournaments. (with M. Beintema, J. Bonn, J. Yucas) Ars Combinatoria 49 (1998) 41--48.
  25. Gorenstein Witt rings II. Canadian Journal of Math. 49 (1997) 499--519.         Download the file gorgor.dvi.
  26. K-regular Witt rings. Proceedings Amer. Math. Soc. 125 (1997) 1309--1313.          Download the file kreg.dvi.
  27. Local Artinian rings and the Fröberg relation. Rocky Mountain Journal of Math. 26 (1996) 1351--1369.
  28. Projective modules over Witt rings. Journal of Algebra 183 (1996) 286--305.
  29. The spectrum of symmetric Krawtchouk matrices. (with P. Feinsilver) Linear Algebra and Its Applications 235 (1996) 121--139.
  30. Characteristic polynomials of symmetric matrices. Linear and Multilinear Algebra 36 (1994) 233--237.
  31. Half factorial Witt rings. Journal of Algebra 155 (1993) 127--136.
  32. Witt rings under odd degree extensions. Pacific Journal of Math.158 (1993) 121--143.
  33. Picard groups of Witt rings. Math. Zeitschrift 206 (1991) 303--319.
  34. Combinatorial techniques and abstract Witt rings III. Pacific Journal of Math. 148 (1991) 39--58.
  35. Linked quaternionic quotients and homomorphisms. Communications in Algebra 18 (1990) 4171- - 4224.
  36. Ideal class groups of Witt rings. Journal of Algebra124 (1989) 506 -520.
  37. Combinatorial techniques and abstract Witt rings II. (with J. Yucas) Rocky Mountain Journal of Math. 19 (1989) 687--708.
  38. On generating linear spans over GF(p). (with J. Yucas) Congressus Numerantium 69 (1989) 55--60.
  39. Gorenstein Witt rings. Canadian Journal of Math. 60 (1988) 1186--1202.
  40. Combinatorial techniques and abstract Witt rings I. (with J. Yucas) Journal of Algebra 114 (1988) 40--52.
  41. Derivation algebras of finitely generated Witt rings. Pacific Journal of Math. 128 (1987) 265--297.
  42. Local factors of finitely generated Witt rings. (with J. Yucas) Rocky Mountain Journal of Math. 16 (1986) 619--627.
  43. Primary ideals in Witt rings. Journal of Algebra 96 (1985) 368--385.
  44. Quadratic forms of height two. Transaction of Amer. Math. Soc.283 (1984) 339--351.
  45. Rotations and Linkage of 2-fold Pfister forms. Proceedings of Amer. Math. Soc. 89 (1983) 19--23.
  46. Witt kernels of function field extensions. Pacific Journal of Math. 109 (1983) 89--106.
  47. Function fields of quadratic forms. Math Zeitschrift 178 (1981) 63--76. 

Math 417: Applied Matrix Theory


 

Days

Time

 Room   

Section

M W F

2

Wham 328

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 12 homework assignments, worth 10 points each, for a total of 120 points possible.

    2. Take-home mid-term, worth 100 points. This will be handed out February 27 and due February 29.

    3. Take-home 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: None—but notes will be handed out. It is important to also have good notes from class.

Topics: (a) Non-negative matrices and the Perron-Frobenius Theorem

(b) Matrix representations of groups and quantum mechanics

 

Calculator: A calculator (such as the TI-85) that can do matrix computations or access to a computer with a symbolic algebra program (such as MAPLE) is needed.

 

Emergency Procedures.  Southern Illinois University Carbondale is committed to providing a safe and healthy environment for study and work. Because some health and safety circumstances are beyond our control, we ask that you become familiar with the SIUC Emergency Response Plan and Building Emergency Response Team (BERT) program. Emergency response information is available on posters in buildings on campus, available on BERT’s website at www.bert.siu.edu, Department of Safety’s website www.dps.siu.edu (disaster drop down) and in Emergency Response Guideline pamphlet. Know how to respond to each type of emergency.

 

Instructors will provide guidance and direction to students in the classroom in the event of an emergency affecting your location. It is important that you follow these instructions and stay with your instructor during an evacuation or sheltering emergency. The Building Emergency Response Team will provide assistance to your instructor in evacuating the building or sheltering within the facility.


Final Exam: 

 Back to the top of the Math 421 page


Homework


#1 p. 20) 8b       p. 34) 5b       p. 41) 2f, 8         p. 76) 17

#2 p. 84) 3, 4      p. 97) 11       p. 117) 3, 6

#3 p. 116) 2d, 4      p. 165) 2f      p. 222) 21      p. 229) 12

#4 p. 258) 8b        p. 279) 2a, b                  p. 322) 2b, 21  

#5 p. 338) 20a       p. 353) 2a, 7       p. 366) 10, 12a

#6 p. 375) 4, 7b      p. 392) 2e

#7 Handout

#8 p. 495) 7 a, b, c, d, e

#9 Handout

#10 p. 546) 2 a,d ,  4 a,c



 

 

 

 

 

 

 

 

 

 
 


Math 109: Trigonometry and Analytic Geometry

 

 

Section 

Day

Time

Room

2

MWF

11

EngrA 420 

 

Syllabus

Office: 379 Neckers

Hours:  MWF 1 - 3

Email: rfitzg@math.siu.edu

Homework: 1. Weekly homework, assigned on Mondays and usually due the following Monday. Each homework is worth 10 points. There will be 11 assignments. I will take the 10 best, giving a total of 100 points possible.

2. There are three exams, each worth 100 points.

First Exam (covers Chapter 6): Monday, September 19

Second Exam (covers Chapter 7): Friday, October 14

Third Exam (covers Chapter 8): Monday, November 7.

 

3. The final exam is worth 200 points. It is comprehensive.

 

Grades:  Grades are curved, with the curve depending on the performance of the class but no stricter than A 90-100, B 80-89, C70-79, D 65-69.

 

Text: Algebra and Trigonometry (4th edition) by Beecher, Penna and Bittinger

 

Topics: Chapters 6, 7, 8 and 10.

 

Calculator: The only calculator allowed on the exams is the TI-30 (although the exams do not require any calculator). Use whatever you want for the homework assignments.

 

 

 

Emergency Procedures SIUC is committed to providing a safe and healthy environment for study and work. Because some health and safety circumstances are beyond our control, we ask that you become familiar with the Emergency Response Plan and the Building Emergency Response Team (BERT) program. Information is available on posters on buildings on campus, BERT's website www.bert.siu.edu, Department of Safety's website www.dps.siu.edu and in the Emergency Response Guideline pamphlet. Know how to respond to each type of emergency.

          Instructors will provide guidance and direction to students in the classroom in the event of an emergency affecting your location. It is important that you follow these instructions and stay with your instructor during an evacuation or sheltering emergency. BERT will provide assistance to your instructor in evacuating the building or sheltering within the facility.

 

 

 

HOMEWORK:

1.     p. 487) 2, 6, 12, 18, 22, 26         p. 499) 20, 22, 26, 36

2.     p. 516) 4, 38, 40, 42, 44, 46, 48, 50         p. 532) 22, 48

3.     p. 549) 8, 10, 12, 20, 22, 24, 26, 30, 64, 76

4.     p. 566) 2, 8, 18, 20, 22, 24, 34, 36, 38, 40

5.     p. 595) 28, 52, 56       p. 603) 14, 20          p. 611) 8, 9, 10, 12, 18

6.     p. 623) 2, 38, 40, 56       p. 636) 2, 11, 14, 30, 32, 34

7.     p. 660) 4, 6, 8, 24, 27     p. 670) 6, 14, 18, 27, 28

8.     p. 683) 16, 34, 52, 56, 62      p. 695) 16, 40, 60, 63, 64

9.     p. 703) 25, 26, 36     p. 716) 2, 10, 12, 14, 46a, 54, 64

10. p. 839) 20, 26    p. 849) 32, 44    p. 859) 8, 26     p. 870) 10, 14, 20, 24

FINAL: Tuesday (December 13) 10:10 AM – 12:10 PM

 

In: Lindegren 133

Rows J – O, R

Even numbered seats

 

Optional review on the weekend before the final:

          Saturday, December 10, 1 – 3 PM in Neckers 218

          Sunday, December 11, 2 – 4 PM in Neckers 218