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

Math 425: Introduction to Number Theory


 

Days

Time

 Room   

Section

M W F

3

EGRA 322

1

 


 
 

 
   


  

 

Syllabus

Office: Neckers 379

Hours:  M W F 1 - 3

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 Chapters 2,5,6 ):                            Wednesday, September 17
Second exam (covers Chapters 10,11):                        Wednesday, October 22

    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:   An Introduction to the Theory of Numbers (5th edition) by G.H. Hardy and E.M. Wright

Topics: Chapters 2,5,6,10,11,16,17

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:   December 12, 3:10 – 5:10 PM, Eng A 322

 Back to the top of the Math 425 page

Homework
Homework #1

Homework #2

Homework #3

Homework #4

Homework #5

Homework #6

Homework #7

Homework #8

Homework #9             plus     TEX file for Homework #9

Homework #10           plus     TEX file for Homework #10

Homework #11           plus     TEX file for Homework #11

 




 
 
 

Math 150: Calculus I

 

 

Section 

Day

Time

Room

6

MWRF

2

EGR D 132 


 

Syllabus

Office: 379 Neckers

Hours:  MWF 12 - 2

WORK : 1. The class meets for an extra hour on Monday, Wednesday and Thursday. Most of these extra periods will be spent on worksheets (see #2), working in groups. The extra periods before an exam will be spent on (ungraded) practice exams. You must attend the lecture to be able to attend the extra period.

 

          2. There will be 33 worksheets, each worth 5 points. I will drop the three lowest scores, for a total of 150 points possible. (Note: for simplicity, the worksheets will be graded out of 20 points. At the end of the year I will divide the total worksheet scores by four).

 

          3. Four exams in class, worth 100 points each.

First exam (covers Chapter 1, sections 2.1-2.2):                 Friday, January 30

Second exam (covers sections 2.3-2.8, 3.1-3.3, 3.5-3.6):    Friday, February 27

Third exam (covers Chapter 4, sections 5.1-5.4):               Friday, April 3

Fourth exam (covers sections 5.5, 7.1-7.3, 7.5):                 Friday, April 24

 

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

 

 

 

GRADING:  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 70-79,  D 60-69.

 

 

 

TEXT:  Essential Calculus   by James Stewart

 

 

 

 

 

 

 

 

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 worksheets.

 

 

TOPICS :     Chapters 1 – 5 and 7. We omit sections 3.4, 3.7, 7.6.

 

 

 

MAKE-UPS : There will be no make-ups on the worksheets. Make-ups on the exams require a doctor's note.

 

 

 

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.

 

 


 Final Exam:  
 

Exam solutions