Ph.D., Univ. of Illinois, Urbana, 1969 (Advisor: J. Rotman)
M.A., Western Washington State, 1965
Dr. Arnold joined the Baylor faculty as the Ralph and Jean Storm Professor of Mathematics in the fall of 1990. Previously, he served as post-doctoral fellow and professor of mathematics at New Mexico State University. In addition, he has been a visiting professor of mathematics and taught classes andseminars at the University of Washington, University of Connecticut, University of Essen (Germany), and Florida Atlantic University.
Academic Interests and Research:
Dr. Arnold's research is in abelian groups, especially torsion-free abelian groups, and related topics in algebra, such as modules over discrete valuation rings, orders, and pullback rings and representations of finite partially ordered sets.
Selected Research Articles:
"Locally free abelian groups of finite rank," Contributions to Module Theory: In Memory of A.L.S. Corner, de Gruyter Press, 2008.
"Subgroups of finite direct sums of Z[1/n]," Houston J. Math., 2008.
"Pi-balanced torsion-free modules over a discrete valuation ring," joint with K.M. Rangaswamy and F. Richman, J. Algebra 295 (2006), no. 1, 269-288.
"Representations of finite partially ordered sets over commutative artinian uniserial rings," joint with Daniel Simson, J. Pure and Appl. Alg. 205 (2006), 640-659.
"Endo-wild representation type and generic representations of finite posets," joint with Daniel Simson, Pacific J. Math. 219 (2005), 101-126.
"Direct sums of local torsion-free abelian groups," Proc. A.M.S. 130 (2002), 1611-1617.
Finite Rank Torsion-free Abelian Groups and Rings, Lecture Notes in Mathematics 931, Springer-Verlag, New York, 1982, 191 pp.
Abelian Groups and Representations of Partially Ordered Sets, CMS Advanced Books in Mathematics, Springer-Verlag, New York, 2000, 244 pp.
- Randy Walters, Torsion free reflexive modules of finite rank, 1975
- Ulrich Albrecht, Ideal conditions in endomorphism rings, 1982
- Joerg Stelzer, Ring theoretical criteria for cancellation, 1983
- Wu-Yen Lee, Co-representing graphs for a class of torsion-free abelian groups, 1986
- External examiner for Anya Elter, Univ.of Essen, Germany, 1996
Grants and Fellowships::
- NSF Graduate Fellowship, Univ. of Illinois, 1967-68
- NSF Summer Research Grants, 1974-1986 (inclusive), 1988-1989, 1991-1992,
- 1994-95 (a total of 18 summers of NSF grant support)
- Study visit grant, Deutscher Akademischer Austauschdienst, Germany, summer, 1983
- German-Israeli Foundation Grant, Germany, spring/summer, 1996
- Meri Hughes, Reed-Solomon Codes, 1995
- David Lauer, Convolutional Codes, 1995
- Rebekah Hahn, Representations of Partially Ordered Sets, 1997
- Amy Tieman, Generalized Interval Systems, 1998
- Matt Shelton, Rijndael:The Advanced Encryption System, 2002
Algebra at all levels, both pure and applied. Undergraduate discrete mathematics including coding theory, cryptography, and mathematics for computer science. Mathematics for liberal arts students, including original sources.
Courses taught at Baylor:
- MTH 1301 – Ideas in Mathematics
- MTH 1302 – College Algebra for Psychology Majors
- MTH 1304 - Pre-Calculus
- MTH 1308 – Business Pre-Calculus
- MTH 1309 – Business Calculus
- MTH 1310 – Discrete Mathematics for Computer Science Majors
- MTH 1321 - Calculus I
- MTH 2311 – Linear Algebra
- MTH 3312 – Foundations of Combinatorics and Algebra
- MTH 4312 – Cryptology
- MTH 4313 – Number Theory
- MTH 4316 – Linear Algebra/Matrix Theory
- MTH 4329 – Complex Variable
- MTH 4V90 – Algebraic Coding Theory
- MTH 5V91 – Algebraic Coding Theory
- MTH 5V91 – Number Theory
- MTH 5310/5311 – Graduate Algebra I and II
- MTH 6V13 – Homological Algebra
- MTH 6V13 – Cryptology