# David Lantz

I study commutative algebra. Much of my work has been joint with Prof. William Heinzer of Purdue University. Together we have studied many kinds of rings (all commutative with unity) that are not quite Noetherian: Laskerian rings, Artinian rings, rings with the ascending chain condition on ideals generated by a fixed number of elements, rings with the ascending chain condition on colon ideals, etc. More recently we have focused on regular local domains (which of course are very Noetherian) and a class of ideals primary for the maximal ideal. We called this class "first coefficient ideals", because they are maximal among those having the same first two coefficients in the Hilbert polynomial. We frequently used the computer algebra system MACAULAY in our study of this class of ideals.

I have taught many of the mathematics courses offered at Colgate; my favorites are both semesters of abstract algebra (especially the second, on Galois theory), geometry and combinatorics. I have used a computer algebra system in several courses, especially in applied mathematics for the social sciences.

I should also mention two more elementary projects in which I have participated: I assisted in the translation of an approximate solution by Casanova (yes, that Casanova) on the Delian Problem ("Construct with straightedge and compass a cube with exactly twice the volume of a given cube"). And an exposition that I wrote for distribution to one of my classes, on why it is impossible to cut a cube into a finite number of polyhedral pieces and reassemble them into a regular tetrahedron, was later published in the South African recreational journal Wistukkie.

My wife Clara and I are very interested in drama, from both sides of the footlights.

Here is a link to the .pdf file of the transparencies I used for the Gehman lecture at the Mathematical Association of America Seaway Section meeting at Queen's University in Kingston, Ontario, on April 1-2, 2005.

Here are links to the web pages of some of the courses I've taught:

• Math 102 /Core 143 : Introduction to Statistics -- based on Freedman, Pisani and Purves, Statistics, Fourth Edition. I am one of several instructors, past and present, who have contributed to the substantial web component of this course. We are proud of the course.
• Math 111 : Calculus I and Math 112 : Calculus II -- based on James Stewart's Single Variable Calculus, Early Transcendentals, Fourth Edition. (For Calc II, Fifth Edition.)
• Math 213: Multivariate Calculus -- based on William G. McCallum et al., Multivariable Calculus.
• Math 320 : Abstract Algebra I -- based on Saracino, Abstract Algebra: A First Course. I supplied a substantial number of graphics; they are linked to this page, and my assignments appear here.
• Math 323 : Real Analysis I -- based on Abbott, Understanding Analysis. Not a "webby" course, at least as I taught it, but you are welcome to look at my assignments and the few graphics linked to this page.
• Math 421 : Abstract Algebra II (Galois theory) -- this is the 37-page "text", in .pdf format, that I wrote for a course on Galois theory using the "Moore method" of teaching mathematics, i.e., a list of definitions, theorems, and discussions, with most of the proofs omitted so that students can be asked to supply them. Michael Weiner, now at Penn State University, Altoona campus, taught the course, using this "text". My sense is that it went well, but I don't have any pedagogical suggestions to make to anyone else who might want to try it. I should note that my colleague Dan Saracino, on whose book this "text" is based, has expanded his book in a second edition to include Galois theory; it should appear shortly.
From the Math Dept's "junior" seminar (now replaced by Math 399):

I much enjoyed the play The Discovery of the Calculus: The Battle Between Wilhelm Leibniz and Isaac Newton, written by H. W. Straley, Charlene B. Straley, and F. A. "Chip" Straley, of Woodberry Forest School, Woodberry Forest, VA. To make the play more available, I have digitized the script and images provided by the Straleys (with their kind permission) and arranged them in several file formats. Here is the index to these files: The Discovery of the Calculus

### Selected Publications:

• (with William Heinzer) Factorization of monic polynomials, Proceedings of the American Mathematical Society, 131(4) (2003), 1049-1052.
• Example of an interpolation domain, Journal of Pure and Applied Algebra, 174 (2002), 149-152.
• (with William Heinzer and Roger Wiegand) Residue fields of a zero-dimensional ring, Journal of Pure and Applied Algebra, 129 (1998), 67-85.
• (with William Heinzer) Ideal theory in two-dimensional regular local domains and birational extensions, Communications in Algebra 23(8) (1995), 2863-2880.
• (with William Heinzer and Sylvia Wiegand) Prime ideals in birational extensions of polynomial rings, Contemporary Mathematics 159 (1994), 73-93.
• (with William Heinzer) ACCP in polynomial rings: a counterexample, Proceedings of the American Mathematical Society 121 (1994), 975-977.
• (with Robert Gilmer and William Heinzer) The Noetherian property in rings of integer-valued polynomials, Transactions of the American Mathematical Society 338 (1993), 187-199.
• (with William Heinzer) Exceptional prime divisors of two-dimensional local domains, in Commutative Algebra: Proceedings of a Microprogram Held June 15 - July 2, 1987 M. Hochster, C. Huneke and J. D. Sally, eds., Springer-Verlag, New York, 1989.
• Finite Krull dimension, complete integral closure and GCD-domains, Communications in Algebra 3(10) (1975), 951-958.

David Lantz
Mathematics Department
Colgate University
13 Oak Drive
Hamilton NY 13346-1398
email: dlantz@mail.colgate.edu
phone: 315-228-7737
fax: 315-228-7004

http://math.colgate.edu/faculty/dlantz.html
Revised: July 9, 2008.