Department of Mathematics
University of Georgia
Athens, GA 30602
Fax: (706) 542-5907
Office: 444 Boyd Graduate Studies
Tuesday 3:15–4:45 (3510 only)
Thursday 11:00–12:15 [except 1/17 and 4/11], 2:00–3:00
Friday 9:00–10:00, 1:30–2:30
or by appointment
I'm Professor of Mathematics at . I have just completed my eight-year term as Associate Head of the Mathematics Department. I have just received the Franklin College Outstanding Academic Advising Award for 2012. I received the Lothar Tresp Outstanding Honors Professor Award in 2002 and 2010, as well as the Honoratus Medal in 1992. I was one of five recipients of the 1997 Josiah Meigs Award for Excellence in Teaching at The University of Georgia. I was the 2000 winner of the Award for Distinguished College or University Teaching of Mathematics, Southeast section, presented by the Mathematical Association of America. My research interests are in differential geometry and complex algebraic geometry. You may consult my current Vita and Publication List and contact me by email if you'd like any preprints or reprints.
If you'd like to see the "text" of my talk at the MAA Southeastern Section meeting, March 30, 2001, entitled Tidbits of Geometry Through the Ages, you may download a .pdf file.
I am the Honors adviser for students majoring in Mathematics at The University of Georgia. I also advise Honors freshmen and sophomores majoring in Computer Science, Physics, Physics & Astronomy, and Statistics. If you would like to see how the Honors Program at The University of Georgia has recently garnered national attention, you might try the cover story of the September 16, 1996 issue of U.S. News & World Report, p. 109. (I have a personal stake in this, of course.)
Long ago, I wrote a senior-level mathematics text, Abstract Algebra: A Geometric Approach, published by Prentice Hall (now Pearson) in 1996. You might want to refer to the list of typos and emendations. Please email me if you find other errors or have any comments or suggestions.
Malcolm Adams and
I recently completed the second
edition of our linear algebra text, Linear
Geometric Approach, published by W.H. Freeman in 2011.
Our approach puts greater emphasis on both geometry and proof
techniques than most books currently available; somewhat novel is
a discussion of the mathematics of computer graphics. As we find
out about them, we will be maintaining a list
of errata and typos.
My textbook Multivariable
Linear Algebra, Multivariable Calculus, and Manifolds
was published by J. Wiley & Sons in 2004. The text integrates
the linear algebra and calculus material, emphasizing the theme of
implicit versus explicit. It includes proofs and
all the theory of the calculus without giving short shrift to
computations and physical applications. There is, as always, the
errata and typos; please email me if you have any
comments or have discovered any errors. Click here
if you want a list of errata in the solutions manual.
I have written some informal class notes for MATH 4250/6250, Differential
Course in Curves and Surfaces. They are available in
.pdf format, and, as usual, comments and suggestions are always
welcome. If you're interested in using them as a class text,
please contact me beforehand for permission. I have recently
revised the notes.
I teach a wide variety of undergraduate and graduate courses, but particularly enjoy teaching:
This is an integrated year-long
course in multivariable calculus and linear algebra. It is now a 4-hour course.
It includes all the material in MATH 2270/2500 and MATH 3000,
along with additional applications and theoretical material.
There is greater emphasis on proofs, and the pace is quick.
Typically the class consists of a blend of sophomores (some of
whom have had MATH 2400(H)–2410(H), others of whom have had MATH
2260 or 2310H and MATH 3200) and freshmen who've earned a 5 on the AP Calculus BC
exam. The text is my book, Multivariable Mathematics:
Linear Algebra, Multivariable Calculus, and Manifolds.
Students who are unsure about what
math class to take should contact me during the summer. Some
students who would like to take MATH 3500(H) but aren't sure
whether they will like it should give it a shot; if your
schedule allows it, we can do a "section change" to MATH 2270
even after two or three weeks. Students who feel like they need
more confidence in writing proofs should consider taking MATH
3200 concurrently in
the fall semester. So far as grades are concerned, students who
master the computational content of the course (the standard
3000 and 2270 material) ordinarily earn at least a B.
Students who would like some
guidance in reading and writing proofs might want to look at a
wonderful new book called How
to Think Like a Mathematician: A Companion to Undergraduate
Mathematics, by Kevin Houston, Cambridge University
Press, 2009. You can get it used for under $25.
MATH 8260 (Riemannian Geometry) — FALL MWF 9:05–9:55
MATH 4250/6250 (Differential Geometry) — SPRING TBAWe will cover standard material on Riemannian manifolds (starting with a "review" of curves and surfaces in R3), the basics of the Levi-Civita connection, geodesics, geodesic polar coordinates, submanifolds and the Gauss and Codazzi equations, and the Cartan-Hadamard Theorem. We will incorporate a moving-frames approach along with the standard covariant derivative approach. There will be some general discussion of connections on vector bundles, homogeneous spaces, and symmetric spaces. Depending on the interests of the clientele, we can cover some complex manifold theory or Gauss-Bonnet and Chern classes via differential forms.
This is an undergraduate introduction to curves and surfaces in R3, with prerequisites of either MATH 2270 (2500) and MATH 3000 or MATH 3510(H). The course is a study of curvature and its implications. The course begins with a study of curves, focusing on the local theory with the Frenet frame, and culminating in some global results on total curvature. We move on to the local theory of surfaces (including Gauss's amazing result that there's no way to map the earth faithfully on a piece of paper) and heading to the Gauss-Bonnet Theorem, which relates total curvature of a surface to its topology (Euler characteristic). As time permits, we'll discuss either hyperbolic geometry or surfaces of constant mean curvature at the end of the course.
Mathematica Primer Once you have Mathematica on your computer, this should open in Mathematica; if for some reason it doesn't, copy and paste it into a Mathematica notebook.
Michael Spivak's brand-new text on Mechanics (the book is now in print for $90 at Amazon!)
Because of rampant paranoia on the part of the UGA administration, I am "obliged" to add the following disclaimer:
The content and opinions expressed on this webpage do not necessarily reflect the views of nor are they endorsed by the University of Georgia or the University System of Georgia.