Allan Donsig's Home Page

Allan Donsig
Associate Professor
Department of Mathematics
University of Nebraska--Lincoln

Office: Avery 307

Office Phone: 402-472-8128

Dept. Phone: 402-472-3731

Dept. Fax: 402-472-8466

E-mail: adonsig1 at unl dot edu (Forgive the non-machine readable address)

preliminary schedule

Office Hours: by appointment

Teaching

Fall 2007: Math 496/896-004 Multivariate Analysis
Spring 2007: Math 106-150 Analytic Geometry and Calculus I; Math 826 Mathematical Analysis II
Fall 2007: Math 104-004 Calculus for Managerial and Social Sciences; Math 825 Mathematical Analysis I
Second Summer Session 2007: Math 221-601 Differential Equations
Spring 2007: Math 107-250 and Math 107-350 Analytic Geometry and Calculus II
Fall 2006: Math 106-350 and Math 106-550 Analytic Geometry and Calculus I

Useful webpages for Mathematics Students

The Most Common Errors In Undergraduate Mathematics
Excerpts from How to Ace Calculus : The Streetwise Guide
HOW DO UNDERGRADUATES DO MATHEMATICS? A guide to studying mathematics at Oxford University Although this study guide is focused on Oxford, much of its advice is relevant (indeed, crucial) to anyone learning mathematics.
A Guide to Writing in Mathematics Classes
If you ever find yourself preparing an abstract or a summary of your own research, you should read How to get your abstract rejected. Heck, read it anyway, it's quite funny and you've probably seen all of the sins it outlines committed in the course texts you've had to read.

My research interests are in operator algebra and operator theory. In particular, most of my papers are about limit algebras, infinite-dimensional operator algebras that are limits of finite-dimensional algebras. In spite of being "almost finite-dimensional", they have some quite suprising properties.

I've put more information, including abstracts of my papers, on a separate page.

Conferences/Events I Help Organize

Operator Algebras Seminar here at UNL.
Nebraska-Iowa Functional Analysis Seminar a local semi-annual conference in functional analysis.
Nebraska Conference for Undergraduate Women in Mathematics
Conferences/Events I Helped Organize
- Nebraska IMMERSE This is a summer program for students starting graduate school in the fall.
Recent Progress in Operator Algebras, a Special Session at the Lincoln, NE meeting of the American Mathematical Society, which I am organizing jointly with David Pitts, also of UNL.
Coordinate Methods in Nonselfadjoint Operator Algebras, a workshop held December of 2003 at the Banff International Research Station for Mathematical Innovation and Discovery, which I organized jointly with Michael Lamoureux of the University of Calgary.

Real Analysis with Real Applications

Together with Kenneth R. Davidson of the University of Waterloo, I have written an introductory analysis textbook, called Real Analysis with Real Applications. The publisher, Prentice Hall, has a webpage for the book.

There is a pdf file available here containing the table of contents and the preface for the book.

There was a third printing of the book in June of 2005. We have lists of errata, one for errors found since the most recent printing and others for the errors fixed in the most recent printing or earlier.

Feel free to email us with comments on the book.

On a related note, I have a short list of articles and books that I've found useful in teaching analysis.

Pi Mu Epsilon

I am faculty advisor for the Nebraska Alpha chapter of Pi Mu Epsilon, a national honorary society dedicated to mathematics. Pi Mu Epsilon is a national honorary society dedicated to mathematics. The Nebraska Alpha chapter, founded in 1928, is restarting. In the past, the chapter has organized math contests, talks, and a variety of mathematical activities. Much of this is now done by the UNL math club, but the Nebraska Alpha chapter will contribute to mathematical scholarship at UNL by

recognizing students with exceptional accomplishments in mathematics,
organizing an inititation ceremony, and
other math related activities, as decided by the members.

If you are interested in becoming a member of the chapter, please fill out the application form. Requirements for membership are listed on the application form. There is a (lifetime) membership fee of $40, which you should pay with your application.

TeX, LaTeX, and AMS-LaTeX

These are typesetting programs that are defacto standards for mathematics and physics papers. The hardest part of getting started with them is finding good model documents to modify. In the absence of better models, I offer a few documents of my own, listed here. There are a multitude of good sites on TeX. I would particularly recommend the Comprehensive TeX Archive Network and the American Mathematical Society's page on TeX Resources.

There are two books I would particularly recommend:

LaTeX: A Document Preparation System by Leslie Lamport, Second Edition, Addison-Wesley, ISBN: 0-201-52983-1.
A Guide to LaTeX 2e by Helmut Kopka and Patrick W. Daly, Second Edition, Addison-Wesley, ISBN: 0-201-42777-X.

The first is the original user's manual by the author of LaTeX.

But what matters most to me, personally, is being able to communicate to others my sense of what mathematical research is all about--the quest for truth and the inner joy that comes from surrendering oneself to it. 1

Alain Connes, Fields Medalist in Operator Algebras