Theodore Shifrin's Home Page

I'm Professor of Mathematics at

. I am now the Associate Head of the Mathematics Department. 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 just completed the second edition of our linear algebra text, Linear Algebra: A 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 Mathematics: 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 obligatory list of 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 Geometry: A First 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.

CLASS WEB PAGES

I teach a wide variety of undergraduate and graduate courses, but particularly enjoy teaching:

MATH 3500(H)–3510(H) ([Honors] Multivariable Mathematics) — MWF 11:15–12:05

This is an integrated year-long course in multivariable calculus and linear algebra. It includes all the material in MATH 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 recent 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 2500 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 2500 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.

Fall semester: MATH 4220/6220 (Differential Topology) — MWF 9:05–9:55

This is an advanced undergraduate/beginning graduate course centered around the application of multivariable calculus (the derivative, inverse and implicit function function theorems, and, ultimately, the change of variables theorem in multiple integrals) to the study of the topology of differentiable manifolds in Rⁿ. The key concept in the course is that of intersection number, with its cousins degree and winding number (which gives the generalization of the intermediate value theorem to higher dimensions). Interesting—and powerful—applications include the Brouwer Fixed Point Theorem, the Jordan Separation Theorem, the Borsuk-Ulam Theorem (not usually proved until an algebraic topology course covering the ring structure of the cohomology of projective space), and the Degree Theorem (relating degree and integrals).

The text for the course will be Guillemin and Pollack's Differential Topology (reissued by AMS Chelsea Publishing, sadly, with none of the typos corrected). Prerequisites for the course: some multivariable analysis (e.g., MATH 3500–3510 or MATH 4120/6120) and some familiarity with basic topology, particularly connectedness and compactness (although I will fill in gaps as needed). John Milnor's Topology from the Differential Viewpoint, originally the inspiration for Guillemin's book, makes a beautiful accompaniment.

MATH LINKS

FAVORITE NON-MATH LINKS

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.

Monday	10-11
Tuesday	11-12, 3-4
Wednesday
Thursday	1-2 [except 4/12]
Friday	10-11, 1-2