Theodore Shifrin

Shifrin pictureTheodore Shifrin
Department of Mathematics
University of Georgia
Athens, GA 30602
(706) 542-2556
Fax: (706) 542-5907
Office: 444 Boyd Graduate Studies
Office hours: no more ...

I'm Professor Emeritus of Mathematics at UGA emblem.  I 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.

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.
starI 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 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.

With gracious thanks to Patty Wagner, Eric Lybrand, Cameron Bjorklund, Justin Payan, and Cameron Zahedi, my lectures in Multivariable Mathematics (MATH 3500(H)–MATH 3510(H)) are available, for better or for worse, on YouTube. We are currently recording the first semester (covering through the basics of linear algebra and differential calculus); the second semester (covering integration, manifolds, and eigenvalues) is already posted.

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. I have recently revised the notes. If you're interested in using them as a class text, all I ask is that the students incur at most a copying fee. I am always happy to hear from people who have used the notes and have comments and suggestions to improve them.


I taught a wide variety of undergraduate and graduate courses, but particularly enjoyed teaching:

During 2014–2015, my last year teaching at UGA, I taught:
bullet MATH 3500(H)–3510(H) ([Honors] Multivariable Mathematics) — MWF 11:15–12:05, T 11:00–12:15

This is an integrated year-long course in multivariable calculus and linear algebra. 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.

bullet MATH 4600/6600 (Probability Theory) — FALL MWF 10:10–11:00

This is an introductory course in Probability Theory. The prerequisites are MATH 2260/3100 and MATH 2270/3510(H). We will cover standard topics, starting with the basics on permutations/combinations, sample spaces, conditional probability, random variables—discrete and continuous, expectation, and some beautiful results like the Law of Large Numbers and the Central Limit Theorem, which have real-life implications. The text will be Sheldon Ross's A First Course in Probability. Jim Pitman's Probability is a good reference.

bullet MATH 4250/6250 (Differential Geometry) — SPRING TR 9:30–10:45

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 calculus of variations at the end of the course.

During 2013–2014, I taught:
bullet MATH 3500(H)–3510(H) ([Honors] Multivariable Mathematics) — MWF 11:15–12:05, T 11:00–12:15
bullet MATH 8260 (Riemannian Geometry) — FALL MWF 9:05–9:55

We 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.

bullet MATH 4250/6250 (Differential Geometry) — SPRING TR 9:30–10:45


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.

Undergraduate Mathematics Information (including advice on majoring in mathematics, job opportunities)

UGA Math Club

Job Opportunities for Mathematics Majors

Alumni Questionnaire

Michael Spivak's brand-new text on Mechanics (the book is now in print for $90 at Amazon!)

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