Theodore ShifrinDepartment of MathematicsUniversity of GeorgiaAthens, GA 30602(706) 542-2556Fax:(706) 542-5907Email:shifrin@math.uga.eduOffice:444 Boyd Graduate StudiesOffice hours: no more ...

I'm Professor Emeritus of Mathematics
at . 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.

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
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:

- MATH 2400(H)-2410(H) ([Honors] Calculus with Theory)
- MATH 2500 (Multivariable Calculus)
- MATH 3000 (Linear Algebra)
- MATH 3500(H)-3510(H) ([Honors] Multivariable Mathematics)
- MATH 4000-4010 (Modern Algebra and Geometry)
- MATH 4220 (Differential Topology)
- MATH 4250 (Differential Geometry)
- MATH 8150-8160 (Complex Variables—graduate version)
- MATH 8250-8260 (Differential Geometry—graduate version)

During 2014–2015, my last year teaching at UGA, I taught:

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.

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'sProbabilityis a good reference.

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

This is an undergraduate introduction to curves and surfaces in

R^{3}, 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:

MATH 3500(H)–3510(H)([Honors] Multivariable Mathematics) — MWF 11:15–12:05, T 11:00–12:15

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

R^{3}), 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.

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 ClubJob Opportunities for Mathematics Majors

Alumni QuestionnaireMichael 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.*