Director of the Center
(This page is like a cathedral: always under reconstruction ;-)
Speaking of photos: here's a link to Rob's class photos.
Current
This spring Rob is teaching honors Differential
Geometry of Curves & Surfaces (Math 563H).
Here is the (quick-loading, even on a slow connection) ASCII file for Math 563H (Curves
and Surfaces) topics & problems .
Rob is also serving as course chair for, and teaching (a double)
section 3 of Introduction
to Linear Algebra (Math 235).
Here is the (again, ASCII) Math 235 (Linear
Algebra) homework schedule for Rob's section.
WebWorK for Spring 2013 will be working soon, but occasionally you'll find a bug! If you're sure that
you've figured out a problem, but WebWorK won't swallow your answer, please
don't waste excessive time guessing and plugging -- each problem is "worth" so little anyway -- and better if you've developed the skill and confidence to KNOW you've found a real bug, and not just made a silly mistake: such is life!
Here's a temporary link to Spring 2012 Math 235 WeBWorK.
The last part of the Spring 2012 linear algebra course used a matrix E whose columns
form a basis of eigenvectors for a matrix A with distinct real
eigenvectors to factor A=EDE^{-1} where D is diagonal (and to compute powers
and the exponential of A). Understanding how to decompose a 2x2 matrix
with complex conjugate eigenvalues (a+bi and a-bi) into aI+bJ where
J^2=-I (or into aI+N where N^2=0 when there is a repeated real
eigenvalue a) to compute powers (and the exponential) of this 2x2
matrix is also good idea to learn. (This approach, suggested by
Prof. Rudvalis, seemed simpler than the approach using complex
eigenvectors discussed in the textbook.)
As in the past, instructors will follow these Math 235
(Linear Algebra) common guidelines.
Math 235 exam and review info:
The Math 235 FINAL EXAM is MAY ? ???DAY ???-??? in ?????? ???.
MAKE-UPS (only pre-approved) on ???day will be arranged privately. As
usual, you may bring a 2-sided, 8.5x11" sheet of notes (in your own
handwriting, please) - no calculators, cell-phones or other devices
(besides a pen or pencil and your brain ;-) are permitted.
Final REVIEW on ?? April ???
***** PRE-MIDTERM REVIEW SESSION with Prof. ??? ?????? *****
********** day ? March 2013 from 6-8pm **********
********** ???? ***********
*** JOINT MIDTERM EXAM ***
********** sday ? March 2013 at 7pm **********
********** ???? ***********
[Please continue to watch here for important developments and announcements!]
!!!!!!!!!!!!!!!!!!MATH NEWSFLASHES!!!!!!!!!!!!!!!!
For you hardcore linear algebraists: the usual multiplication algorithm has complexity O(n^3) for n x n matrices; here's a recent paper on the latest complexity bound: O(n^2.3726...)! (Conjecture: O(n^2) is best.)
And for you W-rated differential geometers: the Willmore conjecture
has been resolved! This is one of what the late Bob Osserman referred
to (in his early 1980s Berkeley Colloquium Lecture) as "Three Obdurate
Conjectures in Differential Geometry" and concerns the total bending
energy W of a closed surface in 3-space. The round sphere achieves the
absolute minimum W=4\pi and it's been known since work of Leon Simon
from the 1980s that for higher genus surfaces the absolute minimum is
strictly greater; indeed Willmore conjectured in
the 1960s that W is at least the area 2\pi^2 of the Clifford minimal
torus in the 3-sphere, and this is what Fernando Coda Marques and
Andre Neves have proven. I've done some work on this problem
myself over the years and believe their methods might help resolve a
related conjecture of mine for closed surfaces in n-space: W exceeds
6\pi for any surface not diffeomorphic to the 2-sphere, with equality
if and only if the surface is a Veronese minimal projective-plane in
the 4-sphere.
Recent
Rob was on leave at the Isaac Newton Institute for Mathematical Sciences
for the Fall 2012 semester.
During Spring 2012, Rob is taught honors Differential
Geometry of Curves & Surfaces (Math 563H).
Here is the Spring 2012 ASCII file for Math 563H (Curves
and Surfaces) topics & problems .
Rob also served as course chair for, and taught both (a double) section 4 and (a single) section 7 of Introduction
to Linear Algebra (Math 235) in Spring 2012.
This wass the Math 235 (Linear
Algebra) homework schedule for Rob's sections.
Here are notes on
Inner Products,
Gram-Schmidt and Ortho'matrices by Jenn Koonz (who gave a few lectures
when Rob was in Germany at the end of March 2012) as well as notes on
Determinants and on
Eigenstuff by Arunas Rudvalis.
Here are links to Math 235 MiniMidtermII solutions (front) and (back) from Tuesday 17 April 2012.
And here are links to Math 235 Midterm solutions (page 1,
2,
3,
4,
5,
and 6)
from Wednesday 7 March 2012.
And links to Math 235 MiniMidtermI solutions (front) and (back) from Monday 13 February 2012.
In Fall 2011 Rob taught (a double) section 2 of Introduction
to Linear Algebra (Math 235), with links to:
Fall 2011 Math 235 (Linear
Algebra) homework schedule
Fall 2011 Math 235 Practice Final Problems
Scanned pages of Fall
Math 235 Common Midterm Solutions (find the sign error)!
Fall 2011 Math 235 Practice Midterm Problems.
And here (temporarily) is a link to the Fall 2011 Math 235 WeBWorK.
In Spring 2011, Rob taught the computational linear algebra (Math313/513-CS513) course while on
sabbatical at Penn, and last fall he taught -- you guessed it! -- Introduction
to Linear Algebra (Math 235) at UMass....
During Spring 2010, Rob taught honors Differential
Geometry of Curves & Surfaces (Math 563H) and a double section of
Linear Algebra (Math 235). Here is the ASCII file for Math 563H (Curves
and Surfaces) topics & problems . (Andrew Reiter and Nicky Reyes
are helping to TeX these now, so please stay tuned!)
Because he was the course chair during a semester when all the other
instructors were graduate students, he and the other instructors
established the following Math 235
(Linear Algebra) common guidelines, which may be useful to future
course chairs.
Here's a link to the Fall 2009 Math 235 Practice Midterm and to sketches of answers!
Here's a link to Fall 2009 Math 235 Midterm Answers.
And here is a link to last year's
Math 235 Practice Midterm.
Finally, here's the Fall 2009 Math 235 practice final , along with Peter Norman's handwritten answers , a link to an old Math 235 practice final and links to older Math 235 practice finals or even older
Math 235 practice finals, including one similar to our practice final with answers ....
Here are some
Quick
and Dirty Differential Equations notes prepared by Peter Norman
last fall (with a little help from me) for use in Math 235.
Older
During Spring 2009, Rob taught a special version of
Math 462
(Geometry and the Imagination) - please visit here for
the
Math 462 topics and comments! He also taught a (double) section of Math 235
(Linear Algebra).
In Fall 2008, Rob taught a double-section of Math 235 (Linear Algebra).
Rob was on sabbatical in Spring 2008, but he taught back-to-back sections
of Math 235 in Fall 2007 -- Linear Algebra is one of his favorite and most popular classes!
In Spring 2007 Rob taught Math 425
(Advanced Calculus) and a section of Math 235
(Linear Algebra). Here are links to the Math 425
(Advanced Calculus) homework schedule. Also,
please have a look at my colleague Roman Federov's
problems for enrichment and review.
Rob organized the undergraduate TAP seminar (Math 191) during the Fall
2006 semester. It met in GANG (LGRT 1535) at lunchtime most Mondays and some Wednesdays. The following people kindly
contributed to the
2006 TAP
Topics. Many thanks to all of you!
More
Watch here
for further developments.
Address
Phone 413 545 6022
Secretary 413 545 2812
Fax 413 545 1801
Electronic Mail kusner@math.umass.edu
Kusner's Math Classes
About the photo: Rob's hair is now a little greyer -- and a little
shorter -- in part because he was elected to the Amherst Select Board a few years ago (having also led a concerted and ultimately successful effort to
preserve Amherst Town Meeting in 2005 :-)!
In academic year 2006-07 Rob again planned to teach a
two-semester course on
Manifolds
(Math 703-4) for graduate students. Due to unforeseen and unfortunate
circumstances, Rob was not be able to offer Math 704 in the spring.
But here is where to find homework problems and informal notes for
that course:
Manifolds I (703) and
Manifolds II
(704), along with older notes from Fall 2002
(703),
Spring 2003 (704) and Spring 2000 (Math 704).
In the Spring 2006 semester Rob taught Advanced
Linear Algebra (Math 545) ; here are the updated problems/notes
for this course. (Please compare with Rob's Spring 2002 advanced linear
algebra problems/notes.)
Rob also pinch-hit all semester for Ordinary
Differential Equations (Math 331) in Spring 2006; here is the Math 331 general
topics list and the Math 331
homework schedule for Rob's section. (This was an ambitious
syllabus, covering more than the other sections did, and not without
some ill-tempered jeers from the bleachers in the final innings -- it
didn't help that Select Board meetings went on till after midnight on
many, many occasions before this early morning course ;)
In the Fall 2005 semester Rob taught
Introduction to Abstract Algebra (Math 411); here are the notes and
homework schedule .
In the Spring 2005 semester Rob was teaching an experimental
version of Geometry and the
Imagination. This was a very popular course, and Rob hopes to
have the opportunity to offer it again soon, perhaps in conjunction
with Math 563 (Differential Geometry of Curves and Surfaces)!
Rob was on sabbatical for 2003-04. During academic year 2002-03 Rob taught a two-semester course on
Manifolds (Math
703-4) for graduate students.
Here is where to find homework problems and notes from that course: Manifolds I (703) and
Manifolds II (704),
along with older notes from my Spring 2000 Math 704.
Rob has taught the basic graduate topology course several times, most recently in Fall 2000,
Click here for the postscript
or the
rawtext
version of the final Topology exam for Fall 2000.
And since this is Greek to me, here's a link to symbols like ε.
1435G Lederle Graduate Research Tower
Department of Mathematics
University of Massachusetts at Amherst
Amherst MA 01003
USA
All material on this website is Copyleft* by Rob Kusner.
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