Michael Joyce

New Orleans, LA

math.tulane.edu/~mjoyce3

Age: 37

I am interested in algebraic combinatorics, especially in the combinatorics of orbits of a Borel subgroup on spherical varieties.
Apr
23
comment Blow-up toric varieties.
I think your suggestions are great, but, at least for #1, it may be better to start with affine space rather than projective space, depending on the sophistication level of the audience.
Apr
22
revised Linear Algebra Proof confirmation
edited title
Apr
20
revised Bourbaki - Algebra Chapter IV - Section 6, Exercise 9(b)
fixed LaTex formatting
Apr
17
comment What is a fair way of constructing exams with tiered levels of difficulty?
Are they only to do a total of 6 out of the 18 problems in your example test?
Apr
14
comment books well-motivated with explicit examples
There is also Silverman and Tate's "Rational Points on Elliptic Curves" which is even more explicit and introduces the subject to undergraduate students.
Apr
13
revised Understanding Faltings's Theorem
corrected the title of Hindry and Silverman's text, in case the OP wants to consult it
Apr
6
revised Why study schemes?
added 3 characters in body
Mar
16
comment How can you be perfect at maths (highschool)?
Great answer. I especially liked this part: "You will make mistakes and you will forget things. We all do. If you want to make yourself good, try to make yourself robust ‐ so that if you forget something, you can reconstruct it based on something else, and if you make a mistake, you can recognize it yourself."
Mar
16
comment Pi or Tau? How should the circle constant be taught?
Another possible compromise: replace the two fundamental constants $e$ and ($\pi$ or $\tau$) with $\pi + e$ and $\tau - e$. The small cost of complete and utter confusion for students is but a small price to pay.
Mar
1
revised Material in a first course in algebraic geometry?
added 3 characters in body
Feb
25
comment How to evaluate $\int_0^1 \frac{\sqrt x}{1+x} dx$?
Hint: $\frac{u^2}{1 + u^2} = \frac{1 + u^2}{1 + u^2} - \frac{1}{1 + u^2}$.
Feb
18
answered Trouble understanding Eisenbud Exercise 2.19a
Feb
6
revised Good ways of explaining the idea of epsilon-delta limits to bio & chem majors?
added 220 characters in body
Feb
6
comment How to create a misuse of calculator!
That's an interesting historical fact that $-25$ was one vote away from being equal to $(-5)^2$. Sounds like it must have been a hotly contested election! :)
Feb
6
answered Good ways of explaining the idea of epsilon-delta limits to bio & chem majors?
Jan
23
comment Combinatorics using a geometric diagram
I assume that in each step you have to move a given row to the row below it? There are multiple ways to interpret what a path is, as written.
Jan
23
comment Proving that $(u+v)×w=u×w+v×w$
If you don't know the number of dimensions, how do you expect us to know the number of dimensions? This sounds like a question of clarification that you should ask your instructor. (That said, the cross product is normally only defined for vectors in $\mathbb{R}^3$, so that's probably a pretty safe assumption. If you don't know the definition of cross product in $\mathbb{R}^3$, you'll surely need to look it up to construct a proof.)
Jan
22
comment Proving that $(u+v)×w=u×w+v×w$
How about writing out the components of the vectors $\vec{u}, \vec{v}, \vec{w}$ and computing each side?
Jan
21
answered Why does eliminating from linear equations work but adding them does not?
Jan
16
revised How to find critical points of the following polynomial?
fixed numerous grammatical and spelling errors
1 2 3 4 5