Michael Joyce

New Orleans, LA

math.tulane.edu/~mjoyce3

Age: 38

I am interested in algebraic combinatorics, especially in the combinatorics of orbits of a Borel subgroup on spherical varieties.
Apr
19
comment How to promote more elegant and beautiful proofs by students?
It takes a long time to develop elegance and beauty in crafting proofs. I think most students need to focus heavily on understanding how to construct rigorous and logically sound proofs, as well as how to formulate useful proof strategies. I would recommend that you include some remarks on elegance in proof writing in class through some well-motivated examples and address elegance/efficiency when appropriate when giving feedback on assignments. But elegance is not something that one can reasonably demand for students who are not fairly strong grad students (or on their way toward that point).
Apr
15
comment Prove that the limit of the line integral is 0.
What branch of the logarithm are you using?
Apr
13
comment Basis for the range and nullspace of the following $T$
Notice that $T(1) = (1,1,1)$, $T(x^2) = (1,4,9)$ and $T(x^3) = (1,8,27)$, so none of the vectors in your purported basis of the null space actually belongs to the null space.
Apr
7
comment Why is the convergence of infinite series covered in Calculus II?
Short answer: inertia.
Apr
7
comment Complex Analysis: why does $\cos(3\theta)$ = $\cos^3\theta - 3\cos\theta \sin^2\theta$.
Many trigonometric identities, including this one, can be derived from exploiting $e^{in\theta} = (e^{i\theta})^n$.
Apr
5
comment Comments on my approach to Group Theory notes?
Motivation is very important. I would suggest including a lot of it. Also, group operations are traditionally written multiplicatively rather than additively if they are not assumed abelian.
Mar
27
awarded Nice Answer
Mar
18
revised How to effectively internalize math?
fixed broken link
Mar
4
revised Matrix computation of products
added 24 characters in body
Feb
26
awarded Electorate
Feb
26
revised Why the image of quadratic Veronese map has the form $v\cdot v$?
added 99 characters in body
Feb
26
awarded Informed
Feb
26
answered Why the image of quadratic Veronese map has the form $v\cdot v$?
Feb
25
reviewed Close system of linear equations in a basic model
Feb
25
reviewed Leave Open How can we prove $\mathbb{Q}(\sqrt 2, \sqrt 3, ..... , \sqrt n ) = \mathbb{Q}(\sqrt 2 + \sqrt 3 + .... + \sqrt n )$
Feb
24
revised Given matrix $A$, a basis for $\mathbb{R}^n$, a subset of which of is a basis for Nul($A$) spans Col($A$)
added 27 characters in body; edited title
Feb
23
awarded Vox Populi
Feb
23
awarded Suffrage
Feb
23
comment If $f(3x)=f(x)+f(3)$, prove that
Hint: Try $x =0$.
Feb
23
awarded Enlightened
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