# 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 productsadded 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 thatHint: Try $x =0$. Feb 23 awarded Enlightened