Michael Joyce

New Orleans, LA

math.tulane.edu/~mjoyce3

Age: 36

I am interested in algebraic combinatorics, especially in the combinatorics of orbits of a Borel subgroup on spherical varieties.
7h
comment Why do we bother with $u$-substitution?
The idea of $u$-substitution is to transform the problem into a simpler coordinate system where it is easier to identify the antiderivative. It is easier to recognize that the function $-\cos u$ is an anti-derivative of $\sin u$ than it is to recognize that $-\cos(x^2)$ is an anti-derivative of $2x \sin(x^2)$.
8h
answered Book recommendation for Linear algebra.
1d
answered Preparation for a graduate commutative algebra course based on Eisenbud
1d
revised Proving that the terms of the sequence $(nx-\lfloor nx \rfloor)$ is dense in $[0,1]$.
Fixed LaTeX formatting
1d
answered 1995 MathCounts State Team #8
2d
comment What is wrong with my contradiction?
A way to think about induction is that it proves infinitely many finite cases. Induction proves statements of the form "For all $n \in \mathbb{N}$, Proposition $P_n$ is true." For example, it proves that an integral of any finite sum of $n$ integrable functions is equal to the finite sum of the integrals of each function; there are infinitely many statements proven (one for each $n$), but not one of the statements involves an infinite sum.
2d
comment What is wrong with my contradiction?
The very example you are studying is one illustration why the additive property of integrals fails for infinite decompositions. Here, in some sense $F(x) = \sum_{q \in \mathbb{Q}} f_q(x)$ where $f_q(x) = 1$ if $x = q$ and $= 0$ otherwise. (The 'in some sense' comment is that you need to define what you mean by an infinite sum of functions, but this can be done rigorously.) Then $\int_a^b \sum_{q \in \mathbb{Q}} f_q(x) \, dx$ does not exist, even though $\sum_{q \in \mathbb{Q}} \int_a^b f_q(x) \, dx = 0$ does. +1 btw for explaining your thought process well in your question.
2d
answered How does this series diverge?
2d
revised What is the nature of this surface?
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2d
answered What is the nature of this surface?
2d
awarded Tumbleweed
2d
revised Defining operations for a vector space
Added linear algebra tag
2d
answered Looking for combinatorial proof for identity $n! = 1 \cdot 1! + 2\cdot 2! ... (n-1) \cdot (n-1)! + 1$
Apr
16
revised How to find the line integral from $(0,0)$ to $(1/8,0)$
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Apr
16
answered Do we have $(G/H)\times H \cong G$ for groups in general?
Apr
14
revised Proof of integral equality
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Apr
14
comment Bruhat order and Schubert cycles
I thought Chevalley's paper also works over $\mathbb{C}$. Have you tried looking in Procesi's book Lie Groups: An Approach Through Invariants and Representations
Apr
14
comment determine if $\sum^{\infty}_{n=1} \frac{n}{e^n}$ converges
Or at least state that the fraction is sufficiently proximate to its approximate.
Apr
14
revised Bruhat order and Schubert cycles
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Apr
14
revised Two path test in calculus
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