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bio website mathcs.holycross.edu/~ahwang
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Jul
19
comment “Deep” maths books in certain subjects
I didn't downvote, but do tend to feel your question is flawed in its hypotheses, aside from being primarily opinion-based. For starters, books don't "give" you insight and mathematical maturity; you yourself acquire these traits (or do not acquire these traits) over many years of experience, and not merely through reading, but by doing mathematics.
Jul
15
awarded  Yearling
Jul
14
comment What exactly is a number?
FWIW, the second edition of Russell's book is at Project Gutenberg (typeset in LaTeX).
Jul
10
comment How does one graph $\sum_{x=0}^{n}$
"$\sum_{x=0}^{n} n$" is not a function of $x$ at all (as Shawn O'Hare notes), but rather equal to $n(n+1)$. Generally, a "graph" in the sense of your question contains only points $(x, y)$ with $x$ an element of the domain of the function being graphed. So even if you really meant $\sum_{k=1}^{n} k$, the graph will consist only of isolated points (as StrangerLoop and Andres Caicedo say).
Jul
8
comment Definition of the algebraic intersection number of oriented closed curves.
Back in the day, the standard introductory reference for intersection theory was Differential Topology by Guillemin and Pollack. Your surmise for "1." is essentially correct; you just need to fix orientations for each curve, as well as for the ambient surface (so that "left-to-right" makes sense). I don't recall whether G-P addresses "2."
Jul
8
answered Double integration:$ \int_0^a \int_0^b e^{max(b^2x^2,a^2y^2)}dydx $
Jul
8
answered rotated hyperbolic cylinder parameterization
Jul
7
reviewed Close Permutation and Combinations (Separation)
Jul
7
reviewed Close Find the remainder
Jul
7
reviewed Close Closed subspace $M=(M^{\perp})^{\perp}$ in PRE hilbert spaces.
Jul
7
reviewed Close prove ${a_n}$ is a Cauchy sequence, provided $a_{n+2} = \frac{a_n + a_{n+1}}{2}$
Jul
7
reviewed Edit suggested edit on How to approximate large sum of exponential variables
Jul
7
revised How to approximate large sum of exponential variables
added 35 characters in body
Jul
7
reviewed No Action Needed Closed subspace $M=(M^{\perp})^{\perp}$ in PRE hilbert spaces.
Jul
7
reviewed Looks OK The relation between orders in a group
Jul
7
reviewed Looks OK Formal Notation - A simple example
Jul
2
comment How to define integration over the boundary of a curve?
Integration of a $0$-form (i.e., a smooth function) over a $0$-chain (i.e., a finite integer linear combination of points) is customarily defined by evaluation. The boundary of $1$-cube $[a, b]$ is defined to be the $0$-chain $(+1)[b] + (-1)[a]$ (the square brackets signifying a formal linear combination, or elements of a free Abelian group if you prefer), so the "integral" of $f$ over this boundary is, by fiat, $f(b) - f(a)$.
Jun
28
comment $f(x)=sec(x)$ inequality inconsistency\trouble
Multiplying (or dividing) by a negative number reverses the sign of an inequality. :)
Jun
26
answered An extension of line bundles splits locally
Jun
25
answered Geodesic on n-dimensional sphere