# muzzlator

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bio website location Perth, Australia age 29 member for 1 year, 10 months seen Dec 1 at 20:39 profile views 453

Studied at UWA, Perth, Western Australia.

Working as a software engineer for Fugro Survey Pty. Ltd.

Interested in mathematics, computer science, and problem solving.

 22 Value of $\sum \limits_{k=1}^{81} \frac{1}{\sqrt{k} + \sqrt{k+1}} = \frac{1}{\sqrt{1} + \sqrt{2}} + \cdots + \frac{1}{\sqrt{80} + \sqrt{81}}$? 8 Show that the difference of two consecutive cubes is never divisible by $3$. 8 Does there exist a unique definition of dot product in $\mathbb R^n$ such that the standard basis is orthonormal? 7 Suppose that $f$ is entire and that for each $z$, either $|f(z)| \leq 1$ or $|f^\prime (z) |\leq 1$. Prove that $f$ is a linear polynomial. 7 why $\iint \sqrt{1+\left(\frac{\partial f}{\partial x}\right)^2+\left(\frac{\partial f}{\partial y}\right)^2}\:dx\:dy$ means surface area?

# 5,423 Reputation

 +10 How to build a smooth “transition function” explicitly? +10 Motivation for the Tensor Product +10 Intuitively, what is the difference between Eigendecomposition and Singular Value Decomposition? +10 How do I completely solve the equation $z^4 - 2z^3 + 9z^2 - 14z + 14 = 0$ where there is a root with the real part of $1$.

# 9 Questions

 12 How does one calculate the product of $\tan 1^{\circ} … \tan 45^{\circ}?$ 10 Checking my understanding of $T^*M$ as a symplectic manifold and the links between the classical description of Lagrangians vs this invariant way. 8 $n \times n$ lattice graph with partial derivatives bounded by $1$ has $n$ equal values. 4 Arbitrary ratio sequences on a partition of $\mathbb{R}$ (Partition regularity of fixed ratio sequences) 3 Names and algorithms for subgraphs with smallest neighbourhoods

# 122 Tags

 75 linear-algebra × 36 31 matrices × 17 57 calculus × 22 27 complex-analysis × 14 52 real-analysis × 20 25 abstract-algebra × 12 37 sequences-and-series × 9 23 general-topology × 9 36 algebra-precalculus × 12 21 integration × 7

# 14 Accounts

 Mathematics 5,423 rep 1430 Mathematica 225 rep 110 Stack Overflow 135 rep 6 Physics 133 rep 6 MathOverflow 111 rep 4