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awwalker.com | ||
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algorithmsoup.wordpress.com
The ``probabilistic method'' is the art of applying probabilistic thinking to non-probabilistic problems. Applications of the probabilistic method often feel like magic. Here is my favorite example: Theorem (Erdös, 1965). Call a set $latex {X}&fg=000000$ sum-free if for all $latex {a, b \in X}&fg=000000$, we have $latex {a + b \not\in X}&fg=000000$. For any finite... |
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nhigham.com
For a polynomial $latex \notag \phi(t) = a_kt^k + \cdots + a_1t + a_0, $ where $latex a_k\in\mathbb{C}$ for all $latex k$, the matrix polynomial obtained by evaluating $latex \phi$ at $latex A\in\mathbb{C}^{n \times n}$ is $latex \notag \phi(A) = a_kA^k + \cdots + a_1A + a_0 I. $ (Note that the constant term is... |
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www.jeremykun.com
This post assumes working knowledge of elementary number theory. Luckily for the non-mathematicians, we cover all required knowledge and notation in our number theory primer. So Three Thousand Years of Number Theory Wasn't Pointless It's often tough to come up with concrete applications of pure mathematics. In fact, before computers came along mathematics was used mostly for navigation, astronomy, and war. In the real world it almost always coincided with the physical sciences. |
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gpfault.net
[AI summary] The text provides an in-depth exploration of various x86-64 instruction set architectures, focusing on arithmetic operations (ADD, SUB, MUL, SMUL, DIV, SDIV), logical operations (AND, OR, XOR, NOT), and control flow instructions. It details the implementation of these instructions in the QBX virtual machine, emphasizing how they emulate real x86-64 instructions while managing the flags register and handling different operand sizes (8-bit and 16-bit). The text also discusses the nuances of flag handling, register operations, and macro-based code generation to streamline instruction implementation. |
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