# Math

Mon, Feb 25, 2019 - 200 Words

These slides are from a talk I gave on many aspects of computing, starting with classical computing (Hilbert’s 10th problem, Church and Turing, Godel, boolean functions, complexity theory, transistors, Moore’s law and demise), then going through physics (relativity, quantum mechanics, quantum field theory), and finally into quantum computing basics (qubits, superposition, entanglement, no cloning, basic gates) and quantum algorithms (Deutsch, Simon, Shor, Grover).

Then I cover advanced quantum topics, such as quantum machines,quantum complexity theory, the Quantum-Church-Turing-Deutsch principle, graph isomorphism, quantum error correction, and quantum security. A final speculative section covers even weirder computation ideas (closed timelike curves, string computing) and how computing seems intertwined with the nature of reality (It from Bit, Simulation Hypthesis, Free Will Theorem).

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Sat, Jul 21, 2018 - 200 Words

This talk is an intro to wireless communications, starting with the basic physics of EM waves and how they interact with materials, then how antennas work, then on to antenna properties and design. Next modulation schemes are discussed, showing how data is encoded and transmitted over noisy channels via modulation, spread spectrum, time and frequency division, and other methods. Noise in the form of doppler, intermodulation, and other causes is covered. Information theory (channel capacity, Shannon entropy, error correction) is covered. Finally specific protocols are analyzed under this framework: FM, NTSC, remotes, WiFi, Bluetooth, ZigBee, satellite radio, GPS, and cellular formats.

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Mon, Apr 2, 2018 - 100 Words

This talk covers cryptography best practices as of April, 2018. Background on each area is covered, with each section ending with a best practices slide. Sections are Symmetric Encryption, Asymmetric Encryption, Key Lengths, Hashing/HMAC, Password usage, Key Exchange, Random number generation, Digital Signatures,

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Wed, Nov 1, 2017 - 300 Words

Here's a math puzzle.

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Mon, May 1, 2017 - 7700 Words

Here's FRACTRAN, a weird fraction based programming language, written in FRACTRAN.

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Sun, Mar 5, 2017 - 1400 Words

How does one generate uniform random numbers in [0,1] using IEEE 754 floating point formats? It's tricky.

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Tue, Feb 21, 2017 - 1200 Words

Here's bit tricks for efficient divisibility testing.

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Tue, Aug 23, 2016 - 900 Words

What's the average length of a segment chosen uniformly by area on a unit square?

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Tue, Aug 23, 2016 - 2300 Words

This is a nicely hard problem in the common prisoners and warden format.

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Tue, Aug 23, 2016 - 500 Words

Here's a result that is completely non-intuitive.

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Fri, Jul 1, 2016 - 100 Words

A post to test site features such as tables, math, code…

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