Math on Lomont.org

MinimalTicTacToe

Fri, 26 Jul 2024 07:50:18 -0400

Derivation of a minimal size tree for playing perfect tic tac toe

Correct alpha and gamma for image processing

Mon, 28 Aug 2023 18:40:19 -0400

This is a note on the correct usage of alpha blending, pre-multiplied alpha, gamma correction, and linear colors for image processing.

A better quadratic formula algorithm

Sat, 27 Aug 2022 08:12:01 -0400

A robust algorithm for computing roots of quadratic equations, much better than common code.

Rtk Gps Project

Mon, 07 Dec 2020 20:25:57 -0500

I built a RTK-GPS gadget and wrote enough software to do basic GNS tasks such as finding distances, decoding GPS NMEA and RTCM messages, finding intersections, and doing boundary detection.

Chris Lomont's Riddle Pages

Thu, 06 Jun 2019 07:55:47 -0400

Summary

Chris Lomont's Riddle Pages

Thu, 06 Jun 2019 07:55:47 -0400

Summary

Computation: Theory, Methods, Limitations, and the Future

Mon, 25 Feb 2019 12:58:12 -0400

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 Hypothesis, Free Will Theorem).

Intro to Wireless Communications

Sat, 21 Jul 2018 12:59:10 -0400

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.

Cryptography Best Practices 2018

Mon, 02 Apr 2018 12:58:39 -0400

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,

The Cosmic Distance Ladder

Sun, 19 Nov 2017 12:58:24 -0400

The Cosmic Distance Ladder is how mankind has determined the distances to various astronomical objects, basically by deducing closer “rungs” on the ladder and using them to determine farther distances (higher rungs on the ladder).

These notes are from Terry Tao, modified by me to suit my audience and to add other topics.

Walking Ant Probability Problem

Wed, 01 Nov 2017 17:08:08 -0400

Here’s a math puzzle.

A Universal FRACTRAN Interpreter in FRACTRAN

Mon, 01 May 2017 17:08:08 -0400

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

Generating Uniform Random Numbers on [0,1]

Sun, 05 Mar 2017 17:08:08 -0400

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

Efficient divisibility testing

Tue, 21 Feb 2017 17:08:08 -0400

Here’s bit tricks for efficient divisibility testing.

Average segment length

Tue, 23 Aug 2016 17:08:08 -0400

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

How many prisoners?

Tue, 23 Aug 2016 17:08:08 -0400

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

Pick a Number

Tue, 23 Aug 2016 17:08:08 -0400

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

Test site features

Fri, 01 Jul 2016 17:08:08 -0400

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