The Mathematics of Duelling
Duelling with pistols. If you were the one issuing the challenge, your dilemma was that custom dictated that your adversary be allowed to shoot first. Only then, if you were still able to shoot, would...
View ArticleTeaching Enriched Mathematics
Thoughts on Teaching Mathematics in an Exploratory, Dialectical, Topical format. (2nd ed. July 13th 2016; 1st ed. Jan 31, 2010) Mathematics is a richly spun tapestry, threaded with interconnections...
View ArticleCoding for pre-schoolers: a ‘Turtle Logo’ in Forth
*New!* (29 Aug 2020) – Turtle Logo v1.8 (portable) is available! Developer kit with source code included. Suitable from ages 3 years to adult. (970 lines of Forth code). 1. Inspiring the next...
View ArticleSum of Integer Powers (Part 3)
(Discrete Mathematics Techniques III) 1st ed. Apr 2nd, 2010 Abstract This is the last in the 3-part series of articles on finding for oneself the solution to the sum of integer power problem, and in...
View ArticleSums of Integer Powers (Part 2)
(Discrete Mathematics Techniques II) 1st ed. Feb 8th, 2010 Abstract We continue the 3-part paper exploring how one might solve for themselves the general case of the sum-of-integer-powers problem for...
View ArticleSums of Integer Powers (Part 1)
2nd ed. January 21, 2018; 1st ed. Feb 8th, 2010 Abstract This three part paper explores solving the sum of powers problem using discrete maths techniques (recurrence relations, matrix systems) to...
View ArticleElectronics in the Junior School – Gateway to Technology
Electronics is a gateway subject to modern technology, along with computer programming and applied mathematics. Getting started in electronics is easier than one may imagine and not prohibitively...
View ArticleBuilding a 13-key analog piano from only resistors, capacitors, and transistors
Building a fully analog electronic piano using only resistors, capacitors, and transistors, is an insightful experiment in electronic sound generation from first principles. I designed and built a...
View ArticleExperimenting with Microcontrollers – an Arduino development kit for under £10
For under £10, you can put together a microcontroller development platform, ready to program directly from your PC over USB using free Arduino software. Once programmed, your microcontroller will run...
View ArticleHow to think about engineered solutions?
Rapid prototyping can be an accelerator for hardware or embedded solutions. But for a successful outcome, follow the recommended checklist / task sequence given below, as all of these steps will likely...
View ArticleMaking Animation from Stills
Hi, my name is Jasmine, and I’m 7 years old. Today I made two animated movies, The Basket (1m 18s long) and Snowbell’s Accident (2m 23s long) (Nov 2nd, new with audio!) Enjoy! I made these by taking...
View ArticleThe Mathematics of Uruk and Susa (c.3500-3000 BCE)
This is Part 2 in the Ancient Mathematics series. (Part 1: The Prehistoric Origins of Mathematics, Part 3: Exploring Cuneiform Culture 8500-2500 BCE) Summary The written mathematics of ancient Iraq...
View ArticleSeven Fields of Computer Programming: A Brief Survey
Written July 7th, 2012, Revised Jan 12th, 2013, Updated & extended Jan 25th, 2020 There are at least seven distinct fields of computer programming that have less to do with languages and more to do...
View ArticleForth, Lisp, & Ruby: languages that make it easy to write your own domain...
Before domain-specific languages (DSLs) and REPL environments (read, execute, print, loop) became fashionable, computing pioneer Charles (Chuck) Moore had built, by 1968, what he viewed as the perfect...
View ArticleExploring cuneiform culture (8500-2800 BCE)
This is Part 3 in the Ancient Mathematics series. (To read earlier parts: Part 1: Prehistoric Origins of Mathematics, Part 2: The Mathematics of Uruk and Susa). This article explores what the people...
View ArticleThe rise of Mathematical Logic: from Demonstration to Laws of Thought to...
Revised Nov 2022, Jan 2023 In this article we look at the evolution of logic from its earliest form in the demonstration of truths to the rapid development of mathematical logic in the 1800s at the...
View ArticleHow Algebra became abstract: George Peacock & the birth of modern algebra...
In this article we look at the ideas of George Peacock whose 700-page opus A Treatise on Algebra (1830) transformed classical algebra into its modern form as an abstract symbolic science, free from the...
View ArticleLOGIC in a Nutshell: Theory & Application (including a Forth simulator, and...
This article looks at Propositional Logic, also called Statement Calculus, from a combinatorial and algebraic point of view (Sections 3-6), its implementation in software (Section 7), and its...
View ArticleFuzzy Classifiers and Quantile Statistics for continuous data monitoring with...
Abstract This brief note explores the use of fuzzy classifiers, with membership functions chosen using a statistical heuristic (quantile statistics), to monitor time-series metrics. The time series can...
View ArticleVoice-controlled Hardware: Making Sensors Talk for Under £5
Voice controlled hardware requires four capabilities: (1) vocal response to trigger events (sensors/calculations-to-brain), (2) speech generation (brain-to-mouth), (3) speech recognition...
View ArticleProgramming Microcontrollers – low power, small footprints, & fast...
This article explains how to use the Arduino toolchain to program microcontrollers from the Arduino IDE using their bootloaders, and also burning bootloaders directly onto bare microcontroller chips....
View ArticleTinyPhoto: Embedded Graphics and Low-Fat Computing
TinyPhoto is a small rotating photobook embedded graphics project that uses the low-power ATtiny85 microcontroller (3mA) and a 128×64 pixel OLED display (c.5-10mA typical, 15mA max). This combination...
View ArticleMathematical Finance and The Rise of the Modern Financial Marketplace
Updated March 21, 2023, following two bank collapses in the US and the collapse of Credit Suisse in Europe. First published July 5, 2010, two years after the start of the Great Recession. Mathematical...
View ArticleThe Benefits of Enriched Mathematics Instruction
2nd ed. June 2023; 1st ed. April 2010 The term “mathematical maturity” is sometimes used as short-hand to refer to a blend of elements that distinguish students likely to be successful in mathematics....
View ArticleWhat is Mathematics?
4th ed. Jan 2024; 3rd ed. May 2023; 2nd ed. Dec 2009; 1st ed. Sep 2004 “It is not philosophy but active experience in mathematics itself that alone can answer the question: `What is Mathematics?'” –...
View ArticleThe Prehistoric Origins of Mathematics
3rd ed. Aug 2023 (expanded appendices). 2nd ed. Nov 2019 (revised to include advances in linguistics, genomics, interpretive theory, and Mesopotamian mathematics); 1st ed. (Dec 29, 2009) Part 1 in...
View ArticleMathematics “from the inside”: mathematicians on mathematics
Revised & Expanded May 2023. First published November 1998. This article provides a selection of quotes, written mostly by mathematicians, that convey especially clearly essential aspects of...
View ArticleKnowledge Engineering & Emerging Technologies*
2nd ed. Jan 2024 (with standalone chapters), 1st. ed. 2005 Overview In the intersection between Mathematics, Modern Statistics, Machine Learning & Data Science, Electrical Engineering &...
View ArticleThe Sacred and the Profane: software engineering & the search for simplicity...
4th ed. (Jan 31st, 2024), 3rd ed. (Jul 20, 2021), 2nd ed. (Apr 9, 2014, addition of GCC history), 1st ed. (May 2, 2010) If you haven’t done so already, you may want to start by reading the Preface to...
View ArticleFreehand Diagrams on Windows, Android, and iOS with MetaMoji Note & the WACOM...
Updated: 2014-11-23 MetaMoji Note: A worthy digital replacement to Pencil & Notebook for creating freehand diagrams on Windows and Android. Pencil & Notebook are hard to beat when diagrams,...
View ArticleSnippets
Below a quick reference for various useful code snippets… Forth LaTeX HTML Forth snippets Forth has many dialects. I use GForth for general purpose Forth, as it is available for both Linux and Windows...
View ArticleForth (Embedded Systems)
“Any [one] can make things bigger, more complex, … It takes a touch of genius, and a lot of courage, to move in the opposite direction.” – Ernst F. Schumacher, 1973, from “Small is Beautiful: A Study...
View ArticleTotal Commander (File Manager)
If you haven’t done so already, you may want to start by reading the Preface to the Computing Series: Software as a Force Multiplier, Sections 1-3. 1. Total Commander: a programmable, extensible,...
View ArticleNotepad++ (Text Editor)
If you haven’t done so already, you may want to start by reading the Preface to the Computing Series: Software as a Force Multiplier, Sections 1-3. 1. Notepad++: a programmable, extensible,...
View ArticleEverything (Desktop Search)
If you haven’t done so already, you may want to start by reading the Preface to the Computing Series: Software as a Force Multiplier, Sections 1-3. “Everything” you need for ultra-fast desktop search...
View ArticleR (for Stats)
R for Statistical Computing: Quick Start & Useful Coding Snippets Assad Ebrahim, http://www.mathscitech.org/articles/computing-toolkits/r-for-stats 2003-2020 This page provides notes/references to...
View ArticleLivia’s Christmas
Livia’s Christmas, by Jasmine Sheherazade Ebrahim, Story in the Livia Series Livia Bell, Maya (Mum), Sam (Dad), Brittany Bell, Roxanne Bell, Alexa Bell, Catherine Bell, Rosalind Bell, Lavender Bell,...
View ArticleLivia’s Life – Season 1
Livia’s Life – Season 1 by Jasmine Sheherazade Ebrahim, In the Livia Series Chapter One “Faster! Higher!” Livia grinned as Lavender patiently pushed the swing. Livia’s legs swung uncontrollably as...
View ArticleLivia’s Life – Season 2
Livia’s Life – Season 2 by Jasmine Sheherazade Ebrahim, from the Livia Series Chapter One Livia was sitting restlessly on the picnic-blanket, complaining every five seconds. “Mum, please,” she moans....
View ArticleLivia All Alone
Livia All Alone By Jasmine Sheherazade Ebrahim, from the Livia Series “Ow!” Livia moaned. “You stood on my foot!” “Budge up!” Roxanne hollered. “That’s my guitar you’re poking at!” “Hey, hey, hey!...
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