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MATH BASICS YOU NEED TO SUCCEED IN TECHNOLOGY
A compilation of one page abstracts (cheat sheets) of many important topics (chapters), essential in college math
by
ZACK BAJIN
Keywords: Aha Experiences, Logical Reasoning, Enlightenment, Blimey! (British: Wow!)
“Sla me op de kop met de klomp” (Dutch: hit me on the head with the clog)
"Jetzt kapier ich's!" (German: Now I get it!)
A Brief Intro
In today’s fast changing world and the resulting information overload, the last thing a person needs is a 1000 pages thick book of a small section from the oldest subject on earth. So here's an attempt to condense the most essential fundamentals to serve as a base from which to grow in almost any profession one choses. Most of it is ancient knowledge tediously pieced together by nerds, who withdrew from and elevated themselves above the daily rut of mere existence, pushing the envelope of consciousness, deriving amazing logical connections from basic facts most people don’t waste their time to overanalyze. Although these envelope pushers, not understood by most of their contemporaries, had the feeling of the importance of their “AHA” experiences, they frequently couldn’t foresee how useful the results of their brain gymnastics would become in the distant future.
One of the least recognized facts is that there are many different symbolic ways, characters, to write the spoken words in languages all over the world (just check the fonts in MS-Word or Google Translate), but practically all use an additional collection of numeric and other mathematical symbols which are the same in all languages and are found on the computer keyboards and many more on the scientific calculators. No matter what and how many old or new languages one knows, knowing the language and symbolism of math enables one to communicate with others, traversing space and time.
This collection of cheat sheets is intended to give the layperson and the expert a condensed summary of basics for most important areas in tech math: Arithmetic, Algebra, Geometry, Trigonometry, Vectors and the oh-so-dreaded Calculus intro. The purpose of each cheat sheet is to provide a drone view (I used to call it bird’s eye view) of every topic. The street view (which I called “bush work”) becomes much easier if there is a logical framework to build on. Exponents & Radicals and Factoring & Fractions alone, are applied in four out of five steps (80%!) on any level of algebraic workout of science and engineering problems. There are additional modern Arithmetic-Algebra subsections, essential for the computer age, such as Binaries, Boolean Algebra and Propositional Logic as well as Operation Analysis basics to handle large scale projects, like operating a big corporation or an airline with profit, building a supercomputer or venturing into space.
To make the most of it, make up your own cheat sheets based on these and other resources, including your own examples, to personalize your own math discovery experience. Even though through frequent use one cannot help but memorize some essential facts and formulae, don’t memorize math on purpose. Exercise your logical reasoning (processor) instead. There are other important things in today’s world which can be mastered primarily by loading up one’s memory banks, such as human and programming languages, legal, technical, chemical, biological or medical terminology, etc.
In the appendix there is an added topic, apparently disconnected from applied mathematics. It is a one-page overview of the International System of measurement units (SI). It’s included here because in this area, information overload exists as well. Too many archaic and redundant measurement units are still being used in technology, promoting compartmentalization and impeding communication between people in different disciplines and countries. SI offers a more streamed, one unit per quantity approach, allowing the users to see connections between disciplines and advance much further with ease. This cheat sheet gives you a direct way to build connections from a few defined base units to practically all derived units employed in science and technology. When used online, this kind of bird’s eye view brings everything within one’s grasp.
At the turn of the millennium, a couple of decades ago, it was already predicted that every professional must expect at least eight career changes during their productive life. Mastery of the oldest subject on earth provides a solid base for lateral career change.
I wish you lot of success in your chosen profession but be well prepared for lateral mobility.
Zack Bajin, professor
George Brown College
Toronto, Ontario, Canada
