History of Computing — Quick Reference Notes

Computing: use of computers to manage, process, and communicate critical information; central to modern industrial technology.
Impact: devices, Internet, WWW, social media improve standard of living.

Babylonians (~ $2000$ BC – $500$ BC): clay cuneiform tables with arithmetic, cubes, square roots; numeral system used two symbols ( $1$ and $10$ ) combined to form others; counting boards akin to an abacus.
Egyptians: base-10 numerals with symbols for $1$ , $10$ , $100$ , $1000$ , $10000$ , $100000$ ; Rhind Papyrus; arithmetic and geometric problems used in building projects.
Greeks (~ $500-600$ BC): Pythagoras and Thales in geometry; Pythagorean theorem; Thales’ theorem: if AC is diameter and A,B,C on circle, then angle ABC is a right angle.
Romans: Roman numerals use letters for numbers; abacus used for calculation; influence visible today (clocks, cornerstones, etc.).

Islamic mathematics (North Africa, Middle East, Spain) advanced algebra beyond Greek geometry.
Algebra developed as objects (rational and irrational numbers) and applied to arithmetic and geometry; study of curves via equations.

Wilhelm Gottfried Leibniz — binary number system; building on Pascal’s calculating machine; The Step Reckoner (1672–1964) could perform $+, - , imes , o$ , and root extraction; first calculator to run basic arithmetic.
Charles Babbage — Difference Engine (1821): aimed to compute polynomial, logarithmic, and trigonometric functions; sought to improve on Pascaline; Ada Lovelace was an analyst for the engine and is often called the first computer programmer; first working Difference Engine prototype completed by George and Edward Schuetz in $1853$ .
Ada Lovelace — often regarded as the first computer programmer (analyst on the Analytical Engine).
George Boole — Boolean algebra: foundation for modern computing; symbolic logic as the basis for switching theory and digital circuit design; introduced 0 and 1; operators $+ , - , \times$ .
Grace Hopper — COBOL (Common Business-Oriented Language) promoted in 1959; helped make COBOL widely adopted by military and private sector; scaling of business-oriented programming.
Katherine Johnson — NASA’s human computer; calculated trajectories for space travel; geometry and orbit calculations pivotal for moon missions (notably 1962).
Gladys Mae West — GPS development; created geodetic model of Earth; enabled precise satellite geodesy and radar altimeter satellite work in the 1960s.

Egyptian numerals: base-10 with symbols for $1$ , $10$ , $100$ , $1000$ , $10000$ , $100000$ .
Roman numerals: $I=1, ext{ } V=5, ext{ } X=10, ext{ } L=50, ext{ } C=100, ext{ } D=500, ext{ } M=1000$ .
Step Reckoner: Leibniz’s machine capable of $+, -, \times, \div, \sqrt{}$ operations.
Difference Engine: Babbage’s design to generate mathematical tables; proto-computing device.

Computing developments arise from contributions across civilizations (Babylonians, Egyptians, Greeks, Romans, Islamic scholars).
Foundational ideas include numeral systems, algebra, logic, and mechanical calculation devices.
Key figures connected the theory (Boolean algebra, logic) with practical programming and computing languages (COBOL) and space-age computing (Katherine Johnson, GPS).
The evolution from manual calculation devices to algebraic and logical frameworks set the stage for modern computers and software.

Binary system: $0,1$ digits underpin digital computation.
Boolean algebra: fundamental to switching theory and digital circuits; operators: $+, -, \times$ .
COBOL: early standardized business language (1959) with broad historical impact.
GPS: based on a detailed Earth geodesy model developed in the 1960s.