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During the Renaissance period in the 16th century, the symbols that we are familiar with, today, were developed. This would include variables and parenthesis.
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Logarithms were discovered by John Napier.
Descartes writes about combining algebra and geometry in his new book, "Discourse on Method". He suggested that we uses a grid with an X and Y axis to create graphs. We call this graphing method, the Cartesian coordinate system
Probabilty theory is developed by Dutchman, Christiaan Huygens, by studying the outcome of dice rolls.
Calculus is discovered by Sir Isaac Newton and later by Leibniz. Calculus is the study of the rate of change on a curve, much like that on a line and exact areas for curved graphs.
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Charles Babbage developed the first computer prototype. The first one, created in 1822, was called the "Difference Machine". It was set up to create math tables.
The next machine was called the "Analyzing Machine", which was started in 1830, but was never completed. It could perform calculations and then more operations based on the first ones. It could also do program loops. That "Analyzing Machine" was never completed. The machine was designed to be used with Jacquard's punched cards. These cards were also used in the early days of computer programming.
Augusta Ada Lovelace worked closely with Babbage and developed a program for the machine. She is credited with making the first computer program.
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