The Scientific Revolution – Mathematics Ajay Kumar, Lyndon Shi, Nicholas Voreas 9-1

Father of Complex Numbers Gerolamo Cardano Father of Complex Numbers

Gerolamo Cardano - Biography Born 1501 Unhappy childhood – illegitimate son Inventor, astrologer, philosopher, algebraist, physician Known as the “Gambling Scholar” for his gambling skills Wrote more than 200 books on subjects that interested him Committed suicide (September 21, 1576)

Complex Numbers An Introduction

Complex Numbers Also known as imaginary numbers A variable (i) stands for the square root of a negative number Always do the i part first when solving

Without Complex Numbers… No iPod No modern advancement No quantum theory

Francois Viete

Life French Mathematician Lived 1540 to 1603 Father of modern symbolic algebra Career as a lawyer, worked on mathematics in spare time Involved in politics, worked for Kings Henry III & IV Decoded messages sent to Philip II of Spain

Books In artem analyticam isagoge (1591) First works – Canon mathematicus, Universalium Inspectionum Liber Singularis, (1579) Trigonometric tables calculated to 9 decimal places Collection of trigonometric formulas In artem analyticam isagoge (1591) Algebraic notation Use of letters for unknowns and constants Vowels are unknowns, letters are constants

Trigonometry Math of triangles Relationships between sides and angles

Symbolic Algebra

John Napier

Life Scottish noble/landowner Lives 1550 to 1617 Protestant Attention to land (inventions) Theologian/astronomer, worked on mathematics in spare time Invented logarithms, Napier’s Bones, decimal point

Books The Plaine Discovery of the Whole Revelation of St. John (1593) Against Papacy A Description of the Wonderful Canon of Logarithms (1614) Explained inventions Logarithmic tables Led to base 10

Logarithms log2(8) = 3 Exponential form How many of one number do we multiply to get another log2(8) = 3

Napiers Bones Multiplication tables

Blaise Pascal Pascal’s Triangle

Blaise Pascal Born: June 19, 1623 (Clermont) Was kept away from mathematics at an early age – led to curiosity on the subject Easily mastered properties of geometry by experimenting himself Invented “arithmetic machine” – could add/subtract Spent some time studying religion Died: August 19, 1662 (Paris)

Pascal’s Triangle

Isaac Newton Born Dec. 25, 1642 in Woolsthorpe, England Father died before he was born, mother moved away Grew up with his uncle Attended Trinity College at the University of Cambridge in 1661, received bachelor of arts in 1665 In 1669, appointed professor of mathematics at Trinity College, and elected to the Royal Society in 1672 Elected to Parliament in 1691, warden of the mint in 1696 Died March 20, 1727

Newton’s Development of Modern Calculus First version of Newton’s calculus published in 1665-6 Seemed to be derived from ideas of motion Considered variables changing with time His calculus was geometrical, as opposed to analytical Used “infinitesimals”, infinitely small but not zero Later replaced by notions

Applied his version of calculus to general physics Included the laws of differentiation and integration, second and higher derivatives, and the notion of an approximating polynomial series Calculus today is used in many ways, some including physical sciences, engineering, computer science and statistics

Gottfried Wilhelm Leibniz Born in 1646 Early years influenced by moral and religious views of mother Attended University of Leipzig at age 14 in 1661 Studied philosophy, mathematics, rhetoric, Latin, Greek and Hebrew Graduated with bachelor’s in 1663, got master’s degree in philosophy the same year Death on November 14, 1716

Development of the Binary System Developed by Gottfried Wilhelm Leibniz Belief that all logic can be translated from a verbal representation to an absolute mathematical condition Ideas were repelled, Leibniz dropped the idea for about 10 years Hope revived when the Book of Change was published, and he found confirmations of his ideas within this book

If such things as yes/no, on/off and male/female could be reduced to straightforward propositions, why couldn’t logic and thought? Went out to define his binary system Transposed numbers into seemingly infinite rows of ones and zeroes At the end of his life he began to believe that his binary number were quasi-religious mysticisms Claimed that it portrayed creation, with one being God, and zero being void

Bibliography   Hartshorne, Robin. "François Viète - Life." Mathematicians. 1998. University of California Berkeley Math Department. 02 Dec. 2012 <http://math.berkeley.edu/~robin/Viete/index.html>. Hartshorne, Robin. "Work." Mathematicians. 1998. University of California Berkeley Math Department. 02 Dec. 2012 <http://math.berkeley.edu/~robin/Viete/work.html>. O'Conner, J. J., and E. F. Robertson. "François Viète." Viete biography. Jan. 2000. School of Mathematics and Statistics University of St Andrews, Scotland. 02 Dec. 2012 <http://www-history.mcs.st-and.ac.uk/Biographies/Viete.html>. O'Conner, J. J., and E. F. Robertson. "John Napier." Napier Biography. School of Mathematics and Statistics University of St Andrews, Scotland, Apr. 1998. Web. 02 Dec. 2012. <http://www-history.mcs.st-andrews.ac.uk/Biographies/Napier.html>. Russel, Deb. "John Napier Biography." John Napier Biography. About.com, 2012. Web. 02 Dec. 2012. <http://math.about.com/library/weekly/blbionapier.htm>.

Bibliography  "1660-1670 Newton and Leibniz, Founders of Modern Calculus." IT Support from MSP Provider in New Jersey RSS. N.p., n.d. Web. 04 Dec. 2012. <http://www.powersolution.com/1660-1670-newton-and-leibniz-founders-of-modern-calculus/>. "Gottfried Wilhelm Leibniz - Biography." Gottfried Wilhelm Leibniz. N.p., n.d. Web. 04 Dec. 2012. <http://www.egs.edu/library/gottfried-wilhelm-leibniz/biography/>. "Gottfried Wilhelm Leibniz (1646 - 1716)." Gottfried Wilhelm Leibniz (1646 - 1716). N.p., n.d. Web. 04 Dec. 2012. <http://www.kerryr.net/pioneers/leibniz.htm>. "The History of Calculus." The History of Calculus. N.p., n.d. Web. 04 Dec. 2012. <http://www.uiowa.edu/~c22m025c/history.html>.

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