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

2. Father of Complex Numbers
Gerolamo Cardano
Father of Complex Numbers

3. 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)

4. Complex Numbers
An Introduction

5. 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

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

7. Francois Viete

8. 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

9. 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

10. Trigonometry
Math of triangles
Relationships between sides and angles

11. Symbolic Algebra

12. John Napier

13. 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

14. 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

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

16. Napiers Bones
Multiplication tables

17. Blaise Pascal
Pascal’s Triangle

18. 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)

19. Pascal’s Triangle

21. 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

22. Newton’s Development of Modern Calculus
First version of Newton’s calculus published in
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

23. 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

24. 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

25. 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

26. 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

27. Bibliography
Hartshorne, Robin. "François Viète - Life." Mathematicians University of California Berkeley Math Department. 02 Dec <
Hartshorne, Robin. "Work." Mathematicians University of California Berkeley Math Department. 02 Dec <
O'Conner, J. J., and E. F. Robertson. "François Viète." Viete biography. Jan School of Mathematics and Statistics University of St Andrews, Scotland. 02 Dec <
O'Conner, J. J., and E. F. Robertson. "John Napier." Napier Biography. School of Mathematics and Statistics University of St Andrews, Scotland, Apr Web. 02 Dec <
Russel, Deb. "John Napier Biography." John Napier Biography. About.com, Web. 02 Dec <

28. Bibliography
 " Newton and Leibniz, Founders of Modern Calculus." IT Support from MSP Provider in New Jersey RSS. N.p., n.d. Web. 04 Dec <
"Gottfried Wilhelm Leibniz - Biography." Gottfried Wilhelm Leibniz. N.p., n.d. Web. 04 Dec <
"Gottfried Wilhelm Leibniz ( )." Gottfried Wilhelm Leibniz ( ). N.p., n.d. Web. 04 Dec <
"The History of Calculus." The History of Calculus. N.p., n.d. Web. 04 Dec <

29. Bibliography
 "Google Images." Google Images. N.p., n.d. Web. 03 Dec <
"Articles with Keyword Pascal. - Answers in Genesis." Articles with Keyword PascalEnter Website Address or Keywords to Cite. - Answers in Genesis. N.p., n.d. Web. 03 Dec < website address or keywords to cite.>.
"Blaise Pascal ( )." Blaise Pascal ( ). N.p., n.d. Web. 03 Dec <
"Gerolamo Cardano, Physician Extraordinaire." World Research Foundation RSS. N.p., n.d. Web. 03 Dec <
"Pascal's Triangle." Pascal's Triangle. N.p., n.d. Web. 03 Dec <