History of Mathematics

Algebra

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Babylonian Mathematics

1800-1600 B.C. Clay tablets with fractions, algebra, and equations.

THE RHIND PAPYRUS OR AHMES PAPYRUS

This document dates back to 1650 B.C. Copied by a scribe, Ahmes, from a copied document that may have been written as far back as 2650 B.C. The written material included simple equations and simple algebra problems.

Diophantus 200-284 A.D.

  • Greek mathematician
  • Found rational solutions to equations with several unknowns
  • Some claim he should be called "The Father of Algebra"
  • Wrote a collection of 13 books called Arithmetica
  • The series included over 100 algebraic problems with solutions
  • He used three types of quadratic equations, instead of one, because he did not have notation for zero
  • He thought out the solutions to problems concerning linear and quadratic equations, using only positive rational solutions
  • There is no evidence that he found two solutions to the quadratic equations
  • He thought negative or irrational square roots were useless

LIU HUI 220-280 A.D.

  • Chinese mathematician that solved linear equations using matrices.
  • Edited and published The Nine Chapters on Mathematical Art in 263 A.D.
  • The contents of the chapters included arithmetic, algebraic and geometric algorithms.
  • He approximated pi as 3.14014 and suggested 3.14 was a practical approximation.

http://www.famous-mathematicians.com/liu-hui/

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ARYABHATA 476-550 A.D.

  • Indian mathematician and astronomer.
  • Published his first book, Aryabhatiya, at age 23
  • The mathematical part of the book covered arithmetic, algebra, plane trigonometry, and spherical trigonometry.
  • He wrote important observations on 4 types of equations. Equations with one variable, quadratic equations, simultaneous equations, and indeterminate equations.

http://akubihar.org/aryabhatta.html

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BRAHMAGUPTA 598-550 A.D.

  • Indian mathematician and astronomer
  • His understanding of the number system went far beyond that of other mathematicians of this period
  • He established rules for zero
  • For example, one plus zero equals zero, one minus zero equals zero, and one times zero equals zero
  • His understanding of the division of zero was not complete
  • He thought positive and negative numbers divided by zero equaled zero or expressed as a fraction and zero divided by zero equaled zero


http://economictimes.indiatimes.com/slideshows/people/indian-maths-wizards-and-their-ideas/brahmagupta-598-670/slideshow/40354409.cms

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AL-HAITHAM (ALHAZEN) 965-1040 A.D.


  • Considered the father of modern optics
  • Alhazen's problem, lead to an equation of the fourth degree
  • He developed analytical geometry by establishing a link between algebra and geometry

(Al h ai z in n)


http://images.rapgenius.com/a474212330aa50e11894253a602afc94.187x227x1.jpg

1100 THE SPREAD OF MATHEMATICS

Arabic and Hindu mathematics spread throughout the Western Europe


http://etc.usf.edu/maps/pages/6800/6866/6866.jpg

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BHASKARA II (1114-1185)

  • Indian mathematician
  • Had an understanding of the number system and solving equations that was not achieved for several centuries
  • He knew that x^2 = 9 had two solutions
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ROBERT RECORDE (1510-1558)

Welch mathematician who published the first English book of Algebra, The Ground of Artes

RENE DESCARTES (1596-1650)

  • French philosopher and mathematician
  • Created the Cartesian coordinate system with axes label x, y, and z (later extended to negative numbers)
  • Algebra could now be linked with geometry

ISAAC NEWTON (1642-1727)

  • Polish philosopher, scientist, astronomer, and mathematician credited for the generalized binomial theorem

LEONARD EULER (1701-1783)

  • Swiss mathematician
  • Wrote The Elements of Algebra
  • f(x) functions
  • The symbol, e, for the base of natural logarithms
  • Sometimes called Euler's number
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CARL FRIEDRICH GAUSS (1777-1825)

  • German mathematician who was credited for the Fundamental Theorem of Algebra
  • The theorem states, if we have an n-th degree polynomial, we will have n-roots
  • Example: A second degree parabola has exactly two roots
  • Note: Complex non-real root are always in pairs
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1827 ALGEBRA EDUCATION

Massachusetts passed a law requiring algebra to be taught in the high school of any town with at least 500 families.
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