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Mathematics in the Modern World > Module 1. History of Mathematics > Flashcards

Module 1. History of Mathematics Flashcards

1
Q

The Mathematics that we know in the modern world has its roots in ancient __, __, and __

A
  • Mesopotamia
  • Egypt
  • Babylonia
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2
Q

Mathematics was then developed in __, and simultaneously in __ and in __

A
  • Greece
  • China
  • India
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3
Q

This ancient Greek mathematics, along with some influence of __ mathematics spread to the neighboring countries in the __ __

A
  • Hindu (mathematics)
  • Middle East
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4
Q

Mathematics was translated into __ and __, and was adopted by __ __

A
  • Arabic and Latin
  • Western Europe
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5
Q
  • first people to assign symbols to group of objects to represent numbers
  • developed the earliest known writing system
A

Sumerians

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6
Q

Sumerians are from

A

Sumer, a region of Mesopotamia

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7
Q

What writing system did the Sumerians develop

A

cuneiform script (pictographic writing system)

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8
Q

When: Sumerians

A

4,000 - 3,000 B.C.E.

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9
Q

first people to develop a numerical system that was based on the number 10

A

Egyptians

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10
Q

What developed in Egypt

A

Hieroglyphic Numerals

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11
Q

When: Egyptians

A

3,000 B.C.E.

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12
Q

used the Sexagesimal System

A

Babylonians

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13
Q

What did the Babylonians use

A

Sexagesimal Numeral System

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14
Q

When: Babylonians

A

2,400 B.C.E.

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15
Q

When was the major Greek progress in mathematics

A

300 BC - 200 AD

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16
Q

What did Euclid write during 300 BC - 200 AD era

A

Elements

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17
Q

compilation of theorems, axioms in Algebra and postulates and theorems in Geometry

A

Elements

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18
Q

With the Elements, Euclid gained the title of

A

Father of Geometry

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19
Q

When: major Greek progress

A

300 B.C.E.

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20
Q
  • a Greek mathematician, physicist, inventor and astronomer
  • derived a range of formulas in Geometry
A

Archimedes of Syracuse

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21
Q

What are the formulas that Archimedes derived

A
  • area of circle
  • surface area and volume of sphere
  • area under a parabola
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22
Q

When: Archimedes of Syracuse

A

200 B.C.E.

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23
Q

Greek astronomer, geographer, and mathematician considered as founder of trigonometry

A

Hipparchus of Nicaea

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24
Q

When: Trigonometry of Hipparchus

A

140 B.C.E.

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25
Q

When: Hindu mathematical works translated to Arabic

A

775 C.E.

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26
Q

How did the Arabic Algebra and Indian numerals come to Western Europe

A

through Muhammad ibn Musa Al-Khwarizmi’s writings

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27
Q

Other Arabic scholars also cultivated Greek mathematics translating the writing of __, __, __, __, etc. into Arabic

A
  • Apollonius
  • Archimedes
  • Euclid
  • Ptolemy
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28
Q

When: Arabic Algebra and Indian numerals came to Western Europe

A

830 C.E.

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29
Q
  • also called Fibonacci
  • wrote Liber Abaci
A

Leonardo of Pisa

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30
Q

Leonardo of Pisa is also called

A

Fibonacci

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31
Q

What did Leonardo of Pisa write

A

Liber Abaci

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32
Q

a book filled with arithmetical and algebraic information which he had collected during his travels

A

Liber Abaci

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33
Q

Liber Abaci was one of the means by which the ___________ was introduced to Western Europe

A

Hindu-Arabic System of Numeration

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34
Q

What is the best known contribution of Hindu mathematics to modern mathematics?

A

decimal position system

35
Q

What did the Hindi mathematics also introduce

A

number zero

36
Q

When: Leonardo of Pisa

A

1202 C.E.

37
Q
  • German mathematician
  • the + and - first appeared in print in his book
A

Johannes Widmann

38
Q

What is the book where the + and - symbols first appeared

A

Mercantile Arithmetic

39
Q

When and where was the Mercantile Arithmetic book published

A

Leipzig in 1489

40
Q

Mercantile Arithmetic referred to

A

surpluses and deficits in business problems

41
Q

When: Johannes Widmann

A

1489 C.E.

42
Q

discovered logarithms

A

John Napier

43
Q

What did John Napier discover

A

logarithms

44
Q

When: John Napier

A

17th century

45
Q
  • given credit for early developments that led to infinitesimal calculus
  • French lawyer and mathematician
A

Pierre de Fermat

46
Q

Pierre de Fermat was given credit for early developments that led to what

A

infinitesimal calculus

47
Q

__ and __ began the mathematical study of probability

A
  • Fermat
  • Pascal
48
Q

What did Fermat and Pascal begin

A

mathematical study of probability

49
Q

laid the foundations of the Probability Theory together with Fermat

A

Blaise Pascal

50
Q

early mechanical calculator

A

Pascaline

51
Q

tool for expanding a binomial

A

Pascal’s Triangle

52
Q

binomial

A

(a + b)^n

53
Q
  • invented the Cartesian coordinate system
  • developed analytic geometry
  • laid foundation for the development of calculus
  • another notable mathematician of the 17th century
A

Rene Descartes

54
Q

Rene Descartes invented the __ __ __

A

Cartesian coordinate system

55
Q

Rene Descartes developed __ __

A

analytic geometry

56
Q

Rene Descartes laid the foundation for the development of __

A

calculus

57
Q

When: Pierre de Fermat, Blaise Pascal, Rene Descartes

A

1629 C.E.

58
Q
  • discovered infinitesimal calculus along with Sir Isaac Newton
  • each one made the discovery alone, not while working together
A

Gottfried Leibniz

59
Q

When: Leibniz’ first paper on the calculus published

A

1684 C.E.

60
Q
  • most important mathematician of the 18th century
  • worked in a wide range of mathematical areas
  • started the Graph Theory, the Calculus of Variations, and Differential Geometry
A

Leonhard Euler

61
Q

Leonhard Euler started the __ __, the __ __ __, and __ __

A
  • Graph Theory
  • Calculus of Variations
  • Differential Geometry
62
Q
  • German mathematician
  • regarded as one of the greatest mathematicians of all time
  • contributed to number theory, geometry, probability theory, planetary, and the theory of functions
  • proved the Fundamental Theorem of Algebra
A

Carl Friedrich Gauss

63
Q

Carl Friedrich Gauss contributed to __ __, __, __ __, __, and the __ _ __

A
  1. number theory
  2. geometry
  3. probability theory
  4. planetary
  5. theory of functions
64
Q

When did Carl Friedrich Gauss prove the Fundamental Theorem of Algebra

A

1799

65
Q

What did Carl Friedrich Gauss prove in 1799

A

Fundamental Theorem of Algebra

66
Q
  • began a rigorous theory of functions and of mechanics toward the end of 18th century
  • played a key role in the creation of the Metric system of weights and measures
A

Joseph Louie Lagrange

67
Q

What did Joseph Louie Lagrange began toward the end of the 18th century

A

rigorous theory of functions and of mechanics

68
Q

Joseph Louie Lagrange played a key role in the creation of the __ __ of weights and measures

A

Metric system

69
Q

introduced the Venn Diagram in 1874 which became a useful tool in Set Theory

A

John Venn

70
Q

What did John Venn introduce in 1874

A

Venn Diagram

71
Q

When did John Venn introduce the Venn Diagram

A

1874

72
Q

The Venn diagram became a useful tool in __ __

A

Set Theory

73
Q

When: Leonhard Euler, Carl Friedrich Gauss, Joseph Louie Lagrange, John Venn

A

18th - 19th Century

74
Q
  • introduced the theory of fractals
  • published The Fractal Geometry of Nature in 1982
A

Benoit Mandelbrot

75
Q

What did Benoit Mandelbrot introduce

A

theory of fractals

76
Q

When did Benoit Mandelbrot publish The Fractal Geometry of Nature

A

1982

77
Q

What did Benoit Mandelbrot publish in 1982

A

The Fractal Geometry of Nature

78
Q

When: Benoit Mandelbrot

A

1975 C.E.

79
Q

proved Fermat’s Last Theorem

A

Andrew Wiles

80
Q

What did Andrew Wiles prove

A

Fermat’s Last Theorem

81
Q

When: Andrew Wiles

A

1994 C.E.

82
Q

What was announced in 2000 C.E.

A

Mathematical challenges of the 21st Century

83
Q

When: Mathematical challenges of the 21st Century announced

A

2000 C.E.

Mathematics in the Modern World (13 decks)

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