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
2
Q
Mathematics was then developed in __, and simultaneously in __ and in __
A
- Greece
- China
- India
3
Q
This ancient Greek mathematics, along with some influence of __ mathematics spread to the neighboring countries in the __ __
A
- Hindu (mathematics)
- Middle East
4
Q
Mathematics was translated into __ and __, and was adopted by __ __
A
- Arabic and Latin
- Western Europe
5
Q
- first people to assign symbols to group of objects to represent numbers
- developed the earliest known writing system
A
Sumerians
6
Q
Sumerians are from
A
Sumer, a region of Mesopotamia
7
Q
What writing system did the Sumerians develop
A
cuneiform script (pictographic writing system)
8
Q
When: Sumerians
A
4,000 - 3,000 B.C.E.
9
Q
first people to develop a numerical system that was based on the number 10
A
Egyptians
10
Q
What developed in Egypt
A
Hieroglyphic Numerals
11
Q
When: Egyptians
A
3,000 B.C.E.
12
Q
used the Sexagesimal System
A
Babylonians
13
Q
What did the Babylonians use
A
Sexagesimal Numeral System
14
Q
When: Babylonians
A
2,400 B.C.E.
15
Q
When was the major Greek progress in mathematics
A
300 BC - 200 AD
16
Q
What did Euclid write during 300 BC - 200 AD era
A
Elements
17
Q
compilation of theorems, axioms in Algebra and postulates and theorems in Geometry
A
Elements
18
Q
With the Elements, Euclid gained the title of
A
Father of Geometry
19
Q
When: major Greek progress
A
300 B.C.E.
20
Q
- a Greek mathematician, physicist, inventor and astronomer
- derived a range of formulas in Geometry
A
Archimedes of Syracuse
21
Q
What are the formulas that Archimedes derived
A
- area of circle
- surface area and volume of sphere
- area under a parabola
22
Q
When: Archimedes of Syracuse
A
200 B.C.E.
23
Q
Greek astronomer, geographer, and mathematician considered as founder of trigonometry
A
Hipparchus of Nicaea
24
Q
When: Trigonometry of Hipparchus
A
140 B.C.E.
25
When: Hindu mathematical works translated to Arabic
775 C.E.
26
How did the Arabic Algebra and Indian numerals come to Western Europe
through Muhammad ibn Musa Al-Khwarizmi's writings
27
Other Arabic scholars also cultivated Greek mathematics translating the writing of __, __, __, __, etc. into Arabic
- Apollonius
- Archimedes
- Euclid
- Ptolemy
28
When: Arabic Algebra and Indian numerals came to Western Europe
830 C.E.
29
- also called Fibonacci
- wrote Liber Abaci
Leonardo of Pisa
30
Leonardo of Pisa is also called
Fibonacci
31
What did Leonardo of Pisa write
Liber Abaci
32
a book filled with arithmetical and algebraic information which he had collected during his travels
Liber Abaci
33
Liber Abaci was one of the means by which the ___________ was introduced to Western Europe
Hindu-Arabic System of Numeration
34
What is the best known contribution of Hindu mathematics to modern mathematics?
decimal position system
35
What did the Hindi mathematics also introduce
number zero
36
When: Leonardo of Pisa
1202 C.E.
37
- German mathematician
- the + and - first appeared in print in his book
Johannes Widmann
38
What is the book where the + and - symbols first appeared
Mercantile Arithmetic
39
When and where was the Mercantile Arithmetic book published
Leipzig in 1489
40
Mercantile Arithmetic referred to
surpluses and deficits in business problems
41
When: Johannes Widmann
1489 C.E.
42
discovered logarithms
John Napier
43
What did John Napier discover
logarithms
44
When: John Napier
17th century
45
- given credit for early developments that led to infinitesimal calculus
- French lawyer and mathematician
Pierre de Fermat
46
Pierre de Fermat was given credit for early developments that led to what
infinitesimal calculus
47
__ and __ began the mathematical study of probability
- Fermat
- Pascal
48
What did Fermat and Pascal begin
mathematical study of probability
49
laid the foundations of the Probability Theory together with Fermat
Blaise Pascal
50
early mechanical calculator
Pascaline
51
tool for expanding a binomial
Pascal's Triangle
52
binomial
(a + b)^n
53
- invented the Cartesian coordinate system
- developed analytic geometry
- laid foundation for the development of calculus
- another notable mathematician of the 17th century
Rene Descartes
54
Rene Descartes invented the __ __ __
Cartesian coordinate system
55
Rene Descartes developed __ __
analytic geometry
56
Rene Descartes laid the foundation for the development of __
calculus
57
When: Pierre de Fermat, Blaise Pascal, Rene Descartes
1629 C.E.
58
- discovered infinitesimal calculus along with Sir Isaac Newton
- each one made the discovery alone, not while working together
Gottfried Leibniz
59
When: Leibniz' first paper on the calculus published
1684 C.E.
60
- 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
Leonhard Euler
61
Leonhard Euler started the __ __, the __ __ __, and __ __
- Graph Theory
- Calculus of Variations
- Differential Geometry
62
- 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
Carl Friedrich Gauss
63
Carl Friedrich Gauss contributed to __ __, __, __ __, __, and the __ _ __
1. number theory
2. geometry
3. probability theory
4. planetary
5. theory of functions
64
When did Carl Friedrich Gauss prove the Fundamental Theorem of Algebra
1799
65
What did Carl Friedrich Gauss prove in 1799
Fundamental Theorem of Algebra
66
- 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
Joseph Louie Lagrange
67
What did Joseph Louie Lagrange began toward the end of the 18th century
rigorous theory of functions and of mechanics
68
Joseph Louie Lagrange played a key role in the creation of the __ __ of weights and measures
Metric system
69
introduced the Venn Diagram in 1874 which became a useful tool in Set Theory
John Venn
70
What did John Venn introduce in 1874
Venn Diagram
71
When did John Venn introduce the Venn Diagram
1874
72
The Venn diagram became a useful tool in __ __
Set Theory
73
When: Leonhard Euler, Carl Friedrich Gauss, Joseph Louie Lagrange, John Venn
18th - 19th Century
74
- introduced the theory of fractals
- published The Fractal Geometry of Nature in 1982
Benoit Mandelbrot
75
What did Benoit Mandelbrot introduce
theory of fractals
76
When did Benoit Mandelbrot publish The Fractal Geometry of Nature
1982
77
What did Benoit Mandelbrot publish in 1982
The Fractal Geometry of Nature
78
When: Benoit Mandelbrot
1975 C.E.
79
proved Fermat's Last Theorem
Andrew Wiles
80
What did Andrew Wiles prove
Fermat's Last Theorem
81
When: Andrew Wiles
1994 C.E.
82
What was announced in 2000 C.E.
Mathematical challenges of the 21st Century
83
When: Mathematical challenges of the 21st Century announced
2000 C.E.
