By Marsigit

C. Probability with relative Frequency

Probability can be explained from the definition of relative frequency. See the explanation below!

• In the experiment of tossing a coin, the ratio between the occurrence of the head and the total number of the experiment is called the relative frequency of obtaining the head.

• If in the experiment, the coin balances enough then the more the experiment is taken out, the more the relative frequency of getting a head is close to .

• In this case, we can tell that in the experiment of throwing a balance coin, the probability of obtaining a head (P(G)) is .

If n is large enough, then the probability of event A is

Where f represents the frequency of event A and n represents the total number of experiment.

Example:

From the experiment of 40 times tossing of 1 coin , the occurrence of head is 22 times. Find the relative frequency of obtaining a head !

Solution :

The total number of experiment (n) is 40 times.

The frequency of the occurrences of the head, f=22

So, the relative frequency of the occurrences of the head is=

Exercises

1. In the experiment of rolling once a six-sided dice , find :

a. the probability of occurrences of the 3-spot side

b. the probability of occurrences of the odd-spot side

2. From tossing a coin 30 times, there are 16 times tail occurrences. Find :

a. the relative frequency of obtaining of the tail

b. the relative frequency of obtaining of the head

3. Expectation Frequency

In an experiment, if A is an event and the probability of event A is P(A) then the expectation frequency of event A for n times experiments is determined by the formula stated below

Example :

A coin was tossed 30 times (assume the coin balances ). What is the expectation frequency of obtaining a head ?

Solution :

The total number of tossing is 30 times. If H is an event of obtaining a head, the probability of obtaining a head is . Hence the frequency of expectation of obtaining a head is

So, the expectation frequency of obtaining the head is 15 times.

Exercises

1. Two coins were tossed together 10 times. What is the expectation frequency of obtaining a head from the first coin and the tail from the other coin?

2. A six-sided dice was thrown 30 times. What is the frequency of expectation of occurrences of the even-spot side?

3. A coin and a dice were rolled together 4 times. What is the expectation frequency of obtaining a tail from the coin and even-spot side from the dice?

4. Two dice were rolled together. How many experiments that have been taken out if the expectation frequency of occurrences of the same side from both of the dice is 10 times?

4. Compound Events

Compound event is an event that contains 2 or more events. In the next explanation, we will discuss about the probability of some compound events contained 2 or more events.

A. Probability Of Non Mutually Exclusive Event

Event A and event B are non mutually exclusive if . Consider the Venn diagram of event A and B that are non mutually exclusive events below

….

The probability of 2 events ( event A and event B) that are non mutually exclusive is as follows

Remember:

is an intersection operation in sets algebra

is an empty sets that is a set which has no elements.

is an union operation in sets algebra

Note:

In mathematics, the union operation is presented by term 'or'. While the intersect operation is presented by term 'and'. For example, P(AUB) is stated as the probability of event A or event B. While P(A∩B) is stated as the probability of event A and event B..

Example

A six-sided dice is rolled once. Find the probability of occurrences of the primary number spot side or the sides with spots less than 5.

Solution:

The sample space of the results of rolling a six sided dice once is S={1,2,3,4,5,6}. So, the total member of sample space S is n(S)=6

If A is an event of obtaining primary number spot side, then A={2,33,5}. So, the total member of event A is n(A)=3.

If B is an event of obtaining the sides with spot less than 5. So, the total member of event B is n(B)=4.

Hence, we can conclude that

So, the total member of event is . So, A and B are non mutually exclusive events.

As a results

The probability of obtaining primary number spot side or sides with spot less that 5 is 5/6

B. Probability of Mutually Exclusive Events

Event A and event B is called mutually exclusive event if . See the Venn diagram of event A and B that are mutually exclusive event below

….

Example

A six sided dice is thrown once. Find the probability of occurrences of the sides with spots less than 3 or the sides with spots greater than or equal to 5!

Solution :

The sample space of the results of throwing a six sided dice once is S={1,2,3,4,5,6}. So the total member of sample space S is n(S)=6

If A is an event of occurrences of the side wit spots less than3, then A={1,2}. The total member of event A is n(A)=2

If B is an event of occurrences of the side with spots greater than or equal with 5 then B={5,6}. The total member of event B is n(B)=2

We can conclude that . So A and B are mutually exclusive events.

as a results

So the probability of occurrences of sides with spots less than 3 or the sides with spots greater then or equal with 5 is 4/6

c. The Probability of Independent Events

Event A and event B are called independent events if the occurrence or non-occurrence of event A is not in any way influenced by the occurrence or non-occurrence of another event. The probability of independent events is as follows

Examples

A basket contains 4 oranges and 6 apples. The other basket contains 5 oranges and 15 apples. What is the probability of obtaining an orange from the first basket and an orange too from the other basket?

Answer :

If,

S1 is sample space of fruits in the first basket, then the number of fruits in the first basket is n(S1)=10

S2 is a sample space of fruits in the second basket, then the number of fruits in the second basket is n(S2)=20

A is an event of obtaining an orange from the first basket n(A)=4

B is an event of obtaining an orange from the second basket, then n(B)=5

So the probability of obtaining an orange from the first basket and an orange from the second basket is 1/10

Exercises

1. A six sided dice was rolled once. Find:

a. the probability of obtaining the even-spot side or the odd-spot side

b. the probability of obtaining the even spot side or the sides with spot less than 3

2. From 52 cards, a card is taken randomly. Determine:

a. the probability that the red card or black card is selected

b. the probability that the red ace card or black ace card is selected

c. the probability that the black card or the 9th card is selected

d. the probability that the red card or the black ace card is selected

3. There are 80 students from a certain school joining some extracurricular programs. It was found that 25 students were joining karate, 15 students were joining swimming and 10 students were joining both karate and swimming program. While the rests were joining the other programs. If we select randomly 1 student from the students that were joining the extracurricular programs, what is the probability that the students which were joining karate or swimming program is selected?

4. Class IX A consists of 40 students. It is found that 10 from 40 students like Biology subject, 20 like English and 5 students like both Biology and English. The other students like the other subject. If we select randomly 1 student from class IX A, what is the probability that the students that like Biology or English is selected?

5. Two six-sided dice were rolled once together. Determine:

a. the probability of occurrences of 1 spot side of the first dice and the primary number spot side of the second dice.

b. the probability of occurrences of 2 spot side of the first dice and 3 spot side of the other dice.

Exercise Chapter 3

A. Chose the correct answer

1. Mrs. Tuti tastes 1 spoon of soup from a bowl of soup. The population from the illustration above is

a. 1 bowl of soup

b. 1 spoon of soup tasted by mrs Tuti

c. 1 pan of soup

d. 1 plate of soup

2. Given the data presented as below

….

The average of the data is....

a. 18

b. 18.25

c. 18.50

d. 18.75

3. Given the data of the student’s age from a certain organization is presented below

The median of the data is ....

a. 13

b. 13.50

c. 15.50

d. 16

4. The data of the weight of a group of athletes is presented below...

The modus of data above is ....

a. 42

b. 44.5

c. 47

d. 42 and 47

5. The average of the art test score from a certain student group consist of 5 students is 75. After a new member join the group, the average turns into 73. The art test score of the new member is....

a. 73

b. 70

c. 63

d. 60

6. See the data of English test score from 50 students presented in the bar diagram below.

The modus of the data of the English test score is ....

a. 5

b. 7

c. 9

d. 5 and 7

7. The money ( in rupiahs ) owned by a student in a week is presented in the diagram below.

The average of the student's money in a week is ....

a. Rp 6000,00

b. Rp 6200,00

c. Rp 6500,00

d. Rp 6800,00

8. If 2 coins were tossed once then the probability of obtaining a tail from one of the coins is ...

a. 1/4

b. 1/2

c. 3/4

d. 1

9. Tono checks his 2 game CD that has not being used for a long time. He wants to know whether his CDs are still working or not. The number of possible outcome that might occur from the checking is....

a. 1

b. 2

c. 4

d. 6

10. The total member of a certain Arisan group is 40 people. Every round, there are 4 people that get the Arisan money. The probability of a member getting the money in the first round is ....

a. 1/10

b. 1/10

c. 1/4

d. 1

11. In the experiment of throwing a coin three times, B is an event of obtaining a tail once. The B event can be expressed as….

a. {T}

b. {THH}

c. {THH, HTH, HHT}

d. {THH, HTH, HHT, HHH}

12. If from 1 pack of cards is taken 1 card randomly, then the probability of obtaining an Ace is ….

a.

b.

c.

d.

13. A box contains 4 red marble, 5 white and 6 green ones. If 1 marble is taken randomly, the probability of occurrences of obtaining a red marble is ….

a.

b.

c.

d.

14. A manager from a certain company gets information that 3 of 100 products from that company are damaged. If 1 product from that company is taken randomly, the probability that the product is good is ….

a.

b.

c.

d.

15. A coin and a six-sided dice are rolled together. The probability of obtaining the 5 spot side is ….

a.

b.

c.

d.

16. Two dices are thrown together. The probability that both of the sides are same is ….

a.

b.

c.

d.

17. A six-sided dice is rolled 18 times. The relative frequency ( the expectation frequency) of obtaining a side with spots less that 4 is ….

a. 2

b. 3

c. 6

d. 9

19. A six sided dice and a coin were rolled together once. The probability of occurrences of obtaining a primary number spot side and the tail from the coin is ….

a. 0.25

b. 0.5

c. 0.75

d. 0.85

20. From 52 cards we took 1 card randomly. The probability of getting a black Ace or a red card is ….

a.

b.

c.

d.

B. Do the exercises below

1. The data of favorite sports of 120 students is presented as a pie diagram below.

a. How many students that like badminton ?

b. What is the modus of student favourite sports? Explain your answer

2. The try out score of Science National Examination from a certain school is presented in table below

a. How many students whose score is more than 5?

b. Calculate the average of the try out score !

c. Determine the median and modus of the data above ?

3. A student is observing whether 3 laboratory equipments are still working or not.

a. Determine the sample space of the observation

b. If A is an event of getting 2 equipment damaged, write the member of event A !

c. Determine the probability of event that 1 equipment is damaged !

4. Given 2 box, each contains 5 balls. The balls in every box were labeled 1 to 5. Then, from each box was taken 1 ball randomly all at once.

a. What is the probability of obtaining that the balls of each box have the same label.

b. What is the probability of obtaining an odd numbered ball from the first box?

5. The probability of a student to be chosen as representatives in the scientific paper competition for teenagers in a certain school is 0.025. How many students that will be the representatives in the competition if the total number of students joining is 720?

Evaluation 1-3

A. Chose the correct answers

1. Two triangles below are congruent in the case of the relation….

a. side, side, side

b. side, side, angle

c. side, angle, angle

d. angle, angle, angle

….

2. Two triangles below are congruent in the case of the relation ….

a. side, side, side

b. side, side, angle

c. side, angle, angle

d. angle, angle, angle

….

3. Two triangles below are congruent in the case of the relation….

a. side, side, side

b. side, side, angle

c. side, angle, angle

d. angle, angle, angle

….

4. Given ABC and CBD. If AB=10 cm and BC=7 cm then the length of BD is ....

a. 10 cm

b. cm

c. cm

d. 4.9 cm

….

5. Given ABC and PQR are similar. CAB=RPQ, ABC= PQR, and BCA=QRP then the length of PR is ….

a. 7.14 cm

b. 3.5 cm

c. 0.56 cm

d. 0.14 cm

….

6. Given ABC and CBD are similar. CAB=DCB=90o and CBA=DBC. If AC=6 cm and BC=10 cm then the length of AB and the length of CD are ….

a. AB=7.5 cm and CD=8 cm

b. AB=8 cm and CD=4.8 cm

c. AB=8 cm and CD=7.5 cm

d. AB=8 cm and CD=13.3 cm

….

7. Given AOB and XOY are similar. If AO=2 cm, XA=3cm, AB=4 cm, and BY=5.1 cm then the length of XY and the length of OB are ….

a. XY=3.4 cm and OB=1.6 cm

b. XY=3.4 cm and OB=10 cm

c. XY=1.6 cm and OB=3.4 cm

d. XY=10 cm and OB=3.4 cm

….

8. Given ABC and DEC are similar. If CD=5 cm and AD=3 cm then the value of is ….

a.

b.

c.

d.

….

9. Given ABX and CDX are similar. If AX= 8 cm XC=10 cm, and BD=27 cm then the length of DX is ….

a. 12 cm

b. 13 cm

c. 14 cm

d. 15 cm

….

10. Given ABC and DEC are similar. If BCA:CAB:ABC = 1:2:1 then the value of DEC is ….

a. 25o

b. 30o

c. 45o

d. 50o

….

11. A cylinder has a radius 6 cm and the side area is 37.86 cm2. The height of the cylinder is ....

a. 12 cm

b. 10 cm

c. 2 cm

d. 1 cm

12. Oil 4.71 liter was poured into a can formed cylinder so the cylinder is filled with the oil until 15 cm high. The diameter of the cylinder is ....

a. 10 cm

b. 15 cm

c. 20 cm

d. 30 cm

13. The side area of a cylinder is 440 cm2. If the height of the cylinder is 10 cm then the top and bottom area of the cylinder are ....

a. 308 cm2

b. 154 cm2

c. 88 cm2

d. 44 cm2

14. A biscuit can has diameter 20 cm and height 10 cm. The surface area of the biscuit can is ....

a. 12,560 cm2

b. 1,256 cm2

c. 628 cm2

d. 125.6 cm2

15. A trumpet made from cardboard and formed a cone has a diameter of 14 cm. If the slant height is 30 cm then the area of the cardboard needed to make the trumpet is ....

a. 1,320 cm2

b. 660 cm2

c. 132 cm2

d. 66 cm2

16. A cone has a slant height of 7 cm and radius 3.5 cm. The surface area of the cone is ....

a. 1,155 cm2

b. 770 cm2

c. 115.5 cm2

d. 77 cm2

17. If the volume of a cone having perpendicular height 9 cm is 462 cm3 then the base area of the cone is ....

a. 44 cm2

b. 154 cm2

c. 1,386 cm2

d. 7,546 cm2

18. Mom has a mold to make jelly formed a half sphere and having a diameter of 21 cm. The volume of the jelly if it was made using the mold is ....

a. 38,808 cm3

b. 19,404 cm3

c. 4,851 cm3

d. 2,425.5 cm3

19. A ball is made from woven rattan. If the total area of woven rattan used to make the sphere is 616 cm2 then the diameter of the ball is ....

a. 4.9 cm

b. 7 cm

c. 9.8 cm

d. 14 cm

20. An aquarium formed a sphere has diameter of 35 cm. The volume of the aquarium is ....

a. 67,375 liter

b. 22,458.33 liter

c. 67.375 liter

d. 22.458 liter

Do number 21-22 based on the table below. We were given a data of weight of an apple from some different trees below.

….

21. The total number of apples that are being measured is….

a. 43 apples

b. 44 apples

c. 48 apples

d. 50 apples

22. If the apples that have weight less than 80 gram are not sold then the total number of apples that are sold is ….

a. 33 apples

b. 26 apples

c. 24 apples

d. 17 apples

Do number 23-25 based on the circle graph below. The data of student favorite activities in their spare time is presented below.

….

23. The value of x is …..

a. 100o

b. 110o

c. 120o

d. 130o

24. The percentage of students that like reading is ….

a. 80 %

b. 40 %

c. 33.33%

d. 22.22%

25. If the number of students who like reading is 40 people, then the number of students who like watching TV is ….

a. 50 students

b. 60 students

c. 80 students

d. 120 students

26. We were given a data of the total number of goal occurrences of 15 soccer games in a certain season

….

The median of the data above is ….

a. 1

b. 2

c. 3

d. 4

27. A box contains 4 red marble, 3 white, and 5 green ones. If we took 1 marble randomly then the probability of obtaining a white marble is ….

a. 0.25

b. 0.33

c. 0.42

d. 0.60

28. If the probability of a student getting scholarship is 0.125 then the probability of a student not getting that scholarship is …

a. 0.875

b. 0.785

c.

d.

29. A six sided dice and a coin were rolled together. The probability of occurrences of odd-spot side of the dice and a tail of the coin is ….

a. 0.75

b. 0.5

c. 0.25

d. 0.125

30. A card is taken randomly from 52 cards. The probability of getting an Ace card is ….

a.

b.

c.

d.

B. Solve the following problems

1. In the afternoon, a boy who has height 1.5 m has a shadow with length of 4.5 m. Tina’s height is 1.3 m. What is the length of Tina’s shadow if she stands in the same time and the same place as the boy?

2. See the picture below. A fisherman wants to know about the distance of his friend boat that sailing in the ocean from the coast line. Based on the position of the boat, the fisherman is located in point D. Then he make another points ABC along the coast according to the sketch below. Determine the length of AA'!

….

3. Prove that ABC and ADC are congruent!

4. A cylinder has maximum capacity of 2.156 liter. If the diameter of the cylinder is 14 cm, then calculate the height of the cylinder!

5. A traditional cap formed a cone has a slant height of 28 cm and radius 21 cm. It is made from woven rattan. Find the area of the woven rattan used to make the traditional cap!

6. A bowl is formed half-sphere with diameter 14 cm. Calculate the volume of the bowl!

7. A ball has a circumference of the mid circle of 66 cm. Determine the total area of material used to cover the leather!

8. A student has a collection of 50 books, consists of 20 school text books, 10 fiction books, 15 motivation books, and 5 biography books of world famous person. Draw a circle graph to illustrate the information!

9. A trader mixes 10 kg oranges that priced Rp 15.000,00 per kg and 5 kg oranges priced Rp 10.000,00. What is the average price of that mixed oranges now?

10. In a certain school, there are 100 students who propose for scholarship. Each student has the probability of 0.25 to get the scholarship. How many students who will get the schoolarship?

## Wednesday, February 25, 2009

## Thursday, December 25, 2008

### Four Postulats of Euclides

Postulat I

For every point P and for every point Q not equal to P there exists a unique line l that passes through P and Q.

Postulate II

For every segment AB and for every segment CD there exists a unique point E such that B is between A and E and segment CD is congruent to segment BE.

Postulate III

For every point O and every point A not equal to O there exist a circle with center O and radius OA.

Postulate IV

All right angles are congruent to each other.

The fifth postulate is really the most one

Greenberg, M.J., 1973, “Euclidean and Non-Euclidean Geometries: Development and History”, San Francisco: W.H. FREEMAN AND COMPANY

For every point P and for every point Q not equal to P there exists a unique line l that passes through P and Q.

Postulate II

For every segment AB and for every segment CD there exists a unique point E such that B is between A and E and segment CD is congruent to segment BE.

Postulate III

For every point O and every point A not equal to O there exist a circle with center O and radius OA.

Postulate IV

All right angles are congruent to each other.

The fifth postulate is really the most one

Greenberg, M.J., 1973, “Euclidean and Non-Euclidean Geometries: Development and History”, San Francisco: W.H. FREEMAN AND COMPANY

### Incommensurability of Mathematics

Posy, C., 1992, noted that commensurability is false (found irrational numbers); if commensurability were true, (1+1)=2 must equal p/q where p and q are natural numbers. Proof that Commensurability is False (first recorded use of reductio ad absurdum proof):

1) Assume 2=p/q, p and q {set of natural numbers}

2) Reduce p/q to lowest terms (can be done with any fraction)

3) p=q2 p2=2q2

4) Thus, p2 is an even number (it is equal to twice an integer)

5) p2 = p is also even (all even sqaures' roots are even)

6) So, p=2k, k {set of natural numbers}

7) (2k)2=2q2 4k2=2q2 2k2=q2

8) Thus, q2 is even, so q is even

9) Both q and p are even, thus they share the common factor of 2; this however, contradicts step #2, that p/q is reduced to lowest terms, thus our assumption that 2=p/q is false.

1) Assume 2=p/q, p and q {set of natural numbers}

2) Reduce p/q to lowest terms (can be done with any fraction)

3) p=q2 p2=2q2

4) Thus, p2 is an even number (it is equal to twice an integer)

5) p2 = p is also even (all even sqaures' roots are even)

6) So, p=2k, k {set of natural numbers}

7) (2k)2=2q2 4k2=2q2 2k2=q2

8) Thus, q2 is even, so q is even

9) Both q and p are even, thus they share the common factor of 2; this however, contradicts step #2, that p/q is reduced to lowest terms, thus our assumption that 2=p/q is false.

### Pythagorean Theorem

In the British museum, it was found one of four Babylonian tablets, which flourished in Mesopotamia between 1900 BC and 1600 BC, which has a connection with Pythagoras's theorem, as the following:

4 is the length and 5 the diagonal. What is the breadth ?

Its size is not known.

4 times 4 is 16.

5 times 5 is 25.

You take 16 from 25 and there remains 9.

What times what shall I take in order to get 9 ?

3 times 3 is 9.

3 is the breadth.

Reference:

O’Connor, J.J and Robertson, E.F., 1999, Pythagoras of Samos, http://www- history.mcs.st-andrews.ac.uk/history/Mathematicians/Pythagoras.html

4 is the length and 5 the diagonal. What is the breadth ?

Its size is not known.

4 times 4 is 16.

5 times 5 is 25.

You take 16 from 25 and there remains 9.

What times what shall I take in order to get 9 ?

3 times 3 is 9.

3 is the breadth.

Reference:

O’Connor, J.J and Robertson, E.F., 1999, Pythagoras of Samos, http://www- history.mcs.st-andrews.ac.uk/history/Mathematicians/Pythagoras.html

## Sunday, December 7, 2008

### Timeline of mathematics

Timeline of mathematics

From Wikipedia, the free encyclopedia.

A timeline of Pure and Applied Mathematics

1. 2450 BC - Egypt, first systematic method for the approximative calculation of the circle on the basis of the Sacred Triangle 3-4-5,

2. 1650 BC - Rhind Papyrus, copy of a lost scroll from around 1850 BC, the scribe Ahmes presents first known aproximate value of π at 3.16 and first attempt at squaring the circle.

3. 530 BC - Pythagoras studies propositional geometry and vibrating lyre strings; his group discovers the irrationality of the square root of two,

4. 370 BC - Eudoxus states the method of exhaustion for area determination,

5. 350 BC - Aristotle discusses logical reasoning in Organon,

6. 300 BC - Euclid in his Elements studies geometry as an axiomatic system, proves the infinitude of prime numbers and presents the Euclidean algorithm; he states the law of reflection in Catoptrics,

7. 260 BC - Archimedes computes π to two decimal places using inscribed and circumscribed polygons and computes the area under a parabolic segment,

8. 225 BC - Apollonius of Perga writes On Conic Sections and names the ellipse, parabola, and hyperbola,

9. 200 BC ?240 BC - Eratosthenes uses his sieve algorithm to isolate prime numbers and finds the number of primes is infinite,

10. 140 BC - Hipparchus develops the bases of trigonometry,

11. 250 - Diophantus uses symbols for unknown numbers in terms of the syncopated algebra,

12. 250 - Diophantus writes Arithmetica the first systematic treatise on algebra,

13. 450 - Tsu Ch'ung-Chih and Tsu Kêng-Chih compute π to six decimal places,

14. 550 - Hindu mathematicians give zero a numeral representation in a positional notation system,

15. 628 - Brahmagupta writes Brahma- sphuta- siddhanta,

16. 750 - Al-Khawarizmi - Considered father of modern algebra. First mathematician to work on the details of 'Arithmetic and Algebra of inheritance' besides the systematisation of the theory of linear and quadratic equations.

17. 895 - Thabit ibn Qurra - The only surviving fragment of his original work contains a chapter on the solution and properties of cubic equations.

18. 975 - Al-Batani - Extended the Indian concepts of sine and cosine to other trigonometrical ratios, like tan¬gent, secant and their reciprocals. Derived the formula: sin α = tan α / (1+tan² α) and cos α = 1 / (1 + tan² α).

19. 1020 - Abul Wafa - Gave this famous formula: sin (α + β) = sin α cos β + sin β cos α. Also discussed the quadrature of the parabola and the volume of the paraboloid.

20. 1030 - Ali Ahmed Nasawi - Develops the division of days into 24 hours, hours into 60 minutes and minutes into 60 seconds.

21. 1070 - Omar Khayyam begins to write Treatise on Demonstration of Problems of Algebra and classifies cubic equations. Invented the second and third degree of quadratic equations.

22. 1202 - Leonardo Fibonacci demonstrates the utility of Arabic numerals in his Book of the Abacus,

23. 1424 - Ghiyath al-Kashi - computes π to sixteen decimal places using inscribed and circumscribed polygons,

24. 1520 - Scipione dal Ferro develops a method for solving cubic equations,

25. 1535 - Niccolo Tartaglia develops a method for solving cubic equations,

26. 1540 - Lodovico Ferrari solves the quartic equation,

27. 1596 - Ludolf van Ceulen computes π to twenty decimal places using inscribed and circumscribed polygons,

28. 1614 - John Napier discusses Napierian logarithms in Mirifici Logarithmorum Canonis Descriptio,

29. 1617 - Henry Briggs discusses decimal logarithms in Logarithmorum Chilias Prima,

30. 1619 - René Descartes discovers analytic geometry,

31. 1629 - Pierre de Fermat develops a rudimentary differential calculus,

32. 1634 - Gilles de Roberval shows that the area under a cycloid is three times the area of its generating circle,

33. 1637 - Pierre de Fermat claims to have proven Fermat's last theorem in his copy of Diophantus' Arithmetica,

34. 1654 - Blaise Pascal and Pierre de Fermat create the theory of probability,

35. 1655 - John Wallis writes Arithmetica Infinitorum,

36. 1658 - Christopher Wren shows that the length of a cycloid is four times the diameter of its generating circle,

37. 1665 - Isaac Newton invents his calculus,

38. 1668 - Nicholas Mercator and William Brouncker discover an infinite series for the logarithm while attempting to calculate the area under a hyperbolic segment,

39. 1671 - James Gregory discovers the series expansion for the inverse-tangent function,

40. 1673 - Gottfried Leibniz invents his calculus,

41. 1675 - Isaac Newton invents an algorithm for the computation of functional roots,

42. 1691 - Gottfried Leibniz discovers the technique of separation of variables for ordinary differential equations,

43. 1693 - Edmund Halley prepares the first mortality tables statistically relating death rate to age,

44. 1696 - Guillaume de L'Hôpital states his rule for the computation of certain limits,

45. 1696 - Jakob Bernoulli and Johann Bernoulli solve brachistochrone problem, the first result in the calculus of variations,

46. 1706 - John Machin develops a quickly converging inverse-tangent series for π and computes π to 100 decimal places,

47. 1712 - Brook Taylor develops Taylor series,

48. 1722 - Abraham De Moivre states De Moivre's theorem connecting trigonometric functions and complex numbers,

49. 1724 - Abraham De Moivre studies mortality statistics and the foundation of the theory of annuities in Annuities on Lives,

50. 1730 - James Stirling publishes The Differential Method,

51. 1733 - Giovanni Gerolamo Saccheri studies what geometry would be like if Euclid's fifth postulate were false,

52. 1733 - Abraham de Moivre introduces the normal distribution to approximate the binomial distribution in probability,

53. 1734 - Leonhard Euler introduces the integrating factor technique for solving first-order ordinary differential equations,

54. 1736 - Leonhard Euler solves the problem of the Seven bridges of Königsberg, in effect creating graph theory,

55. 1739 - Leonhard Euler solves the general homogenous linear ordinary differential equation with constant coefficients,

56. 1742 - Christian Goldbach conjectures that every even number greater than two can be expressed as the sum of two primes, now known as Goldbach's conjecture,

57. 1748 - Maria Gaetana Agnesi discusses analysis in Instituzioni Analitiche ad Uso della Gioventu Italiana,

58. 1761 - Thomas Bayes proves Bayes' theorem,

59. 1762 - Joseph Louis Lagrange discovers the divergence theorem,

60. 1789 - Jurij Vega improves Machin's formula and computes π to 140 decimal places,

61. 1794 - Jurij Vega publishes Thesaurus Logarithmorum Completus,

62. 1796 - Carl Friedrich Gauss presents a method for constructing a heptadecagon using only a compass and straightedge and also shows that only polygons with certain numbers of sides can be constructed,

63. 1796 - Adrien-Marie Legendre conjectures the prime number theorem,

64. 1797 - Caspar Wessel associates vectors with complex numbers and studies complex number operations in geometrical terms,

65. 1799 - Carl Friedrich Gauss proves that every polynomial equation has a solution among the complex numbers,

66. 1805 - Adrien-Marie Legendre introduces the method of least squares for fitting a curve to a given set of observations,

67. 1807 - Joseph Fourier announces his discoveries about the trigonometric decomposition of functions,

68. 1811 - Carl Friedrich Gauss discusses the meaning of integrals with complex limits and briefly examines the dependence of such integrals on the chosen path of integration,

69. 1815 - Siméon-Denis Poisson carries out integrations along paths in the complex plane,

70. 1817 - Bernard Bolzano presents the intermediate value theorem---a continuous function which is negative at one point and positive at another point must be zero for at least one point in between,

71. 1822 - Augustin-Louis Cauchy presents the Cauchy integral theorem for integration around the boundary of a rectangle in the complex plane,

72. 1824 - Niels Henrik Abel partially proves that the general quintic or higher equations cannot be solved by a general formula involving only arithmetical operations and roots,

73. 1825 - Augustin-Louis Cauchy presents the Cauchy integral theorem for general integration paths -- he assumes the function being integrated has a continuous derivative,

74. 1825 - Augustin-Louis Cauchy introduces the theory of residues in complex analysis,

75. 1825 - Johann Peter Gustav Lejeune Dirichlet and Adrien-Marie Legendre prove Fermat's last theorem for n = 5,

76. 1825 - André-Marie Ampère discovers Stokes' theorem,

77. 1828 - George Green proves Green's theorem,

78. 1829 - Nikolai Ivanovich Lobachevsky publishes his work on hyperbolic non-Euclidean geometry,

79. 1831 - Mikhail Vasilievich Ostrogradsky rediscovers and gives the first proof of the divergence theorem earlier described by Lagrange, Gauss and Green,

80. 1832 - Évariste Galois presents a general condition for the solvability of algebraic equations, thereby essentially founding group theory and Galois theory,

81. 1832 - Peter Dirichlet proves Fermat's last theorem for n = 14,

82. 1835 - Peter Dirichlet proves Dirichlet's theorem about prime numbers in arithmetical progressions,

83. 1837 - Pierre Wantsel proves that doubling the cube and trisecting the angle are impossible with only a compass and straightedge,

84. 1841 - Karl Weierstrass discovers but does not publish the Laurent expansion theorem,

85. 1843 - Pierre-Alphonse Laurent discovers and presents the Laurent expansion theorem,

86. 1843 - William Hamilton discovers the calculus of quaternions and deduces that they are non-commutative,

87. 1847 - George Boole formalizes symbolic logic in The Mathematical Analysis of Logic, defining what are now called Boolean algebras,

88. 1849 - George Gabriel Stokes shows that solitary waves can arise from a combination of periodic waves,

89. 1850 - Victor Alexandre Puiseux distinguishes between poles and branch points and introduces the concept of essential singular points,

90. 1850 - George Gabriel Stokes rediscovers and proves Stokes' theorem,

91. 1854 - Bernhard Riemann introduces Riemannian geometry,

92. 1854 - Arthur Cayley shows that quaternions can be used to represent rotations in four-dimensional space,

93. 1858 - August Ferdinand Möbius invents the Möbius strip,

94. 1859 - Bernhard Riemann formulates the Riemann hypothesis which has strong implications about the distribution of prime numbers,

95. 1870 - Felix Klein constructs an analytic geometry for Lobachevski's geometry thereby establishing its self-consistency and the logical independence of Euclid's fifth postulate,

96. 1873 - Charles Hermite proves that e is transcendental,

97. 1873 - Georg Frobenius presents his method for finding series solutions to linear differential equations with regular singular points,

98. 1874 - Georg Cantor shows that the set of all real numbers is uncountably infinite but the set of all algebraic numbers is countably infinite. Contrary to widely held beliefs, his method was not his famous diagonal argument, which he published three years later. (Nor did he formulate set theory at this time.)

99. 1878 - Charles Hermite solves the general quintic equation by means of elliptic and modular functions

100. 1882 - Carl Louis Ferdinand von Lindemann proves that π is transcendental and that therefore the circle cannot be squared with a compass and straightedge,

101. 1882 - Felix Klein invents the Klein bottle,

102. 1895 - Diederik Korteweg and Gustav de Vries derive the KdV equation to describe the development of long solitary water waves in a canal of rectangular cross section,

103. 1895 - Georg Cantor publishes a book about set theory containing the arithmetic of infinite cardinal numbers and the continuum hypothesis,

104. 1896 - Jacques Hadamard and Charles de La Vallée-Poussin independently prove the prime number theorem,

105. 1899 - Georg Cantor discovers a contradiction in his set theory,

106. 1899 - David Hilbert presents a set of self-consistent geometric axioms in Foundations of Geometry,

107. 1900 - David Hilbert states his list of 23 problems which show where some further mathematical work is needed,

108. 1901 - Élie Cartan develops the exterior derivative,

109. 1903 - Carle David Tolme Runge presents a fast Fourier Transform algorithm,

110. 1903 - Edmund Georg Hermann Landau gives considerably simpler proof of the prime number theorem,

111. 1908 - Ernst Zermelo axiomizes set theory, thus avoiding Cantor's contradictions,

112. 1908 - Josip Plemelj solves the Riemman problem about the existence of a differential equation with a given monodromic group and uses Sokhotsky - Plemelj formulae,

113. 1912 - Luitzen Egbertus Jan Brouwer presents the Brouwer fixed-point theorem,

114. 1912 - Josip Plemelj publishes simplified proof for the Fermat's last theorem for exponent n = 5,

115. 1914 - Srinivasa Aaiyangar Ramanujan publishes Modular Equations and Approximations to π,

116. 1919 - Viggo Brun defines Brun's constant B2 for twin primes,

117. 1928 - John von Neumann begins devising the principles of game theory and proves the minimax theorem,

118. 1930 - Casimir Kuratowski shows that the three cottage problem has no solution,

119. 1931 - Kurt Gödel proves his incompleteness theorem which shows that every axiomatic system for mathematics is either incomplete or inconsistent,

120. 1931 - Georges De Rham develops theorem in cohomology and characteristic classes,

121. 1933 - Karol Borsuk and Stanislaw Ulam present the Borsuk-Ulam antipodal-point theorem,

122. 1933 - Andrey Nikolaevich Kolmogorov publishes his book Basic notions of the calculus of variations (Grundbegriffe der Wahrscheinlichkeitsrechnung) which contains an axiomatization of probability based on measure theory,

123. 1940 - Kurt Gödel shows that neither the continuum hypothesis nor the axiom of choice can be disproven from the standard axioms of set theory,

124. 1942 - G.C. Danielson and Cornelius Lanczos develop a Fast Fourier Transform algorithm,

125. 1943 - Kenneth Levenberg proposes a method for nonlinear least squares fitting,

126. 1948 - John von Neumann mathematically studies self-reproducing machines,

127. 1949 - John von Neumann computes π to 2,037 decimal places using ENIAC,

128. 1950 - Stanislaw Ulam and John von Neumann present cellular automata dynamical systems,

129. 1953 - Nicholas Metropolis introduces the idea of thermodynamic simulated annealing algorithms,

130. 1955 - Enrico Fermi, John Pasta, and Stanislaw Ulam numerically study a nonlinear spring model of heat conduction and discover solitary wave type behavior,

131. 1960 - C. A. R. Hoare invents the quicksort algorithm,

132. 1960 - Irving Reed and Gustave Solomon present the Reed-Solomon error-correcting code,

133. 1961 - Daniel Shanks and John Wrench compute π to 100,000 decimal places using an inverse-tangent identity and an IBM-7090 computer,

134. 1962 - Donald Marquardt proposes the Levenberg-Marquardt nonlinear least squares fitting algorithm,

135. 1963 - Paul Cohen uses his technique of forcing to show that neither the continuum hypothesis nor the axiom of choice can be proven from the standard axioms of set theory,

136. 1963 - Martin Kruskal and Norman Zabusky analytically study the Fermi-Pasta-Ulam heat conduction problem in the continuum limit and find that the KdV equation governs this system,

137. 1965 - Martin Kruskal and Norman Zabusky numerically study colliding solitary waves in plasmas and find that they do not disperse after collisions,

138. 1965 - James Cooley and John Tukey present an influential Fast Fourier Transform algorithm,

139. 1966 - E.J. Putzer presents two methods for computing the exponential of a matrix in terms of a polynomial in that matrix,

140. 1967 - Robert Langlands formulates the influential Langlands program of conjectures relating number theory and representation theory,

141. 1968 - Michael Atiyah and Isadore Singer prove the Atiyah-Singer index theorem about the index of elliptic operators,

142. 1976 - Kenneth Appel and Wolfgang Haken use a computer to prove the Four-Color Theorem,

143. 1983 - Gerd Faltings proves the Mordell conjecture and thereby shows that there are only finitely many whole number solutions for each exponent of Fermat's last theorem,

144. 1983 - the classification of finite simple groups, a collaborative work involving some hundred mathematicians and spanning thirty years, is completed,

145. 1985 - Louis de Branges de Bourcia proves the Bieberbach conjecture,

146. 1987 - Yasumasa Kanada, David Bailey, Jonathan Borwein, and Peter Borwein use iterative modular equation approximations to elliptic integrals and a NEC SX-2 supercomputer to compute π to 134 million decimal places,

147. 1991 - Alain Connes and John W. Lott develop non-commutative geometry,

148. 1994 - Andrew Wiles proves part of the Taniyama-Shimura conjecture and thereby proves Fermat's last theorem,

149. 1998 - Thomas Hales (almost certainly) proves the Kepler conjecture,

150. 1999 - the full Taniyama-Shimura conjecture is proved.

151. 2000 - the Clay Mathematics Institute establishes the seven Millennium Prize Problems of unsolved important classic mathematical questions,

152. 2002 - Manindra Agrawal, Nitin Saxena, and Neeraj Kayal of Indian Institute of Technology (IIT), Kanpur, India, present a unconditional deterministic polynomial time algorithm to determine whether a given number is prime,

153. 2002 - Yasumasa Kanada, Y. Ushiro, Hisayasu Kuroda, Makoto Kudoh and a team of nine more compute π to 1241 billion digits using a Hitachi 64-node supercomputer,

154 2003

155 2004

156 2005 - 2007

From Wikipedia, the free encyclopedia.

A timeline of Pure and Applied Mathematics

1. 2450 BC - Egypt, first systematic method for the approximative calculation of the circle on the basis of the Sacred Triangle 3-4-5,

2. 1650 BC - Rhind Papyrus, copy of a lost scroll from around 1850 BC, the scribe Ahmes presents first known aproximate value of π at 3.16 and first attempt at squaring the circle.

3. 530 BC - Pythagoras studies propositional geometry and vibrating lyre strings; his group discovers the irrationality of the square root of two,

4. 370 BC - Eudoxus states the method of exhaustion for area determination,

5. 350 BC - Aristotle discusses logical reasoning in Organon,

6. 300 BC - Euclid in his Elements studies geometry as an axiomatic system, proves the infinitude of prime numbers and presents the Euclidean algorithm; he states the law of reflection in Catoptrics,

7. 260 BC - Archimedes computes π to two decimal places using inscribed and circumscribed polygons and computes the area under a parabolic segment,

8. 225 BC - Apollonius of Perga writes On Conic Sections and names the ellipse, parabola, and hyperbola,

9. 200 BC ?240 BC - Eratosthenes uses his sieve algorithm to isolate prime numbers and finds the number of primes is infinite,

10. 140 BC - Hipparchus develops the bases of trigonometry,

11. 250 - Diophantus uses symbols for unknown numbers in terms of the syncopated algebra,

12. 250 - Diophantus writes Arithmetica the first systematic treatise on algebra,

13. 450 - Tsu Ch'ung-Chih and Tsu Kêng-Chih compute π to six decimal places,

14. 550 - Hindu mathematicians give zero a numeral representation in a positional notation system,

15. 628 - Brahmagupta writes Brahma- sphuta- siddhanta,

16. 750 - Al-Khawarizmi - Considered father of modern algebra. First mathematician to work on the details of 'Arithmetic and Algebra of inheritance' besides the systematisation of the theory of linear and quadratic equations.

17. 895 - Thabit ibn Qurra - The only surviving fragment of his original work contains a chapter on the solution and properties of cubic equations.

18. 975 - Al-Batani - Extended the Indian concepts of sine and cosine to other trigonometrical ratios, like tan¬gent, secant and their reciprocals. Derived the formula: sin α = tan α / (1+tan² α) and cos α = 1 / (1 + tan² α).

19. 1020 - Abul Wafa - Gave this famous formula: sin (α + β) = sin α cos β + sin β cos α. Also discussed the quadrature of the parabola and the volume of the paraboloid.

20. 1030 - Ali Ahmed Nasawi - Develops the division of days into 24 hours, hours into 60 minutes and minutes into 60 seconds.

21. 1070 - Omar Khayyam begins to write Treatise on Demonstration of Problems of Algebra and classifies cubic equations. Invented the second and third degree of quadratic equations.

22. 1202 - Leonardo Fibonacci demonstrates the utility of Arabic numerals in his Book of the Abacus,

23. 1424 - Ghiyath al-Kashi - computes π to sixteen decimal places using inscribed and circumscribed polygons,

24. 1520 - Scipione dal Ferro develops a method for solving cubic equations,

25. 1535 - Niccolo Tartaglia develops a method for solving cubic equations,

26. 1540 - Lodovico Ferrari solves the quartic equation,

27. 1596 - Ludolf van Ceulen computes π to twenty decimal places using inscribed and circumscribed polygons,

28. 1614 - John Napier discusses Napierian logarithms in Mirifici Logarithmorum Canonis Descriptio,

29. 1617 - Henry Briggs discusses decimal logarithms in Logarithmorum Chilias Prima,

30. 1619 - René Descartes discovers analytic geometry,

31. 1629 - Pierre de Fermat develops a rudimentary differential calculus,

32. 1634 - Gilles de Roberval shows that the area under a cycloid is three times the area of its generating circle,

33. 1637 - Pierre de Fermat claims to have proven Fermat's last theorem in his copy of Diophantus' Arithmetica,

34. 1654 - Blaise Pascal and Pierre de Fermat create the theory of probability,

35. 1655 - John Wallis writes Arithmetica Infinitorum,

36. 1658 - Christopher Wren shows that the length of a cycloid is four times the diameter of its generating circle,

37. 1665 - Isaac Newton invents his calculus,

38. 1668 - Nicholas Mercator and William Brouncker discover an infinite series for the logarithm while attempting to calculate the area under a hyperbolic segment,

39. 1671 - James Gregory discovers the series expansion for the inverse-tangent function,

40. 1673 - Gottfried Leibniz invents his calculus,

41. 1675 - Isaac Newton invents an algorithm for the computation of functional roots,

42. 1691 - Gottfried Leibniz discovers the technique of separation of variables for ordinary differential equations,

43. 1693 - Edmund Halley prepares the first mortality tables statistically relating death rate to age,

44. 1696 - Guillaume de L'Hôpital states his rule for the computation of certain limits,

45. 1696 - Jakob Bernoulli and Johann Bernoulli solve brachistochrone problem, the first result in the calculus of variations,

46. 1706 - John Machin develops a quickly converging inverse-tangent series for π and computes π to 100 decimal places,

47. 1712 - Brook Taylor develops Taylor series,

48. 1722 - Abraham De Moivre states De Moivre's theorem connecting trigonometric functions and complex numbers,

49. 1724 - Abraham De Moivre studies mortality statistics and the foundation of the theory of annuities in Annuities on Lives,

50. 1730 - James Stirling publishes The Differential Method,

51. 1733 - Giovanni Gerolamo Saccheri studies what geometry would be like if Euclid's fifth postulate were false,

52. 1733 - Abraham de Moivre introduces the normal distribution to approximate the binomial distribution in probability,

53. 1734 - Leonhard Euler introduces the integrating factor technique for solving first-order ordinary differential equations,

54. 1736 - Leonhard Euler solves the problem of the Seven bridges of Königsberg, in effect creating graph theory,

55. 1739 - Leonhard Euler solves the general homogenous linear ordinary differential equation with constant coefficients,

56. 1742 - Christian Goldbach conjectures that every even number greater than two can be expressed as the sum of two primes, now known as Goldbach's conjecture,

57. 1748 - Maria Gaetana Agnesi discusses analysis in Instituzioni Analitiche ad Uso della Gioventu Italiana,

58. 1761 - Thomas Bayes proves Bayes' theorem,

59. 1762 - Joseph Louis Lagrange discovers the divergence theorem,

60. 1789 - Jurij Vega improves Machin's formula and computes π to 140 decimal places,

61. 1794 - Jurij Vega publishes Thesaurus Logarithmorum Completus,

62. 1796 - Carl Friedrich Gauss presents a method for constructing a heptadecagon using only a compass and straightedge and also shows that only polygons with certain numbers of sides can be constructed,

63. 1796 - Adrien-Marie Legendre conjectures the prime number theorem,

64. 1797 - Caspar Wessel associates vectors with complex numbers and studies complex number operations in geometrical terms,

65. 1799 - Carl Friedrich Gauss proves that every polynomial equation has a solution among the complex numbers,

66. 1805 - Adrien-Marie Legendre introduces the method of least squares for fitting a curve to a given set of observations,

67. 1807 - Joseph Fourier announces his discoveries about the trigonometric decomposition of functions,

68. 1811 - Carl Friedrich Gauss discusses the meaning of integrals with complex limits and briefly examines the dependence of such integrals on the chosen path of integration,

69. 1815 - Siméon-Denis Poisson carries out integrations along paths in the complex plane,

70. 1817 - Bernard Bolzano presents the intermediate value theorem---a continuous function which is negative at one point and positive at another point must be zero for at least one point in between,

71. 1822 - Augustin-Louis Cauchy presents the Cauchy integral theorem for integration around the boundary of a rectangle in the complex plane,

72. 1824 - Niels Henrik Abel partially proves that the general quintic or higher equations cannot be solved by a general formula involving only arithmetical operations and roots,

73. 1825 - Augustin-Louis Cauchy presents the Cauchy integral theorem for general integration paths -- he assumes the function being integrated has a continuous derivative,

74. 1825 - Augustin-Louis Cauchy introduces the theory of residues in complex analysis,

75. 1825 - Johann Peter Gustav Lejeune Dirichlet and Adrien-Marie Legendre prove Fermat's last theorem for n = 5,

76. 1825 - André-Marie Ampère discovers Stokes' theorem,

77. 1828 - George Green proves Green's theorem,

78. 1829 - Nikolai Ivanovich Lobachevsky publishes his work on hyperbolic non-Euclidean geometry,

79. 1831 - Mikhail Vasilievich Ostrogradsky rediscovers and gives the first proof of the divergence theorem earlier described by Lagrange, Gauss and Green,

80. 1832 - Évariste Galois presents a general condition for the solvability of algebraic equations, thereby essentially founding group theory and Galois theory,

81. 1832 - Peter Dirichlet proves Fermat's last theorem for n = 14,

82. 1835 - Peter Dirichlet proves Dirichlet's theorem about prime numbers in arithmetical progressions,

83. 1837 - Pierre Wantsel proves that doubling the cube and trisecting the angle are impossible with only a compass and straightedge,

84. 1841 - Karl Weierstrass discovers but does not publish the Laurent expansion theorem,

85. 1843 - Pierre-Alphonse Laurent discovers and presents the Laurent expansion theorem,

86. 1843 - William Hamilton discovers the calculus of quaternions and deduces that they are non-commutative,

87. 1847 - George Boole formalizes symbolic logic in The Mathematical Analysis of Logic, defining what are now called Boolean algebras,

88. 1849 - George Gabriel Stokes shows that solitary waves can arise from a combination of periodic waves,

89. 1850 - Victor Alexandre Puiseux distinguishes between poles and branch points and introduces the concept of essential singular points,

90. 1850 - George Gabriel Stokes rediscovers and proves Stokes' theorem,

91. 1854 - Bernhard Riemann introduces Riemannian geometry,

92. 1854 - Arthur Cayley shows that quaternions can be used to represent rotations in four-dimensional space,

93. 1858 - August Ferdinand Möbius invents the Möbius strip,

94. 1859 - Bernhard Riemann formulates the Riemann hypothesis which has strong implications about the distribution of prime numbers,

95. 1870 - Felix Klein constructs an analytic geometry for Lobachevski's geometry thereby establishing its self-consistency and the logical independence of Euclid's fifth postulate,

96. 1873 - Charles Hermite proves that e is transcendental,

97. 1873 - Georg Frobenius presents his method for finding series solutions to linear differential equations with regular singular points,

98. 1874 - Georg Cantor shows that the set of all real numbers is uncountably infinite but the set of all algebraic numbers is countably infinite. Contrary to widely held beliefs, his method was not his famous diagonal argument, which he published three years later. (Nor did he formulate set theory at this time.)

99. 1878 - Charles Hermite solves the general quintic equation by means of elliptic and modular functions

100. 1882 - Carl Louis Ferdinand von Lindemann proves that π is transcendental and that therefore the circle cannot be squared with a compass and straightedge,

101. 1882 - Felix Klein invents the Klein bottle,

102. 1895 - Diederik Korteweg and Gustav de Vries derive the KdV equation to describe the development of long solitary water waves in a canal of rectangular cross section,

103. 1895 - Georg Cantor publishes a book about set theory containing the arithmetic of infinite cardinal numbers and the continuum hypothesis,

104. 1896 - Jacques Hadamard and Charles de La Vallée-Poussin independently prove the prime number theorem,

105. 1899 - Georg Cantor discovers a contradiction in his set theory,

106. 1899 - David Hilbert presents a set of self-consistent geometric axioms in Foundations of Geometry,

107. 1900 - David Hilbert states his list of 23 problems which show where some further mathematical work is needed,

108. 1901 - Élie Cartan develops the exterior derivative,

109. 1903 - Carle David Tolme Runge presents a fast Fourier Transform algorithm,

110. 1903 - Edmund Georg Hermann Landau gives considerably simpler proof of the prime number theorem,

111. 1908 - Ernst Zermelo axiomizes set theory, thus avoiding Cantor's contradictions,

112. 1908 - Josip Plemelj solves the Riemman problem about the existence of a differential equation with a given monodromic group and uses Sokhotsky - Plemelj formulae,

113. 1912 - Luitzen Egbertus Jan Brouwer presents the Brouwer fixed-point theorem,

114. 1912 - Josip Plemelj publishes simplified proof for the Fermat's last theorem for exponent n = 5,

115. 1914 - Srinivasa Aaiyangar Ramanujan publishes Modular Equations and Approximations to π,

116. 1919 - Viggo Brun defines Brun's constant B2 for twin primes,

117. 1928 - John von Neumann begins devising the principles of game theory and proves the minimax theorem,

118. 1930 - Casimir Kuratowski shows that the three cottage problem has no solution,

119. 1931 - Kurt Gödel proves his incompleteness theorem which shows that every axiomatic system for mathematics is either incomplete or inconsistent,

120. 1931 - Georges De Rham develops theorem in cohomology and characteristic classes,

121. 1933 - Karol Borsuk and Stanislaw Ulam present the Borsuk-Ulam antipodal-point theorem,

122. 1933 - Andrey Nikolaevich Kolmogorov publishes his book Basic notions of the calculus of variations (Grundbegriffe der Wahrscheinlichkeitsrechnung) which contains an axiomatization of probability based on measure theory,

123. 1940 - Kurt Gödel shows that neither the continuum hypothesis nor the axiom of choice can be disproven from the standard axioms of set theory,

124. 1942 - G.C. Danielson and Cornelius Lanczos develop a Fast Fourier Transform algorithm,

125. 1943 - Kenneth Levenberg proposes a method for nonlinear least squares fitting,

126. 1948 - John von Neumann mathematically studies self-reproducing machines,

127. 1949 - John von Neumann computes π to 2,037 decimal places using ENIAC,

128. 1950 - Stanislaw Ulam and John von Neumann present cellular automata dynamical systems,

129. 1953 - Nicholas Metropolis introduces the idea of thermodynamic simulated annealing algorithms,

130. 1955 - Enrico Fermi, John Pasta, and Stanislaw Ulam numerically study a nonlinear spring model of heat conduction and discover solitary wave type behavior,

131. 1960 - C. A. R. Hoare invents the quicksort algorithm,

132. 1960 - Irving Reed and Gustave Solomon present the Reed-Solomon error-correcting code,

133. 1961 - Daniel Shanks and John Wrench compute π to 100,000 decimal places using an inverse-tangent identity and an IBM-7090 computer,

134. 1962 - Donald Marquardt proposes the Levenberg-Marquardt nonlinear least squares fitting algorithm,

135. 1963 - Paul Cohen uses his technique of forcing to show that neither the continuum hypothesis nor the axiom of choice can be proven from the standard axioms of set theory,

136. 1963 - Martin Kruskal and Norman Zabusky analytically study the Fermi-Pasta-Ulam heat conduction problem in the continuum limit and find that the KdV equation governs this system,

137. 1965 - Martin Kruskal and Norman Zabusky numerically study colliding solitary waves in plasmas and find that they do not disperse after collisions,

138. 1965 - James Cooley and John Tukey present an influential Fast Fourier Transform algorithm,

139. 1966 - E.J. Putzer presents two methods for computing the exponential of a matrix in terms of a polynomial in that matrix,

140. 1967 - Robert Langlands formulates the influential Langlands program of conjectures relating number theory and representation theory,

141. 1968 - Michael Atiyah and Isadore Singer prove the Atiyah-Singer index theorem about the index of elliptic operators,

142. 1976 - Kenneth Appel and Wolfgang Haken use a computer to prove the Four-Color Theorem,

143. 1983 - Gerd Faltings proves the Mordell conjecture and thereby shows that there are only finitely many whole number solutions for each exponent of Fermat's last theorem,

144. 1983 - the classification of finite simple groups, a collaborative work involving some hundred mathematicians and spanning thirty years, is completed,

145. 1985 - Louis de Branges de Bourcia proves the Bieberbach conjecture,

146. 1987 - Yasumasa Kanada, David Bailey, Jonathan Borwein, and Peter Borwein use iterative modular equation approximations to elliptic integrals and a NEC SX-2 supercomputer to compute π to 134 million decimal places,

147. 1991 - Alain Connes and John W. Lott develop non-commutative geometry,

148. 1994 - Andrew Wiles proves part of the Taniyama-Shimura conjecture and thereby proves Fermat's last theorem,

149. 1998 - Thomas Hales (almost certainly) proves the Kepler conjecture,

150. 1999 - the full Taniyama-Shimura conjecture is proved.

151. 2000 - the Clay Mathematics Institute establishes the seven Millennium Prize Problems of unsolved important classic mathematical questions,

152. 2002 - Manindra Agrawal, Nitin Saxena, and Neeraj Kayal of Indian Institute of Technology (IIT), Kanpur, India, present a unconditional deterministic polynomial time algorithm to determine whether a given number is prime,

153. 2002 - Yasumasa Kanada, Y. Ushiro, Hisayasu Kuroda, Makoto Kudoh and a team of nine more compute π to 1241 billion digits using a Hitachi 64-node supercomputer,

154 2003

155 2004

156 2005 - 2007

## Sunday, November 30, 2008

### Pengumuman/Announcement

Kepada yang kubanggakan semua follower dan para mahasiswa/mahasiswi, untuk kepentingan penningkatan performa dan komunikasi international saya berkeinginan untuk menampilkan Blog-blog dari follower di link yang sesuai, namun saya belum menemukan caranya. Sementara yang saya tempuh adalah melakukan blocking bagi setiap blog yang muncul di halaman muka. Untuk itu saya sarankan agar anda mendaftarkan untuk jadi follower bukan pada alamat utama. Alamat utama Blog ini adalah http://powermathematics.blogspot.com/, melainkan daftarkan ke alamat blog sesuai dengan kriteria. Untuk Sejarah di http://sejarahmatematika.blogspot.com/; untuk Psikology di http://marsigitpsiko.blogspot.com/; untuk Guru dan Pembelajaran Matematika di http://pbmmatmarsigit.blogspot.com/, sedang untuk Filsafat, Blognya sedang dalam proses pembuatan. Jika anda telah menjadi follower di blog utama dan sekarang mengalami pemblokiran, saya sarankan anda membuat askes follower Blog anda sesuai dengan kriteria di atas. Pengumuman tambahan tentang Comment, agar digunakan betul-betul untuk komentar dengan bahasa pendek dan jelas syukur in English. Comment bukan untuk mengirimkan tugas. Tugas anda silahkan anda taruh di Blog masing-masing. Untuk itu maka mulai sekarang saya harus menyeleksi setiap Comment yang layak ditampilkan. Demikian harap maklum. Dan jangan lupa saya selalu membanggakan bagi anda yang telah berpartisipasi dalam Blog ini. Selamat buat anda semua. Mohon maaf kiranya, semua dalam rangka peningkatan mutu. (Marsigit)

## Tuesday, November 25, 2008

### We invite our students to contribute writing the history of mathematics

We invite our students to write your writing on the history of mathematics (Marsigit)

Subscribe to:
Posts (Atom)