2.  In 18th century mathematics is already a modern science  Mathematics begins to develop very fast because of introducing it to schools  Therefore everyone have a chance to learn the basic learnings of mathematics

3.  Thanks to that, large number of new mathematicians appear on stage  There are many new ideas, solutions to old mathematical problems,researches which lead to creating new fields of mathematics.  Old fields of mathematics are also expanding.

4. FAMOUS MATHEMATICIANS

5. LEONHARD EULER

6. Leonhard Paul Euler (1707-1783)  He was a Swiss mathematician  Johann Bernoulli made the biggest influence on Leonhard  1727 he went to St Petersburg where he worked in the mathematics department and became in 1731 the head of this department  1741 went in Berlin and worked in Berlin Academy for 25 years and after that he returned in St Ptersburg where he spent the rest of his life.

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8.  Euler worked in almost all areas of mathematics: geometry, calculus, trigonometry, algebra,applied mathematics, graph theory and number theory, as well as, lunar theory, optics and other areas of physics.  He introduced several notational conventions in mathematics  Concept of a function as we use today was introduced by him;he was the first mathematician to write f(x) to denote function  He also introduced the modern notation for the trigonometric functions, the letter e for the base of the natural logarithm (now also known as Euler’s number), the Greek letter Σ for summations and the letter i to denote the imaginary unit Σ

9.  He wrote 45 books an over 700 theses.  His main book is Introduction in Analisyis of the Infinite.

10. Analysis  He discovered ways to express various logarithmic functions using power series, and he successfully defined logarithms for negative and complex numbers  He also defined the exponential function for complex numbers, and discovered its relation to the trigonometric functions

11. EULER’ S FORMULA For any real number x, Euler’s formula states that the complex exponential function satisfies

12. Number theory  He contributed significantly to the theory of perfect numbers, which had fascinated mathematicians since Euclid.  His prime number theorem and the law of quadratic reciprocity are regarded as fundamental theorems of number theory.

13. Geometry  Euler (1765) showed that in any triangle, the orthocenter, circumcenter, centroid, and nine- point center are collinear.  Because of that the line which connects the points above is called Euler line.

15. Seven bridges of Konigsberg

18.  This was old mathematical problem.  The problem was to decide whether it is possible to follow a path that crosses each bridge exactly once and returns to the starting point.  1736 Euler solved this problem, and prooved that it is not possible.  This solution is considered to be the first theorem of graph theory

19.  Euler was very importnat for further development of mathematics  Next quotation tells enough about his importance:  “Lisez Euler, lisez Euler, c'est notre maître à tous ”(Read Euler, read Euler, he is the master of us all.) Pierre-Simon Laplace

20. GABRIEL CRAMER

21. GABRIEL CRAMER (1704-1752)  Swiss mathematician  He give the solution of St. Peterburg paradox  He worked on analysis and determinants  He is the most famous by his rule (Cramer’s rule) which gives a solution of a system of linear equations using determinants.

22. THOMAS SIMPSON

23.  He received little formal education and taught himself mathematics while he was working like a weaver.  Soon he became one of the most distinguished members of the English school  Simpson is best remembered for his work on interpolation and numerical methods of integration.  He wrote books Algebra, Geometry, Trigonometry, Fluxions, Laws of Chance, and others THOMAS SIMPSON (1710-1761)

24. JEAN LE ROND D’ALAMBERT

25.  He dealt with problems of dinamics and fluids and especially with problem of vibrating string which leads to solving partial diferential equations  During his second part of life, he was mainly occupied with the great French encyclopedia JEAN LE ROND D’ALAMBERT (1717-1783)

26. For this he wrote the introduction, and numerous philosophical and mathematical articles; the best are those on geometry and on probabilities. For this he wrote the introduction, and numerous philosophical and mathematical articles; the best are those on geometry and on probabilities.

27. JOSEPH LOUIS LANGRANGE

28.  He didn’t show any intersts for mathematics untill his 17.  From his 17, he alone threw himself into mathematical studies  Already with 19, he wrote a letter to Euler in which he solved the isoperimetrical problem which for more than half a century had been a subject of discussion. JOSEPH LOUIS LANGRANGE (1736-1813)

29.  Lagrange established a society known as Turing Academy, and published Miscellanea Taurinesia, his work in which he corrects mistakes made by some of great mathematicians  He was studing problems of analytical geometry, algebra, theory of numbers, differential eqations, mechanics, astronomy, and many other...  Napoleon named Lagrange to the Legion of Honour and made him the Count of the Empire in 1808.

30.  On 3 April 1813 he was awarded the Grand Croix of the Ordre Impérial de la Réunion. He died a week later.

31. PIERRE SIMON LAPLACE

32. FFFFrench mathematician and astronomer HHHHis most known works are Traite de mecanique celeste and Theory analytique des probabiliteis HHHHis name is also connected with the “Laplace transform” and with the “Laplace ex pansion” of a determint HHHHe is one of the first scientists to postulate the existence of black holes. HHHHe is one of only seventy-two people to have their name engraved on Eiffel Tower. PIERRE-SIMON LAPLACE (1749-1827)

33.  It is also interesting to say the difference between Laplace and Lagrange  For Laplace, mathematics was merely a kit of tools used to explain nature  To Lagrange, mathematics was a sublime art and was its own excuse for being

34.  He is remembered as one of the greatest scientists of all time, sometimes referred to as a French Newton or Newton of France  He became a count of the First French Empire in 1806 and was named a marquis in 1817

35. GASPARD MONGE

36.  French mathematician also known as Comte de Péluse  Monge is considered the father of differential geometry because of his work Application de l'analyse à la géométrie where he introduced the concept of lines of curvature of a surface in 3-space. GASPARD MONGE (1746-1818)

37.  His method, which was one of cleverly representing 3-dimensional objects by appropriate projections 2- dimensional plane, was adopted by the military and classified as top secret

38. ADRIEN – MARIE LEGENDRE

39.  He made important contributions to statistics, number theory, abstract algebra and mathematical analysis.  Legendre is known in the history of elementary methematics principially for his very popular Elements de geometrie  He gave a simple proof that π(pi) is irrational as well as the first proof that π2(pi squared) is irrational. ADRIEN – MARIE LEGENDRE (1752-1833)

40. JEAN BAPTISTE JOSEPH FOURIER

41.  French mathematician, physicist and historian  He studied the mathematical theory of heat conduction. JEAN BAPTISTE JOSEPH FOURIER (1768-1830)

42.  Fourier established the partial differential equation governing heat diffusion and solved in by using infinite series of trigonometric functions

43. JOHANN CARL FRIEDRICH GAUSS

44. JOHANN CARL FRIEDRICH GAUSS (1777 – 1855)  He worked in a wide variety of fields in both mathematics and physics incuding number theory, analysis, differential geometry, geodesy, magnetism, astronomy and optics.  “Mathematics is the queen of the sciences and number theory is the queen of mathematics.”

46. AUGUSTIN LOUIS CAUCHY

47.  Cauchy started the project of formulating and proving the teorems of calculus in a rigorous manner and was thus an early pioneer of analysis  He also gave several important theorems in complex analysis and initiated the study of permutation groups AUGUSTIN LOUIS CAUCHY (1789-1857)

48.  He also researched in convergence and divergence of infinite series, differential equations, determinants, probability and mathematical physics.  He was first to prove Taylor’s theorem, he brought a whole new set of teorems and definitions, he dealed with mechanics, optics, elasticity and many other problems

49.  His last words were: “Men pass away, but their deeds abide.”

50. Anela Bocor Mateja Jelušić Ivan Jelić Vojislav Đuračković Boris Dokić