The document summarizes mathematics in the 18th and 19th centuries. It profiles influential mathematicians such as Euler, Gauss, Lagrange, and Cauchy in the 18th century who made advances in calculus, analysis, mechanics and number theory. In the 19th century, it describes advances in abstract mathematics and the origins of theories like group theory and non-Euclidean geometry due to mathematicians like Galois, Bolyai, Riemann, Venn and Fourier.

3. Mathematics
in
18th & 19th
Century

4. Objectives:
• To understand the 18th and 19th
century mathematics .
• To identify the contributions and
ideas of the mathematicians in the
18th and 19th century.

5. GROUP
Dalumpines,
Joruss
Bugna, Wymvee
Clair
Empeño, Szai
Shanley
Gallevo, Desiree
Celiz
Pagsuguiron,
Jericho

6. GROUP
Vequiso, Jake
Clayford
Unos, Suraida
Tan, Francis
Lanada, Gwen
Shady

7. The 18th Century Mathematics
•In this century, mathematics is already a modern science and it has a
strong emphasis on analysis and mechanics.
•Also, in this century, CALCULUS is much known.
•Mathematics begins to develop very fast because of introducing it to
schools. Therefore everyone have a chance to learn the basic learnings of
mathematics.
•There are many new ideas mathematical problems, researches which lead
to creating new fields of mathematics. Old fields of mathematics are also
expanding.

8. Mathematicians
in the
18th Century

9. Leonhard Euler
• Considered as the “Greatest Mathematician of the 18th century”
• Said to have produced one mathematical paper every week on average.
• His collected works nearly tallied to 900 books.
• Said to have impeccable mental calculation skills and photographic
memory
• His interests covered geometry, calculus, mechanics, and Number Theory.
• Created, Standardized, or Popularized the following Mathematical
Notations: - e (Euler’s Number) - i (Imaginary unit) - f(x) ( Function) - ∑
(Sigma) - constants( a,b, and c) - unknowns(x, y, and z) - π (Pi) -
Trigonometric Functions (Sin, Cos, Tan,Cot, Sec, Csc)

10. Leonhard Euler
• Euler’s Theorem - a result on the curvature of curves on a surface.
- proved by Leonhard Euler on 1760
• Graph Theory
• Calculus of Variations

11. • was a German mathematician who contributed in many fields of
mathematics and science and is touted as one of history's most influential
mathematicians.
• referred as the” prince of mathematicians”
• published work on number theory, the mathematical theory of map
construction.
• Discovered that every positive integer can be expressed as the sum of at
most 3 triangular numbers.
• Gauss' formula is a result of counting a quantity in a clever way.
Johann Carl Friedrich Gauss

12. • Italian Mathematician and Astronomer, later neutralized French
• Born on January 25, 1736 in Turin, Italy
• He made significant contributions to the fields of: * Analysis *
Number Theory * Both Classical and Celestial Mechanics
• Lagrange Major Contributions in Mathematics: * Calculus of
Variations *Solution of Polynomial Equations * Power Series and
Functions
Joseph Louis Lagrange

13. • French Mathematician, engineer and physicist
• August 21, 1789
• He made pioneering contributions to several branches of
Mathematics: * Mathematics Analysis * Continuum
Mechanics * Real and Complex Analysis * Theory of
Permutation Groups
Baron Augustin-Louis Cauchy

14. • A british mathematician and inventor
• Born: August 20, 1710, Market Bosworth, United Kingdom
Died: May 14, 1761, Market Bosworth, United Kingdom
• He is known for the eponymous Simpson's rule to approximate
definite integrals.
• Most of his important works are the Doctrine and Application
of Fluxions (1750), Mathematical Dissertations (1743), and
Miscellaneous Tracts (1757).
Thomas Simpson

15. • A French mathematician
• Born on 9 May 1746 in Beaune, Côte-d'Or, France
• Died: July 28, 1818, Paris, France
• He invented descriptive geometry, and technical
drawing.
• Subjects Of Study: curvature descriptive geometry
surface
Gaspard Monge

16. The 19th Century Mathematics
•The 19th century of mathematics was a golden age of prosperity
and new ideas.
• Most of the powerful abstract mathematical theories in use today
originated in the 19th century.
• In 19th century, saw an unprecedented increase in the breadth and
complexity of mathematical concepts.

17. Mathematicians
in the
19th Century

18. John Venn
• He was an English mathematician, logician and
philosopher.
• He invented the Venn Diagram, a method of utilizing
diagrams to demonstrate set theory.
• A Venn diagram is a widely used diagram style that
shows the logical relation between sets.

19. Joseph Frourier
• He was a French mathematician and physicist born in
Auxerre.
• He demonstrated how to analyze heat conduction in
solid bodies using an infinite mathematical series now
called by his name, the Fourier series.
• A Fourier series is a sum that represents a periodic
function as a sum of sine and cosine waves.

20. Evariste Galois
• Famous for his contribution to the part of higher algebra and discovered
the hidden structure of polynomial equations.
• Developed the Galois theory, now known as the group theory.
• He realized the relation between the algebraic solution to a polynomial
equation and the structure of a group of permutations associated with the
roots of the polynomial.

21. János Bolyai
• Hungarian mathematician
• One of the founders of non-Euclidean geometry
• Developed a geometric concept of complex
numbers
• Explored hyperbolic geometry and curved
spaces

22. Bernhard Riemann
• German mathematician
• Introduced Riemann Zeta Function & Riemann
Hypothesis
• Argued the fundamental ingredients for geometry
• Provided mathematical function for the 4D
geometry of spacetime
Riemann Zeta
Function

23. Mathematicians in the 18th Century
• Leohard Euler
>Number Theory, Graph Theory, Applied Mathematics
2. Carl Gauss
>Systematic text of algebraic number theory
3. Joseph Lagrange
>Calculus of variation, solutions of polynomial equations, power
series, and function
4. Augustin Cauchy
>Real and Complex analysis, The study of permutation groups
5. Thomas Simpson
>Interpolation, Numerical methods of Integration
6. Gaspard Monge
>Descriptive Geometry

24. Mathematicians in the 19th Century
1. John Venn
>Venn Diagram
2. Joseph Fourier
>Mathematical theory of heat conduction
3. Evariste Galois
>Galois theory
4. Janos Bolyai
>Absolute Geometry
5. Bernhard Reimann
>Complex analysis, Real analysis, Differential Geometry