2. Introduction
→ Introduction
→ His life
→ His most important works
→ Conclusion
3. His life
Born in Basel in 1707
At 16 : Master of Philosophy
Received lessons from Bernouilli
In 1727 he went to St Petersburg
4. His life
1731 : professor of physics
1733 : head of the mathematics department
1741 : he went to Berlin Academy
1766 : came back in St Petersburg
He died in 1783
5. Mathematical notations
The concept of a function, notation f(x)
The letter e ''Euler's number'' use to define the
Exponential function : ex
The greek letter Ʃ for summations
The famous greek letter π
The letter i to denote the imaginary unit
6. Analysis
n
x ∞ x
e =∑ n =0 n !
∞
1 ²
∑ n2 = 6 '' The Basel Problem ''
n=1
i
e =cos i sin '' The Euler's formula ''
i
e 1=0 '' The Euler's identity ''
7. Number Theory
The infinitude of prime numbers
The sum of the reciprocals of the primes diverges
The totient function : φ(n)
The Euler's theorem
231 − 1 = 2,147,483,647 is a Mersenne prime
