METU Department of Mathematics Math 304 History of Math Concepts Spring 2011

Makeup

June 10 2011, 15:30 – 16:30

Name and the student number:

Q 1. Describe the principal events, names and dates related to solution of cubic and quartic equations, and to the proof of impossibility to solve the equations of higher degrees.

Q 2. Which names, dates and events related to discovery and development of Calculus and Mathematical Analysis do you know ?

Q 3. Which names, dates and events mark the development of Geometry: projective, analytical, algebraic, and non-Euclidean ?

Q 4. When did the following mathematical ideas and theories appear ? Who were the authors ?

Logarithms. The Fundamental Theorem of Algebra. Probability theory. Generalized binomial theorem. Theory of convergence of power series. Analytic number theory. Riemann Geometry Quadratic Reciprocity Law Variational calculus. Group theory Theory of determinants Topology

Q 5. What are Fermat’s primes and Mersenne’s primes ? What is their relation to the perfect numbers ?

Q 6. Formulate the Little Fermat Theorem and the Great Fermat theorem. When the latter was proved and by whom ?

Q 7. Approximate time of life and characterize mathematical interests of the following mathematicians.

Leonardo of Pisa Descartes Fermat Pascal Newton Leibniz Euler Cauchy Gauss Riemann Hilbert Poincare Q 8. Formulate the Fifth Postulate of Euclid in three equivalent ways. What is known about sum of angles of a triangle in non-Euclidean Geometry ?

Q 9. What is the Riemann’s zeta-function? Formulate the Riemann Conjecture.

Q 10. Formulate the Set-theoretical paradoxes which caused a crisis of foundations in mathematics. Which ways to overcome this crisis were proposed and by whom ?

Q 11. When was the first International Congress of Mathematicians ? When and where did Hilbert presented his famous problems ?

Q 12. What is the Four-color Theorem ? Who formulated it and when ? Who proved it and when ?