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

Midterm 1

April 5 2010, 17:30 – 18:40

Name and the student number:

Q 1. Which mathematicians of Middle Ages do you know ? In which century did they live ?

Q 2. When (approximately) and where a solution of cubic equation was found ? Whose names are related to this discovery and what was the conflict related to the authorship ?

Q 3. Which discoveries are related to the scientific revolution ? When (approximately) did they happen ?

Q 4. When (approximately) did live Newton and Leibniz, and what is their principal mathematical contribution ? What was the scandal between them and when (approximately) did it happen ?

Q 5. Approximate time (at least the century) of the following events.

Foundation of the first universities in Europe. The Black Death. Fall of Constantinople. The first books printed. Establishing of the first Academies of Science in Europe.

Q 6. Who is related to the following mathematical discoveries ? Approximate time of these events.

Theory of perspective and projective geometry. Logarithms. Solution of equations of the forth degree. Discovery of the complex numbers. The coefficients of polynomials are denoted by letters. The Fundamental Theorem of Algebra. Coordinate system and analytic geometry. Calculus. Probability theory. Generalized binomial theorem. Analytic number theory.

Q 7. Approximate time of life of the following scientists. Characterize their mathematical interests and discoveries. Indicate the title of their principle works, if you know any.

Leonardo of Pisa Descartes Fermat Pascal Newton Leibniz Euler Q 8. What is the Tartaglia-Cardano method of solution of cubic equations ? Demonstrate it on the example x^{3}−6x−9 = 0. What is the discriminant of a cubic equation and what does it characterize ?

Q 9. What are the results of Fermat related to perfect numbers? Formulate the Little Fermat Theorem. What is the Great Fermat theorem ?

Q 10. Formulate Euler’s formula for polyhedra. Justify it for a tetrahedron and a cube.