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

Final

May 26 2011, 17:30 – 19:00

Name and the student number:

Q 1. What was the contribution of Weierstrass to the analysis ? Which of his results has surprised his contamporary mathematicians ? Which outstanding students of him do you know ?

Q 2. Which discovery related to cubic surfaces was made in XIX-th century ? What do you know about the history of this discovery and the works which followed it ?

Q 3. What are the Cayley-Klein and the Poincare models of a hyperbolic plane ? What the the ”lines” in these two models ?

Q 4. Which breakthrough in mathematics is Cantor famous for ? Who opposed him, and why ? When did he publish his theory ?

Q 5. Who proved that numbers π and e are irrational ? Who proved their transcendence ?

Q 6. When and where did Hilbert presented his famous problems ? How many problems ? Which properties of a “good problem” did Hilbert formulate ?

Q 7. What was the reason of the crisis in foundations of mathematics ? When did it happen ? Which camps of mathematicians appeared and how did they proposed to resolve the crisis ?

Q 8. Which works related to the special relativity theory did appear before Einstein’s ? When it happened ? How do you understand the mathematical meaning of special relativity theory ?

Q 9. When was the first International Congress of Mathematicians ? When the first Fields medals were awarded ?

Q 10. When and where N.Bourbaki group of mathematicians appeared ? Whom of its members do you know ? What was their contribution ?

Q 11. Explain briefly the following mathematical notions quaternions generators of a hyperboloid x^{2} + y^{2} − z^{2} = 1 (give the formulas) Dedekind section transcendent number

Q 12. Whose names (in XIX-th century, or earlier) are related with the following theories.

Probability Theory Graph Theory Solution of algebraic equations Abstract Algebra Linear Algebra Projective Geometry Hyperbolic Geometry

Q 13. What were the mathematical interests of the following mathematicians ? Describe their famous results. (Give the names of their works and years of publication, if you know any).

Poincare

Hilbert

Dedekind Q 14. What is the Gödel theorem about ? When it was proved ? What did Cohen prove about the Continuum hypothesis ?

Q 15. Who formulated the Four-color Theorem, and when ? Who proved it and when ? What was special about the proof: why it is still raising questions?

Q 16. What are the finite “simple groups” ? When they were classified and whom of the principal contributors to the proof do you know ? What was special about this proof ? Which examples of the simple groups do you know ?

Q 17. Who proved the Last Fermat Theorem and when ? Which other mathematicians made an important contributions to its solution, and what was this contribution ?