Tuesday and Thursday 12:30 - 1:45 in MONT 217 Syllabus

Textbook: Laubenbacher, Reinhard; Pengelley, David. Mathematical expeditions. Chronicles by the explorers.

Office: MSB M312 Phone: (860)
486-3850
e-mail: kaufmann@math.uconn.edu

Office hours: Tuesday & Thursday 2:00 pm- 3:00 pm and by
appointment

New Deadline Nov 18

Deadline for the revised version Dec 8

Please select one of the following topics.

The Hilbert problems as a guide to 20th century mathematics

The History of a one particular Hilbert problem

The History of one of the millennium/Clay prize Problems

or maybe: The History of the Navier-Stokes Equation

or any of the other problems)

The History of the Prize Problems of the Paris Academy of Sciences

Logicism, Formalism and Intuitionism, three approaches to mathematics

Homework Assignments

For the lecture on |
Numbers or assignments |

Sep 9 | 1.14, 1.15 |

Sep 14 |
1.16 |

Sep 21 |
1.21-1.26 |

Sep 28 |
Review naive set theory and the
definitions of and N,Z,Q and R |

Sep 30 |
Think of a 1-1 correspondence
between R and (0,1), read the section on Cantor |

Oct 5 |
2.14, 2.16 (harder) |

Oct 12 |
2.17, 2.21, 2.23, 2.25 (try if
you like) |

Oct 20 |
Read on the symptom of the
parabola and conic sections. Do 3.1. Try 3.8, 3.9, do 3.11, 3.12. |

Oct 26 |
Read the section on Cavalieri |

Oct 28 |
3.21 |

Nov 2 | 3.27, 3.28, 3.30, 3.31 |

Nov 11 |
4.7, 4.8, 4.10, 4.11, 4.16 |

Nov 16 |
4.18, try 4.21, do 4.22
(assuming a,b>0), optional 4.25 |

Dec 6 |
5.1, 5.5, 5.12, try 5.13 |

Dec8 |
5.14 , 5.15, 5.17 |

**Interesting and useful links for the course**

Euclid's Elements:

Byrne's
Edition (Facsimile of a 1847 edition)

Joyce's
Edition (Electronic edition with comments in Java illustrated
diagrams)

Archimedes' Quadrature of the Parabola

A page of The Method

**Links to definitions and animations:
**

Hyperbolic
triangles

Hyperbolic
drawing applet

Naive set
theory- Wikipedea

On
the symptom of a parabola

On conic sections: a definition from Mathworld ,
and animation

Links to pages discussing the work of mathematicians

A link on
Bolyai including his definition of parallels

Very
nice page about Archimedes

A page
on Zeno's paradoxes and another
page with animations.

Link to the millennium/Clay prizes:
click here

Geometry I | Geometry II | Set theory I | Set Theory II | Analysis I | Analysis II | Number Theory I | Number Theory II | Algebra I | Algebra II |

Euclid
Legendre Gauss J. Bolyai Lobachevsky |
Beltrami
Klein Poincaré |
Zeno
Bolzano Cantor Russell Frege |
Gödel
Zermelo Fraenkel P. Cohen |
Archimedes
Cavalieri Leibniz Newton Cauchy |
Riemann
Lebesgue Robinson |
Euclid
Diophantus Fermat Euler Germain |
Kummer
Faltings Wiles |
Euclid
al Khwarizimi del Ferro Tartaglia Cardano Ferrari |
Lagrange
Galois |

Links back to my homepage at UConn and the Department of Mathematics at the University of Connecticut