History of Mathematics
MATH 242W

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

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

Ralph M. Kaufmann

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


Topics for the "Long Paper"
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
(Disclaimer: do not just list the Hilbert Problems!)

The History of a one particular Hilbert problem
(The choice is yours)

The History of one of the millennium/Clay prize Problems
(E.g. History in the making: The Poincaré conjecture
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

Overhead slides (PowerPoint) for selected lectures

Geometry Set Theory
Analysis Number Theory Algebra
Slides for Lecture 1
Euclid slides
Slides for Lecture 2
Slides for Lecture 3
Slides for Lecture 4
Non Euclidean Parallels
Slides for Lecture 5
Study Guide 1
 Slides for Lecture 6
Slides for Lecture 7
Slides for Lecture 8
Slides for Lecture 9
Slides for Lecture 10
Study Guide 2
 Slides for Lecture 11
Slides for Lecture 12
Slides for Lecture 13
Slides for Lecture 14
Slides for Lecture 15
Study Guide 3

 Slides for Lecture 16
Slides for Lecture 17
Slides for Lecture 18
Slides for Lecture 19
Slides for Lecture 20
Study Guide 4
 Slides for Lecture 21
Slides for Lecture 22
Slides for Lecture 23
Slides for Lecture 24
Study Guide 5


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

Original Sources:

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

Biographies of Mathematicians
 
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