Note that this schedule will be updated frequently in the course of the semester!
The HW column tells you when the homework will be handed out. Usually, they are handed out on Thursdays and are due the following Tuesday.
Week  Date  Lec #  HW  Topic  Supplementary Reading 
1  Tu, Aug 25  1  General remarks, administrative points  
Th, Aug 27  2  Everything follows from a contradiction Hippocrates' quadrature of the lune 
p.117 of handout on Hippocrates  
Functions: examples and terminology  
2  Tu, Sep 1  3  Systematic connection between parts I and II of the
course Hippocrates' quadrature of the lune (contd.) Erastothenes' determination of the circumference of the earth 
Finish handout on Hippocrates Poetry of the universe, Chapter 1 Discuss "the impossibility of squaring the circle" in group, and write a brief summary of the argument 

Th, Sep 3  4  #1  Presentation: the impossibility of squaring the circle  Rewiew "the impossibility of squaring the circle", read Geometry civilized p.4971  
Sets and ordered pairs  
3  Tu, Sep 8  5  Structure of impossibility arguments ; Euler's theorem 
Read Chapter~II, Encompassing the Earth, in Osserman's
book; Homework #1 due 

Relations  
Th, Sep 10  6  #2  Euler's theorem (contd.) Geomertry: loci 
Problems 4b) and 4c) of Homework #1 are due  
Functions  
4  Tu, Sep 15  7  Euclid's proofs I.1, I.2, I.9, I.10  
Th, Sep 17  8  #1  Reflection: what have we been doing? Review: ordered pairs, relations, functions 
Euclid's proof of the Pythagorean Theorem  
5  Tu, Sep 22  9  Form and structure of Euclid's proofs: I.15, I.32, I.41, I.46  Euclid's proof of the Pythagorean Theorem  
Th, Sep 25  10  #2B  Structure of proofs Proof that two sets of points are equal Proof for the Pythagorean Theorem 

Inverse, and injective functions  
6  Tu, Sep 29  11  The development of logical calculi: Natural Deduction Calculus; Hilbert's axiomatization of geometry  Arguments in and on logic (handout)  
Th, Oct 1  12  #3  The language of predicate logic; Discussion of Euclid's common notions; Hilbert's axiom system for geometry  
Surjective and bijective functions  
7  Tu, Oct 6  13  Hilbert's axiom system for geometry  
Th, Oct 8  Midterm (1h)  
8  Tu, Oct 13  14  Recap: functions; Midterm Part A; Cantor's Theorem 

Th, Oct 15  15  #4  Midterm review: Internal organization (proofs), context of applications, functions  
9  Tu, Oct 20  16  Provability of the Parallel Postulate?  The NonDenumerability of the Continuum  
Th, Oct 22  17  #5  Syntax and Semantics; Geometry on the shere; Calculable functions  Courant/Robbins: What is mathematics? pp.214227 (handout)  
10  Tu, Oct 27  18  Modern axiomatic presentations of mathematics The sum of the angles of a triangle on a sphere,and the ratio of circumference/diameter Calculable functions (multiplication) 
Think about: the sum of the angles of a triangle on a sphere,and the ratio of circumference/diameter!  
Th, Oct 29  19  #6  Counterexamples to inferences Interpretations of geometry (hyperbolic geometry) 

11  Tu, Nov 3  20  Universe of discourse; Hyperbolic geometry; Turing Machines 

Th, Nov 5  21  #7  Distance in hyperbolic geometry  
12  Tu, Nov 10  22  Curvature; Logical Calculi  
Th, Nov 12  23  #8  Entscheidungsproblem; Example for ORelimination: Proof  Hilbert: The foundations of geometry  
13  Tu, Nov 17  24  Fitchrepresentation; Semantics for sentential logic  
Th, Nov 19  25  Gödel numbering; FitchDiagrams  Church: An unsolvable problem of elementary number theory, Review of Turing (1936); Post: Finite combinatory processes; Turing: On computable numbers, Computing machinery and intelligence  
14  Tu, Nov 24  26  #9  Gödel's Incompleteness Theorems  Gödel: On undecidable propositions of formal mathematical systems 
Th, Nov 26  Thanksgiving! Happy Holiday!  
15  Tu, Dec 1  27  Turing's analyis of computability and calculability  Turing: On computable numbers  
Th, Dec 3  28  Unsolvability of the Halting Problem; Learning Machines  Turing: Computing Machinery and Intelligence, Sec. 35 and 7  
Mo, Dec 7  Review Session (with Wilfried), 4:00  
Th, Dec 10  Question Session (with Dirk), 1:00  
Fr, Dec 11  Final (3h) 5:308:30 
[ 80101 Home page  course description  requirements  schedule  literature  related links ]
© Dirk Schlimm, Last modified: August 24, 1998