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Note that this schedule will be updated frequently in the course of the semester!




Lecture 1: January 16 Introduction, general remarks, administrative points. Early history of mathematics. 
Lecture 2: January 18 The origins of mathematics: Egypt, Babylonia, Greece 

Lecture 3: January 23 Early mathematics. Proof that the square root of 2 is irrational. 
Lecture 4: January 25 Proof that there are infinitely many primes. Mathematical notation. 

Lecture 5: January 30 The notion of proof: deductive validity. 
Lecture 6: February 1 More about arguments: possibility, objectiveness, forms of arguments, inductive/deductive reasoning. 

Lecture 7: February 6 (Early course evaluations). Proofs by contradiction. 
Lecture 8: February 8 Definitions. 

Lecture 9: February 13
(Early course evaluation results). Axiomatic theories. 
Lecture 10: February 15
Consistency and independence. 

Lecture 11: February 20
Axiomatizations of geometry. Axiomatizations of number theory. 
Lecture 12: February 22
Philosophical and mathematical limitations of axiomatizations. 

Lecture 13: February 27
Let's Make a Deal problem. Axioms of Probability. 
Lecture 14: March 1
Review. Bring your own questions! 

Midterm, March 6
Midterm exam 
March 8


Lecture 15: March 13
Conditional probability. Bayes' Theorem. Deductive solution to the problem. 
Lecture 16: March 15
Another application of probability theory. 

Lecture 17: March 20
Aristotle's syllogisms. Terminology 
Lecture 18: March 22
Propositional logic 
March 27

March 29



Lecture 19: April 3
More propositional logic: Knights & Knaves, Natural Deduction 
Lecture 20: April 5
Quantifiers. 

Lecture 21: April 10
Nonclassical logics. Mathematical Induction (I) 
Lecture 22: April 12
Deadline: Essay topic has to be approved. Mathematical Induction (II) 

Lecture 23: April 17
Set Theory. Functions. 
Lecture 24: April 19
Deadline: Essay outline has to be handed in. Cardinality of N, Z, Q. 

Lecture 25: April 24
Cardinality of R. 
Lecture 26: April 26
Deadline:Essay due. Philosophy of mathematics 

May 1
Bring your own questions! 
May 3

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© Dirk Schlimm, Last modified: Tue May 1 10:32:47 EDT 2001