Schedule

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

Week
Tuesday
Thursday
1
 Lecture 1: January 16
Introduction, general remarks, administrative points.
Early history of mathematics.
  • Handout: Syllabus & Overview
    		• Lecture 2: January 18
    The origins of mathematics: Egypt, Babylonia, Greece
  • Handout 1: The Language of Numbers. (Dehaene)
  • Homework: No. 1  
    		•
    2
    		 Lecture 3: January 23
    Early mathematics. Proof that the square root of 2 is irrational.
  • Handout 2: Measuring the Unmeasurable. (Osserman)  
    		•  Lecture 4: January 25
    Proof that there are infinitely many primes. Mathematical notation.
  • Quiz: No. 1, Homework: No. 2
  • Handout 3: From mystery to history. (Barrow)
  • Handout 4: Counting with base 2, 5, 60. (Barrow)
    • 3
    		 Lecture 5: January 30
    The notion of proof: deductive validity.
  • Handout 5: Terminology for proofs and arguments. (Schlimm)
  • Handout 6: Deductive arguments. (Weston)  
    		•  Lecture 6: February 1
    More about arguments: possibility, objectiveness, forms of arguments, inductive/deductive reasoning.
  • Quiz: No. 2, Homework: No. 3
  • Handout 7: Sceptical doubts ... (Hume)
  • Handout 8: Proofs by contradiction. (Mancosu)  
    		•
    4
    		 Lecture 7: February 6
    (Early course evaluations). Proofs by contradiction.
  • Handout 9: Letter to Russell (Frege)
  • Handout 10: Proofs (Glymour)
  • Handin Portfolios.
     
    		•  Lecture 8: February 8
    Definitions.
  • Quiz: No. 3, Homework: No. 4  
    		•
    5
    		 Lecture 9: February 13
    (Early course evaluation results). Axiomatic theories.
  • Handout 11: Axiom systems. Models. Consistency and Independence. (Berlinghoff)  
    		•  Lecture 10: February 15
    Consistency and independence.
  • Quiz: No. 4, Homework: No. 5
  • Handout 12: Foundations of geometry. (Hilbert)
  • Handout 13: Space and the Geometrization of Mathematics. (Shaw)  
    		•
    6
    		 Lecture 11: February 20
    Axiomatizations of geometry. Axiomatizations of number theory.
  • Handout 14: Natural numbers. (Landau)
  • Handout 15: The series of natural numbers (Russell).  
    		•  Lecture 12: February 22
    Philosophical and mathematical limitations of axiomatizations.
  • Quiz: No. 5, Homework: No. 6a, b
  • Handout 16: Example of the axiomatic method in practice. (Bochenski)
  • Handout 17: Gödel's Incompleteness Theorems.  
    		•
    7
    		 Lecture 13: February 27
    Let's Make a Deal problem. Axioms of Probability.
  • Handout 18: Probability.  
    		•  Lecture 14: March 1
    Review. Bring your own questions! 
    8
    		 Midterm, March 6
    Midterm exam
  • Homework: No. 7
  • Handout 19: Descartes's Myth. (Ryle)
    		• March 8
    Mid-semester break
    9
    		 Lecture 15: March 13
    Conditional probability. Bayes' Theorem. Deductive solution to the problem.     		 Lecture 16: March 15
    Another application of probability theory. 
  • Quiz: No. 6, Homework: No. 8
  • Handout 20: Aristotle's logic.
    • 10
    		 Lecture 17: March 20
    Aristotle's syllogisms. Terminology    		 Lecture 18: March 22
    Propositional logic
  • Quiz: No. 7, Homework: No. 9
    •   March 27
    Spring break
    		 March 29
    Spring break
    11
    		 Lecture 19: April 3
    More propositional logic: Knights & Knaves, Natural Deduction
  • Handout 21: Natural Deduction rules.
    		•  Lecture 20: April 5
    Quantifiers.
  • Quiz: No. 8, Homework: No. 10
    		•
    12
    		 Lecture 21: April 10
    Non-classical logics. Mathematical Induction (I)    		 Lecture 22: April 12
    Deadline: Essay topic has to be approved.
    Mathematical Induction (II)
  • Handout 22: Mathematical induction problems.
  • Quiz: No. 9, Homework: No. 11
    • 13
    		 Lecture 23: April 17
    Set Theory. Functions.
  • Handout: Sample solutions for Homework 10.
  • Handout 23: Important definitions: Sets & functions
    		• Lecture 24: April 19
    Deadline: Essay outline has to be handed in.
    Cardinality of N, Z, Q.
  • Handout 24: The Non-Denumerability of the Continuum
  • Quiz: No. 10, Homework: No. 12
    • 14
    		 Lecture 25: April 24
    Cardinality of R.    		 Lecture 26: April 26
    Deadline:Essay due.
    Philosophy of mathematics
  • Homework: No. 13
    • 15
    		 May 1
    Review
    Bring your own questions!
    		 May 3
    Final exam

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