• Final instructions for portfolio.

  • Schedule

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

    Week Date Lec # Topic Reading Homework/ Quiz
    History & Motivation
    1 Mo, Jul 3 1 Introduction, general remarks, administrative points Handout: The Language of Numbers. (Dehaene) (No.1)
      Tu, Jul 4   Independence Day. No class.    
      We, Jul 5 2 The origins of mathematics Handout: Measuring the unmeasurable. (Osserman) (No.2)
      Th, Jul 6 3 Early mathematics: Proof that the square root of 2 is irrational Handout: From mystery to history. (Barrow) (Quiz 1)
      Fr, Jul 7 4 Early mathematics: Proof that there are infinitely many prime numbers. Mathematical notation. Handout: Counting with base 2, 5, 60. (Barrow) (No.3)
    Kinds of reasoning/arguments
    2 Mo, Jul 10 5 Deductive vs. inductive reasoning Handouts:
  • Deductive Arguments. (Weston)
  • On Induction. (Hume)
  • Terminology
  • (No.4)
      Tu, Jul 11 6 Deductive validity Handouts:
  • Letter to Russell. (Frege)
  • Proofs by contradiction. (Mancosu)
  • (Quiz 2), (No.5)
      We, Jul 12 7 Proofs by contradiction. Syllabus update: New guidelines for portfolio glossary/index.  
      Th, Jul 13 8 More about arguments Handout: Proofs. (Glymour) (Quiz 3)
    The structure of mathematical theories
      Fr, Jul 14 9 Definitions.
    (Early course evaluations).
    The Language of First-Order Logic (FOL): p. 9-13 and Section 2.8 (p. 24-28). (No.6)
    3 Mo, Jul 17 10 Axiomatic systems
  • FOL: Sections 2.4-2.7 (p.15-22).
  • Handout: Axiom systems. Models. Consistency and Independence. (Berlinghoff et al.)
  • (No.7)
      Tu, Jul 18 11 Axiomatizations of geometry Handouts:
  • Foundations of geometry. (Hilbert)
  • Space and the Geometrization of Mathematics. (Shaw)
  • (Quiz 4)
      We, Jul 19 12 Axiomatizations of number theory Handouts:
  • Natural numbers. (Landau)
  • The series of natural numbers (Russell).
  • (No.8)
      Th, Jul 20 13 Limits of axiomatizations Handouts:
  • Example of the axiomatic method in practice. (Bochenski)
  • Gödel's Incompleteness Theorems.
  • (Quiz 5)
      Fr, Jul 21 14 Review. Handout: Sample solutions to Homework 8, Problem 3. (No.9)
    4 Mo, Jul 24 15 Midterm exam.    
    Case study I: Probability theory
      Tu, Jul 25 16 Let's Make a Deal problem. Axioms of Probability.    
      We, Jul 26 17 Deductive solution to the problem.
  • FOL: Sections 3.1-3.6
  • Handout: Probability. (Eels)
  • (No. 10)
      Th, Jul 27 18 Another application   (Quiz 6)
    The nature of mathematical proof
      Fr, Jul 28 19 Aristotle's syllogisms. Terminology
  • FOL: Sections 3.7, 3.8, 3.12
  • Handout: Aristotle's logic. (Glymour)
  • (No. 11)
    5 Mo, Jul 31 20 Propositional logic FOL: Sections 4.1-4.4, 4.7 (No. 12)
      Tu, Aug 1 21 More propositional logic Handout: Natural deduction rules (Quiz 7)
      We, Aug 2 22 Quantifiers. Non-classical logics. FOL: Sections 5.1-5.10, 5.13, and 6.1-6.5 (No. 13)
      Th, Aug 3 23 Mathematical Induction (I)   (Quiz 8)
      Fr, Aug 3 24 Mathematical Induction (II) FOL: Sections 9.1, 9.3, and 8.1-8.4.
    Handouts: Sample solutions for Homework 12. Claims to prove by mathematical induction.
    (No. 14)
    Case study II: Set theory
    6 Mo, Aug 7 25 Set Theory. Functions. Handouts:
  • Important definitions: Sets & Functions.
  • The Non-Denumerability of the Continuum. (Dunham)
  • (No. 15)
      Tu, Aug 8 26 Cardinality of N, Z, Q   (Quiz 9)
      We, Aug 9 27 Cardinality of R    
    Review
      Th, Aug 10 28 Review. Last day of classes!    
      Fr, Aug 11 29 Final exam.    


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    © Dirk Schlimm, Last modified: August 4, 2000