1 January 14 (Lecture 1)
Topic: Introduction
Handout: Syllabus & Overview
January 16 (Lecture 2)
Topic: The origins of mathematics
Homework: Problem set 1
January 18 (Lecture 3)
Topic: The importance of notation: Chinese number words; Roman and Babylonian number systems.
2 January 21
Martin Luther King day
(No class)

January 23 (Lecture 4)
Topic: Early mathematics. Proof that the square root of 2 is irrational.
Homework: Problem set 2
January 25 (Lecture 5)
Topic: More proofs: Proof that there are infinitely many prime numbers.
3 January 28 (Lecture 6)
Topic: The notion of proof: Deductive validity.
Handout #1: Terminology for proofs and arguments (pdf)
January 30 (Lecture 7)
Topic: More about arguments: Possibility, objectivity, forms of arguments.
Homework: Problem set 3
Handout #2: Deductive arguments (Weston)
February 1 (Lecture 8)
Topic: Deductive vs. inductive reasoning.
4 February 4 (Lecture 9)
Topic: Proofs by contradiction.
February 6 (Lecture 10)
Topic: Definitions.
Homework: Problem set 4
Handin Journal.
Handout #3: Proofs (Glymour)
February 8 (Lecture 11)
Topic: Feedback on journals. Mathematical theories.
5 February 11 (Lecture 12)
Topic: Feedback on early course evaluations. Axiomatic theories, and properties of axiom systems.
Handout #4: Axiom systems. Models. Consistency and Independence. (Berlinghoff,
February 13 (Lecture 13)
Topic: Consistency and independence.
Homework: Problem set 5
February 15 (Lecture 14)
Topic: Axiomatization of geometry. Non-Euclidean geometries.
6 February 18 (Lecture 15)
Topic: More Non-Euclidean geometries. Axioms of arithmetic.
Handout #5: Foundations of geometry (Hilbert)
Handout #6: Foundations of analysis (Landau)
February 20 (Lecture 16)
Topic: Axiomatizations; the situation in mathematics at the beginning of the 20th century
Handout #7: Axiomatization of sentential logic (Bochenski)
Handout #8: Introduction to mathematical philosophy, Ch.1 (Russell)
Handout #9: Hilbert and Gödel (pdf)
February 22 (Lecture 17)
Topic: Limitations of formal systems: Gödel's incompleteness theorems
Homework: Problem set 6, Extra problem (pdf)
7 February 25 (Lecture 18)
Topic: Philosophical implications of Gödel's theorems. Let's Make a Deal problem. Axioms of probability theory.
Handout #10: Probability (Eels).
February 27 (Lecture 19)
Topic: Conditional probability. Bayes' Theorem.
Handout #11: Conditional probabilities and Cherry pies (pdf)
Homework: Problem set 7
March 1 (Lecture 20)
Topic: Deductive solution to the Let's Make a Deal problem. Empirical confirmation. Concept map.
8 March 4 (Review session)
Review for exam: Bring your own questions!
More questions.
March 6
Midterm exam
March 8
Mid-semester Break
9 March 11 (Lecture 21)
Topic: Another example for the application of probability theory
March 13 (Lecture 22)
Topic: Discussion of midterm exam
Handout #12: Aristotle's logic (Glymour).
Homework: Problem set 8
March 15 (Lecture 23)
Topic: Aristotle's syllogisms
10 March 18 (Lecture 24)
Topic: The language of logic. Syntax and semantics.
March 20 (Lecture 25)
Topic: Propositional logic. Truth tables.
Homework: Problem set 9 (A)
Homework: Problem set 9 (B)
Note, you need to do only (A) or (B).
March 22 (Lecture 26)
Choose your topic:
Lecture A (Dirk) Fun with truth tables
Lecture B (Henrik): BH 231 A Compactness, non-standard models
11 March 25 (Lecture 27)
Topic: Syntactic reasoning: Natural Deduction
Handout #13: Natural Deduction rules (pdf)
March 27 (Lecture 28)
Topic: Soundness, completeness, quantifiers
Homework: Problem set 10 (A)
Homework: Problem set 10 (B)
Note, you need to do only (A) or (B).
March 29 (Lecture 29)
Choose your topic:
Lecture A (Dirk) More on quantifiers
Lecture B (Henrik): BH 231 A Quantifiers in intuitionistic logic
  April 1
Spring Break
April 3
Spring Break

April 5
Spring Break
12 April 8 (Lecture 30)
Topic: Non-classical logics
April 10 (Lecture 31)
Topic: Mathematical induction (I): Recursive definitions
Homework: Problem set 11
April 12 (Lecture 32)
Topic: Mathematical induction (II)
Handout #14: Mathematical induction problems.
13 April 15 (Lecture 33)
Essay outline due
Topic: Introduction to the theory of sets
April 17 (Lecture 34)
Topic: Functions and cardinality
Homework: Problem set 12
Handout #15: Sets and functions (pdf)
April 19
Spring Carnival

14 April 22 (Lecture 35)
Topic: Cardinalities of the natural numbers, integers, rational numbers
April 24 (Lecture 36)
Topic: The cardinality of the continuum
Homework: Problem set 13
Handout #16: The Non-Denumerability of the Continuum
April 26 (Lecture 37)
Topic: Paradoxes of set theory
15 April 29 (Lecture 38)
Topic: Questions in philosophy of mathematics
May 1 (Lecture 39)
Topic: Summary of course, concept map
May 3 (Last day of classes)
Review for exam: Bring your own questions!
Essay due
Exam May 6
Final Exam
8:30am-11:30am, HH B131

Handin Journal

© Dirk Schlimm, Last modified: 5/3/02