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: |
(No.4) |
Tu, Jul 11 | 6 | Deductive validity | Handouts: |
(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 | (No.7) | |
Tu, Jul 18 | 11 | Axiomatizations of geometry | Handouts: |
(Quiz 4) | |
We, Jul 19 | 12 | Axiomatizations of number theory | Handouts: |
(No.8) | |
Th, Jul 20 | 13 | Limits of axiomatizations | Handouts: |
(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. | (No. 10) | ||
Th, Jul 27 | 18 | Another application | (Quiz 6) | ||
The nature of mathematical proof | |||||
Fr, Jul 28 | 19 | Aristotle's syllogisms. Terminology | (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: |
(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. |