640:300:H1–Spring 2015

Lecture Notes for 300H.

The main reference for this course are lecture notes by Professor Saks. These notes are being revised as the semester proceeds. New installments and revisions will appear as they become available.

As these notes are a work in progress, your suggestions and corrections are very welcome. If you find mistakes please notify me by email. If there are parts you find confusing or difficult to read please let me know.

Lecture notes

Section Title Version date
Section 1 Introduction:Thinking and communicating about mathematics 9-4-16
Section 2 What do Mathematicians Study? 10-1-16
Section 3 Universal Principles in Mathematics: An introduction 9-22-16
Section 4 Communicating Mathematics I: Assertions 9-26-16(7PM)
Section 5 Mathematical Scenarios 9-26-16(7PM)
Section 6 Tools from Logic 9-26-16(7PM)
Section 7 First Proofs: Elementary Set Theory 10-1-16
Section 8 Proof Mechanics: Simplifying the Goal 10-1-16
Section 9 Using and abusing variables 10-11-16
Section 10 Binary Relationships and Binary Relations 10-20-16
Section 11 Introduction to Mathematical Induction 11-3-16
Section 12 A glimpse of number theory 11-10-16
Section 13 Basic proofs involving real numbers 12-13-16
Section 14 Cardinality:Comparing the sizes of sets 12-13-16