Announcements
 07/08/12 — I uploaded a document to give you LaTeX practice. Try to recreate this output yourself and see me if you're having trouble. It will help you learn many important LaTeX commands and tricks.
 Office hour schedules for myself and my TA are posted above!
 I have created a page on how to install and get started with LaTeX, the math typesetting program.
 06/30/2012 — There are detailed instructions on the textbook materials page about how to register and login to the textbook viewing app.
Course Summary
Welcome to Concepts of Mathematics! This course is a prerequisite for any theoretical course here at CMU in mathematics, computer science, and the natural sciences. It will train you how to reason and think about mathematical problems, as well as give you a base of knowledge, techniques, and mathematical fluency that will aid in your understanding of more advanced mathematics.
See the course syllabus for more information about Concepts of Mathematics, in general, and a description of this summer session (content, assessment, policies, etc.), in particular.
Useful Links
 An introduction to LaTeX: how to download it, how to use it
 CMU Mathematics Department
 CMU HUB
 CMU Academic Integrity Policy
 CMU Peer Tutoring
Course Calendar
Note: to use any of the LaTeX files I provide, you will need the preamble I import: preamble.tex
In the preamble of your .tex file, include the line "\input{/*****/preamble.tex}", where ***** is the directory path to where preamble.tex is stored on your computer.
NOTE: None of these links work anymore because the course is over. Sorry! I gotta keep my secrets, ya know?
Monday  Tuesday  Wednesday  Thursday  Friday 

2
Notes: PDF
Intro + Syllabus
What is math? Puzzles 
3
Notes: PDF
What is a proof?
Axioms 
4

5
Notes: PDF
Inductive arguments
Sets Examples 
6

9
Notes: PDF
Set equalities
Logical Statements 
10

11
Notes: PDF
Proof Strategies
Proof Examples 
12
Notes: PDF
Using proof strategies
Workshop 
13

16

17
Notes: PDF
More on Induction
Generalized strategies Structural Induction 
18
Notes: PDF
Relations
Examples Properties 
19
Notes: PDF
Equivalence Relations
Equivalence Classes Modular Arithmetic 
20

23
Notes: PDF
Functions
Examples Images + Preimages 
24
Notes: PDF
HW5 due! PDF/LaTeX
Injections + Surjections
Proof Strategies Bijections 
25
Notes: PDF
Composing Functions
Inverses 
26
Notes: PDF
Cardinality
Finite Sets Countable Sets 
27
Notes: PDF
HW6 due! PDF/LaTeX
Infinite Sets
Uncountable Sets Cantor's Argument 
30
Exam 2! Prep Q's: PDF/LaTeX

31
Notes: PDF
Counting
Rule of Sum Rule of Product 
1
Notes: PDF
Counting Objects
Proof Strategies Combinatorial Identities 
2
Notes: PDF
Counting in 2 ways
Reading Proofs Pirates & Gold 
3
Notes: PDF
HW7 due! PDF/LaTeX
Pigeonhole Principle
Inclusion/Exclusion 
6
Notes: PDF
Probability Theory
Spaces and Functions Results 
7
Notes: PDF
Conditional Probablity

8
Notes: PDF
HW8 due! PDF/LaTeX
Graph Theory
Definitions Properties 
9
Notes: PDF
Graph Colorings
Probabilistic Method Ramsey Theory 
10
Exam 3! Prep Q's: PDF/LaTeX
