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 log-in 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
|
