We've made it to the end of the course! "FINALLY," you say. MISSION ACCOMPLISHED!!!


Well hold your horses there, buster brown. We're not out of the woods yet. We have, of course... the DREADED FINAL EXAM to worry about!!!



No, there's no use running.


Or, perhaps you may be saying, "Alex, I spent an entire semester in this class and I don't remember anything!" or "I don't feel like I learned anything."

Like flames... at the side of your face.


Well I'm here to say: POPPYCOCK.
You remember plenty, and you've probably learned lots of things! Here, I'll guide you by the hand and list some of the stuff that you probably know and don't even know you know!




Don't worry, I'll STEP you through it. Hahahahahahahaha



Look at all the stuff we learned!

Chapter 1 was on logic:
  • Natural Deduction in Propositional Logic
  • Existencial and Universal Quantifiers
  • Natural Deduction in First-Order Logic
  • Building Proof Trees
  • The difference between intuitionistic and classical logic
  • The law of the excluded middle
  • Proof by contradiction
  • Variables, propositions, atoms, constants
  • Homework: DeMorgan's Laws
  • Homework: Double Negation
  • The Project: The Gentzen System



Building proof trees: somewhat painful!

Chapter 2 was on set theory
  • What's a set?
  • Set equivalence, subsets, and elements
  • Russell's paradox
  • Power sets
  • Unions, Intersections
  • Cardinality
  • The definition of the Natural Numbers
  • Countable/uncountable infinities
  • The Axiom of Choice?!?
  • Complete (strong) induction, weak induction
  • Homework: Big Unions/Intersections




Chapter 3 was all about functions
  • What is a function?
    • Ordered pairs, cartesian products
    • Relations
  • Function composition
  • Recursion and the Fibonnaci/Lucas numbers
  • Inverses of functions
  • Images and inverse images
  • Injections, Surjections, Bijections
  • The Pigeonhole Principle
  • Hilbert's Space Filling Curve
  • How do we REALLY prove things?
  • Homework: The Triangular Numbers
  • Homework: Hilbert's Hotel!




Chapter 4 was an introduction to graphs
  • What are graphs?
    • Verticies and Edges
    • Directed, Undirected
  • Paths and Strongly Connected Components
  • Node degrees, in degree and out degree
  • Cycles, Connectivity
  • Trees and Forests
  • Spanning Trees
  • Graph Isomorphism


TREEEEEES!!!


And that's it! If you know all of that, you're surely set for the final. And look how much you know! Maybe you knew some of it before, maybe some of it will fall out of your head soon, but that's OK! You've surely gained something from the class.

I'll be having office hours next week for any questions you have.

It's been delightful being your TA this semester, you guys were great, even if you did bombard me with 100000000 emails.

I guess it's time to say goodbye...



No no, don't worry about me, I'll be fine.


Haha, just kidding! It is time for RIDICULOUS DANCING.


Enjoy your winter break!
Allons-y! Back to CIS160 Page