コンピュータサイエンス理論: Python による離散数学と確率 (サマーキャンプ)

In this course, students will be exposed to the language of higher mathematics(Proofs!) and connecting them to the real world by programming these models in Python. This is a great course for students who have math PTSD since it exposes analytical concepts that aren't just brute force, mechanical calculation. We'll be diving into things like graph theory, number theory, probability, and their applications. Think of this as an English class for Math!

Day 1: We'll answer questions like what is Math, Applied Math, and Computer Science.
We'll set the groundwork for this class by going over--
Logic: Conjunction, Disjunction, Negation, Implications, and Truth Tables.
Basic Mathematical Structures: Sets(Intersections, Unions, and Complements)
Basic Mathematical Notation.
We'll write some small programs that demonstrate De Morgan's Law and
solve the Green Eyed, Blue Eyed island problem!

Day 2:  Proof by Induction -- one of the hardest proof methods
We'll go over loops(in programming), an advanced concept called recursion,
and go over things like the fibonacci sequence. 
We'll also start going into Graphs, the four colored map theorem, and
other applications like binary search and stable marriage.

Day 3: Basic Number Theory and modular arithmetic -- Fizzbuzz edition
We'll go over one of the world's most popular coding interview problems,
learn about modulus and a little bit of number theory. At the end of this
session, your student should have a rough idea of how basic cryptography
works and hopefully will have a small demo to show off too!

Day 4: Graphs, and Trees -- the bread and butter of Facebook and Google
We'll go over basic properties and terminology for these structures
and by the end we'll have them coded up using different representations.
We'll learn a few basic algorithms to traverse them.
Programming wise: we'll learn about object oriented programming with
classes!

Day 5: Counting, Combinatorics, and Probability Theory.
We'll go over these concepts under the guise of common dice
and card games. We'll formally prove these concepts and go
over the popular Monty Hall problem. 
At the end of this day, your student will have a programming
simulation of dice and Monty Hall!