It's not just numbers: Journeys into proof-based mathematics
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6 sessions
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+16
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This series is part of Schoolhouse Summer Camp! Explore Summer Camp
About
I believe everyone should be given a space to practice their proof-based math skills, since it teaches you to think logically on your feet, explore, and build/challenge arguments.
PREREQUISITES: This series is meant to be accessible to a broad audience. In reality, much of what we consider to be "college-level math" is completely reachable for students with just a basic proficiency with high school algebra. If any of these sessions require any more advanced prerequisites, I will say so in the description. If you don't have the background knowledge, I encourage you to attend anyway, but also feel free to ask for an excused absence.
Each session, we will explore a different topic in mathematics. These topics are likely unlike any math you've seen before. With this series, I hope to help expand your horizons of what math really is, outside of the classroom. Topics include, but are not limited to, set theory, combinatorics, graph theory, geometry, and more.
These sessions will be proof- and discussion-based, so I would like all participants to engage as much as they are comfortable with! I will provide the basic definitions, pose motivating questions, and provide hints as needed, but the exploration is entirely up to you.
I will add more sessions to this series as we go, so if you have any ideas for future sessions, please feel free to suggest them!
Also, if you're interested in this series but the current set time doesn't work for you, feel free to suggest a better time period that works for you, and if there's enough interest, I can see if I can switch times.
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✋ ATTENDANCE POLICY
Each session will be mostly independent from the others, so don't worry if you need to miss a few. However, if you do, please give me as much advance notice as possible.
SESSION 1
25
Jul
SESSION 1
Even More Math
Even More Math
Fri 12:30 AM - 1:30 AM UTCJul 25, 12:30 AM - 1:30 AM UTC
Title: Some infinities are just built different
Is infinity a number? If not, what is it? Are all infinities the same? (well, clearly not, given the title)
In this session, we will discuss cardinality, a way to conceptualize of the "size" of a collection of objects. We will apply this concept to various infinite sets to try to understand their sizes.
SESSION 2
29
Jul
SESSION 2
Even More Math
Even More Math
Tue 12:30 AM - 1:30 AM UTCJul 29, 12:30 AM - 1:30 AM UTC
Title: One step at a time
Mathematical induction is a very powerful technique for proving many classes of mathematical statements. Induction is extremely simple: If I'm trying to prove a statement for every natural number, I need to show that it's true for n = 1 and that if it's true for n = k, then it must be true for n = k + 1. If both of these things are true, then the statement is proven.
In this session, we will review the basic definition of induction, go through an example or two, and then explore some interesting problems to try to come up with an induction-based solution.
SESSION 3
30
Jul
SESSION 3
Even More Math
Even More Math
Wed 12:30 AM - 1:30 AM UTCJul 30, 12:30 AM - 1:30 AM UTC
Title: Mathematicians love coloring and connect-the-dots
Graphs are mathematical representations of networks. A very common flavor of question in the theory of graphs is: if I assign a color to each node in this graph, what is the minimum number of colors I need so that no two connected nodes are the same color?
In this session, we'll explore the concept of chromatic numbers of different graphs, trying to develop an intuition for what a graph's chromatic number says about the graph's structure. I will also mention an open problem in this area, which we can dig deeper into in a later session!
SESSION 4
1
Aug
SESSION 4
Enrichment
Enrichment
Fri 12:30 AM - 1:30 AM UTCAug 1, 12:30 AM - 1:30 AM UTC
Title: The state of math education
Based on a few requests from you all, this session, we will have a more open-ended discussion about your experiences in math education. I'm curious to hear your perspectives about what you think worked well and what didn't work well, for you and for others, in your classroom math experience!
SESSION 5
5
Aug
SESSION 5
Even More Math
Even More Math
Tue 12:30 AM - 1:30 AM UTCAug 5, 12:30 AM - 1:30 AM UTC
Title: The math that makes your computer secure
In this session, we'll explore the basics of modular arithmetic and primality in an effort to understand the RSA cryptographic algorithm that forms the basis of all modern computer security.
SESSION 6
6
Aug
SESSION 6
Even More Math
Even More Math
Wed 12:30 AM - 1:30 AM UTCAug 6, 12:30 AM - 1:30 AM UTC
Title: Integration, but fancy and French
The Lebesgue Integral is an improvement upon the Riemann integral, making almost all conceivable functions integrable (for example, the Dirichlet function; look it up, it's weird).
NOTE: If you don't have any Calculus experience, this session may be a bit hard to follow. I will try to make it as accessible as possible, so please feel free to still join, and don't be discouraged if you don't understand.