We kick off the academic year with some competition-style problems gathered from AMC, AIME, and Olympiads.
We will introduce Gaussian integers in order to decide which prime numbers can be written as a sum of two squares.
We will wrap up the discussion of Gaussian integers and prove which prime numbers are the sum of two squares.
We will study the limitations of polynomials as prime generating functions.
We will study recursive formulas for generating primes.
We will take our first peak into algorithms, with the goal of discussing the P vs NP problem the following week.
We continue our unit on algorithms by discussing the most famous open problem in the field, P vs NP.
The Fundamental Theorem of Algebra... Everyone's heard of it. If it's so fundamental then why haven't we seen a proof?! Look no further, we consider complex polynomials and graphing techniques to prove that every complex polynomial has a root.
To start off the new year we are going to split the class into two competing groups. There will be a variety of problems to work on and it will be up to the teams to organize how they feel is best.
We start our unit on graphs with a dive into planar graphs and the Euler characteristic.