ORMC Meetings • 2020-2021 Academic Year

We will start the year with a wide variety of competition style problems.

We will introduce Gaussian integers in order to decide which integers can be written as a sum of two squares.

We will wrap up the discussion of Gaussian integers and prove which integers 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 introduce some classic algorithms and the notion of runtime.

Following the introduction to algorithms, we are able to discuss the nuances of the P vs. NP problem.

We prove the Fundamental Theorem of Algebra with a focus on graphing.

The students battle it out in a full class Kahoot competition.

We will attempt to determine when a given graph is planar, culminating in Kuratowski's Theorem.

We will explore many interesting results about graph coloring.

We will finish the study of graph coloring and introduce basic ideas in Ramsey Theory.

Continued fractions are an interesting way to represent real numbers. We will develop an algorithm for computing continued fractions and attempt to classify periodic continued fractions.

We introduce the taxicab metric, a new way of measuring distance in Euclidean space. We will study its properties and figure out how it relates to the Euclidean metric.

We generalize different notions of distances, as motivated by the taxicab distance, into something called a metric space. We then discuss convergence of sequences in metric spaces.

In economics, the Gini index is a measure intended to represent income inequality. We will take a mathematical approach to the study of the Gini index.

Students will learn what an error of measurement is and how the said error propagates through computations that use the result of the measurement. In the process, the students will derive the sum, product, and quotient rules for the derivative using an engineering approach instead of taking limits.

Students will learn what an error of measurement is and how the said error propagates through computations that use the result of the measurement. In the process, the students will derive the sum, product, and quotient rules for the derivative using an engineering approach instead of taking limits.

We will show that certain regions of Euclidean space must contain integer lattice points.

We will develop and study different types of binary codes that detect when a user has made an error. These will include ISBN, repeating codes, Hamming's square code, and Hamming's [7,4]-code. We will also be able to compare the efficiency of these codes.

We will develop and study different types of binary codes that detect when a user has made an error. These will include ISBN, repeating codes, Hamming's square code, and Hamming's [7,4]-code. We will also be able to compare the efficiency of these codes.