LAMC Meetings • 2019-2020 Academic Year

Today we will be looking at how to optimally divide cakes among any amount of people by using an ancient Egyptian technique of breaking fractions into their unit parts but doing so in a specific way, which we will work with and then prove to be optimal.

This week we continue from last week and try to prove a mathematical algorithm, which is a very important activity in mathematics.

This week we begin on a very very very important topic in mathematics; Modular Arithmetic. Although the importance of this topic is not fully realized until a course in Abstract Algebra, it is still a very important topic because it can instill an understanding that the mathematics or arithmetic that we see commonly is not the only way of operating and that mathematics can be far more general and far reaching.

A continuation of next week. Please use this week's sheet as a a set of problems that build stronger arithmetic skills and provide insight into other ways of "counting."

This week we are working with some logic problems in the guise of "real world" sentences. The hope is that students can see that a basic logical structure is embedded in common speech, and that logical structure is the basis for mathematics and is taken to its most pure form and to its greatest lengths. Please use these worksheets as a warm up for the logical skills needed for induction next week.

This week we are starting induction! If these problems are challenging (they most likely are) do not panic. These are meant to be attempted to the best of everyone's ability and asking questions is extremely encouraged.

This week we are continuing on induction proofs. It is fully expected that these problems are challenging, but they are extremely important to attempt, not necessarily get correct. The point of these two weeks is to 1. prepare students for induction proofs (the basis of discrete math and many proofs about finite objects) and 2. to challenge them to see the power of mathematical logic to prove an infinite amount of statements in a finite time.

This week we are working on finding the perimeter of some interesting shapes. These problems are designed to prepare students to quickly recognize the shapes they are looking at and how they can break them into easily solvable pieces.

This week we are playing a Math Circle classic! The rules are attached. Hope everyone has a great time :).

This week we will be looking at geometrical numbers and the successive difference found in the sequence of these numbers. Interestingly, these types of numbers have been studied for thousands of years ever sense the Ancient Greeks. These sorts of problems are very useful to build strategies for induction proofs and pattern spotting.

This week we will be working on some very interesting logical problems. These sorts of problems, although not generalization to higher mathematical theory, are very useful in practicing mathematical logic and intuition.

This week we will be playing a game with the Math Kangaroo Practice tests. The Math Kangaroo is a math test for young mathematicians and is usually held in the middle of the year.

The game we are playing this week will encourage team work, communication, and dieligent justification of answers.

This week we start on the topic of Graph Theory! This topic considers a particular object of mathematics, the Graph, which is defined by its vertices and the edges connecting them. We will be considering the degree of the vertices as well a particular type of Graph, the Bipartite Graph.

Please use the worksheet from last week.

This week we completed the rest of the Graph Theory packet, going over topics such as the coloring of a graph, which is the least number of colors required to fully "color" a graph. An interesting theory associated with this is that if one considers ANY map that separates the area into counties, states, cities, etc. then one can color that map with four colors such that no two adjacent counties, states, cities, etc. have the same color. This theorem was proved using computers!

This week we will be solving the instant insanity puzzle. This puzzle is a mathematicians favorite as it is difficult to solve by “brute force,” but permits a very simple and elegant mathematical solution. We will begin by trying brute force tactics and when that fails us we will find a way to use graph theory to solve the puzzle very simply.

here is the amazon link to the puzzle: Winning Moves Games Instant Insanity https://www.amazon.com/dp/B004KCN6EQ/ref=cm_sw_r_cp_api_i_QwSuEb6C13BXG

This week we will be working with probability! We will be learning how to calculate the expected value of a given game. This sort of "average" thinking is used all the time by everyone unconsciously and explicitly.