|10/7/2018| [Show less]
For our first week of the year, we'll be working on a handout containing olympiad problems from a long time ago. The problems do not follow any particular theme other than general knowledge of algebra.
|10/14/2018| [Show less]
This week we'll develop a theory for converting fractions to decimals and vice versa. Everyone knows that lots of things can be represented by both a fraction or decimal, but most people are at least a little fuzzy on how the two are related. This week we'll cut through the fuzz and by the end you'll be a pro at fractions and decimals.
|10/21/2018| [Show less]
The students ventured away from our decimal system and explored binary, trinary, and hexadecimal base systems. These form the basis of communication between modern computers, and also allow for encryption of English messages much more simply than the decimal system would, so it is important that our students are familiar with them.
|10/28/2018| [Show less]
This weekend we will be continuing our study of place-value systems that are not base 10. Last week was a nice gentle introduction to the topics that consisted of a lot of computation. This week we are going to use some of the intuition that we built up last week to solve some more theoretical questions, and come to some surprising conclusions!
|11/4/2018| [Show less]
Last week we finished talking about place value systems, and this week we'll be letting out hair down and doing some good, old fashioned, problem solving. There is no specific theme for this week but we will be using some of the things that we developed in the past couple of weeks.
|11/11/2018| [Show less]
This weekend we are going to start a multi-week study of the topic of permutations. We are going to start our study by defining what a mathematical permutation is, learn how mathematicians notate permutations and prove some elementary results.
|11/18/2018| [Show less]
This weekend we will be continuing our study of permutations. Now that we have a basic understanding conceptualization of permutations and have some basic notation down, we are going to apply that notation to better understand the 15 puzzle. By the end of the class we won't have solved the puzzle, but we will be a lot closer.
|11/25/2018| [Show less]
Have a happy Thanksgiving!
|12/2/2018| [Show less]
Today we are going to finish up our study of permutations and finally resolve the case of the 15 puzzle. After that is done, we will take a look back at what we have done, and take note of some interesting results that we have proved along the way.
|12/9/2018| [Show less]
This weekend we are going to have our final class for the quarter. For the first hour we are going to take stock of everything that we have proved so far about the 15 puzzle, and the second half will be a class-wide relay with prizes!
|1/13/2019| [Show less]
This weekend we are going to start our study of geometry starting waaaay back at the start of Greek mathematics. This weekend we'll be (re)learning how to use a compass and straight edge. As such, please remember to being a compass and straightedge with you to class today! I hope that you are all as excited to resume the LAMC as I am.
|1/20/2019| [Show less]
Today we are going to continue our studies of Geometry, and learn more about what you can do using a compass and ruler, and finally talk about geometry as you have seen it in school. Today will be a nice mix of hands on drawing/calculation with the compass and ruler, as well as a bit of proving using claim / reason charts.
|1/27/2019| [Show less]
Today will be out third and likely final Geometry session of the quarter. During the first week we got some practice using the straightedge and compass, during the second we had a gentle introduction to two column proofs, and for this last week we'll be solving problems using some of what we have learned. Not all of the problems look like they are 'classic' straightedge and compass problems, but we will find that using just those two implements, you can do more than you might think. For this final week please bring your straightedge and compass with you to class.
|2/3/2019| [Show less]
Today we will be working with vectors, and connecting them to the previous work that we have been doing on geometric constructions. Vectors are in some ways just like the counting numbers, and in other ways are very geometric, unlike the counting numbers. This dual nature of vectors makes them both interesting and useful. We will start to uncover this duality today!
|2/10/2019| [Show less]
This week we are going to do something completely different from what we have been working on the past month. We are making a hard right turn from geometry and instead we will be focusing on problem solving with an emphasis on solving problems for the upcoming math kangaroo competition. You certainly don't have to aim to take the exam to enjoy this weekend's class, indeed When I was still in school, I enjoyed these contests no so much because I was competitive, but more because the questions themselves were often quite beautiful.
You do not need anything special for this week's lesson!
|2/17/2019| [Show less]
On account of the holiday, there will be no Math Circle this weekend.
See you next week!
|2/24/2019| [Show less]
Today we are going to talk about a subject of math that really counts, combinatorics. Combinatorics is known as the math of counting, however the counting itself is usually not the point. The point is the clever arguments that allow the counting to be done at all. Combinatorics is a mainstay of mathematical puzzles and competitions alike, as it is an extremely rich field of math which is still elementary.
|3/3/2019| [Show less]
This week we will be continuing what we stared last week and talk more about combinatorics. We will be starting with a brief review of what we spoke about last week, before moving onto completely new problems.
|3/10/2019| [Show less]
Today we'll be taking a break from our normally scheduled content to talk about everyone favorite geometric constant, pi! Pi is of course one of the most well known mathematical constants and has been studies from ancient Greece until now. We'll do a couple problems about Pi and compute a whole bunch of things geometrically.
|3/17/2019| [Show less]
For our last meeting of the quarter, we will be having another math relay! As we did last quarter, we'll be splitting people up into teams an seeing which team can get through the most problems.
|4/7/2019| [Show less]
We've all seem some pretty big numbers in our day. Sure maybe you've seen a 81, a 104 or maybe even (if you are very worldly) 3841. But, jut how big are big numbers really? How big is a number like 52!, the number of ways to arrange the number of cards in a 52 card deck? What about the number of times you would have to flip 200 coins before you got all heads? Can you even say which one is larger? Today we'll answer this question and more, by introducing the logarithm, a function that is extremely useful for making sense of the super massive.
|4/14/2019| [Show less]
Maybe on the whole you felt like last week was entirely too much. Maybe you thought that the numbers that we spoke about last time were too large, logarithms were too confusing and you are ready to take a mathematical break and return to a more pastoral existence. Good news! This next week we are talking about goats. That's right goats, everyone's favorite ornery, stubborn, ravenous livestock. We will find that making sure that goats have enough to eat is more mathematical then you might have thought. This just goes to show that you can try and leave math, but math will always find you!
|4/21/2019| [Show less]
Logic puzzles are a mainstay of recreational mathematics, and today we'll be solving problems involving people that always tell the truth (knights), always lie (knaves), and sometimes tell the truth and other times lie (knormals). Solving these problems can be challenging, but we'll learn how to approach them is a systematic way so that you can always find the answer. Although these problems seem like all fun and games, they actually have some connections to mathematical logic; the most fundamental branch of modern math.