| 09/30/2012 | We will visit the planet Heptadium in a galaxy far, far away. The planet makes one full spin around its axis in 7 heptahours, so the folks inhabiting the planet divide the dials of their clocks into 7 parts. A heptahour is divided further into 49 heptaminutes, a heptaminute has 49 heptaseconds. We will study the Heptadium way of timekeeping and the related mod 7 and mod 49 arithmetics. ⊟Details |
| 10/7/2012 | First, we will finish discussing the previous handout, from Problem 12 on. Be prepared to present your solutions of Problems 12 - 16 at the board! Next, we will begin learning coordinates on lines and surfaces, from a segment of a straight line to a sphere. Also, come ready for a great naval battle. A good understanding of coordinates will be needed to win! ⊟Details |
| 10/14/2012 | We will study the most elementary, and the most important, functions of one variable, linear, affine, absolute value, and quadratic. ⊟Details |
| 10/21/2012 | We will continue the study of functions and graphs. ⊟Details |
| 10/28/2012 | At the beginning of the class, we will solve a Halloween cryptarithm. Then we will continue working through the fourth handout starting from Problem 8. If time remains, we will prove the Pythagoras' theorem and use it as a tool for figuring out distances between points. ⊟Details |
| 11/04/2012 | We will have a quiz at the beginning of the class. Once finished, we will learn two different proofs of the Pythagoras Theorem and apply the theorem to figuring out distances between points in the Euclidean plane, see Handout 5 from page 7 on. ⊟Details |
| 11/11/2012 | For the first hour, we will solve a variety of problems, including taking roots of numbers, drawing a graph of a function, constructing a right angle by means of a rope, and figuring out the winners of a fencing competition. In the second part of the class, we will prove the triangle inequality for the Euclidean plane. We will further use it as a tool for finding the shortest paths between points in the Euclidean plane and on a cylinder. ⊟Details |
| 11/18/2012 | We will learn that there are infinitely many geodesic lines ("straight lines") connecting two points in general position on a cylinder. We will use this information to construct triangles on a cylinder. We will also learn that there exist two types of circles on a cylinder. One of them is just like a circle in the Euclidean plane, the other looks more like the number 8. ⊟Details |
| 12/02/2012 | During the first hour, we will try to find a winning strategy for a game they sometimes use for starters in a game theory course. During the second hour, we will learn what the average value is and apply the knowledge to solving various problems. ⊟Details |
| 12/09/2012 | The students will be given a test on all the topics covered during the quarter. The duration of the test is an hour and a half. Then, the test will be quickly graded and the highest-scoring students will be given awards. ⊟Details |
| 01/13/2013 | We will begin this quarter with a few classes on probability theory. The probability of an event is a number in between zero and one, ends included, so the working knowledge of fractions is a necessity. We will give the students a 15-min-long diagnostic quiz at the beginning of the first class to estimate how good they are with fractions. The degree of their success will tell us how to split the class time between learning fractions and using them to compute probabilities. Since the results of the quiz will only be available after the first class, we will study fractions till the end of the first hour. We will begin learning the probability theory during the second half of the class. ⊟Details |
| 01/20/2013 | For the first 70 min. of the class, the students will be given a Math Kangaroo test for 5th and 6th graders from one of the years passed. Even if your child doesn't plan to take part in the actual Math Kangaroo competition this year, it's very beneficial to solve the problems, they are non-trivial and fun!
After a 5 min. break, we will run a simulation of the Monty Hall Paradox. Please see the following URL for more.
http://en.wikipedia.org/wiki/Monty_Hall_problem
It is possibly the most famous paradox of elementary probability theory. To make it more striking, we will use ten doors (or rather playing cards) instead of only three from the original version. ⊟Details |
| 01/27/2013 | We will solve a few word problems on fractions at the beginning of the class. Then we will continue our study of probabilities, learning the properties of complementary, mutually exclusive, and independent random events. ⊟Details |
| 02/03/2013 | We will study permutations and combinations and then apply them to counting probabilities. ⊟Details |
| 02/10/2013 | We will continue learning combinatorial probability. In particular, we will finish studying the handout for the previous class. ⊟Details |
| 02/24/2013 | We will first recall the basic compass-and-ruler constructions we have done in the past. We will further move to proving the existence of an incircle, circumcircle, etc. for any triangle in the Euclidean plane. ⊟Details |
| 03/03/2013 | We will begin with Problem 6 of the previous class handout and proceed to the end of it. The very few students who have worked the handout to the end during the previous class will be given a new one. ⊟Details |
| 03/10/2013 | The students will solve a Math Kangaroo test from one of the years past and a few extra problems collected for us by Samir's mom, Sarita. ⊟Details |
| 03/17/2013 | The class will be split into four teams competing against one another in solving the problems given by the instructors. The winning team will get some prizes. ⊟Details |
| 04/07/2013 | At the end of the previous quarter, we considered the following problem. Prove that medians of any triangle in the Euclidean plane intersect at one point and that the intersection point divides them in the ratio 2:1 counting from the corresponding vertex. We are going to give three different proofs to the theorem, each coming from a distinct, and very important, branch of mathematics. In the process, we will learn a bit of geometry of masses and barycentric coordinates, linear algebra, and classical (Greek-style) geometry of the Euclidean plane. ⊟Details |
