We will begin a mini-course on place-value numerical systems. We will study the numerals base ten (decimals), base two (binaries), base three (trinaries), base eight (octal numbers), and base sixteen (hexadecimals or just hexs).

This week we will begin to explore properties of the decimal representations of fractions. The goal for this week is to prove that certain fractions have a terminating decimal equivalent.

We will be spending one more week solving problems that have appeared on Russian math olympiads. This will help the kids strengthen their individual problem solving skills as well as prepare them for thinking outside the box, of which we will ask a lot this year!
NOTE: HOMEWORK DUE: Previous week's handout, Problem 9 and Problem 11. For problem 11, I asked students to come up with as many distinct solutions as they could. Attempting problem 12 is not necessary because it will appear again on this week's set.

About 25% of the students have finished, or nearly finished, working through the first handout during the first session. These students will be given the second handout with various olympiad-style problems at the beginning of the class. The rest of the students will resume studying the first handout at problem 14 on page 14. Once finished, they will be given the second handout with the olympiad-style problems.

This week we will work on equations, through looking at balancing scales. Please remember to bring your kids on time so we can start class right away! Thanks!

This week we will continue working with balancing scales. We are introducing how binary and trinary searches work by finding the minimum number of trials to find one fake coin among real (equal) coins by using a scale. Remember to have kids explain their solutions to you at home!

We will go over the games played two weeks ago and discuss winning strategies. For more details, you can check out the wonderful online notes on game theory by Prof. Ferguson
http://www.math.ucla.edu/~tom/Game_Theory/Contents.html

We will be continuing with Math Induction this week. PLEASE MAKE SURE LAST WEEK'S HANDOUT IS BROUGHT TO CLASS, WITH PROBLEMS 1-4 COMPLETED. Handout is here: http://www.math.ucla.edu/~radko/circles/lib/data/Handout-561-694.pdf

We will go over all the problems in the second and third handout that some students could not figure out themselves. It will be mostly students explaining their solutions to fellow students. The teachers will only help if there is on one else to solve a problem.
If any time remains, we will do some olympiad-style problems on the pigeonhole principle.

This week we will be introducing Roman numerals to the class. We will learn what they are and how to add and subtract them. Please remember to bring your kids on time! Thanks :)

To celebrate the 170 years (+4 days) anniversary of Sir William Rowan Hamilton's discovery, we will take a look at the quaternions, a cousin of the complex numbers.

We will be doing two lessons from the book, "Sideways Arithmetic from Wayside School" by Louis Sachar. The topics include cryptarithms and some logic T/F problems.

Today we will finish up our study of metric spaces, by looking at metrics on sets other than the real numbers. PLEASE look at homework problem 2 from last week's handout, and bring last week's handout this week!

No, not peanut butter, celery, and raisins. This week we will take a look at some classic and not so classic problems about crawling bugs, as well as problems to do with tiling a region in the plane.

This week we will be doing a diverse set of problems that all fit the Halloween theme!
Handout corrections:
#4: The question should be, "At which house will both groups visit?"

Students will take a test on place-value numerals with two problems on the Pigeonhole Principle at the end. The best way to prepare is to study the first and third handouts for the place-value numerals and the fourth handout for the principle. The test may take the stronger students about an hour to complete while weaker students may need two hours. The students finished working on the test will be asked to move to the neighboring room where some more problems on the Pigeonhole Principle will be discussed.

We will discuss how to divide a polygonal pizza between friends, pearl
necklaces between pirates, and other fair division problems.
Continuity plays a major role in all these problems.

We will be working through a full-length AMC practice exam to help with general problem solving skills as well as prep for those who will be participating in the AMC soon after.

We will study some basic properties of parallelograms. Our studies will be based on the April 15, 2012 Junior Circle handout. Please see the following
URL.
http://www.math.ucla.edu/~radko/circles/lib/data/Handout-345-431.pdf

This week we will continue working on binary numbers. We will learn how to count in binary by using our fingers. We will also learn how to add and subtract in binary.

Today we will explore how complex numbers can be applied to geometry. We will focus on how to view transformations of the plane as functions of complex numbers.
Please review the handout from last week in preparation for this week!

We will discuss how to inscribe circles, triangles, rhombi and squares
into more complicated figures. Again, the continuity will play a
major role, but the arguments will turnout to be more sophisticated
while still elementary.

Most of the students didn't move past Problem 6 from the last week's handout. This time we will resume at Problem 7. We will continue proving properties of parallelograms using the Claim ? Reason charts.

Imagine in the future that we are able to build a spacecraft that is able to travel 186,250 miles per second. Suppose that a father goes on holiday to a nearby planet. His daughter takes him to the spaceship and bids him farewell. He tells her that he will be back in a year and to keep an eye on the house. When he comes back, he sees a strange old lady living in his house. He asks her, \Who are you and what are you doing in my house?" She says, "I'm your daughter, Dad." What is going here? By the end of this lecture, we will have an answer to this question.

Imagine in the future that we are able to build a spacecraft that is able to travel 186,250 miles per second. Suppose that a father goes on holiday to a nearby planet. His daughter takes him to the spaceship and bids him farewell. He tells her that he will be back in a year and to keep an eye on the house. When he comes back, he sees a strange old lady living in his house. He asks her, \Who are you and what are you doing in my house?" She says, "I'm your daughter, Dad." What is going here? By the end of this lecture, we will have an answer to this question.

As usual, we will solve a few warm-up problems at the beginning of the class. Then we will learn how to divide a straight line segment into any (positive integral) number of parts, using a compass and ruler as tools. We will further employ a Claim-Reason chart to prove that our method works. In the next part of the class, we will introduce vectors as pointed segments, or arrows, and begin studying their properties.

To start out the quarter, we will be developing logic skills by looking at problems with hats and doors. The goal of this handout is to learn how to make an assumption, test the assumption, and readjust the original assumption if necessary.

We will use vector algebra to re-prove some important theorems we have proven in the past; to slide a heavy box over the floor in an efficient manner; and to steer a spaceship. All that after a warm-up that includes a cool card trick.

We will continue our study of the algebra of vectors. To better understand multiplication of vectors by some irrational numbers, we will also recall the Pythagoras theorem and use it compute some lengths. Finally, we will refresh our understanding of rational vs. irrational numbers.

In this lesson we introduced the class to function machines and how they work. The class worked through several different examples of functions. For homework, each student is making their own function machine.

We will solve a bunch of warm-up problems and then switch back to studying vector algebra. We will work on Problems 7 through 17 from our 1/19/2014 session. We did not solve them back then. We will solve them this time.

In this class we learned about functions being 1-1, as well as how to compose functions. Kids also introduced their own function machines and worked with them throughout the class.

This week, we will continue our discussion on the distance formula. In particular, we will look at how we can solve problems using graphs of distance vs. time. We will also solve some problems involving people working together to complete tasks.

We will be starting a two-week study of taxicab geometry this week!
Handout titled "bonus" is for those who finish the main taxicab handout. It will not be required knowledge for next week's handout, though it's an interesting problem.

First, we will use vector algebra to prove the median theorem, the one we had skipped last time. Then we will see how vectors make clear the three laws of Newton. In the process, we will help Captain Solo defeat the Death Star and save the galaxy, again!

If your child is interested in attending a selective college, you need to understand how today's college admissions has changed since you applied. This talk will cover topics including what you need to know about curriculum, testing, grades, extracurriculars, college essays, recommendations, interviews, and more.

Today we will continue our study of sequences from last week, and introduce the related concept of a series. Please review last week's handout in preparation for this week. In particular, students should be comfortable with at least questions 0:a-h, 1:a-f, 2:a-c, and 3.

This week, we will be looking at graphs to determine speeds of objects. In addition, we will introduce graphing lines and determining equations of lines.

We will be solving problems that will help us prepare for the upcoming Math Kangaroo exam. In addition, we will discuss some strategies for taking the exam.

The students will be given a test covering the topics we have studied this quarter, vectors, velocity and acceleration, Newtonian laws, Pythagorean theorem, rational and irrational numbers, floor and ceiling of a number, and the inclusion-exclusion principle. In addition, there will be a few olympiad-style problems that require no special knowledge, but are non-trivial and fun to solve on the test.

We will be learning some important things about quadratics this week. Please bring this handout back next week, as we will be picking up with the Vieta's Theorem section!

For warm-up, we will discuss the 27 card trick. Then we will begin our study of permutations. Our main goal will be to learn solving the 15 puzzle in the cases where a solution exists.

We will be continuing last week's study of quadratic equations, with an emphasis on Vieta's Theorem. Please make sure to bring last week's handout as we will be finishing that up this week.

This week we will continue to look at tessellations. In particular, we will look at tessellations made by combining regular hexagons, squares, and triangles.

How hard can it be to count? The answer to that question may depend on how
much stamina you have. It might, for example, take an awfully long time to
count how many 125-element subsets there are of {1, 2, ..., 250} by simply
listing all of them. There are faster ways to calculate this number, but
even then, at first glance it may appear to require a substantial amount of
computation in order to determine even the last digit of "250 choose 125".
In this talk, we will find this last digit, and explore some related
topics. (Hint: the last digit is not zero - that would be too easy!)

In 2012, UCLA Professor Emeritus Lloyd Shapley won the Nobel Prize in Economics. The award was in recognition of the Gale-Shapley Algorithm. You will learn that algorithm and also another of Shapley's important concepts called the Shapley Value.

We will continue our discussion of "insect worlds", and work with graphs. We will discuss properties of paths, circuits, Euler Circuits, and Euler paths.

The students who have finished working through the second handout on permutations will be given some olympiad-style problems to solve. Other student will join as soon as they finish the permutations handout.

We will make one more step towards understanding the 15 puzzle - learn what a parity of a permutation is and how to compute it. If time permits, we will also solve some more olympiad-style problems.

In these lectures we will explore an area of mathematics called knot theory. A knot is a closed loop in three dimensional space, and two knots are called equivalent if they can be deformed into each other. We can distinguish knots by assigning to them certain quantities, called invariant.

Not every proof needs to have two columns for "statements" and "reasons," or an assumption that is contradicted. We'll learn about a different way this week; if you don't want to tell me how, show me how -- with a picture!

A USC physics professor and the father of one of our students, Vitaly Kresin, is going to show the class some cool experiments related to the Newtonian Laws of motion we studied at the end of the 2014 Winter quarter. Once he is finished, we will get back to the 15 puzzle and learn the last tool we need to unravel it, taxicab geometry.

We will continue our discussion of modular arithmetic this week. We will look at addition and multiplication tables, as well as determining divisibility rules for some numbers.

We will learn the last tool we need to figure out why Sam Loyd's configuration of the 15 puzzle is not solvable. Called the taxicab (a.k.a. L_{1}) geometry, it is important in various areas of math and physics and quite entertaining in its own right. In particular, we will see that a taxicab geometry circle is ... a square! Once finished, we will solve some cool olympiad-style problems.

This lecture is about tilings of plane polygons by other plane polygons. We shall see many examples of impossible tilings but the proofs will get more and more involved. Colouring argument is a simple yet strong argument. However, there are problems that colouring argument alone cannot solve. One way of tackling tiling problems is using Conway's tiling group. This method transforms tiling problems into creating specific group structures.

This lecture is about tilings of plane polygons by other plane polygons. We shall see many examples of impossible tilings but the proofs will get more and more involved. Colouring argument is a simple yet strong argument. However, there are problems that colouring argument alone cannot solve. One way of tackling tiling problems is using Conway's tiling group. This method transforms tiling problems into creating specific group structures.

Students will take a 2-hour test on permutations, taxicab distance, and the 15 puzzle. At the end of the test, there will be four olympiad-style problems, the last of them extra credit.

We will meet at 3:30 PM at the lawn near the 5th floor Math Building entrance and take pictures of the class. We will get down to the classrrom, split the students into four teams, and start the competition afterwards. The winning teams will get prizes. Some special prizes will be given to the most useful team member on every team.

We will learn to multiply permutations. Finishing the first handout, we will figure out what configurations of the 3 puzzle are solvable and what are not. If time permits, we will finish the lesson solving some olympiad-style problems.