Los Angeles Math Circle
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LAMC Calendar // 2016-2017 Academic Year. Jump to:

For meetings prior to Fall 2016, visit the Circle Archive.

AdvancedEarly ElementaryHigh School IHigh School IIIntermediateJunior Circle
We will start with a few beautiful warm-up problems and proceed to learn some bare minimum of graph theory needed to fully understand the winning MathMovesU presentation Dan Tsan made last year.
Handouts: handout
We will continue the study of the 10/2 handout.
Handouts: handout
We will discuss planar graphs, Euler characteristic, and related topics.
Dan Tsan will give us a lecture based on his award-winning MathMovesU presentation for the first hour. Then we will study planar graphs, Kuratowski Theorem and Euler characteristic of a graph.
The majority of the class have stopped working in the vicinity of Problem 9 from the 10/9 handout. We will resume from there, study the Euler characteristic of planar graphs and prove that the graphs K_3,3 and K_5 are not planar. The faster students who are finished or nearly finished with the handout will be given a bunch of Math-Olympiad-style problems to solve.
Handouts: handout
We will finish studying the 10/30 handout. If time permits, we will use graph theory to solve the Instant Insanity puzzle.
We will attempt to finish the 10/30 handout. If/when finished, we will study the final handout of the Intro to Graphs mini-course, Introduction to Ramsey Theory.
Handouts: handout
We will discuss problem 9 of the 10/30 handout for warm-up and then get back to studying graph theory.
We will resume studying the 10/30 handout at problem 12. Once finished, we will begin studying the next, and final, handout of the mini-course.
We will resume at Problem 14 of the 10/30/2016 handout and proceed to Ramsey theory if time permits.
We will finish the proof of Theoprem 1 from the 10/30 handout. Then we will begin and, hopefully, finish the last handout of the Intro to Graphs course, the one on Ramsey Theory.
We study a bit of Ramsey theory during the first hour of the classes.
The students will be given a two-hour test that covers the Intro to Graphs course we just have finished. Preparing for the test is a good way to review the course. The tests' results will give the students and the instructors the much-needed feedback. The top five performers will get great math books as prizes!
Handouts: test
We will study the theory of quadratic equations and solve a few surprisingly hard problems on the topic.
Handouts: handout
We will continue stidying the 2/12 handout.
We will resume studying the 2/17 handout at Problem 13.
Last time, many of our students felt uncomfortable with the weighted sums in the formula defining a convex function. To alleviate the feeling, we will take a second look at the topic we studied in April 2013, Barycentric Coordinates. Then we will get back to Problem 17 of the 2/17 handout.
Handouts: handout
We will start with refreshing problem 18 from the 2/12 handout. http://www.math.ucla.edu/~radko/circles/lib/data/Handout-1272-1283.pdf We will then use the derived formula as a tool to solve Problems 19 and 20. Then we will finish the handout and proceed to the next one.
We will see how the Vieta formulas for quadratic equations enable one to solve qubic equations as well.
Handouts: handout
We will review the derivation of the Cardano formula, then learn long division of polynomials, and then solve some cubic equations.The students finished with the current handout will be given a set of very hard geometry problems.
We will continue the study of the Cardano formula, based on the handout posted on 4/9.
We will see how symmetries of an equilateral triangle act on roots of cubic equations. 
Handouts: handout
We will be revisiting the algebra curriculum of a function and introduce the idea of a function between general sets. In addition, we will define the notions of one-to-one and onto for a function. Then, we will look at a particular type of functions between n ordered objects known as permutations. We will then look at some enumeration results on permutations including the hat matching Combinatorics problem.

Handouts: handout
Handouts: handout