|10/2/2016| [Show less]
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.
|10/9/2016| [Show less]
We will continue the study of the 10/2 handout.
|10/16/2016| [Show less]
We will discuss planar graphs, Euler characteristic, and related topics.
|10/23/2016| [Show less]
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.
|10/30/2016| [Show less]
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.
|11/6/2016| [Show less]
We will finish studying the 10/30 handout. If time permits, we will use graph theory to solve the Instant Insanity puzzle.
|11/13/2016| [Show less]
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.
|11/20/2016| [Show less]
We will discuss problem 9 of the 10/30 handout for warm-up and then get back to studying graph theory.
|12/4/2016| [Show less]
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.
|1/15/2017| [Show less]
We will resume at Problem 14 of the 10/30/2016 handout and proceed to Ramsey theory if time permits.
|1/22/2017| [Show less]
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.
|1/29/2017| [Show less]
We study a bit of Ramsey theory during the first hour of the classes.
|2/5/2017| [Show less]
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!
|2/12/2017| [Show less]
We will study the theory of quadratic equations and solve a few surprisingly hard problems on the topic.
|2/26/2017| [Show less]
We will continue stidying the 2/12 handout.
|3/5/2017| [Show less]
We will resume studying the 2/17 handout at Problem 13.
|3/12/2017| [Show less]
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.
|3/19/2017| [Show less]
We will start with refreshing problem 18 from the 2/12 handout.
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.
|4/9/2017| [Show less]
We will see how the Vieta formulas for quadratic equations enable one to solve qubic equations as well.
|4/16/2017| [Show less]
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.
|4/23/2017| [Show less]
We will continue the study of the Cardano formula, based on the handout posted on 4/9.
|4/30/2017| [Show less]
We will see how symmetries of an equilateral triangle act on roots of cubic equations.
|5/14/2017| [Show less]
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.
|5/21/2017|| [Show less] |