Notes related to classes

Here we summarize the activities of classes. The summaries will be sporadically updated. So you are encouraged to check this page every now and then!

In this file, you can find notes related to problems and topics discussed in math league. Please share your comments, suggestions, and corrections with us. If you have a solution to a problem mentioned in these notes, please share it with us. We might include it in the notes and mention your name. So far we have the following topics in the notes or in class.

Problems that are discussed in the information night.
Solutions of the problems mentioned in the info night and related theorems: Heron's formula, importance of transformations in problems in geometry, etc.
Placement test.
Solutions of problems in placement test and related theorems and techniques: Vieta's formulas, sieve of Eratosthenes, triangulation of a polygon, the inclusion-exclusion principle, Euler phi-function, basics of dilations, etc.
Problems on algebraic manipulations.
Problems on multiplicative functions.
Problems on counting and probability.
Using the concept of weighted mass points to solve certain problems in geometry.
Practice Mathcount.
Practice AMC 10.

We have different activities in our Power and Factorial classes. Here are some of the topics that are discussed in the Power class.

Pythagorean theorem.
Pythagorean triples and ways to find all such triples.
Congruence arithmetic and how to use it to find the remainder of large powers of a number divided by another.
Pigeonhole principle and how it can be used in conjunction with congruence arithmetic.
Counting: permutations, choose function, number of ways one can go from the bottom left corner of a grid to the top right corner by just going to the right or up, etc.
Shoelace theorem.
Power of a point.
Ptolemy's theorem.
Telescopic sums, geometric sums, etc.

Here are some of the topics that are discussed in the Factorial class.

Algebraic manipulations and using them to do arithmetic. Worksheet.
Counting numbers in a given sequence.

Here are extra resources from MathCount.