LAMC Meetings • 2019-2020 Academic Year

For meetings prior to Fall 2019, visit the Circle Archive.

10/6/2019	Olympiads 1: Problems about Digits and Base Representations More ... We will discuss a few properties concerning representations of nonnegative integers and rationals in a general base (such as divisibility criteria), and particularly in base 10. Then we will apply this knowledge to several Olympiad-type Number Theory problems. Handouts: Handout \| Solutions [Show less]
10/13/2019	Olympiads 1: Length and Areas in Olympiad Geometry More ... We will solve a variety of geometry problems involving the computation of a length or an area, or using notions about areas to prove an identity. The problems range in difficulty from introductory to fairly challenging. Handouts: Handout [Show less]
10/20/2019	Olympiads 1: Graphs and Trees More ... We solve a couple of introductory problems to Graph Theory and several harder ones. The lesson spans over two weeks. Handouts: Handout [Show less]
10/27/2019	Olympiads 1: Graphs and Trees, Part 2 More ... We continue the lesson from last week with a few Olympiad-type problems in Graph Theory. Handouts: Handout [Show less]
11/3/2019	Olympiads 1: Inequalities with Integers More ... We discuss various techniques for solving problems involving integer inequalities, specific to Olympiad Number Theory. Handouts: Handout [Show less]
11/10/2019	Olympiads 1: Inequalities with Integers, Part 2 More ... We continue the lecture from last time, with a few additional Olympiad-type Number Theory problems. Handouts: Handout [Show less]
11/17/2019	Olympiads 1: Geometric Combinatorics and Convexity More ... We define convexity, convex hulls and triangulations, then solve a few Olympiad-type problems in Geometric Combinatorics. Handouts: Handout [Show less]
11/23/2019	Olympiads 1: Trigonometry in Olympiad Geometry More ... We define and discuss basic concepts from trigonometry, including the law of sines and the law of cosines. We then apply these notions to solving several Olympiad-type geometry problems. Handouts: Handout [Show less]
1/12/2020	Olympiads 1: Problem Session 1 More ... We state and prove Ceva's theorem, then solve a few Olympiad-type problems. Handouts: Handout [Show less]
1/19/2020	Olympiads 1: Practice Test 1 More ... The students took a 2-hour long practice exam for BAMO-type competitions. There were 3 problems (in Geometry, Combinatorics and Number Theory). Handouts: Handout [Show less]
1/26/2020	Olympiads 1: Problem Session 2 More ... Today we discussed the solutions for Practice Exam 1, and then solved three other problems. Handouts: Handout [Show less]
2/2/2020	Olympiads 1: Practice Test 2 More ... The students took an Olympiad-style practice exam with 3 problems (in Geometry, Algebra, and Combinatorics). Handouts: Handout [Show less]
2/9/2020	Olympiads 1: Problem Session 3 More ... Today we went through the solutions for the practice exam, and we solved a few extra problems in class. Next time there will be no class (President's Day) Handouts: Handout [Show less]
2/23/2020	Olympiads 1: Practice Test 3 More ... We solve five final practice problems for the Bay Area Mathematical Olympiad. Handouts: Handout [Show less]
3/1/2020	Olympiads 1: Complex Numbers More ... We introduce and study the basic properties of complex numbers, with the goal of using them to solve geometry problems. Handouts: Handout [Show less]