Los Angeles Math Circle

LAMC Meetings • 2019-2020 Academic Year

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

Advanced 1AAdvanced 1BAdvanced 2AAdvanced 2BBeginners 1ABeginners 1BBeginners 2ABeginners 2BBNPIntermediate 1A
Intermediate 1BIntermediate 2AIntermediate 2BOlympiads 1Olympiads 2
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.

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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.

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We solve a couple of introductory problems to Graph Theory and several harder ones. The lesson spans over two weeks.

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We continue the lesson from last week with a few Olympiad-type problems in Graph Theory.

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We discuss various techniques for solving problems involving integer inequalities, specific to Olympiad Number Theory.

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We continue the lecture from last time, with a few additional Olympiad-type Number Theory problems.

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We define convexity, convex hulls and triangulations, then solve a few Olympiad-type problems in Geometric Combinatorics.

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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.

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We state and prove Ceva's theorem, then solve a few Olympiad-type problems.

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The students took a 2-hour long practice exam for BAMO-type competitions. There were 3 problems (in Geometry, Combinatorics and Number Theory).

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Today we discussed the solutions for Practice Exam 1, and then solved three other problems.

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The students took an Olympiad-style practice exam with 3 problems (in Geometry, Algebra, and Combinatorics).

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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)

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We solve five final practice problems for the Bay Area Mathematical Olympiad.

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We introduce and study the basic properties of complex numbers, with the goal of using them to solve geometry problems.

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