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Summer Lectures 2022

Although the BCA Math Team is typically geared towards high school students, it has recently begun offering lecture series during the summer to help prepare rising high school freshmen and middle schoolers. This summer, four lecture series will be offered in Algebra, Combinatorics, Geometry, and Number Theory throughout August.

Each lecture series will meet four times from 4:00pm to 5:30pm EDT via Zoom. Homework assignments and class materials will be managed on each series' respective Google Classroom.

If you have any questions or would like to join a lecture series, please contact joyren24@bergen.org and/or nikmud23@bergen.org.

#### Algebra - David Wang

In this course, we we will discuss ways of approaching and solving various flavors of algebra problems which may show up on high school math competitions. Some topics that will be covered include polynomials and Vieta's formulas, trigonometric identities and their applications, and techniques to recognize and solve problems faster.

**Dates:** August 3, 10, 17, and 24

#### Combinatorics - Joy Ren

This course will cover various combinatorics topics ranging from the basics of counting to combinations and probability. We will go over interesting techniques such as PIE, challenging problems dealing with symmetry and distinguishability, and techniques to simplify complicated problems or exploit patterns in problems.

**Dates:** August 2, 9, 16, and 23

#### Geometry - Nikhil Mudumbi

In this course, we will discuss various topics in introductory geometry and their applications. Topics will include angle cahsing, congruent and similar triangles, the Pythagorean Theorem, special right triangles, circles, and Power of a Point. While we will derive and explain these concepts from fundamental principles, we will gradually work up to problems at about the AMC 10 level.

**Dates:** August 4, 11, 18, and 25

#### Number Theory - Justin Zhang

In this course, we will walk through many fundamental topics in Number Theory and how to apply them to contest problems. Topics covered will include bases, divisor problems/Euclidean Algorithm, modular arithmetic, and solving linear congruences/Chinese Remained Theorem. We will start from the fundamental theory and progress to applying the concepts to AMC 10 level problems.

**Dates:** August 5, 12, 19, and 26