INTRODUCTION TO GEOMETRY

This is an introductory level course for students who have not taken a geometry class in school and want to learn the geometry concepts necessary for competitions such as AMC8 and MathCounts. Content includes the fundamental concepts and theorems covering points, lines, angles, area, etc. Student will study various geometric shapes such as triangles, quadrilaterals, and circles and learn their basic properties. This course will prepare students for more advanced classes such as Math Challenge I-A and I-B.

MATH CHALLENGE I-A

This is an introductory level course for 6-8 grade students who have no experience in in-depth problem solving nor math competitions. Students learn skills to apply the concepts they learn in school math classes into problem solving. Content includes pre-algebra, beginning algebra, fundamental geometry, basic number theory concepts and counting and probability. Students develop skills in creative thinking, logical reasoning, analytical and problem solving skills. Students are exposed to beginning contests such as AMC 8, MathCounts and Math Olympiads for Elementary and Middle School MOEMS.

MATH CHALLENGE I-B

Students learn math skills at a deeper level with topics in Beginning Algebra, Fundamental Geometry, Basic Number Theory concepts and Counting strategies, as well as Logic and Probabilities. The students not only learn practical skills of challenging problem solving that are supplemental to their school curricula, but also develop skills in creative thinking, logical reasoning, oral and written presentation, and team work. This course helps 6th to 8th graders to participate in the American Mathematics Competition (AMC) 8, MathCounts and Math Olympiads for Elementary and Middle School MOEMS. Through the effective guidance and direction by our experienced teachers, students develop strong problem solving skills that make them perform well in those Contests.

MATH CHALLENGE II-A

This course is for students who are preparing for the AMC 10 contest. Students are required to have fundamental knowledge in Algebra I, Geometry, Basic Number Theory and Counting and Probability up to the 10th grade level. Topics include polynomials, inequalities, special algebraic techniques, triangles and polygons, collinearity and concurrency, vectors and coordinates, numbers and divisibility, modular arithmetic,  advanced counting strategies, binomial coefficients, sequence and series, and various other topics and problem solving techniques involved in math contests such as the AMC 10, advanced MathCounts, ARML, and ZIML.

MATH CHALLENGE II-B

In Math Challenge II-B, students learn and practice in areas such as algebra and geometry at the high school level, as well as advanced number theory and combinatorics. Topics include polynomials, inequalities, special algebraic techniques, trigonometry, triangles and polygons, collinearity and concurrency, vectors and coordinates, numbers and divisibility, modular arithmetic, residue classes, advanced counting strategies, binomial coefficients, pigeonhole principle, sequence and series, and various other topics and problem solving techniques involved in math contests such as the American Mathematics Competition (AMC) 10, 12 and ARML, and also the beginning AIME.

MATH CHALLENGE III

This course is for students who are qualified to participate in the AIME contest, or at the equivalent level of experiences. The topics includes everything covered in MC-II with more depth, and the focus is more on various problem solving strategies, including pairing, change of variables, some advanced techniques in number theory and combinatorics, advanced probability theory and techniques, solid geometry, geometrical transformations, etc. Through the effective guidance and direction by our experienced teachers, students develop strong problem solving skills that make them perform well in contests such as AIME and ARML.

MATH CHALLENGE IV

This course is for experienced students who can solve at least a few problems in the AIME contest and qualify or almost qualify for USAMO. In this course, the students learn more in-depth math concepts and problem-solving strategies that involve more rigorous mathematical writing and a broad range of topics. Students are trained to comfortably solve the AIME problems to qualify for USA(J)MO, also to comfortably write mathematical proofs for problems at the USA(J)MO level, aiming to win USA(J)MO and get into the prestigious MOSP. The topics include everything covered in MC-III with more depth, and additional topics such as quadratic residue, diophantine equations, recurrence, proving inequalities, mathematical induction, functional equations, generating functions, inversion, projective geometry, and rigorous proof-writing practices. Through the effective guidance and direction by our experienced teachers, students develop strong problem solving skills that make them perform well in AIME and USA(J)MO.

This is a multi-year class.  Students may continue to enroll in MC-IV for up to 3 years and all the major math olympiad sub-topics shall be covered.  Since the size of this class is small, the topics are customized according to the knowledge level of the enrolled students.

INTRO TO PHYSICS

This is an introductory Physics course that explains the concepts in Physics, including Mechanics, Electricity and Magnetism, Thermodynamics, Modern Physics, etc. It builds the foundation for students to advance to the problem solving for the Physics Olympiad, Physics Bowl, SAT II and AP Physics. There are four 10-week sessions planned for one school year. Recommended to enroll in this course prior or concurrent with the Physics Challenge II and III courses.

PHYSICS CHALLENGE II: AP PHYSICS & PHYSICS OLYMPIAD

This year-long AP course provides a solid and thorough review for students to prepare for both the Advanced Placement (AP) Physics C exams in Mechanics and Electricity & Magnetism and both of the F=ma and Semi-Final exams for the USA Physics Olympiad (USAPhO). The syllabus covers the Mechanics portion of AP Physics in two terms for the Summer and Fall and Electricity & Magnetism in one term for Winter.

The Mechanics section will include a discussion of kinematics; Newton’s laws of motion; work, energy and power; systems of particles  and linear momentum; circular motion and rotation and oscillations and gravitation. The section on Electricity & Magnetism includes a discussion of electrostatics, conductors, capacitors and dielectrics; electric circuits, magnetic fields and electromagnetism.

All of the course content will focus on areas that will be tested in the AP Physics exams. There will be a partial lab component along with a full discussion of the scientific method and the real-world nature of analyzing experimental data. The course consists of class lectures with engaging student-to-teacher participation, an online homework system, as well as physics and general test preparation in order to ace the AP Physics and Physics Olympiad exams with material that can be useful for the SAT II: Physics test, the Physics Bowl and other science bowls.

COMPUTER SCIENCE FUNDAMENTALS

Students will learn a brief history of Computer Science, and the evolution of software development environment and programming languages. Students will be exposed to the lower level languages to understand how a machine worked under limited hardware resources. Students will be exposed to the latest professional software development technologies as well.

PROGRAMMING CONCEPTS

Students learn the concepts of programming, data structure, various programming methodologies, structures of computer programs.  The Java programming language is introduced, along with some other popular languages.  Software development life cycle Modern software engineering concepts and are introduced.  Topics covered: data types, variables, statements, input/output, operators, control flows (conditional statements, loops, switches), files, object oriented programming.

RESEARCH WORKSHOP FOR PROJECT BASED RESEARCH & SCIENCE FAIR

Students learn Scientific Research Method, and use it as a guideline to conduct a systematic research on an interested field and narrow down to a specific project under the guidance of the adviser. Students will then develop the problems to solve, survey the latest research status in the field, design his/her own experiments, determine the procedure and materials to use, carry out the experiments, collect relevant data and analyze the data to identify the pattern in order to reach the result. During the scheduled live sessions, the instructor will facilitate the methods and teach the theoretical knowledge needed to conduct research in depth, and facilitate the brainstorming for solving problems at the particular stage. Two or more hours a week self study and research efforts are expected outside of the live sessions. Students are expected to produce a presentable project submitted to science and engineering fairs or other science competitions.

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