# Course Catalog

### Subject Areas

###### Accelerated Math

### Courses

**Advanced High School Math with AMC 10/12 Problems***This course prepares students for American Mathematics Competitions 10 and 12 and the non-proof parts of AIME. The topics taught include***the entire high school curriculum including trigonometry, advanced algebra, precalculus and advanced geometry,**but exclude calculus. Our curriculum also includes some additional challenging and brain-stimulating topics outside of the traditional school curriculum.**Recommended Grade Levels:**Although we do not limit students by grade level, this course is typically recommended for advanced 7th and 8th graders and high school students.**Course Description:**This course will familiarize students with the essential concepts and techniques in Algebra II, PreCalculus, Combinatorics, Number Theory, and Geometry. We will have a specific emphasis on problem solving where the students will constantly be challenged to think creatively.**Contest Preparation:**AMC 10/12, AIME, ARML, Mandelbrot, Purple Comet.**Course Objectives:**As of the completion of this course, students will:1. Have complete mastery of concepts covered in standard Algebra II and PreCalculus courses, as well as more advanced topics (such as Vieta’s formulas, Complex Numbers, and manipulation of Series).

2. Be able to explain and employ important theorems and techniques used in Combinatorics, Number Theory, and Geometry.

3. Be able to reduce unfamiliar problems to basic principles, and cleverly employ techniques they’ve learned to find shortcuts in solution methods.

**Teaching Philosophy:**We believe that building good problem-solving skills is as (if not more) important than knowing lots of theorems. As such, although the course will cover a considerable amount of material, the main emphasis will be on building problem-solving intuition and training students to think creatively when faced with classes of problems they’ve never seen before.**Class Participation:**Students are expected to actively participate in class. We will employ the Socrates method, which is a cooperative dialogue between the students and teacher to stimulate critical thinking. Students will also collaborate with classmates while solving challenging problems.**Curriculum:**The course curriculum is owned and copyright by CyberMath Academy. The class material is composed of unique blends of problems hand picked from prestigious competitions from around the globe, along with many historical problems and fascinating puzzles.**Information on Summer Camp Attendance Options (Academic Year Courses cover all topics)****Full-Day Program:**Students who would like to master all topics should register for full-day program**Half-Day Program:**Students who would like to master only Algebra II or PreCalculus topics alongside Number Theory can choose this option. Students can also choose to enroll only in morning classes.**Topics Covered In This Course****Algebra**– Quadratics/Discriminants & Conic Sections

– System of Equations

– Polynomial Division

– Rational Root Theorem

– Fundamental Theorem of Algebra

– Vieta’s Formulas

– Sequences and Series

– Induction

– Radicals and Rationalizing Denominators

– Algebraic Factorizations

– Complex Numbers

– Inequalities

– Functions

– Exponents and Logarithms**Combinatorics**– Basic Counting: Constructive and Complimentary

– Sets, Bijections, and Logic

– Principle of Inclusion Exclusion

– Combinations and Permutations

– Pascal’s Triangle

– Binomial Theorem

– Combinatorial Identities

– Pigeonhole Principle

– Expected Value

– Stars & Bars

– Recursion

– Fibonacci Numbers**Number Theory**– Prime Factorization

– Divisibility Rules

– Euclidean Algorithm

– Diophantine Equations

– Bezout’s Identity

– Modular Arithmetic & Exponentiation

– Fermat’s Little Theorem

– Wilson’s Theorem

– Chinese Remainder Theorem

– Multiplicative Functions

– Euler’s Theorem**Geometry**– Congruent & Similar Triangles

– Special Parts of a Triangle

– Triangle Area Formulas

– Quadrilaterals

– Angles in Polygons

– Inscribed Angles in Circles

– Power of a Point

– Three-Dimensional Geometry

– Trigonometry for Right Triangles

– Unit Circle & Radians

– Trigonometric Identities

– Extended Law of Sines & Law of Cosines

– Polar Coordinates & Geometry of Complex Numbers**Click below to see sample lecture notes****AUTHORS****Justin Stevens:**Accelerated Math Program Coordinator

University of Alberta – jstevens@cybermath.academy – (909) 713-4398**Forest Kobayashi:**Curriculum Designer, Harvey Mudd College**Alex Toller:**Curriculum Designer**Advanced Middle School Math with MathCounts/AMC 8-10 Problems***This course covers the main topics in middle school math. Students will be mastering these topics while solving challenging problems at the level of or from MathCounts, AMC-8, AMC 10 and similar competitions. Students go above and beyond Common Core standards in this brain-stimulating course. Students will also solve mathematical puzzles and cyphers and learn topics that are typically not covered at traditional school settings.***Recommended Grade Levels:**Although we do not limit students by grade level, this course is typically recommended for students in grades 4th-8th.**Course Description:**This course will familiarize students with the essential concepts and techniques in Pre-Algebra, Algebra I, Geometry, Number Theory and Combinatorics. We will have a specific emphasis on problem solving where the students will constantly be challenged to think creatively.**Contest Preparation:**MathCounts, AMC 8, AMC 10.**Course Objectives:**As of the completion of this course, students will:1. Have complete mastery of concepts covered in standard Pre-Algebra, Algebra I and Geometry courses, as well as topics not covered in traditional school curriculum.

2. Be able to explain and employ important theorems and techniques used in Combinatorics, Number Theory, and Geometry.

3. Be able to reduce unfamiliar problems to basic principles, and cleverly employ techniques they’ve learned to find shortcuts in solution methods.

**Teaching Philosophy:**We believe that building good problem-solving skills is as (if not more) important than knowing lots of theorems. As such, although the course will cover a considerable amount of material, the main emphasis will be on building problem-solving intuition and training students to think creatively when faced with classes of problems they’ve never seen before.**Class Participation:**Students are expected to actively participate in class. We will employ the Socrates method, which is a cooperative dialogue between the students and teacher to stimulate critical thinking. Students will also collaborate with classmates while solving challenging problems.**Curriculum:**The course curriculum is owned and copyright by CyberMath Academy. The class material is composed of unique blends of problems hand picked from prestigious competitions from around the globe, along with many historical problems and fascinating puzzles.**Information on Summer Camp Attendance Options (Academic Year Courses cover all topics)****Full-Day Program:**Students who would like to master all topics should register for full-day program**Half-Day Program:**Students who would like to master only Pre-Algebra and ALgebra-I topics alongside Number Theory can choose this option. Students can also choose to enroll only in morning classes.**Algebra**• Ratios and Proportions

• Algebraic Expressions

• Linear Equations

• Functions

• Inequalities

• Polynomial Expressions

• Pascal’s Triangle

• Binomial Theorem

• Quadratic Equations**Combinatorics**• Counting

• Statistics

• Probability

• Permutations

• Combinations**Number Theory**• Divisibility

• GCD and LCM

• Prime Factorization

• Radicals and Exponents

• Modular Arithmetic

• Sequences and Series

• Gauss’s Formula**Geometry**• Angles

• Triangles

• Pythagorean Theorem

• Polygons

• Circles

• Perimeter, Area and Volume

• Coordinate Geometry

• 3D Geometry###### Math Olympiad Courses

### Courses

To find out what course is best for you, please look at the information below:

There are two tracks in this course:

**Advanced AIME with Proofs:**For students who can comfortably qualify for the

AIME and solve the first half of problems on the exam. These students might be

aiming to qualify for USA(J)MO and have a pleasant start on the olympiad.

**USA(J)MO:**For students who can already comfortably qualify for USA(J)MO, and

are aiming to score highly on it.**First: Please determine your level below**(1) Starting out on AMC, trying to qualify for AIME

(2) Can solve 2 problems on AIME, hoping to solve 8

(3) Can solve 6+ problems on AIME, hoping to solve 13

(4) Can qualify for USA(J)MO, hoping to solve a problem or two

(5) Can solve one or two USA(J)MO problems and solve hard USAJMO or medium USAMO problems

(6) Aiming to solve the final P3 / P6 problems on USAMO

**Second:Learn about the tracks in our Math Olympiad Program**Our Math Olympiad Program has two tracks:

*Entry Level Math Olympiad Course with Computations (Advanced AIME with Proofs)** Prerequisites: 6+ on AIME

* Aiming for high AIME scores, and a couple problems on USA(J)MO

*Advanced Math Olympiad Course (USAJMO)** Prerequisites: consistently qualify for USA(J)MO

* Aiming to score 14+ on USAMO

**Third: Placement**– If you are in levels 1 or 2, you should sign up for our Advanced High School Math with AMC 10/12 Problems course. It covers AMC 10/12 and the non-proof problems on AIME.

– If you are in levels 3 or 4, you should sign up for our Advanced AIME with Proofs course.

– If you are in levels 5 or 6, you should sign up for our USA(J)MO course.

Have questions? E-mail our Math Olympiad Program Coordinator Evan Chen at echen@cybermath.academy

**Math Olympiad Program Curriculum**There are two tracks in this course:

**Advanced AIME with Proofs:**For students who can comfortably qualify for the

AIME and solve the first half of problems on the exam. These students might be

aiming to qualify for USA(J)MO and have a pleasant start on the olympiad.

**USA(J)MO:**For students who can already comfortably qualify for USA(J)MO, and

are aiming to score highly on it.These two tracks overlap in any given year. The curriculum runs in a three-year cycle.

**Contest preparation:**AIME, HMMT, USA(J)MO, IMO.**Curriculum:**The course operates on a three-year cycle, so students can repeat the course up to three times total, across both tracks. The summer and year-round materials

are disjoint.A detailed listing of topics covered appears below. Not all topics occur in all years. Most topics occur in multiple years, but they will have different examples and problems each time they appear over the three-year cycle.

Each iteration of the course contains several practice exams.

**1- Topics appearing only in Advanced AIME with Proofs****Algebra***Symmetric Polynomials.*Vieta’s formulas, Newton sums, fundamental theorem of elementary symmetric polynomials.*Logarithms.*Computational problems and equations involving logarithms.*Trig Equation.*Algebraic problems involving trig functions.*Intro Functional Equation.*Introduction to olympiad-style functional equations. Substitutions, injectivity and surjectivity, Cauchy’s functional equation.*Inequalities.*Introduction to olympiad-style inequalities. AM-GM and Cauchy-Schwarz.

**Combinatorics***Computations with Probability.*Random variables, expected value, linearity of expectation.*Enumeration.*Computational counting problems.- Monovariants and Invariants.
*Finite processes.*

*Computational Geometry.*AIME-style problems in Euclidean geometry.

Angle Chasing.*Trig in Geometry.**Elementary Geometry.*Angle chasing, power of a point, homothety.*Basics of Complex Numbers. Introduction to complex numbers in geometry.*

**Number theory***Computations with Modular Arithmetic.*Fermat, Wilson, Chinese Remainder theorem.*Diophantine Equations.*Introduction to olympiad-style Diophantine equations.*Chinese Remainder Theorem.*

**2- Topics appearing in both tracks****Algebra***Generating Functions.*Their uses in combinatorial sums.*Linear Recursions and Finite Differences.**Sums.*Swapping order of summation.*Polynomials.*Fundamental theorem of algebra, factorizations, roots.

**Combinatorics***Weights and Colorings.**Induction and Recursion.**Linearity of Expectation and Double-Counting.**Algorithms.*Combinatorial problems involving discrete-time processes.*Graph Theory.*Definitions and problems.*Ad-Hoc Constructions.**Problems on Rectangular Grids.*

**Geometry***Power of a Point.**Homothety**Common Congurations.**Divisibility and Euclidean Algorithm.*Bounding the remainders.*Look at the Exponent.*p-adic evaluation, lifting the exponent.*Orders. Primes of the form a2 + b2.*Primitive roots.*Functional Equations.*More difficult functional equations at the USAMO/IMO level.*Advanced Inequalities.*Jensen and Schur. Fudging, smoothing.*Analysis and Calculus.*Understanding the complete theorem statements in calculus and how they can be applied to olympiad problems. Differentiation and the relation

to multiplicity of roots. Lagrange multipliers. Compactness.*Advanced Graph Theory.*More difficult olympiad problems involving graphs.*Advanced Algorithms.**Games and Processes.**Projective Geometry.*Harmonic bundles, poles and polars.*Inversion.**Spiral Similarity.**Complex Numbers.*Applications to problems.*Barycentric Coordinates.*Applications to problems.*Constructions in Number Theory.**Integer Polynomials.*Irreducibility, minimal polynomials, a taste of Galois theory.*Quadratic Reciprocity.*Legendre symbols.

**Number theory****3- Topics appearing only in USA(J)MO****Algebra****Combinatorics****Geometry****Number theory***Coding**Courses**Learn to deal with common algorithmic problems. Beginners will learn the basics of programming and will be able to write codes that solve beginner level computer science problems. Students with programming experience will improve their skills to solve challenging projects.***Recommended Grade Levels:**4th-12th**Prerequisites:**None**Topics Covered**– Variables and Operators

– Conditionals

– Loops

– Arrays

– Strings

– Functions

– Files

– Matrices*The Perfect Introductory Programming Course for Students in Grades 4-8 !***Java Processing***This course teaches students programming in Java Processing. In this course, students will learn object-oriented programming in a fun and exciting way, that will effectively prepare them for learning any C-based programming language.***Recommended Grade levels: 4th-8th.**This course is designed for students who are comfortable with the math level (Pre-Algebra), and is NOT proficient in any programming languages. Block-based and introductory programming experience are fine, if the student is proficient in any programming languages, they should enroll in our USACO and AP Computer courses.AP Computer Science Principles: The breadth of concepts this course covers effectively prepares students for the AP Computer Science Principles exam.

*The Processing software is used by thousands of visual designers, artists, and architects to create their works. Projects created with Processing have been featured at the Museum of Modern Art in New York, the Victoria and Albert Museum in London, the Centre Georges Pompidou in Paris, and many other prominent venues. Processing is used to create projected stage designs for dance and music performances; to generate images for music videos and film; to export images for posters, magazines, and books; and to create interactive installations in galleries, in museums, and on the street. Some prominent projects include the House of Cards video for Radiohead, the MIT Media Lab’s generative logo, and the Chronograph projected software mural for the Frank Gehry-designed New World Center in Miami. But the most important thing about Processing and culture is not high-profile results – it’s how the software has engaged a new generation of visual artists to consider programming as an essential part of their creative practice.***Course Description:**This course is a collaborative and project-based introduction to object-oriented computer programming through MIT’s Java-based computer language Processing, with an emphasis on problem solving, visual arts, graphic design, and animation.**What is Java Processing?:**Processing is a visual arts based open source language developed at MIT.Please watch this video for a better understanding:

And to see examples of what professionals have done with it, please visit this page:

Processing is essentially an extremely visual front-end to Java. When you click “Run”, the program converts your code into Java code and then runs it. It was built for two purposes:

1. To be an easy to learn but powerful language for beginning developers and artists.

2. To be easy to code visual ideas. That is, it’s much faster to code the same concept in Processing than in Java or C++.

Because of its convenience, Processing is mainly used for data visualization, visual art/design, app development, and education. Its educational accessibility means the skills from coding in Processing very easily translate to any other C-based language (C, C++, C#, Java, Javascript, Python, Ruby).

**Art/design:**Art and design are half the point of the language. The class will mostly deal with 2D but we’ll also spend a couple lessons doing 3D.**Why Processing?:**Processing is a fantastic first programming language for 2 reasons:1. The syntax is easy and it’s easy to understand.

2. The incredible visual component and speed of compilation. When you click run, you almost immediately see what you just coded.

This makes programming interesting and accessible in a way no other language does. It’s very satisfying to make things appear and interact with you with only basic understanding of the language.

**Prerequisites:**Students should be reasonably skilled in mathematical reasoning at a 5th/6th grade level; the class has a high problem solving component. Two important topics students should know:– Coordinate grid: Student must be able to understand plotting on a Cartesian plane (x and y coordinates). Knowing how to graph things is unnecessary.

– Basic pre-algebra: Student must be able to solve basic algebraic equations like 250 = x + w/2 where w = 50 (answer: x = 225).

Also:

– Decent typing skills: or the student will fall behind. Student doesn’t have to be a professional typewriter, just the ability to touch type. Students shouldn’t have to think too hard about the keyboard when they should be thinking about what’s on the screen.**Topics**– Fundamentals of Computer Programming

– The Basics of Data Types

– Control Flow

– Iteration and Functional Programming

– Recursion

– Classes

– Objects and Methods,**Connections to Other Subject Areas**– Cartesian Geometry,

– Number Bases (binary and hexadecimal),

– Pseudorandomness,

– Kinematics,

– Fractals, and

– Mathematical Problem Solving With ComputersPrior understanding of computer programming not required.

**Class projects:**This course features projects that are independent and collaborative design and development of games and interactive animations. There will be 10 projects, on, in order:– Drawing things with basic shapes,

– Interactive 2D/3D animations (moving an object, basic text editor, solar system model)

– Designing modifiable single player games, and

– Mathematical art.**Capabilities:**Students will gain the skills to design, code, and debug basic animations and games in the language Processing, while also gaining programming skills to be well-prepared for further computer science study and independent programming projects and problem solving.*AP Computers and USACO**Courses**The Perfect Introductory Programming Course for Students in Grades 4-8 !***AP Computer Science Principles and Java Processing***This course teaches students programming in Java Processing. In this course, students will learn object-oriented programming in a fun and exciting way, that will effectively prepare them for learning any C-based programming language.**AP Computer Science Principles: The breadth of concepts this course covers effectively prepares students for the AP Computer Science Principles exam.***Recommended Grade levels: 4th-8th.**This course is designed for students who are comfortable with the math level (Pre-Algebra), and is NOT proficient in any programming languages. Block-based and introductory programming experience are fine, if the student is proficient in any programming languages, they should enroll in our USACO and AP Computer courses.*The Processing software is used by thousands of visual designers, artists, and architects to create their works. Projects created with Processing have been featured at the Museum of Modern Art in New York, the Victoria and Albert Museum in London, the Centre Georges Pompidou in Paris, and many other prominent venues. Processing is used to create projected stage designs for dance and music performances; to generate images for music videos and film; to export images for posters, magazines, and books; and to create interactive installations in galleries, in museums, and on the street. Some prominent projects include the House of Cards video for Radiohead, the MIT Media Lab’s generative logo, and the Chronograph projected software mural for the Frank Gehry-designed New World Center in Miami. But the most important thing about Processing and culture is not high-profile results – it’s how the software has engaged a new generation of visual artists to consider programming as an essential part of their creative practice.***Course Description:**This course is a collaborative and project-based introduction to object-oriented computer programming through MIT’s Java-based computer language Processing, with an emphasis on problem solving, visual arts, graphic design, and animation.**What is Java Processing?:**Processing is a visual arts based open source language developed at MIT.*Please watch this video for a better understanding:**And to see examples of what professionals have done with it, please visit this page:**Processing is essentially an extremely visual front-end to Java. When you click “Run”, the program converts your code into Java code and then runs it. It was built for two purposes:**1. To be an easy to learn but powerful language for beginning developers and artists.**2. To be easy to code visual ideas. That is, it’s much faster to code the same concept in Processing than in Java or C++.**Because of its convenience, Processing is mainly used for data visualization, visual art/design, app development, and education. Its educational accessibility means the skills from coding in Processing very easily translate to any other C-based language (C, C++, C#, Java, Javascript, Python, Ruby).***Art/design:**Art and design are half the point of the language. The class will mostly deal with 2D but we’ll also spend a couple lessons doing 3D.**Why Processing?:**Processing is a fantastic first programming language for 2 reasons:*1. The syntax is easy and it’s easy to understand.**2. The incredible visual component and speed of compilation. When you click run, you almost immediately see what you just coded.**This makes programming interesting and accessible in a way no other language does. It’s very satisfying to make things appear and interact with you with only basic understanding of the language.***Prerequisites:**Students should be reasonably skilled in mathematical reasoning at a 5th/6th grade level; the class has a high problem solving component. Two important topics students should know:*– Coordinate grid: Student must be able to understand plotting on a Cartesian plane (x and y coordinates). Knowing how to graph things is unnecessary.**– Basic pre-algebra: Student must be able to solve basic algebraic equations like 250 = x + w/2 where w = 50 (answer: x = 225).**Also:*

– Decent typing skills: or the student will fall behind. Student doesn’t have to be a professional typewriter, just the ability to touch type. Students shouldn’t have to think too hard about the keyboard when they should be thinking about what’s on the screen.**Topics***– Fundamentals of Computer Programming*

– The Basics of Data Types

– Control Flow

– Iteration and Functional Programming

– Recursion

– Classes

– Objects and Methods,**Connections to Other Subject Areas***– Cartesian Geometry,*

– Number Bases (binary and hexadecimal),

– Pseudorandomness,

– Kinematics,

– Fractals, and

– Mathematical Problem Solving With Computers*Prior understanding of computer programming not required.***Class projects:**This course features projects that are independent and collaborative design and development of games and interactive animations. There will be 10 projects, on, in order:*– Drawing things with basic shapes,*

– Interactive 2D/3D animations (moving an object, basic text editor, solar system model)

– Designing modifiable single player games, and

– Mathematical art.**Capabilities:**Students will gain the skills to design, code, and debug basic animations and games in the language Processing, while also gaining programming skills to be well-prepared for further computer science study and independent programming projects and problem solving.**C++ Programming and USACO Bronze***In this course, while learning coding in C++, students will be trained to master the fundamental skills to correctly understand the questions on USACO Bronze competitions and design and implement algorithms to solve them. These skills will be practiced extensively to help students meet the time limits set for each problem.***USACO is the most prestigious pre-college Computer Science competition in the states. For more information, please see our AP Computers and USACO page.***While your program must solve the problem presented on a USACO competition, it must also do it fast. Your program must be submitted within the specified time period and should not produce any compilation or run-time errors. There will be a number of test cases that your program will be judged on.***Prerequisites/Requirements:**Students must be good in math and they need a laptop.**Topics Covered***– Introduction to C++*

– Variables and Operators

– Conditionals

– Loops

– Arrays

– Strings

– Functions

– Files

– Matrices**USACO Silver and AP Computer Science A***This course prepares students for the USACO Silver Contest and AP Computer Science A Exam through comprehensive lectures and practice problems from national and international competitions, taught and guided by an expert instructor. In this course, students hone their problem solving skills while they advance their algorithm designs and implementation. It’s a fun and friendly challenging environment which mathematically advanced students experience the thrill of solving real-life like problems through computer programming.***Prerequisites***At least one of the following requirements needs to be satisfied. The student:**– Has taken a computer programming course before (contact us for details, please)*

– Has taken the USACO Bronze class, or

– Has scored 400+ in a USACO Bronze contest.**Topics Covered***Sorting*

Searching (Sequential Search, Binary Search)

Brute Force

Silver Level Techniques (FloodFill, RMQ, Prefix Sums)

String Algorithms (Silver Level)

Data Structure (Stack, Queue, Vector, Set, Map, PriorityQueue- Silver Level)

Recursion

Depth first Search

Breadth first Search

Bitset & Binary Operations

Object-Oriented Program Design**USACO Gold***This course prepares students for USACO Gold contests.***Prerequisites***At least one of the following requirements needs to be satisfied. The student:**Successfully completed a USACO Silver course before**Scored more than 600 in a USACO Silver contest,**is already a USACO Gold contestant*

**Topics Covered***Bitset & Binary operations**Data Structure*- Stack
- Queue
- Vector
- Set
- Ma
- PriorityQueue- Gold Level Applications

*Graph Theory*- DFS
- BFS
- Topological Sort
- Minimum Spanning Tree(Prim)
- Shortest Path-(Dijkstra, Bellman-Ford,)
- All Shortest Paths(Floyd-Warshall)

*Dynamic Programming*- Introduction
- Basic Problems(Longest Increasing Subsequence, Maximum Subarray Sum, Longest Common Subsequence)
- Knapsack
- Coin Change
- Subset Sum
- String Edit Distance
- USACO Dynamic Programming Questions

*Introductory Geometric Algorithms**Greedy Problems*

**USACO Platinum***This course prepares students for USACO Platinum contests.***Prerequisites***At least one of the following requirements needs to be satisfied. The student:**Successfully completed a USACO Gold course before**Scored more than 600 in a USACO Gold contest,**is already a USACO Platinum contestant*

**Topics Covered***Advanced DP problems*- Inclusion Exclusion
- Convex Hull Trick
- Divide and Conqueror

*Advanced Binary Search Problems**Advanced String Algorithms*- KMP
- Manacher
- Rabin-Karp
- Suffix Trie
- Suffix Array
- Aho Corasick

*Advanced Data Structures*- Heavy-Light Decomposition
- RMQ
- Segment Trees
- Treap
- Persistent Segment Tree

*Advanced Graph Algorithms*- 2-SAT
- Kosaraju
- Bipartite Maximum Matching
- Blossom
- Tarjan’s SCC
- DSU
- LCA
- Tarjan’s offline LCA
- Fleury

*Greedy Approaches and Math Tricks**Square Root Decomposition Trick**Centroid Decomposition Trick*

*Robotics and Electronics**Courses**Students will learn LEGO Mindstorms and prepare for the FIRST LEGO League competitions.***Recommended Grade Levels:**4th-8th**Topics Covered***Moving Straight*- Motors
- Sequences of Commands,
- Block Settings
- Downloading and Running Programs
- Move Steering Block

*Turning Turning*- Types of Turns
- Move Steering vs. Move Tank Block

*Move Until Touch*- Sensors
- Wait For Block
- Touch Sensor
- Move Until Behaviors

*Move Until Near*- Ultrasonic Sensor
- Thresholds

*Turn for Angle*- Gyro Sensor
- Compensating for Sensor Error

*Move until Color*- Color Sensor

*Loops*- Loops
- Patterns of Behavior

*Switches*- Switches,
- Conditional Reasoning

*Switch-Loops*- Obstacle Detection Behavior,
- Repeated Decisions Pattern

*Line Follower*- Line Following (a Repeated Decisions Pattern Behavior)

*Final Challenge*- Cumulative Application of Skills and Knowledge

*In this course, students will learn basics of electronics while building amazing gadgets.***Topics Taught****Introduction: Basics of Electronics**- Inputs and Outputs: Control images, sound, and motion
- Loops: Make animated images
- Logic: Add choices to a game
- Variables: Create and use image, number, and coordinates variables
- Functions: Make custom blocks to level-up a game

**Ultimate Shootout****Hot Potato…of Doom!**- Students will use loops, conditional logic and variables to create a new spin on the game of Hot Potato.

**Rockstar Guitar**- Students will design a musical instrument that makes it easy for anyone, even for those who cannot read music, to play simple songs.

**Tug of War**- Students will create and remix the Tug of War game to explore how functions are used to structure code.

**Change the World Arcade**- Students design and prototype a game that will help make life easier for people in their community. At the end, each group will present their prototypes at a “Change the World Arcade” that will be open to students and parents.

**Self-Driving Car**- Students will create and test a circuit containing a power source, inputs, outputs and wires, construct a prototype of a self-driving vehicle.
- Systematically categorize the energy of the car for different settings of the slide dimmer by adding a Number Bit in VALUE or VOLTS mode to the circuit.
- Test their prototypes and make improvement, self-assess their work based on the outlined success criteria and constraints.
- Conclude the activity with a class “car show” to allow students to explain and show off the best features of their designs.

**Build a Microwave**- Students will build a microwave from scratch.

**Security Device**- Students will use an understanding of the basics of circuitry and environmental sensors to construct a backpack alarm that protects students’ belongings.
- Students will then modify their alarms to make them function for different users and environments.
- Conclude the activity by having students create 30-second commercials to pitch their product.

**Earthquake Machine**- Students will create a machine to simulate earthquakes, gather and record data from an experiment and analyze the effects of simulated earthquakes on objects.

**Satellite Dish**- Students will learn the science behind satellites and make your own parabolic reflector.

**Mars Rover**- Students will build a replica of NASA’s Mars Rover and test its movements.

*Physics and Biology**Courses***AP Physics A and USAPhO F=m*a***Our Physics Olympiad Course aims to prepare students with little to only basic high school knowledge of Physics to take the USAPhO F=m*a exam and the AP Physics A Test.***Topics Covered***Motion Along a Straight Line**Motion in two or three dimensions**Equilibrium**Newton’s Laws of motion**Work and Energy**Momentum and Collisions**Rigid Body Dynamics**Gravitation**Periodic Motion**Waves**Electrostatics**Electrical Circuits*

**Recommended Grade Levels:**Upper Middle and High School Students**Prerequisites:**Knowledge of Mathematics at the algebra 2 level (with some omissions) is required.**AP Biology and USA Biology Olympiads***Our Biology Olympiad Course aims to prepare students with little to only basic high school knowledge of Biology to take the USABO Open exam and the AP Biology Test. Each Unit is broken down into 4 subjects each of which should take about half to one hour to cover.***Topics Covered***Chemistry of Life*- Basic Principles of Chemistry
- Water
- Carbon
- Macromolecules

*Cells and Communication*- Organelles
- Cell Communication
- Cellular Respiration
- Photosynthesis

*Genetics*- Mitosis and Meiosis
- Mendelian Genetics
- Chromosomal Inheritance
- Population Genetics

*Molecular Biology*- Gene to Protein
- Regulation of Gene Expression
- Genomics
- Biotechnology and Methods

*Plants*- Plant Systematics
- Plant Growth and Nutrition
- Plant Reproduction and Life Cycles
- Plant Hormones

*Anatomy and Physiology*- Digestive System
- Circulatory and Respiratory System
- Excretory System
- Immune System
- Endocrine System

*Animal Development*- Reproductive System
- Animal Development
- Comparative Anatomy
- Animal Systematics

*Neurobiology and Ethology*- Cellular Neurobiology
- Whole System Neurobiology
- Skeletal Muscular System
- Ethology (Animal Behavior)

*Ecology*- Population Ecology
- Community Ecology
- Ecosystem Ecology
- Quantitative Ecology

**Recommended Grade Levels:**Upper Middle and High School Students**Prerequisities:**No prerequisites