Mathematics

Counting and Probability

Chapter 1: Review of Counting and Probability Basics
arrow
Review of basic counting and probability, expected value, Pascal’s Triangle and Binomial Theorem, and the summation notation
Chapter 2: Sets and Logic
arrow
Sets, logics, quantifiers
Chapter 3: A Piece of PIE
arrow
Principle of Inclusion and Exclusion
Chapter 4: Constructive Counting and 1-1 correspondances
arrow
Constructive counting, count by finding1-1 correspondances
Chapter 5: Pigeonhole Principle
arrow
Pigeonhole Principle
Chapter 6: Constructive Expectation
arrow
Linearity of Expectation
Chapter 7: Distributions
arrow
Count the number of ways to place indistinguishable items into distinguishable boxes
Chapter 8: Mathematical Induction
arrow
Induction
Chapter 9: Fibonacci Number
arrow
Introduction and application for Fibonacci Numbers
Chapter 10: Recursion
arrow
Recursion, Catalan Numbers
Chapter 11: Conditional Probability
arrow
Conditional Probability, and their applications
Chapter 12: Combinatorial Identities
arrow
Strategies of proving Combinatorial Identities
Chapter 13: Events with states
arrow
State diagrams, random walks, events with infinite states
Chapter 14: Generating Functions
arrow
Definition, and applications in deriving the binomial theorem, as well as formulas for distribution, partitions, and Fibonacci numbers
Chapter 15: Graph Theory
arrow
Definitions, Basic Properties, Cycles and Paths, Planar Graphs, Eulerian and Hamiltonian paths
Chapter 16: Challenge Problems
arrow
Hard problems in counting that use combinations of topics above

Learn from the best

Passion for tech. Unmatched expertise. Personality that brings out the absolute best in your child. We know there's no replacement for the best teacher. It's no surprise that iconic companies like Google, Amazon, Microsoft, and Disney hire the same talent we do. Our Geek Certified instructors possess the whole package of skills that inspires students for the Tech World!

university icon
Recruited from top universities and leading IT companies
verified icon
Rigorous background and reference checks
certified icon
Geekedu Certified professional level
experienced icon
Verified teaching experience

What our parents say

This course is for students who have completed our Introduction to Counting and Probability course.

Graph Icon - Education X Webflow Template
Level: 
AGES 14  - 18
Star Icon - Education X Webflow Template
Lifetime Access
Phone Icon - Education X Webflow Template
Online 1-on-1 Private Sessions

This course typically takes 3-6 months to complete. This depends on the student's experience and how fast they can master the concepts and the knowledge. Our instructors move at the pace of the student, it may take extra time for some students to reinforce what they have learned.

Sign up and get a 60-minute free assessment class

Book A FREE Trial
Other courses

You Might Also Be Interested In Our Elective Courses

Python Level 1
AGES 10 - 15

Designed for beginners, this level is designed to teach the basic fundamentals and design principles of Python, with the help of Turtle graphics and PyGame. This includes: variables, conditional statements, loop basics, and functions.

These concepts are transferable to any other programming language. Throughout the way, students will create projects in order to apply the concepts they have learned, and to solidify their knowledge.

Python Level 2
AGES 10 - 15

Level 2 dives deeper into the basics of Python for a more thorough understanding and introduces advanced topics. Students will build on knowledge from Level 1 and work with data structures, advanced loops, algorithms, and object-oriented programming, and create games based on what they learn.

Students will complete the course with a solid understanding of Python fundamentals.

Java Level 1
AGES 10 - 15

This beginner-friendly course serves as an introduction to the Java programming language. Students will learn the fundamentals of Java along with core computer science concepts.