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A Comprehensive Guide to Combinatorics
Rating: 4.6 out of 5(88 ratings)
3,564 students

A Comprehensive Guide to Combinatorics

Easily master combinatorics through nine succinct videos
Created byDeyan Kassev
Last updated 8/2019
English
English [Auto],

What you'll learn

  • Master the fundamental counting principle
  • Derive the formulas for permutations and combinations and learn the differences between these two types of arrangements
  • Discuss special types of arrangements (Combinations with repetitions, Distinguishable and circular permutations)
  • Discover Pascal's Triangle and its numerous applications
  • Learn the laws of probability
  • Fully understand binomial experiments
  • Learn how to calculate expected value
  • Apply your new knowledge by solving interesting problems

Course content

1 section • 9 lectures • 1h 35m total length

  • Introduction3:29

    Explore combinatorics as the study of arranging elements under rules, using examples like magic squares and letter arrangements, and applying it to coding, cryptography, and DNA sequencing.

  • The Fundamental Counting Principle and Factorials7:46

    Explore the fundamental counting principle and factorials by multiplying options across independent and dependent events, illustrated with outfits, car orders, surveys, and license plates.

  • Permutations and Combinations15:45

    Discover how permutations and combinations differ, derive their factorial-based formulas from the fundamental counting principle, and apply them to ordered and unordered selections.

  • Distinguishable Permutations and Problem Solving15:45

    Learn to count distinguishable permutations by accounting for identical elements, and apply combinatorial methods to problems involving circular arrangements, grid paths, polygon diagonals, factorization, and complementary events.

  • Probabilities13:07

    Explore probability and counting as you enumerate outcomes, distinguish theoretical and experimental probability, and apply formulas for independent and dependent events, complementary events, and mutually exclusive events.

  • Pascal's Triangle8:39

    Explore Pascal's triangle and uncover its patterns, symmetry, and applications in combinatorics, including binomial coefficients, the choose function, and binomial expansions.

  • Binomial Experiments10:14

    Explore binomial experiments through coin flip and dice problems, defining success as heads or a given outcome, using independence, probability, and binomial formulas such as n choose k.

  • Expected Value15:14

    Explore expected value as the weighted average of a random variable’s outcomes, using arithmetic mean and probability distributions, with coin, dice, roulette, and stock investment examples.

  • Combinations with Repetitions5:11

    Distinguish permutations from combinations and apply dividers to count with repetition. Derive and apply the combinations with repetition formula to donuts and digit-sum problems.

Requirements

  • An understanding of fundamental mathematical operations
  • A positive, can-do attitude and a desire to learn and enhance your math skills

Description

Welcome to a “Comprehensive Guide to Combinatorics.”

My name is Deyan Kassev and I am a high school student from the United States. For as long as I can remember, I have been fascinated with mathematics. I have participated in countless math competitions including Math Olympiad, AMC 8 and 10, Mathcounts, and various regional math leagues. I have also tutored aspiring middle school mathletes. Through my competition career I have come to find that many of the most interesting and challenging problems involve combinatorics, a field of mathematics concerned with creating, counting, analyzing, and optimizing arrangements.

Whether you are a mathlete looking to enhance your competition skills or a high school student preparing for an Algebra II test, I have the perfect solution for you. I have complied a class or nine videos that, together, form a complete and well-structured guide to combinatorics. While comprehensive, my series of videos, is concise and time friendly. It is accompanied by relevant examples that will augment your learning experience. I go over clever ways to derive and remember counting concepts and discuss common problem types that appear throughout competition math and the high school curriculum. All information is presented in an easy to follow visual manner.

Over the course of my nine videos, students will cover concepts ranging from permutations and combinations to Pascal’s triangle, exploring the many interesting topics within the field of combinatorics. After completing my course, you will be a master at combinatorics and will be ready to confidently tackle any counting problem that you encounter.

Who this course is for:

  • Middle and high school mathletes
  • Students preparing for Algebra II
  • Anyone who wants to learn more about counting techniques and combinatorics

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