Learn the multiplication rule, permutations, combinations, n choose r with repetition, multinomial, the principle of inclusion and exclusion, partitions, and derangements. John will take you through the ideas and techniques you need to get a firm handle on counting concepts and applications. This course is perfect for people wanting to learn counting strategies for tests such as the John mentions some extra applications that require some knowledge of numbers such as "e," but these applications can easily be skipped with no loss of continuity.
Read more
Learn the multiplication rule, permutations, combinations, n choose r with repetition, multinomial, the principle of inclusion and exclusion, partitions, and derangements. John will take you through the ideas and techniques you need to get a firm handle on counting concepts and applications. This course is perfect for people wanting to learn counting strategies for tests such as the John mentions some extra applications that require some knowledge of numbers such as "e," but these applications can easily be skipped with no loss of continuity.
Learn the multiplication rule, permutations, combinations, n choose r with repetition, multinomial, the principle of inclusion and exclusion, partitions, and derangements. John will take you through the ideas and techniques you need to get a firm handle on counting concepts and applications. This course is perfect for people wanting to learn counting strategies for tests such as the John mentions some extra applications that require some knowledge of numbers such as "e," but these applications can easily be skipped with no loss of continuity.
Combinatorics is a growing field utilized in data science, computer science, statistics, probability, engineering, physics, business management, and everyday life. This course is a great introduction with some specialized topics. It is best for someone getting started. If you are more experienced, this course is not for you unless you want to revisit the core concepts. Please see the list of topics.
*Although this course covers only the topics listed, the material can be challenging and demand time to fully absorb.
This is paced as "Beginner" for a US College Course. But, on UDEMY the course rated 5.0 until a student rated the it a 1.0 due to the difficulty. A few other students commented that they loved the course but that it was set at a difficulty level greater than "Beginner" with respect to many UDEMY courses. To be consistent with the platform, the class has been adjusted to an "Intermediate" level course. However, if you are taking a university course in the US on combinatorics, this course would be the equivalent of the first part of a combinatorics class.
What's inside
Learning objectives
- You will be able to handle counting problems necessary for tests such as the gre, gmat, dat, etc.
- You will have a firm foundation for pursuing more combinatorics.
- You will be comfortable with permutations, combinations, binomial coefficients, ordering with repetition, choosing with repetition, pie, etc.
- You will be comfortable with the combinatorics needed for beginning a data science career.
- You will be able to handle counting problems necessary for tests such as the gre, gmat, dat, etc.
- You will have a firm foundation for pursuing more combinatorics.
- You will be comfortable with permutations, combinations, binomial coefficients, ordering with repetition, choosing with repetition, pie, etc.
- You will be comfortable with the combinatorics needed for beginning a data science career.
Syllabus
After this section you should be comfortable with different applications of the multiplication principle, the addition rule, and other fundamental counting strategies.
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Syllabus
This short, self-contained course gives you the basics on counting necessary to be successful in probability, stats, genetics, GMAT, GRE, etc. The multiplication principle, additional rule, permutations, combinations, counting strategies, binomial coefficients, multinomial coefficients, inclusion & exclusion, and derangements are covered. In a follow up course, we will cover more involved topics such as generating functions and Polya's counting theory. Abbreviations for applicability to different tests: DAT, GRE, GMAT, MSG (Math Subject GRE), OAT (O), ISSE (I).
Here is a quick bonus problem taken from a class lecture John gave.
From this quiz on: n "choose" r will be written as nCr.
In this bonus lesson, we will apply our knowledge of combinatorics to probability. For the problem we look at, it is enough to know that the probability can be computed by diving the number of ways of getting "what we want" by the "total number of possibilities" [WANT/TOTAL]. Here, we take for granted that each possibility is equally likely to occur.
A bonus lecture showing two interesting ways of picking 3 nonconsecutive numbers from the numbers 1-10!
For standardized tests, this quiz and topic, really, are not necessary (with the possible exception of the MSG). For combinatorics, this is a must!
An application to Fibonacci numbers!
John does a quick video on Burnside's Lemma (an advanced topic for this course). Let us know if you want a more extensive explanation!
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Reviews summary
Foundational combinatorics for technical studies
Examples and checks are helpful.
Covers essential counting principles.
Builds strong base for applications.
Instructor makes concepts accessible.
Activities
Review Basic Set Theory
Show steps
Strengthen your understanding of set theory, which provides a foundation for understanding counting principles and inclusion-exclusion.
Browse courses on
Set Theory
Show steps
-
Review definitions of sets, subsets, and power sets.
-
Practice set operations like union, intersection, and complement.
-
Solve problems involving Venn diagrams to visualize set relationships.
Read 'Discrete Mathematics and Its Applications' by Kenneth H. Rosen
Show steps
Supplement your learning with a comprehensive textbook that covers combinatorics in detail.
View
Discrete Mathematics and Its Applications
on Amazon
Show steps
-
Obtain a copy of 'Discrete Mathematics and Its Applications'.
-
Read the chapters related to counting principles and combinatorics.
-
Work through the examples and exercises in the book.
Participate in a Combinatorics Study Group
Show steps
Reinforce your learning by discussing concepts and solving problems with peers.
Show steps
-
Find other students who are also taking the course.
-
Schedule regular study sessions to discuss course material.
-
Work together to solve practice problems and answer questions.
Four other activities
Expand to see all activities and additional details
Show all seven activities
Create a Combinatorics Cheat Sheet
Show steps
Consolidate your understanding by creating a concise cheat sheet summarizing key formulas and techniques.
Show steps
-
Review the formulas and techniques covered in the course.
-
Organize the information into a clear and concise format.
-
Include examples to illustrate each concept.
Solve Combinatorial Problems on Project Euler
Show steps
Apply your knowledge by solving challenging combinatorial problems that require creative problem-solving skills.
Show steps
-
Visit the Project Euler website.
-
Select combinatorial problems to solve.
-
Implement your solutions in a programming language.
Read 'Combinatorial Problems and Exercises' by László Lovász
Show steps
Challenge yourself with a collection of advanced combinatorial problems to solidify your understanding.
View
Combinatorial Problems and Exercises
on Amazon
Show steps
-
Obtain a copy of 'Combinatorial Problems and Exercises'.
-
Select problems related to the topics covered in the course.
-
Attempt to solve the problems independently before consulting the solutions.
Design a Counting Algorithm
Show steps
Deepen your understanding by designing and implementing an algorithm to solve a specific counting problem.
Show steps
-
Choose a counting problem, such as counting the number of ways to arrange objects with constraints.
-
Design an algorithm to solve the problem efficiently.
-
Implement the algorithm in a programming language.
-
Test the algorithm with various inputs.
Review Basic Set Theory
Show steps
Strengthen your understanding of set theory, which provides a foundation for understanding counting principles and inclusion-exclusion.
Browse courses on
Set Theory
Show steps
- Review definitions of sets, subsets, and power sets.
- Practice set operations like union, intersection, and complement.
- Solve problems involving Venn diagrams to visualize set relationships.
Read 'Discrete Mathematics and Its Applications' by Kenneth H. Rosen
Show steps
Supplement your learning with a comprehensive textbook that covers combinatorics in detail.
View
Discrete Mathematics and Its Applications
on Amazon
Show steps
- Obtain a copy of 'Discrete Mathematics and Its Applications'.
- Read the chapters related to counting principles and combinatorics.
- Work through the examples and exercises in the book.
Participate in a Combinatorics Study Group
Show steps
Reinforce your learning by discussing concepts and solving problems with peers.
Show steps
- Find other students who are also taking the course.
- Schedule regular study sessions to discuss course material.
- Work together to solve practice problems and answer questions.
Create a Combinatorics Cheat Sheet
Show steps
Consolidate your understanding by creating a concise cheat sheet summarizing key formulas and techniques.
Show steps
- Review the formulas and techniques covered in the course.
- Organize the information into a clear and concise format.
- Include examples to illustrate each concept.
Solve Combinatorial Problems on Project Euler
Show steps
Apply your knowledge by solving challenging combinatorial problems that require creative problem-solving skills.
Show steps
- Visit the Project Euler website.
- Select combinatorial problems to solve.
- Implement your solutions in a programming language.
Read 'Combinatorial Problems and Exercises' by László Lovász
Show steps
Challenge yourself with a collection of advanced combinatorial problems to solidify your understanding.
View
Combinatorial Problems and Exercises
on Amazon
Show steps
- Obtain a copy of 'Combinatorial Problems and Exercises'.
- Select problems related to the topics covered in the course.
- Attempt to solve the problems independently before consulting the solutions.
Design a Counting Algorithm
Show steps
Deepen your understanding by designing and implementing an algorithm to solve a specific counting problem.
Show steps
- Choose a counting problem, such as counting the number of ways to arrange objects with constraints.
- Design an algorithm to solve the problem efficiently.
- Implement the algorithm in a programming language.
- Test the algorithm with various inputs.
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