Combinatorics and Probability
- Offered byCoursera
Combinatorics and Probability at Coursera Overview
Duration | 20 hours |
Start from | Start Now |
Total fee | Free |
Mode of learning | Online |
Difficulty level | Beginner |
Official Website | Explore Free Course  |
Credential | Certificate |
Combinatorics and Probability at Coursera Highlights
- Shareable Certificate Earn a Certificate upon completion
- 100% online Start instantly and learn at your own schedule.
- Course 2 of 5 in the Introduction to Discrete Mathematics for Computer Science Specialization
- Flexible deadlines Reset deadlines in accordance to your schedule.
- Beginner Level
- Approx. 20 hours to complete
- English Subtitles: Arabic, French, Portuguese (European), Chinese (Simplified), Greek, Italian, Vietnamese, German, Russian, English, Spanish
Combinatorics and Probability at Coursera Course details
- Counting is one of the basic mathematically related tasks we encounter on a day to day basis. The main question here is the following. If we need to count something, can we do anything better than just counting all objects one by one? Do we need to create a list of all phone numbers to ensure that there are enough phone numbers for everyone? Is there a way to tell that our algorithm will run in a reasonable time before implementing and actually running it? All these questions are addressed by a mathematical field called Combinatorics.
- In this course we discuss most standard combinatorial settings that can help to answer questions of this type. We will especially concentrate on developing the ability to distinguish these settings in real life and algorithmic problems. This will help the learner to actually implement new knowledge. Apart from that we will discuss recursive technique for counting that is important for algorithmic implementations.
- One of the main `consumers? of Combinatorics is Probability Theory. This area is connected with numerous sides of life, on one hand being an important concept in everyday life and on the other hand being an indispensable tool in such modern and important fields as Statistics and Machine Learning. In this course we will concentrate on providing the working knowledge of basics of probability and a good intuition in this area. The practice shows that such an intuition is not easy to develop.
- In the end of the course we will create a program that successfully plays a tricky and very counterintuitive dice game.
- As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students.
Combinatorics and Probability at Coursera Curriculum
Basic Counting
Why counting
Rule of Sum
How Not to Use the Rule of Sum
Convenient Language: Sets
Generalized Rule of Sum
Number of Paths
Rule of Product
Back to Recursive Counting
Number of Tuples
Licence Plates
Tuples with Restrictions
Permutations
Slides
Slides
Listing All Permutations
Slides
Rule of Sum in Programming
Numbers Divisible by 2 or 3
Operations with Sets
Generalized Rule of Sum
Puzzle: Number of Paths
Rule of Product in Programming
Applications of the Rule of Product
Tuples
Counting with Restrictions
Binomial Coefficients
Previously on Combinatorics
Number of Games in a Tournament
Combinations
Pascal's Triangle
Symmetries
Row Sums
Binomial Theorem
Practice Counting
Generating Combinatorial Objects: Code
Slides
Slides
Slides
Number of Segments and Diagonals
Forming Sport Teams
Number of Iterations of Nested For Loops
Sum of the First Six Rows of Pascal's Triangle
Expanding (3a-2b)^k
Practice Counting
Advanced Counting
Review
Salad
Combinations with Repetitions
Distributing Assignments Among People
Distributing Candies Among Kids
Numbers with Fixed Sum of Digits
Numbers with Non-increasing Digits
Splitting into Working Groups
Salads
Slides
Slides
Salads
Combinations with Repetitions
Distributing Assignments Among People
Distributing Candies Among Kids
Numbers with Fixed Sum of Digits
Numbers with Non-increasing Digits
Splitting into Working Groups
Problems in Combinatorics
Probability
The Paradox of Probability Theory
Galton Board
Natural Sciences and Mathematics
Rolling Dice
More Probability Spaces
Not Equiprobable Outcomes
More About Finite Spaces
Mathematics for Prisoners
Not All Questions Make Sense
What Is Conditional Probability?
How Reliable Is The Test?
Bayes' Theorem
Conditional Probability: A Paradox
Past and Future
Independence
Monty Hall Paradox
`Our Position'
Slides
Slides
Slides
Slides
Concentration for Galton Board
Computing Probabilities for Two Dice
Computing Probabilities: More Examples
Fair Decisions and Imperfect Coins
Puzzle: Prisoner and King
Inclusion-Exclusion Formula
Computing Conditional Probabilities
Prisoner, King and Conditional Probabilities
More Conditional Probabilities
More About Independence
Monty Hall Gone Crazy
Random Variables
Random Variables
Average
Expectation
Linearity of Expectation
Birthday Problem
Expectation is Not All
From Expectation to Probability
Markov?s Inequality
Application to Algorithms
Average Value of a Dice Throw: Experiment
Slides
Slides
Dice Game Experiment
Slides
Slides
Random Variables
Average
Expectations
Linearity of Expectation
Bob?s Party
More Linearity
Average Income
Bob?s Party Revisited
Alice?s tests
Project: Dice Games
Dice Game
Playing the Game
Project Description
Experiment: Dice Game
Slides
Slides
Final Project: Dice Game
Combinatorics and Probability at Coursera Admission Process
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