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Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Course Overview
Here most standard combinatorial settings are addressed in the Combinatorics and Probability course that can help answer questions of this nature. In particular, this course focuses on improving the ability to differentiate these settings from algorithmic problems in real life. This will assist candidates to apply new knowledge in practice. Besides that recursive counting technique that is necessary for algorithmic implementations is also addressed here.
The Combinatorics and Probability course is part of Introduction to Discrete Mathematics for Computer Science Specialisation. There are total of five courses in it and Combinatorics and Probability is the second one. The language of computer science is known as Discrete Mathematics. In many areas including data science, software engineering and machine learning, one needs to work fluently. Via a fun approach, candidates are introduced to this language. Firstly they will solve several interactive puzzles that are specially designed especially for this online specialisation. Then actual solving methods and significant ideas will be introduced to them. It is sure that candidates will gain a deeper understanding in this way and will appreciate the beauty of the underlying concepts better. Programming examples, projects and problems are integrated into the specialisation in order to get the knowledge closer to IT applications.
The Highlights
- Approx. 23 hours to complete
- Available in diversified language subtitles
- Offered by University of California San Diego
- Offered by National Research University Higher School of Economics
- The certificate can be electronically shared
- 100% online
- Beginners level
Programme Offerings
- online learning
- videos
- Practice Exercises
- assignments.
Courses and Certificate Fees
| Certificate Availability | Certificate Providing Authority |
|---|---|
| yes | UC San DiegoCoursera |
Fee details of the Combinatorics and Probability course are:
Head | Amount |
1 Month | Rs. 6,757 |
3 Months | Rs. 13,514 |
6 Months | Rs. 20,271 |
Note: There is a free trial of 7 days available for everyone. The fee is to be paid only after 7 days. Candidates can cancel the subscription any time during the free trial. There will not be any charge for cancellation.
Eligibility Criteria
Education
Candidates must have a basic understanding of Maths and Python.
Certification Qualifying Details
For getting the certificate of completion candidates to have to subscribe to the specialisation by paying the required fee. Along with that, it should be a successful completion as well. The Combinatorics and Probability course is a week's training. All candidates should complete them all to become qualified for certification.
What you will learn
After completing the Combinatorics and Probability course candidates will have knowledge in these:
- Candidates will gain skills like random variables, probability interpretation, probability, combinatorics which can be applied in real life.
- Candidates will learn to build a dice game and several other skills as well.
Who it is for
Application Details
For applying to the Combinatorics and Probability course candidates are required to follow these steps.
Step 1: Visit the course page to enroll for this programme. https://www.coursera.org/learn/combinatorics
Step 2: Click on “Enroll for free” button.
Step 3: Candidates have to sign up on the website either with Google, Facebook or Apple account. If an account was created already please log in.
Step 4: Candidates can audit the course for free or can subscribe to the specialization. Select the option according to the need.
Step 5: Pay the announced fee.
After the payment candidates will be registered successfully.
The Syllabus
Readings
- Companion e-book
- 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
Assignments
- Rule of Sum in Programming
- Operations with Sets
- Generalized Rule of Sum
- Rule of Product in Programming
- Applications of the Rule of Product
- Tuples
- License Plates
- Counting with Restrictions
- Numbers Divisible by 2 or 3
- Puzzle: Number of Paths
- Number of passwords
Videos
- Previously on combinatorics
- Number of Games in a Tournament
- Combinations
- Pascal's Triangle
- Symmetries
- Row Sums
- Binomial Theorem
- Practice Counting
Readings
- Generating Combinatorial Objects: Code
- Slides
- Slides
- Slides
Assignments
- Number of Segments and Diagonals
- Forming Sport Teams
- Sum of the First Six Rows of Pascal's Triangle
- Expanding (3a-2b)^k
- Practice Counting
- Number of Iterations of Nested For Loops
Readings
- Review
- Salads
- Combinations with Repetitions
- Distributing Assignments
- Distributing Candies Among Kids
- Counting Credit Card PINs
- Splitting into Working Groups
Assignments
- Salads
- Combinations with Repetitions
- Problems in Combinatorics
- Distributing Assignments Among People
- Distributing Candies Among Kids
- Numbers with Fixed Sum of Digits
- Numbers with Non-increasing Digits
- Splitting into Working Groups
Videos
- 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'
Readings
- Slides
- Slides
- Slides
- Slides
Assignments
- 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
Readings
- Random Variables
- Average
- Expectation
- Linearity of Expectation
- Birthday Problem
- Expectation is Not All
- From Expectation to Probability
- Markov’s Inequality
Assignments
- Random Variables
- Average
- Expectations
- Linearity of Expectation
- Bob’s Party
- More Linearity
- Average Income
- Bob’s Party Revisited
- Alice’s tests
- Birthday Problem
Ungraded Lab
- Birthday Problem Simulation
Readings
- Dice Game Problem
- Optimal Strategy
Assignment
- Final Project: Dice Game