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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

Fees Informations	Certificate Availability	Certificate Providing Authority
INR 6486	yes	Coursera

The fee for the Combinatorics and Probability course is Rs. 6,486 per month.

Fee details of the Combinatorics and Probability course are:

Head	Amount
1 Month	Rs. 6,486
3 Months	Rs. 12,973
6 Months	Rs. 12,973

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

Mathematical skill

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

Data ScientistComputer ProgrammerSoftware EngineerPython ProgrammerIT EngineerIT Analyst

Application Details

For applying to the Combinatorics and Probability course candidates are required to follow these steps.

Step 1: Visit the course page to enrol for this programme. https://www.coursera.org/learn/combinatorics

Step 2: Click on “Enrol 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 specialisation. Select the option according to the need.

Step 5: Pay the announced fee.

After the payment candidates will be registered successfully.

The Syllabus

Readings

Why counting
How Not to Use the Rule of Sum
Rule of Sum
Convenient Language: Sets
Number of Paths
Generalized Rule of Sum
Rule of Product
Number of Tuples
Back to Recursive Counting
License Plates
Permutations
Tuples with Restrictions
Rule of Sum in Programming
Operations with Sets
Numbers Divisible by 2 or 3
Generalized Rule of Sum
Applications of the Rule of Product
Rule of Product in Programming
Counting with Restrictions
Tuples

Practice Exercises

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
Number of passwords
Tuples
License Plates
Counting with Restrictions

Videos

Previously on combinatorics
Number of Games in a Tournament1
Combinations
Pascal's Triangle
Symmetries
Row Sums
Binomial Theorem
Practice Counting

Readings

Generating Combinatorial Objects: Code
Slides
Slides
Slides

Practice Exercises

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

Readings

Review
Salads
Combinations with Repetitions
Distributing Assignments
Distributing Candies Among Kids
Counting Credit Card PINs
Splitting into Working Groups

Practice Exercises

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

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

Practice Exercises

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

Practice Exercises

Random Variables
Average
Expectations
Linearity of Expectation
Bob’s Party
Birthday Problem
More Linearity
Average Income
Bob’s Party Revisited
Alice’s tests

Readings

Dice Game Problem
Optimal Strategy

Practice Exercises

Final Project: Dice Game

Instructors

UC San Diego Frequently Asked Questions (FAQ's)

1: What are the advantages of subscribing to the specialisation?

Candidates will get access to all the courses in the specialisation by enrolling in the course, and after finishing the programme, they will receive a certificate. The electronic certificate can be printed or shared through email and LinkedIn.

2: What is the charge for enrollment?

Coursera enrollment is free. The fee is applicable only for the subscription of the specialisation. After enrolment candidates can audit the course for free. Most of the contents will be available on free audit mode.

3: When will the learning process start?

Candidates can start learning at the next moment after the enrolment. But the access to the contents depends upon the method of enrolment. Only paid subscription has the full access of contents including assignments. Auditing for free lectures will be available but there won’t be assignments and certification.

4: Does Coursera provide scholarships?

Coursera provides financial aid to eligible candidates. For availing of financial aid, candidates are required to apply through the website. The application review process will take a minimum of 15 days.

5: Can I apply for the course with 10+2 qualification?

This course is designed for people working or willing to work in the IT profession. Candidates from high school can even apply. But they should have basic knowledge of mathematics and Python programming.

6: Will I get the University credit?

No. There will not be any university credit provided. Coursera is responsible for the certification.