Discrete Mathematics
Enrol in the Discrete Mathematics programme by Coursera to learn about mathematical objects and the mathematical foundation of computer and information science.
Intermediate
Online
11 Weeks
Free Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Course Overview
Coursera’s Discrete Mathematics online training programme uncovers the fundamentals of discrete mathematics, and how it also forms the mathematical foundation of information and computer science. You will be familiarized with a wide range of mathematical aspects such as functions, graphs, relations, sets, etc. which are ubiquitous and thoroughly involved in computer science.
The online programme, Discrete Mathematics, is an intermediate-level course and attempts to teach through rigorous methods while also trying to avoid being extra formal. For this, the course not only introduces the concepts and gives the full proof, but also makes the process interesting by showing at least one non-trivial result. Examples and figures will be used whenever possible to avoid extremely formal representation.
The Shanghai Jiao Tong University offers the Discrete Mathematics online course and is known to be one of China’s fastest developing universities. The course curriculum features online video lectures, course readings, quizzes, assignments, and interactive feedback. Moreover, it also provides flexible deadlines for a self-paced learning experience. Upon completion, you will also earn the e-certificate, which can be shared across your LinkedIn profile, CV, or printed resume.
The Highlights
- Flexible deadlines
- Computer and information sciences
- Completion in about 41 hours
- 100% online course
- Shareable certificate
- Self-paced learning
- Intermediate-level course
- Subtitles in English, Russian, Spanish, Portuguese (Brazilian), and French
Programme Offerings
- Intermediate-level Course
- Shareable Electronic Certificate
- video lectures
- Flexible Deadlines
- financial aid
Courses and Certificate Fees
| Fees Informations | Certificate Availability | Certificate Providing Authority |
|---|---|---|
| INR 2480 | yes | Coursera |
Discrete Mathematics Fees Structure :
| Course | Fees |
| Discrete Mathematics (Certificate) | Rs. 2,480 |
What you will learn
After completing the Discrete Mathematics online training by Coursera, you will be able to thoroughly understand:
- What discrete mathematics is and how it differs from the other fields because of the way its “flavour” is.
- How to prove non-trivial and fundamental facts about partial orders.
- Be able to perform enumerative combinatorics
- Analyze algorithms by using the binomial coefficients (n choose k)
- The concept of asymptotics and the O-Notation
- Basic principles of graph theory such as cycles, degree, isomorphism, paths, graphs, etc. and apply it in discrete mathematics
- The class of graphs called trees and their various equivalent characterizations.
- How to detect whether two trees are isomorphic by using an efficient algorithm
- The characterization of Eulerian graphs, Hamiltonian paths, and their existence with Ore’s and Dirac’s theorem
- How to prove Cayley’s formula and find a graph’s minimum spanning tree with edge costs
- How to prove Hall’s Theorem and Konig’s theorem and prove Dilworth’s theorem using Konig’s theorem.
- Formal statements, their proofs, establishing rigorous proofs, creating interesting results.
Who it is for
Admission Details
To enrol yourself for the Discrete Mathematics training course by Coursera follow the steps given below:
- Visit the Course page.
- Type in ‘Discrete Mathematics’ in the search bar and open your course.
- Select the “Enroll for free” tab, and the sign-up page will appear.
- Open an account on Coursera or log in via Google, Facebook, or Apple. If you have registered before, log in and get the course material.
Application Details
To be able to apply for the Discrete Mathematics course by Coursera, there is no need to fill extensive forms with intricate details. Simply, register by logging in and get access to the course material.
The Syllabus
Videos
- Introduction to the course
- Sets, Relations, Functions
Assignment
- Sets, relations, and functions
Peer Reviews
- Exercises for introduction lesson
- Sets, Relations, Functions
Videos
- Partial orderings: basic notions
- Mirsky's and Dilworth's Theorem
Assignment
- Partial orders, maximal and minimal elements, chains, antichains
Peer Review
- Partial orders, maximal and minimal elements, chains, antichains
Videos
- How to Count Functions, Injections, Permutations, and Subsets
- Evaluating Simple Sums
- Pascal's Triangle
Assignment
- Counting Basic Objects
Peer Review
- Counting Basic Objects
Videos
- Combinatorial Identities
- Estimating the Binomial Coefficient
- Excursion to Discrete Probability: Computing the Expected Minimum of k Random Elements from {1,...,n}
Assignment
- An Eagle's View of Pascal's Triangle
Peer Reviews
- Combinatorial Identities
- Digging Into Pascal's Triangle
Video
- Asymptotics and the O( )-Notation
Assignment
- The Big-O-Notation
Peer Reviews
- Basic Facts
- Classes that often occur in complexity theory
Videos
- Basic Notions and Examples
- Graph Isomorphism, Degree, Graph Score
- Graph Score Theorem
Assignment
- Graphs, isomorphisms, and the sliding tile puzzle
Peer Reviews
- Graphs and Isomorphisms
- The Graph Score Theorem
Videos
- Graphs and Connectivity
- Cycles and Trees
- An Efficient Algorithm for Isomorphism of Trees
Assignment
- Cycles and Trees
Peer Reviews
- Cycles and Trees
- Spanning Tree Exchange Graph
Videos
- Eulerian Cycles
- Hamilton Cycles - Ore's and Dirac's Theorem
Assignment
- Hamiltonian Cycles and Paths
Peer Review
- Hamiltonian Cycles and Paths
Videos
- Minimum Spanning Trees
- The Number of Trees on n Vertices
Assignment
- Spanning Trees
Peer Reviews
- Minimum Spanning Trees
- Counting Trees on n Vertices
Videos
- Flow Networks, Flows, Cuts: Basic Notions and Examples
- Flow Networks: The Maxflow - Mincut Theorem
Assignment
- Network flow
Peer Review
- Network Flows
Videos
- Matchings in Bipartite Graphs - Basic Notions and an Algorithm
- Matchings in Bipartite Graphs: Hall's and König's Theorem
- Partial Orders: Dilworth's Theorem on Chains and Antichains
Peer Review
- Matchings in Bipartite Graphs
Instructors
SJTU Frequently Asked Questions (FAQ's)
Yes. The course is held entirely online without any physical interaction needed.
Purchasing the certificate will help you link it to your LinkedIn profile, or you can include it in your resume, CVs, and other documents.
No. universities do usually accept this certification as a base for credit.
The Discrete Mathematics training course is an eleven-week one, which will take approximately 41 hours to complete.