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Discrete Mathematics 

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Discrete Mathematics
 at 
Coursera 
Overview

Duration

42 hours

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Total fee

Free

Mode of learning

Online

Difficulty level

Intermediate

Official Website

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Credential

Certificate

Discrete Mathematics
 at 
Coursera 
Highlights

  • Shareable Certificate Earn a Certificate upon completion
  • 100% online Start instantly and learn at your own schedule.
  • Flexible deadlines Reset deadlines in accordance to your schedule.
  • Intermediate Level
  • Approx. 42 hours to complete
  • English Subtitles: Arabic, French, Portuguese (European), Italian, Vietnamese, German, Russian, English, Spanish
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Discrete Mathematics
 at 
Coursera 
Course details

More about this course
  • Discrete mathematics forms the mathematical foundation of computer and information science. It is also a fascinating subject in itself.
  • Learners will become familiar with a broad range of mathematical objects like sets, functions, relations, graphs, that are omnipresent in computer science. Perhaps more importantly, they will reach a certain level of mathematical maturity - being able to understand formal statements and their proofs; coming up with rigorous proofs themselves; and coming up with interesting results.
  • This course attempts to be rigorous without being overly formal. This means, for every concept we introduce we will show at least one interesting and non-trivial result and give a full proof. However, we will do so without too much formal notation, employing examples and figures whenever possible.
  • The main topics of this course are (1) sets, functions, relations, (2) enumerative combinatorics, (3) graph theory, (4) network flow and matchings. It does not cover modular arithmetic, algebra, and logic, since these topics have a slightly different flavor and because there are already several courses on Coursera specifically on these topics.
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Discrete Mathematics
 at 
Coursera 
Curriculum

Introduction - Basic Objects in Discrete Mathematics

Introduction to the course

Sets, Relations, Functions

Sets, relations, and functions

Partial Orders

Partial orderings: basic notions

Mirsky's and Dilworth's Theorem

Partial orders, maximal and minimal elements, chains, antichains

Enumerative Combinatorics

How to Count Functions, Injections, Permutations, and Subsets

Evaluating Simple Sums

Pascal's Triangle

Counting Basic Objects

The Binomial Coefficient

Combinatorial Identities

Estimating the Binomial Coefficient

Excursion to Discrete Probability: Computing the Expected Minimum of k Random Elements from {1,...,n}

An Eagle's View of Pascal's Triangle

Asymptotics and the O-Notation

Asymptotics and the O( )-Notation

The Big-O-Notation

Introduction to Graph Theory

Basic Notions and Examples

Graph Isomorphism, Degree, Graph Score

Graph Score Theorem

Graphs, isomorphisms, and the sliding tile puzzle

Connectivity, Trees, Cycles

Graphs and Connectivity

Cycles and Trees

An Efficient Algorithm for Isomorphism of Trees

Cycles and Trees

Eulerian and Hamiltonian Cycles

Eulerian Cycles

Hamilton Cycles - Ore's and Dirac's Theorem

Hamiltonian Cycles and Paths

Spanning Trees

Minimum Spanning Trees

The Number of Trees on n Vertices

Spanning Trees

Maximum flow and minimum cut

Flow Networks, Flows, Cuts: Basic Notions and Examples

Flow Networks: The Maxflow - Mincut Theorem

Network flow

Matchings in Bipartite Graphs

Matchings in Bipartite Graphs - Basic Notions and an Algorithm

Matchings in Bipartite Graphs: Hall's and Konig's Theorem

Partial Orders: Dilworth's Theorem on Chains and Antichains

Discrete Mathematics
 at 
Coursera 
Admission Process

    Important Dates

    May 25, 2024
    Course Commencement Date

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    Discrete Mathematics
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