Discrete Mathematics
- Offered byCoursera
Discrete Mathematics at Coursera Overview
Duration | 42 hours |
Start from | Start Now |
Total fee | Free |
Mode of learning | Online |
Difficulty level | Intermediate |
Official Website | Explore Free Course |
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
Discrete Mathematics at Coursera Course details
- 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.
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
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