Discrete Mathematics
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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Syllabus
Syllabus - What you will learn from this course
Week 1
Introduction - Basic Objects in Discrete Mathematics
Week 2
Partial Orders
Week 3
Enumerative Combinatorics
Week 4
The Binomial Coefficient
Week 5
Asymptotics and the O-Notation
Week 6
Introduction to Graph Theory
Week 7
Connectivity, Trees, Cycles
Week 8
Eulerian and Hamiltonian Cycles
Week 9
Spanning Trees
Week 10
Maximum flow and minimum cut
Week 11
Matchings in Bipartite Graphs
FAQ
When will I have access to the lectures and assignments?
Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:
The course may not offer an audit option. You can try a Free Trial instead, or apply for Financial Aid.
The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.
What will I get if I purchase the Certificate?
When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.
Is financial aid available?
Yes. In select learning programs, you can apply for financial aid or a scholarship if you can’t afford the enrollment fee. If fin aid or scholarship is available for your learning program selection, you’ll find a link to apply on the description page.
Reviews
This course includes the most difficult assignments I have ever had. In the end, but every question has the simplest solution. It was... fun.
sometimes all of the answers are labeled as "correct" - so the multiple choice questions you cannot get right, but other than that it's very good lectures.
This course is good to comprehend relation, function and combinations.
This course requires some background knowledge of mathematics, and the exercises require some hard work. It's interesting, engaging, and has a lot of knowledge on offer!
