Discrete Mathematics (Full 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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⭐⭐Time Stamp ⭐⭐

0:00:00 Introduction Basic Objects in Discrete Mathematics
0:26:36 partial Orders
0:54:45 Enumerative Combinatorics
1:29:44 The Binomial Coefficient
2:24:38 Asymptotics and the o notation
2:38:44 Introduction to Graph Theory
3:19:29 Connectivity Trees Cycles
3:55:46 Eulerian and Hamiltonian Cycles
4:22:59 Spanning Trees
4:52:22 Maximum Flow and Minimum cut
5:21:45 Matchings in Bipartite Graphs
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⭐ Important Notes ⭐
⌨️ this course is created in collaboration with Shanghai Jiao Tong University this material produced by Dominik Scheder

✨✨PLEASE IGNORE THESE TAGS✨✨
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#discretemathematicsanditsapplications,
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[MyLesson]

⭐⭐Time Stamp ⭐⭐

0:00:00 Introduction Basic Objects in Discrete Mathematics
0:26:36 partial Orders
0:54:45 Enumerative Combinatorics
1:29:44 The Binomial Coefficient
2:24:38 Asymptotics and the o notation
2:38:44 Introduction to Graph Theory
3:19:29 Connectivity Trees Cycles
3:55:46 Eulerian and Hamiltonian Cycles
4:22:59 Spanning Trees
4:52:22 Maximum Flow and Minimum cut
5:21:45 Matchings in Bipartite Graphs

[youMatterItDoesGetBetter]

Mathematics literally opens our eyes to the world around us. It’s truly mind blowing. 3rd year CS student here. Y’all math majors are super human.

[kal_bibi]

This is my first time taking a discrete math class. this video gives a good introduction on what excatly is discret math is. Thank you so much.

[PS-]

Did Discrete Math in 2nd year CS degree course in university. Enjoyed it very much as it was an interesting course with topics on sets, graphs, trees, algorithms, relations, etc. Helped me in other courses like Data Structures, Operations Research, Translators & Compilers. It was supposed to help me in Automata Theory course but it didn't. I found Automata Theory to be the hardest course I took in CS.

[afah]

excellent video, it's a shame that it doesn't have the likes it deserves.

[poshimukaka]

no fancy editing, just straight value.

[vansf]

If your major is CS at university level, you must learn discrete maths

[Wanderlust]

The most interesting math class I took in college (an eternity ago).

[thedeathofbirth]

Hello Dominik, do you have a course that is prerequisite to this one. Because when you say recall this, I am not sure from what? If you do can I please have the URL for it? thank you.

[kevinstreeter]

I did not take this course to get my BS. I wish I had.

[gravity]

Cdefgabc-
C—cdefgab
B-c—cdefga
A-b-c—cdefg
G-a-b-c—cdef
F-g-a-b-c—cde
E-f-g-a-b-c—cd
D-e-f-g-a-b-c—c

Check, if C is black and in row 1 column 1 and c- is white in row 1 column 8 then I have made a sequence where if C is not seen; then it is possible to cut two squares (opposite and opposing squares) in a 8 x 8 with consistency and a smooth function… you’re welcome

[strohtaler]

1:43:30 How got to ? Left side of equal: m->k but on right side n->k - shouldn't n->n (or in other words, what is the value of k in the resulting formula?)

[CairosNaobum]

a full university course is at least 30-40 hours long.
This is a fifth of a full course if we're being very generous. Thanks !

[tao-of-wellbeing]

I like this, but are there solution to the exercises? I want to know about the coin puzzle near the start.

[Ninjaskeptic]

I haven't recovered since realizing numbers don't actually exist. And zero isn't a number 🤯

[consciouspi]

I measured size of earth, before. I measured solstice shadow on north side of home..244.5 inches. Your computer came up with close to same number in this excercise.. . is a scream... 1600 mi. For each real time zone. ....kmiles

[matschbirne]

1:32:06 shouldnt k start at 1 here if the comitee has to have a speaker?

[MathinD]

This is most definetely not a full course. Overly-rushed. 2 out of 5 stars

[taxidude]

Is discrete mathematics doing your algebra in a locked room where no one can see you?

[richross]

What is "discrete" mathematics. I know the word discreet, that is all.
If im wrong, id like to be corrected as i enjoy mathematics.
Adieu.