⭐⭐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
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.
Well, not really. Mathematics makes understand things better, because Math is easy. Other branches of knowledge, questions outside Mathematics, are way more complex than most of the problems we study in Math. One of the reasons is because in Math almost everything is well defined. Outside Math, almost nothing is well defined. But I have to agree Math is mind blowing, anyway, despite its simplicity. Strongly disagree with "math majors are super human". Math majors are actually a little weird, mostly normal people. It's undesirable to think Math majors are more than other people. It makes some people think they can't study Math. Any person can study Math.
Math is not easy for most of us. Most people have trouble counting change back and no amount of hard work is going to get them to the level of solving derivates and integrals. Nice humble brag though! Also, I'm learning to love the "weird" math/engineer people. My coworker won't touch money, he uses a napkin. Smartest guy I've ever met... and can hardly talk to a cashier in a drive thru. @@samueldeandrade8535
100%. I've been in sales my whole life, so I naturally have strong people skills and I'm a whiz at languages and memorization/intuition. Logic and actually APPLYING things to problems is a WAY different ball game. Currently transitioning into an Engineering role (stress finally got to me in sales) and although I absolutely am loving it, it's not for the faint of heart. Calc 2 can go %$&# itself. @@miikke0
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.
1:43:30 How \sum_{m=0}^{n}m^{\underline{k}}=\frac{(n+1)^{\underline{k+1}}}{k+1} got to \sum_{k=1}^{n}k^{\underline{2}}=\frac{(k+1)^{\underline{3}}}{3} ? 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?)
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
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
Your emoji is so silly. It suggests that you think he NEEDS TO give us the answer. He doesn't. But, I can tell you what I thought. Think about three coins, A, B and C, in any triangular configuration. The area of the triangle is the same after moving any coin. To see that, let's say we will move "B jumping above C". The area of the triangle is the base BC times the height which is the (perpendicular) distance between A and the line BC. When B jumps above C, we still will have the same values for base and height. So the area is the same. This means the riddle is impossible. We can't obtain a triangular configuration with bigger area. In the square case, the same reasoning works for any 3 points. This implies that if we take a coin for reference, the area of the triangles having it as vertices any two other coins will always have the same area. At the beginning, any triangle will have the same value, that must be constant after moves. For any square configuration bigger than the initial one, the triangles would have a bigger value. Impossible!
@@samueldeandrade8535 I thought the solution might be impossible. I spent a long time trying to find any possibility. I wanted a confirmation, though...
@@samueldeandrade8535i agree with you in the triagular case but not the square case, with 4 point you can change the area of any triagular. i find the proof after a week but it not hard at all, just like the chess board and domino problem.
@@congnguyenthanh8910 hum why do you disagree? The same reasoning is valid. The area of triangles formed by 3 of the 4 initial points will be the same. The area of a quadrilateral may change, because its area is formed by the triangles, possibly overlapping. I didn't said that in the previous comment, because it is not necessary for the proof.
@@congnguyenthanh8910 if you prefer, the area formed by a quadrilateral formed by the four points will be constant or less. But the argument about triangles is valid too. And more simple. What proof did you find?
Export the Quantum, Chat GPT, Revit, Plant 3D, Civil 3D, Inventor, ENGI file of the Building or Refinery to Excel, prepare Budget 1 and export it to COBRA. Prepare Budget 2 and export it to Microsoft Project. Solve the problems of Overallocated Resources, Planning Problems, prepare the Budget 3 with which the construction of the Building or the Refinery is going to be quoted.
If you want to understand why God does what he does, learn his language. What is a number? It is a location in spacetime. It has three physical dimensions AND a time coordinate. That is why they predict the universe with perfect accuracy.
math that deals with discrete values and variables rather than continuous ones. Calculus deals with continuous variables, things that are measured. On the other hand discrete variables are things that can be counted. The number of students in a class is a discrete value. The range of students heights is a continuous value as it is something that must be measured rather than counted and it covers a continuous range rather than distinct values like the count of the number of students.
37:45 are the symbols the othet way around? x is maximal if no y is bigger, but he wrote that for every y in S, y is bigger than x, which is the exact opposite
I heavily disagree with that definition of proof! A proof does not require anything to be “agreed” the laws of logic are not arrived at in consensus! At all! The laws of logic are arrived at by direct evidence of the senses. Which are valid. All laws of logic are in accordance with the law of identity.
@@skyisbluexd,@joelsanderson2021, @kevinstreeter6943, @alexubokwe7933 My dear friends, what we have there is just a p1ec3 of sh1t being a p1ec3 of sh1t. Don't care about people like that. Don't reply to IT.
⭐⭐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
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.
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.
Took Compilers & Automata theory last semester. It was hell :( but we passed!!!
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.
Well, not really. Mathematics makes understand things better, because Math is easy. Other branches of knowledge, questions outside Mathematics, are way more complex than most of the problems we study in Math. One of the reasons is because in Math almost everything is well defined. Outside Math, almost nothing is well defined.
But I have to agree Math is mind blowing, anyway, despite its simplicity.
Strongly disagree with "math majors are super human". Math majors are actually a little weird, mostly normal people. It's undesirable to think Math majors are more than other people. It makes some people think they can't study Math. Any person can study Math.
Math is not easy for most of us. Most people have trouble counting change back and no amount of hard work is going to get them to the level of solving derivates and integrals. Nice humble brag though!
Also, I'm learning to love the "weird" math/engineer people. My coworker won't touch money, he uses a napkin. Smartest guy I've ever met... and can hardly talk to a cashier in a drive thru. @@samueldeandrade8535
100%. I've been in sales my whole life, so I naturally have strong people skills and I'm a whiz at languages and memorization/intuition. Logic and actually APPLYING things to problems is a WAY different ball game. Currently transitioning into an Engineering role (stress finally got to me in sales) and although I absolutely am loving it, it's not for the faint of heart. Calc 2 can go %$&# itself. @@miikke0
@@miikke0 you are talking about Math as the subject of the terrible teaching we have. I thought we were talking about the real OG Math here.
That's why I love maths solving hard problems gives me a rush of dopamine
excellent video, it's a shame that it doesn't have the likes it deserves.
no fancy editing, just straight value.
Discrete Mathematics for Computer Science Specialization : th-cam.com/play/PLtS8Ubq2bIlXO4qEM5BOsBy6xWQNVFu8l.html
Thank you very much for your hard work, love from Saint Petersburg State University Russia 🇷🇺
If your major is CS at university level , you must learn discrete maths
Super, thank you very much !
Here before midterms tomorrow :)
How did you do?
@@jarrodanderson2124not good.
The most interesting math class I took in college (an eternity ago).
Interestint, this is very good.
I like this, but are there solution to the exercises? I want to know about the coin puzzle near the start.
I did not take this course to get my BS. I wish I had.
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.
1:32:06 shouldnt k start at 1 here if the comitee has to have a speaker?
1:43:30 How \sum_{m=0}^{n}m^{\underline{k}}=\frac{(n+1)^{\underline{k+1}}}{k+1} got to \sum_{k=1}^{n}k^{\underline{2}}=\frac{(k+1)^{\underline{3}}}{3} ? 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?)
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
(-) opposite of the original color
(-) is the opposites opposite color …… lol … or a (+) of the original color. For simplicity sake
that was great thank you
Well video❤❤❤❤
Learning from Cisco Ramone :D
I haven't recovered since realizing numbers don't actually exist. And zero isn't a number 🤯
thank you!
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
Okay, what's the solution for the 4 coin riddle at 15:44? 🙄I don't think he told the solution...
Your emoji is so silly. It suggests that you think he NEEDS TO give us the answer. He doesn't.
But, I can tell you what I thought. Think about three coins, A, B and C, in any triangular configuration. The area of the triangle is the same after moving any coin. To see that, let's say we will move "B jumping above C". The area of the triangle is the base BC times the height which is the (perpendicular) distance between A and the line BC. When B jumps above C, we still will have the same values for base and height. So the area is the same. This means the riddle is impossible. We can't obtain a triangular configuration with bigger area.
In the square case, the same reasoning works for any 3 points. This implies that if we take a coin for reference, the area of the triangles having it as vertices any two other coins will always have the same area. At the beginning, any triangle will have the same value, that must be constant after moves. For any square configuration bigger than the initial one, the triangles would have a bigger value. Impossible!
@@samueldeandrade8535 I thought the solution might be impossible. I spent a long time trying to find any possibility. I wanted a confirmation, though...
@@samueldeandrade8535i agree with you in the triagular case but not the square case, with 4 point you can change the area of any triagular. i find the proof after a week but it not hard at all, just like the chess board and domino problem.
@@congnguyenthanh8910 hum why do you disagree? The same reasoning is valid. The area of triangles formed by 3 of the 4 initial points will be the same. The area of a quadrilateral may change, because its area is formed by the triangles, possibly overlapping. I didn't said that in the previous comment, because it is not necessary for the proof.
@@congnguyenthanh8910 if you prefer, the area formed by a quadrilateral formed by the four points will be constant or less. But the argument about triangles is valid too. And more simple. What proof did you find?
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 !
Is discrete mathematics doing your algebra in a locked room where no one can see you?
This is most definetely not a full course. Overly-rushed. 2 out of 5 stars
Export the Quantum, Chat GPT, Revit, Plant 3D, Civil 3D, Inventor, ENGI file of the Building or Refinery to Excel, prepare Budget 1 and export it to COBRA. Prepare Budget 2 and export it to Microsoft Project. Solve the problems of Overallocated Resources, Planning Problems, prepare the Budget 3 with which the construction of the Building or the Refinery is going to be quoted.
why so many antichains🤔😮🤯😎🤓
Jackson Sharon Anderson Linda Williams Thomas
If you want to understand why God does what he does, learn his language. What is a number? It is a location in spacetime. It has three physical dimensions AND a time coordinate. That is why they predict the universe with perfect accuracy.
the earth is flat
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.
math that deals with discrete values and variables rather than continuous ones. Calculus deals with continuous variables, things that are measured. On the other hand discrete variables are things that can be counted. The number of students in a class is a discrete value. The range of students heights is a continuous value as it is something that must be measured rather than counted and it covers a continuous range rather than distinct values like the count of the number of students.
@@enderthexenocide760
Much obliged
37:45 are the symbols the othet way around? x is maximal if no y is bigger, but he wrote that for every y in S, y is bigger than x, which is the exact opposite
nevernind, I just noticed that the "arrow" is actually a negation lol
drezz wede tireyze
Kag tiles
Kag tiles
Tiles
I heavily disagree with that definition of proof! A proof does not require anything to be “agreed” the laws of logic are not arrived at in consensus! At all! The laws of logic are arrived at by direct evidence of the senses. Which are valid. All laws of logic are in accordance with the law of identity.
🤔
this one got the noggin joggin
Scam
why
@@skyisbluexd fr its an introduction video bruh bugging
How? You are not paying anything for it.
What do you mean by calling this scam.
@@skyisbluexd,@joelsanderson2021, @kevinstreeter6943, @alexubokwe7933
My dear friends, what we have there is just a p1ec3 of sh1t being a p1ec3 of sh1t. Don't care about people like that. Don't reply to IT.
Speak chinese please !