Discrete Mathematical Structures, Lecture 1.1: Basic set theory

Discrete Mathematical Structures, Lecture 1.1: Basic set theory

In this lecture, we see some basic definitions and concepts in set theory. We begin with Russell's paradox to see why we need to be careful about what is a set and what isn't. After that, we introduce standard set notation for both general sets and specific sets (e.g., natural numbers, integers, rational numbers, real numbers, complex numbers). We also look at set operations such as complements, power sets, unions, and intersections, and conclude with the distributive laws relating unions of intersections, and vice-versa.

[MrIgnitus]

Thankyou for providing these lectures. I am finally getting educated in math thanks to youtube.

[yiuyiufung]

Hi Prof. I am a biological researcher who recently found interest in understanding biological networks. Needless to say discrete math is essential in this interdisciplinary area. I hope I can catch up the progress and do some awesome research projects in the future. I thank you for making free long series of lectures instead of brief introductions so that we can actually build a stronger math foundation outside school.

[guliyevshahriyar]

This is one of the best and top 3 most "effective" Discrete Mathematics course in the world. Maybe the first one with this compactness.

[AliRaza-tvyf]

Prof. Macauley THANK YOU for these wonderful lectures.

[chrislove]

Woah the russel paradox literally fried my brain 7 mins in to the video

[eugeniagurrola]

THANKS...I am starting Math Grad school soon and absolutely Love your lessons!

[guliyevshahriyar]

Quality lecture, thank you very much professor.

[davidpage]

With symmetric difference (indicated with @), in the case of A @ B @ C aren't elements inside the intersection of A, B, C also a member of A @ B @ C ? If so, then the rule of appearing in exactly one of A, B, C doesn't always hold true. Perhaps it should be extended to appearing in exactly one of A, B, C or appearing in all of A, B, C. In the example given at 54:30 3 should be a member of a A @ B @ C as it appears in A, B and C.

[yesupathammuthuselvan]

"find the number of n digit binary sequence that have the pattern 010 occurring for the first time at the n th digit" please upload this video sir

[Eihell]

I took Calc 3 do I need anything else to understands

[aharonwsmith]

Cant man A shave the barber and the barber doesnt shave man A? Its meets the specs of the scenario, does it not?

[MrBugz]

I feel like I have to disagree that the barber is a paradox. He shaves every man that doesn't shave himself. It doesn't say that he doesn't shave any man that shaves himself.

Or the barber could be a woman