Discrete Mathematics

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Discrete Mathematics

Lectures and Accompanying MCQ keyboard_arrow_down
- check_circle Lecture 1 45:32
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- check_circle Lecture 2 45:52
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- check_circle Lecture 3 40:26
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- check_circle Lecture 4 40:42
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- check_circle Lecture 5 41:20
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- check_circle Lecture 6 41:50
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- check_circle Lecture 7 56:25
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- check_circle Lecture 8 42:07
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- check_circle Lecture 9 38:05
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- check_circle Lecture 10 35:38
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- check_circle Lecture 11 34:35
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- check_circle Lecture 12 34:29
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- check_circle Lecture 13 40:44
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- check_circle Lecture 14 42:33
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- check_circle Lecture 15 39:43
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- check_circle Lecture 16 27:05
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- check_circle Lecture 17 44:35
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- check_circle Lecture 18 37:31
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- check_circle Lecture 19 41:50
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- check_circle Lecture 20 45:28
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- check_circle Lecture 21 40:11
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- check_circle Lecture 22 38:30
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- check_circle Lecture 23 35:04
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- check_circle Lecture 24 36:45
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- check_circle Lecture 25 38:58
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- check_circle Lecture 26 36:50
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- check_circle Lecture 27 39:35
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- check_circle Lecture 28 40:03
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- check_circle Lecture 29 43:14
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- check_circle Lecture 30 40:08
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What You Will Get

Subject-Wise High Quality Lectures by Experts
Accompanying Content for Each Lecture
Lecture-Wise Multiple Choice Questions for Each Subject

About this Subject

Defining discrete mathematics is hard because defining mathematics is hard. What is mathematics? The study of numbers? In part, but you also study functions and lines and triangles and parallelepipeds and vectors and . . . . Or perhaps you want to say that mathematics is a collection of tools that allow you to solve problems. What sort of problems? Okay, those that involve numbers, functions, lines, triangles, . . . . Whatever your conception of what mathematics is, try applying the concept of “discrete” to it, as defined above. Some math fundamentally deals with stuff that is individually separate and distinct. In an algebra or calculus class, you might have found a particular set of numbers (maybe the set of numbers in the range of a function). You would represent this set as an interval: [0, ∞) is the range of f (x) x 2 since the set of outputs of the function are all real numbers 0 and greater. This set of numbers is NOT discrete.

The numbers in the set are not separated by much at all. In fact, take any two numbers in the set and there are infinitely many more between them which are also in the set. Discrete math could still ask about the range of a function, but the set would not be an interval. Consider the function which gives the number of children of each person reading this. What is the range? I’m guessing it is something like {0, 1, 2, 3}. Maybe 4 is in there too. But certainly, there is nobody reading this that has 1.32419 children. This output set is discrete because the elements are separate. The inputs to the function also form a discrete set because each input is an individual person. One way to get a feel for the subject is to consider the types of problems you solve in discrete math.

In this course 0.1. What is Discrete Mathematics? 3 we will study four main topics: combinatorics (the theory of ways things combine; in particular, how to count these ways), sequences, symbolic logic, and graph theory. However, there are other topics that belong under the discrete umbrella, including computer science, abstract algebra, number theory, game theory, probability, and geometry (some of these, particularly the last two, have both discrete and non-discrete variants). Ultimately the best way to learn what discrete math is about is to do it.

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