Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions). Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumerated by integers; more formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets (finite sets or sets with the same cardinality as the natural numbers). However, there is no exact definition of the term "discrete mathematics". The set of objects studied in discrete mathematics can be finite or infinite. The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deals with finite sets, particularly those areas relevant to business. Research in discrete mathematics increased in the latter half of the twentieth century partly due to the development of digital computers which operate in "discrete" steps and store data in "discrete" bits. Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development. Conversely, computer implementations are significant in applying ideas from discrete mathematics to real-world problems. Although the main objects of study in discrete mathematics are discrete objects, analytic methods from "continuous" mathematics are often employed as well. In university curricula, "Discrete Mathematics" appeared in the 1980s, initially as a computer science support course; its contents were somewhat haphazard at the time. The curriculum has thereafter developed in conjunction with efforts by ACM and MAA into a course that is basically intended to develop mathematical maturity in first-year students; therefore, it is nowadays a prerequisite for mathematics majors in some universities as well. Some high-school-level discrete mathematics textbooks have appeared as well. At this level, discrete mathematics is sometimes seen as a preparatory course, not unlike precalculus in this respect. The Fulkerson Prize is awarded for outstanding papers in discrete mathematics. (Wikipedia).
This video explains what is taught in discrete mathematics.
From playlist Mathematical Statements (Discrete Math)
Maths for Programmers: Introduction (What Is Discrete Mathematics?)
Transcript: In this video, I will be explaining what Discrete Mathematics is, and why it's important for the field of Computer Science and Programming. Discrete Mathematics is a branch of mathematics that deals with discrete or finite sets of elements rather than continuous or infinite s
From playlist Maths for Programmers
Intro to Discrete Math - Welcome to the Course!
Welcome to Discrete Math. This is the start of a playlist which covers a typical one semester class on discrete math. I chat a little about why I love discrete math, what you should expect, and how an online discrete math course is structured. FULL PLAYLIST: https://www.youtube.com/watch
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
Formal Definition of a Function using the Cartesian Product
Learning Objectives: In this video we give a formal definition of a function, one of the most foundation concepts in mathematics. We build this definition out of set theory. **************************************************** YOUR TURN! Learning math requires more than just watching vid
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
[Discrete Mathematics] Surjective Functions Examples
In these video we look at onto functions and do a counting problem. LIKE AND SHARE THE VIDEO IF IT HELPED! Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW *--Playlists--* Discrete Mathematics 1: https://www.youtube.com/playlist?list=PLDDGPdw7e6Ag1EIz
From playlist Discrete Math 1
INTRODUCTION to SET THEORY - DISCRETE MATHEMATICS
Today we introduce set theory, elements, and how to build sets. This video is an updated version of the original video released over two years ago. Hopefully the higher pen quality and refined explanations are beneficial for your learning. If you'd like to see more videos redone in the se
From playlist Discrete Math 1
[Discrete Mathematics] Finite State Machines
We do a quick introduction to finite state machines, creating our own, understanding what they do, and abstracting the purpose of these machines. Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW *--Playlists--* Discrete Mathematics 1: https://www.youtu
From playlist Discrete Math 1
The formal definition of a sequence.
We have an intuitive picture of sequences (infinite ordered lists). But there is a formal definition of sequences based out of the idea of a specific function between sets, specifically from the positive integers to the real numbers. ►Full DISCRETE MATH Course Playlist: https://www.youtu
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
The Discrete Charm of Geometry by Alexander Bobenko
Kaapi with Kuriosity The Discrete Charm of Geometry Speaker: Alexander Bobenko (Technical University of Berlin) When: 4pm to 6pm Sunday, 22 July 2018 Where: J. N. Planetarium, Sri T. Chowdaiah Road, High Grounds, Bangalore Discrete geometric structures (points, lines, triangles, recta
From playlist Kaapi With Kuriosity (A Monthly Public Lecture Series)
Notation and Basic Signal Properties
http://AllSignalProcessing.com for free e-book on frequency relationships and more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Signals as functions, discrete- and continuous-time signals, sampling, images, periodic signals, displayi
From playlist Introduction and Background
Discrete Math Book for Beginners
This is a really good discrete math book for beginners. I think this is easier to read than some of the other discrete math books out there. If you are taking discrete math I highly recommend this one. The book is called Discrete Mathematical Structures and it was written by Kolman, Busby
From playlist Book Reviews
The Abel Prize announcement 2021 - Avi Wigderson and László Lovász
0:49 The Abel Prize announced by Hans Petter Graver, President of The Norwegian Academy of Science and Letters 1:38 Citation by Hans Munthe-Kaas, Chair of the Abel committee 10:22 Popular presentation of the prize winners work by Alex Bellos, British writer, and science communicator 17:43
From playlist The Abel Prize announcements
Discrete Mathematics for Computer Science
In this video I will show you an older book on Discrete Mathematics. This is a course that Computer Science majors take in college in the United States. Discrete Math is considered a very tough course as many people struggle with it because it is very different from Calculus. I hope this h
From playlist Book Reviews
[Discrete Mathematics] Proof by Cases Examples
We do a problem that could be done with cases, but is easier as a direct proof. We also then look at a proof with min and max that requires cases. LIKE AND SHARE THE VIDEO IF IT HELPED! Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW *--Playlists--*
From playlist Discrete Math 1
In this video I do a speed run of some of my math books. I go through math books covering algebra, trigonometry, calculus, advanced calculus, real analysis, abstract algebra, differential geometry, set theory, discrete math, finite math, graph theory, combinatorics, number theory, galois t
From playlist Book Reviews
Oxford Mathematics Roger Penrose Public Lecture: Carlo Rovelli - Spin networks: the quantum structure of spacetime from Penrose's intuition to Loop Quantum Gravity Leading Physicist and best-selling author Carlo Rovelli pays tribute to one of his scientific heroes, Roger Penrose, as he t
From playlist Oxford Mathematics Public Lectures
[Discrete Mathematics] Counting Practice
We wrap up the section on counting by doing a few practice problems and showing the intuitions behind solving each problem. Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW *--Playlists--* Discrete Mathematics 1: https://www.youtube.com/playlist?list=P
From playlist Discrete Math 1
Discrete Mathematics Book I Used for Self Study
This is a book that I used for self study when I was learning discrete mathematics. In this video I go over the pros and cons of this book. The book is called Discrete and Combinatorial Mathematics: An Applied Introduction and it is written by Ralph P. Grimaldi. Here is the book on amaz
From playlist Cool Math Stuff