Definition
Discrete Mathematics deals with the study of Mathematical structures. It deals with objects that can have distinct separate values. It is also called Decision Mathematics or finite Mathematics. It is the study of mathematical structures that are fundamentally discrete in nature and it does not require the notion of continuity.
Objects that are studied in discrete mathematics are largely countable sets such as formal languages, integers, finite graphs, and so on. Due to its application in Computer Science, it has become popular in recent decades. It is used in programming languages, software development, cryptography, algorithms etc. Discrete Mathematics covers some important concepts such as set theory, graph theory, logic, permutation and combination as well. [1]
Who
TBS
What
Discrete Mathematics Topics
Set Theory: Set theory is defined as the study of sets which are a collection of objects arranged in a group. The set of numbers or objects can be denoted by the braces {} symbol. For example, the set of first 4 even numbers is {2,4,6,8}
Graph Theory: It is the study of the graph. The graph is a mathematical structure used to pair the relation between objects. Graphs are one of the prime objects of study in Discrete Mathematics.
Logic: Logic in Mathematics can be defined as the study of valid reasoning. There are three types of logic gates. They are AND(∧), NOT(~), and OR(∨)
Permutation: The different arrangements that can be made with a given number of sets taking some or all of them in a particular sequence at a time are called Permutation. For example, there are six permutations of the set {5,6,7}, namely (5,6,7), (5,7,6), (6,5,7), (6,7,5), (7,5,6), and (7,6,5).
Combination: The selection of a number of objects taking some or all of them at a time is called combination. The order of selection does not matter for the combination.
Sequence: According to some definite rules, a set of numbers arranged in a definite order is called a Sequence. A sequence is a function whose domain is the countable set of natural numbers. There are arithmetic sequences and geometric sequences.
Series: A series is the sum of the terms of a sequence. The result of adding all the terms together: s1+s2+s3+s4… is the sum of the series. [1]
Why
Why Discrete Math Is Important
- Discrete math is essential to college-level mathematics and beyond.
- Discrete math is the mathematics of computing.
- Discrete math teaches mathematical reasoning and proof techniques.
- Discrete math is fun. [3]
Discrete Math is Not Hard: Here Are The Reasons
1. It Is Practical
Theoretical classes seem dull and of no use, right? I mean, can you apply the linear algebra theoretical knowledge in real-life situations daily? Many students are thus discouraged with this. With discrete math, however, a student can be able to apply it to everyday intriguing, and exciting challenges. Doesn’t this sound fascinating now?
2. It Enables You Think Mathematically And Prove This
Memorizing a long list of formulas is the order of the day in calculus or algebra. Do you still remember the equations you learned in your first year or sophomore now that you are in your final year? Hectic, right? Nevertheless, discrete math introduces a concept so important, yet lacking in the other mathematical concepts. That is, thinking creatively in a precise manner. Creativity, at its best, will enable you to solve problems in discrete math as opposed to the rigid formulas in calculus and linear algebra.
3. Discrete Math Gives You An Added Advantage
What will make you stand out in a contest or interview? Is it that neatly combed hair with a three-piece suit directly from the tailor’s shop? No. It’s the unique quality that you have above all the other applicants or competitors. Discrete math does justice to this. Topics such as probability and counting in discrete math will broaden the students’ mindset in tackling any other mathematical problem. These topics are the core of mathematics. There will be two or three questions on the same in case of a contest.
4. It Is Exciting
Who else wants to sit down for an hour or so to listen or watching a math lecturer scribble down lines of numbers and signs unfamiliar to them? Well, geometry and linear algebra does just this, but not discrete math. The practicality of discrete math makes it interactive and, ultimately, fun! Number theory, probability, and counting give room for the teacher and students to mingle and excitingly solve problems.
5. Like Any Other Mathematical Concept, Attitude Matters
According to statistics, most students’ fear’ or ‘hate’ mathematics as a whole. Discrete math thus falls victim to this as well. If you get a captivating and inspirational mathematics teacher, you will love the subject. Every concept will be simplified, and you will comfortably sail like a boat on a calm, warm, sunny day in a sea. The case might be worse if the teacher is hard on you. Interest may slowly fade away, and you will develop a negative attitude towards the subject. [2]
See Theoretical Knowledge Vs Practical Application.
How
Many of the References and Additional Reading websites and Videos will assist you with understating and applying discrete mathematics.
As some professors say: “It is intuitively obvious to even the most casual observer.“
References
[1] “Discrete Mathematics – Topics, Applications and Examples”. 2023. BYJUS. https://byjus.com/maths/discrete-mathematics/.
[2] “Is Discrete Math Hard?”. 2023. assignmentgeek.com. https://assignmentgeek.com/blog/is-discrete-math-hard/.
[3] “Why Discrete Math Is Important”. 2023. artofproblemsolving.com. https://artofproblemsolving.com/blog/articles/discrete-math.
Additional Reading
“Discrete Mathematics | Brilliant Math & Science Wiki”. 2023. brilliant.org. https://brilliant.org/wiki/discrete-mathematics/.
“Discrete Mathematics — From Wolfram MathWorld”. 2023. mathworld.wolfram.com. https://mathworld.wolfram.com/DiscreteMathematics.html.
“Discrete Mathematics – Wikipedia”. 2015. en.wikipedia.org. https://en.wikipedia.org/wiki/Discrete_mathematics.
“Discrete Mathematics”. 2023. en.wikibooks.org. https://en.wikibooks.org/wiki/Discrete_Mathematics.
The subject of mathematics is committed to rigorous reasoning. This book aims to raise your confidence in the manipulation and interpretation of formal notations, as well as to train you to solve problems that are fundamentally discrete: problems like chess, in which the moves you make are exact; problems where fields like calculus fail because there’s no continuity; problems that appear frequently in games, puzzles, and computer science. We hope you’ll enjoy discovering discrete mathematics here, and we hope you’ll find this a good reference for quickly picking up the details you may forget.
“Discrete Mathematics”. 2023. LibreTexts. https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_(Levin).
This text aims to give an introduction to select topics in discrete mathematics at a level appropriate for first or second year undergraduate math majors, especially those who intend to teach middle and high school mathematics. A difference between this text and most other discrete math books is that this book is intended to be used in a class taught using problem oriented or inquiry based methods.
⭐ “Discrete Mathematics Tutorial – GeeksForGeeks”. 2022. GeeksForGeeks. https://www.geeksforgeeks.org/discrete-mathematics-tutorial/.
Discrete Mathematics is a branch of mathematics that is concerned with “discrete” mathematical structures instead of “continuous”. Discrete mathematical structures include objects with distinct values like graphs, integers, logic-based statements, etc. In this tutorial, we have covered all the topics of Discrete Mathematics for computer science like set theory, recurrence relation, group theory, and graph theory.
“Discrete Mathematics Tutorial – javaTpoint”. 2023. javatpoint.com. https://www.javatpoint.com/discrete-mathematics-tutorial.
Discrete mathematics Tutorial provides basic and advanced concepts of Discrete mathematics. Our Discrete mathematics Structure Tutorial is designed for beginners and professionals both.
Discrete mathematics is the branch of mathematics dealing with objects that can consider only distinct, separated values. This tutorial includes the fundamental concepts of Sets, Relations and Functions, Mathematical Logic, Group theory, Counting Theory, Probability, Mathematical Induction, and Recurrence Relations, Graph Theory, Trees and Boolean Algebra.
“Discrete Structures: What Is Discrete Math?”. 2023. cse.buffalo.edu. https://cse.buffalo.edu/~rapaport/191/S09/whatisdiscmath.html.
Videos
“Discrete Math II/Combinatorics (entire course)”. 2023. youtube.com. https://www.youtube.com/playlist?list=PLl-gb0E4MII0sGLCJeqDB3y63HZ6lM5LJ.
This playlist follows a typical 2nd course in Discrete Mathematics/Combinatorics. The focus is on enumeration, or finding the number of ways an event can occur.
This playlist uses Discrete Mathematics and Its Applications, Rosen 8e Power Point slide decks to accompany the videos can be found here:
https://bellevueuniversity-my.sharepoint.com/:f:/g/personal/kbrehm_bellevue_edu/Ei9DcmrOBTlAuMxWUoq9ZqsB14M60jcpob-xdAYS6ruVWw?e=uP9KN0
⭐ I suggest that you read the entire reference. Other references can be read in their entirety but I leave that up to you.
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Mathematical Mysteries 