Discrete Mathematics: Books and Computer Science Applications

Discrete mathematics is a division of mathematics that usually involves disconnected elements that use arithmetic and algebra.

In other words, the branch of mathematics only deals with objects capable of assuming separated and distinct values. Most practical fields such as computer science heavily apply this type of mathematics. Discrete

Is Discrete Math Important?

Most middle and high schools use a type of curriculum that deals with a combination of elements such as trigonometry, algebra, and geometry.

These elements of learning are usually combined and spread over the learning period.

Nonetheless, this type of combination has a minimal emphasis on discrete mathematics.

Lately, there has been a great push to have more configuration of discrete mathematics in middle and high schools to the level of progress exams.

Times are changing and discreet Math is going to be a consideration for college admission exams if the emerging proposals are anything to go by.

The Following are Reasons why this Branch of Mathematics is Progressively Becoming Vital in Schools:

1. The Backbone of Computer Science

Without a doubt, discrete mathematics has applications that are extremely significant in computer science. To put it differently, it is the mathematical language of today’s computer science.

Almost all the branches of computer science directly rely on the notations and concepts derived from discrete mathematics.

You need these concepts to be able to describe different problems in programming, software development, computer algorithms, and cryptography among others.

This is a clear indication that if you do not understand discrete mathematics, it can be an uphill task to study computer science. Nurture your love for mathematics.

Modern computer science has graph theory and combinatorics. All these are also directly dependable on discrete mathematics.

As an aspiring student of computer programming, you need to build a significant background in discrete math so that it becomes easier for you to learn all the essential algorithms.

In some universities, discrete mathematics is now one of the fundamental requirements if you want to pursue a degree in computer science.

2. Data Analytics

In big data analytics, discrete mathematics has a vital role. The concepts of this branch of mathematics are widely useful in converting large data into meaningful information that is knowledgeable.

For you to achieve this, you need a variety of powerful methods and mathematics tools.

This is what will enable you to comprehend and manage high-dimensional data.

Only a solid foundation in discrete mathematics can enable you to understand inference systems and algorithms that are necessary when computing large data.

That is to say, discrete mathematics is the present mathematical language of modern data science.

3. It Teaches the Proof of Techniques and Enhances Mathematical Reasoning

Discrete mathematics is one of the subject areas that can improve a student’s thinking abilities. You will not only think flexibly but also be more creative.

The area has few formulas that you need to memorize unlike in continuous mathematics. You only need to master important concepts and apply them in other areas of study.

The absence of geometry in discrete mathematics is one of the reasons why it promotes creative mathematical thinking.

There are no series of formulas that you will need to remember every time in class. The same case applies to proof of exercises and other definitions that you need to master in geometry.

Discrete math only involves fundamental concepts that you can easily master.

Is Discrete Math Useful?

As aforementioned, the significance of discrete mathematics in middle and high schools is gaining momentum. For instance, all mathematics competitions for this level of school have almost half of the questions focusing on discrete mathematics.

A good example is the America Mathematics Competition which has been dedicating about 40% of the questions to discrete mathematics.

This is because of the ability of these questions to have a positive impact on the thinking abilities of the student.

The usefulness of discrete mathematics is also evident in high-level mathematics contests.

All participants who do not have adequate knowledge of discrete mathematics always perform poorly in these competitions. But is it really hard?

Following this, course curriculums are now adapting and putting more emphasis on discrete mathematics. At least a third of the studies are now in discrete mathematics, especially in number theory and graph theory.

In the evolving technological society, discrete mathematics is a useful vehicle that can help you to achieve your goals. In the end, you will not only boast of good reasoning abilities but also amazing problem-solving skills.

You will be ready for any math-related career that needs good analytical and technical skills. Ideally, learners should start putting effort into discrete mathematics as early as the 6th grade.

This is the right stage to start learning fundamental discrete math. At this stage, a student can begin learning discrete geometry, probability, graph, and number theory.

Examples of Application for Discrete Math in the Real World

1. Programming

Discrete math is simply the mathematical language of computer programming. You will need a solid knowledge of discrete mathematics to design good algorithms which are necessary for programming.

The steps that are necessary for an algorithm to complete will need a good knowledge of discrete mathematics. As a building necessity for logical thinking, this branch of mathematics is an essential tool for any computer programmer.

It is equally applicable in software design specifications and other mathematically practical applications.

2. Logistics

Logistics is work that involves the organization of the flow of goods, services, and information. These procedures cannot be practical without the application of discrete mathematics.

In logistics, graphs are widely used and this is a subject that is part of discrete math’s graph theory. This theory is necessary for solving complex logistical situations.

The problem can be split into graphs that have several lines and nodes. A cursory analysis of these graphs makes it easy to solve logistical situations when determining appropriate shipping routes.

3. Cryptography

Cryptography is a sensitive field that involves the creation of security structures. These structures involve the formation of passwords for electronic systems such as computers.

To be an expert in this field, solid background knowledge in discrete mathematics is mandatory.

The knowledge of number theory that is studied in discrete mathematics will help you to create numerical passwords.

As a cryptographer, you can effortlessly encryption methods or provide effective passwords if you are good in number theory.

Best Discrete Math Books

1. Discrete Mathematics with Application

If you need a good explanation of complex concepts in discrete mathematics, this is the book for you.

Written by Susanne Epp, the book covers recursive thinking, combinatorics, computability, and algorithm analysis among other topics.

2. Discrete Mathematics; An open Introduction

This book covers all the exciting themes in discrete mathematics. Apart from counting, you will also learn graph theory, sequences, and logic.

3. Practical Discrete Mathematics

A look at this book introduces you directly to discrete math principles necessary for machine learning and computer science. As the perfect book for beginners, at the end of it, you will be able to tackle algorithm development.

4. 2000 Solved Problems in Discrete Mathematics

As the title suggests, there are thousands of problems you can work on if you opt for this book. However, you need to be familiar with the basics of discrete mathematics before you can start reading the book.

It is a good book for students with experience who want to put their skills into practice.

Is discrete math calculus?

Since calculus is essential in continuous mathematics, you don’t need to understand discrete math. However, your tutor might require calculus in some discrete math homework problems where necessary.

Is discrete math useful for computing?

Virtually every important area of computing needs an indispensable foundation in discrete math. Because modern computer programming is based on graph theory and combinatorics, discrete math is very important.

Is discrete math algebra?

Discrete math is algebra because it partially involves separate elements that deploy algebra when solving problems.