Gain insights into connecting discrete mathematics with programming. Explore variables, expressions, data structures, and algorithm design to enhance your problem-solving and implementation skills.

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momoexp4.tar.gz

java and C++

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Discrete mathematics is the basis of several popular algorithms. This course shows the discreteness of data structures and algorithms. It can benefit programmers with a non-CS background looking to strengthen their foundations by connecting theoretical concepts with practical programming scenarios.

The course starts with discussing relating discrete mathematics with algorithms and data structures. You will have examples demonstrating variables, conditional expressions, and arrays as basic building blocks of programming. Then, you will use classes and objects to define and implement linear data structures. You will also learn about the binary tree traversals and templates and the topics of time complexity, set difference, and rearranging the values in a string.

By the end of the course, you will have a strong grasp of algorithm design, data structure implementation, and overall problem-solving.

Programming Discrete Math Concepts for Beginners

# Introduction to discrete mathematics

We need to understand what discrete mathematics is and its relationship with computer science before we learn how to implement discrete mathematical concepts in the various fields of computer science. 


As mentioned before, we’ve tried to implement discrete mathematical concepts in algorithms and data structures so we can better understand these concepts.

**Discrete mathematics (DM)** is a branch of mathematics. To be very particular, it’s the study of mathematical structures and objects that are discrete.

People, animals, chairs, and everything we see around us fall under this mathematical study. Why? Because they’re discrete and distinct. They’re not continuous. 



Real numbers consist of rational and irrational numbers or a continuous number line, which is not a part of discrete mathematics. Instead, natural numbers (N), like 0, 1, 2, etc., which are discrete, fall under this category. 
Discrete mathematical conceptions handle distinct and separated values. The opposite of discrete mathematics is **continuous mathematics**, such as calculus or Euclidean geometry. However, the Euclidean algorithm that helps us find the greatest common divisor of two positive natural numbers (GCD) is discrete. We’ll see an example in a minute.



Have you found any contradiction in the above statement? 

We’ve found one, and before proceeding further, we think we should make it clear. We’ve just said that real numbers, or a number line where there are infinite numbers between 1 and 2, cannot be discrete. However, when we declare positive natural numbers like 1, 2, and 3, which are distinct and separated, they belong to discrete mathematics. 1, 2, or 51, every positive natural number is also an actual number. Right? They belong to the number line. Right? Then where do we stand? We are contradicting ourselves.

Therefore, we can conclude that there’s no exact definition of discrete mathematics.

At best, we can say that the opposite of continuous mathematics is discrete mathematics.


In mathematics, several concepts exhibit noncontinuity; examples include set theory, as well as the x and y coordinates, which denote distinct quadrant positions without being continuously interconnected. We can think of the greatest common divisor (GCD) and the least common multiple (LCM). They’re always discrete.
Consider logical statements, such as true or false. They’re discrete. Also, the binary code 0s and 1s, the core concepts of computer science, are discrete.
Moreover, every new object in any object-oriented programming language is also discrete.
That’s why discrete mathematical concepts are closely related to every field of computer science. However, in this course, we’ll only consider algorithms and data structures.


# A simple algorithm

Let’s compute the number of molecules in a hydrocarbon. First, we’ll write a program and calculate the number of molecules using Java; then, we’ll use C++ to calculate the same number of molecules.

The two images below highlight the critical differences in how Java and C++ take input and show output.


Learn how discrete mathematics is related to programming.

Course Introduction

Programming Language and Boolean Algebra

Logical Expressions and Algorithms

Arrays and Discrete Mathematics

Classes, Objects, and Methods

Linear Data Structures

Tree, Algorithms, and Templates

Time Complexity

Propositional Logic

Combinatorics

Wrapping Up

What is Discrete Mathematics?

Introduction to discrete mathematics