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

Discrete Mathematical Algorithms and Data Structures-02-02.png

momoexp4.tar.gz

java and C++

OnlyPython

OnlyJava

OnlyCplusplus

OnlyC

JavaLang3

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

# Logical expressions

We can create a compound expression by combining logical operations. De Morgan’s laws are based on this paradigm. Consider the following expression:

```java
not(a or b)
```

The compound expression above is true or false depending on different combinations. If `a` and `b` are false, the negation of subexpression `(a or b)` is true. If any one of them is true, then the value will be false, and this combination might take different shapes according to the truth table.

A major part of discrete mathematical operations is based on Boolean algebra and the associated logical expressions. To recap, we need to remember that there are three basic logical operators. The following symbols/operators are used in Python and other languages:
- Conjunction: `and` in Python; `&&` in Java, C++, C, Dart, and PHP
- Disjunction: `or` in Python; `||` in Java, C++, C, Dart, and PHP
- Negation: `not` in Python; `!` in Java, C++, C, Dart, and PHP


Logical operators manipulate the logical values. In the same way, **relational operators** also manipulate the logical values.
There are two kinds of relational operators: equality and order.

The two **equality operators** are:
- `==` 
- `!=` 

The `==` operation is true when the two operands have the same value. In the same way, the `!=` operation is true when two operands have different values.

The **ordering operators** test the relative size of two values. They are: 

- `<` (less than)
- `>` (greater than)
- `>=` (greater than or equal to)
- `<=` (less than or equal to)


Explore the logical operators in Python and their use as short-circuit evaluators.

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

Logical Expression and Short-Circuit Evaluation

Logical expressions