Discrete Mathematics

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Key Features

Discrete Mathematics is the study of mathematical structures that are discrete rather than continuous.

Discrete Mathematics is concerned with the investigation of mathematical structures

It deals with objects that can have multiple distinct values.

It's also referred to as Decision Mathematics or Finite Mathematics.

It is the study of fundamentally discrete mathematical structures that do not require the concept of continuity.

In discrete mathematics, the set of objects studied can be finite or infinite.

Discrete Mathematics Homework and Assignment Help

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Key Topics

    Sets, Relations, and Functions

    a) Sets: A set is a collection of objects or numbers. The elements of a set can be the same or different. For example, the set of positive integers 1, 2, 3 and 4 are all different while they are still part of the same set.

    There are two different ways of representing a set. They include:
    Set-builder notation: This is a way of representing a set by defining a specific property that members of the set have in common. Set-builder notation is described as
    A={x:p(x)}
    Our assignment helpers will help you write a set-builder notation for any given collection of objects or numbers. Set-builder notation is also called set comprehension.

    b) Relations: Relations are a way of describing the relationship between objects of the same set or between objects of two or more sets. Relations can be very simple or complex.

    We will help you:
    • Learn types of relations
    • How to represent relations using graphs in your assignment

    c) Functions: Functions are a way of describing the relationship between one or more sets. Functions can be very simple or complex.

    A function is defined as f: X→Y where f is the function, X is the domain and Y is the Codomain of function ‘f.
    Functions can be represented using a graph or an equation. In this section, we will help you learn how to represent functions using graphs in your assignment.

    d) Mathematical Logic: Mathematical logic is the study of the principles of reasoning. It is used in all areas of mathematics, as well as many other fields, such as computer science and philosophy.

    e) Propositional Logic: Propositional logic is a branch of mathematical logic that deals with the study of propositions and their truth values. A proposition is an assertion that can be either true or false. Propositional logic studies the properties of such assertions and how they can be combined using logical connectives to form complex statements.

    f) Predicate Logic: A predicate specifies the relationship between one or more variables and values from a given domain. A predicate with variables can be made into a proposition by assigning values to the variables or quantifying them.

    g) Rules of Inference: Rules of Inference tell us how to construct arguments from statements we already have.

    Group Theory: Group theory is a branch of mathematics that studies the properties of groups. A group is a set of elements with an operation that combines any two elements with another element in such a way that the result is independent of order. Group Theory has applications in many areas, including computer science.

    Counting Theory: Counting theory is a branch of mathematics that studies the properties and relationships between numbers. Its goal is to develop methods for counting or enumerating discrete objects, such as the number of different arrangements of a deck of cards. Counting theory has many applications in computer science, including algorithms for searching through lists and tree-based data structures like binary search trees.

    Probability: Probability studies the likelihood that an event will occur. It’s important because it underlies many computer science algorithms, such as those for finding the shortest path between two points in a graph, sorting data, and searching through lists of items. Probability also provides a theoretical foundation for statistics, which is used to analyze real-world data sets.

    Mathematical Induction and Recurrence Relations

    Mathematical induction and recurrence relations are two methods for proving results about lists of numbers. They’re both useful for proving the properties of algorithms that iterate through a sequence of values (like those used in sorting and searching).

    a) Graph Theory: Graphs consist of points, called nodes or vertices, connected by lines.

    Graph theory is part of many disciplines, including mathematics and computer science.

    Graph theory has many applications in computer science, including for the analysis of algorithms and data structures. It’s also used to model networks, like social networks or the internet.

    b) Boolean Algebra: Boolean algebra is a branch of mathematics that describes logical operations on binary values. It’s used in computer science to analyze algorithms and data structures, as well as in coding theory and cryptography. The most common applications of Boolean algebra include logic gates and circuits, which are fundamental components of electronic devices like computers and cell phones.

    What Is The Best Way To Learn Discrete Mathematics?

    Solving as many questions as possible is the best way to learn Discrete Mathematics. Begin by devoting time to graph theory and combinatorics early on. What you must do is as follows:
    • Make a habit of working through logic and proof
    • Avoid making common logical mistakes
    • Verify solutions using mathematical induction
    • Participate in classes and lectures
    • Begin solving combinatorial problems as soon as possible
    • Take note of the notation
    • To answer correctly, pay attention to the exact wording of each question.
    Aside from that, you must be under the supervision of qualified professionals such as ourselves. It is critical to seek discrete math assistance as soon as possible in order to resolve any doubts that may arise. As a result, you should rely on our knowledgeable experts, who are adept at handling all student-related issues and making learning enjoyable.

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