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Introduction to Discrete Mathematics

LESSON 1: WHAT IS DISCRETE MATHEMATICS?
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The World of Integers

Discrete mathematics is the study of countable things.
It is not a branch of mathematics.
Rather, it is a group of branches with a common property: the study of discrete objects.
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Main Questions

Discrete mathematics aims to answers a variety of problems:
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  • What is known?
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  • What can be summarized?
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  • What can be computed?
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    Information

    Logic, discrete structures and graphs all allow the verification and storage of information.
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    Summarization

    Combinatorics, set theory and mathematical proofs allow the study of emerging properties.
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    Computation

    From a set of rules, iterative and recursive computations can be done and verified.
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    History

    Integers were first used with tally marks (3400 BC), and negative numbers were introduced with the Chinese number rod system (200 BC).
    Many mathematicians have had an important influence on modern discrete mathematics, including:
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    Discrete Mathematics Today

    Nowadays, discrete mathematics is strongly associated with technology.
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    Why Study Discrete Mathematics?

    High-school mathematics mostly overlooks discrete mathematics in favor of continuous mathematics.
    Reasons to study discrete mathematics:
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  • Calculate discrete phenomena efficiently
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  • Understand computation
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  • Use and store information
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  • Develop your mathematical reasoning
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    About This Course

    This course is designed to be an introduction to many fields of mathematics and computer science.
    This exploration is facilitated by the use of Wolfram Language, a language with discrete computation as its core philosophy.
    This course is separated into seven small sections:
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  • Logic
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  • Discrete Structures
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  • Counting
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  • Algorithms
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  • Proofs and Recursion
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  • Recurrence Relations
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  • Graphs
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    Who Is This Course For?

    The Wolfram U course on discrete mathematics is most useful for:
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    Summary

    As a mathematical subject, discrete mathematics is essentially the study of countable objects.
    As a professional skill, it helps you analyze, store and compute information, all to conquer many tasks.
    As an educational hurdle, it provides the toolset necessary to excel in computer science courses.
    In the next lesson, the course will begin with the two simplest discrete values: true or false.
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