Discrete Mathematics from Udemy

WHAT IS THIS COURSE ABOUT?

Discrete Mathematics (DM), or Discrete Math is the backbone of Mathematics and Computer Science. DM is the study of topics that are discrete rather than continuous, for that, the course is a MUST for any Math or CS student. The topics that are covered in this course are the most essential ones, those that will touch every Math and Science student at some point in their education. The goal of this course is to build the mathematical foundation for computer science courses such as data structures, algorithms, relational and database theory, and for mathematics courses such as linear and abstract algebra, combinatorics, probability, logic and set theory, and number theory.

Discrete Mathematics gives students the ability to understand Math language and based on that, the course is divided into the following sections:

Sets
Logic
Number Theory
Proofs
Functions
Relations
Graph Theory
Statistics
Combinatorics
and Sequences and Series

I know visually seeing a problem getting solved is the easiest and the most direct way for a student to learn so I designed the course keeping this in mind. The materials are delivered through videos to make complex subjects easy to comprehend. More details on certain lessons are delivered through text files to provide more explanations or examples. The course is taught in plain English, away from cloudy, complicated mathematical jargon, to help the student learn the material rather than getting stuck on fancy words.

HOW DO I LEARN BETTER?

There are quizzes after each lecture so you can test your knowledge and see how much of the material has sunk in. I suggest you go through each lesson several times to better understand the content.

What's inside

Learning objectives

You will learn and develop the ability to think, read and write abstractly and mathematically.
You will learn the fundamentals of set theory including set builder notation, and set operations and properties.
You will learn tautologies, contradictions, de morgan's laws in logic, logical equivalence, and formulating quantified statements.
You will lear how to create truth tables and tell the falsehood and truthfulness of a compound statements.
You will know how to write, read and prove mathematical statements using a variety of methods.
You will understand boolean expressions, black boxes, logical gates and digital circuits.
You will understand the fundamental theorem of arithmetics, modular arithmetic, and learn how to find gcd & lcm.

You will acquire a solid foundation in functions, function composition & combination, bijective and inverse functions.
You will learn how to find equivalence relations and equivalence classes.
You will learn essential concepts in statistics and combinatorics.
You will master arithmetic and geometric sequences, and partial sums.
You will learn the fundamental concepts in graph theory like incidence and adjacency matrices, walks, eccentricity, connectedness, and ore's theorem.
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You will learn and develop the ability to think, read and write abstractly and mathematically.
You will learn the fundamentals of set theory including set builder notation, and set operations and properties.
You will learn tautologies, contradictions, de morgan's laws in logic, logical equivalence, and formulating quantified statements.
You will lear how to create truth tables and tell the falsehood and truthfulness of a compound statements.
You will know how to write, read and prove mathematical statements using a variety of methods.
You will understand boolean expressions, black boxes, logical gates and digital circuits.
You will understand the fundamental theorem of arithmetics, modular arithmetic, and learn how to find gcd & lcm.
You will acquire a solid foundation in functions, function composition & combination, bijective and inverse functions.
You will learn how to find equivalence relations and equivalence classes.
You will learn essential concepts in statistics and combinatorics.
You will master arithmetic and geometric sequences, and partial sums.
You will learn the fundamental concepts in graph theory like incidence and adjacency matrices, walks, eccentricity, connectedness, and ore's theorem.
Show more
Show less

Syllabus

Sets

Intro

Definition of a Set

Quiz

Number Sets

Set Equality

Set-Builder Notation

Types of Sets

Subsets

Power Set

Ordered Pairs

Cartesian Products

Cartesian Plane

Venn Diagrams

Set Operations (Union, Intersection)

Properties of Union and Intersection

Set Operations (Difference, Complement)

Properties of Difference and Complement

De Morgan’s Law

Partition of Sets

Extra Practice Problems

Logic

Introduction

Statements

Compound Statements

Truth Tables

Examples

Logical Equivalences

Tautologies and Contradictions

De Morgan’s Laws in Logic

Logical Equivalence Laws

Conditional Statements

Negation of Conditional Statements

Converse and Inverse

Biconditional Statements

Digital Logic Circuits

Black Boxes and Gates

Boolean Expressions

Truth Tables and Circuits

Equivalent Circuits

NAND and NOR Gates

Quantified Statements - ALL

Quantified Statements - THERE EXISTS

Negations of Quantified Statements

Number Theory

Parity

Divisibility

Prime Numbers

Prime Factorization

GCD & LCM

Proofs

Terminologies

Direct Proofs

Proofs by Contrapositive

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Introduces fundamental concepts in abstract Mathematics and Computer Science

Provides a solid foundation for future studies in Math and Science

Taught in plain English, making it accessible to students with varying levels of mathematical background

Emphasizes hands-on learning through quizzes and exercises

Suitable for beginners with little to no prior knowledge in Discrete Mathematics

Covers a wide range of topics, providing a comprehensive overview of Discrete Mathematics

Reviews summary

Easy-to-understand discrete math

According to students, Discrete Mathematics is considered easy to understand. Students appreciate that the instructor provides clear explanations and examples. Students say it's well-paced and suitable for beginners.

Instructor provides clear explanations.

"อธิบายพร้อมยกตัวอย่างได้ดีและละเอียด"

Course is well paced.

"ค่อยๆสอนไปเรื่อยๆ"

Instructor provides good examples.

"อธิบายพร้อมยกตัวอย่างได้ดีและละเอียด"

Suitable for beginners.

"ค่อยๆสอนไปเรื่อยๆ สอนเข้าใจง่ายๆ สำหรับคนไม่มีพื้นฐานก็เรียนได้"

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Discrete Mathematics with these activities:

Review mathematical symbols and notation

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Brings back to mind important concepts that are essential to understanding discrete mathematics.

Browse courses on Mathematical Notation

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Re-familiarize yourself with mathematical symbols for sets, logical operators, and functions.
Review common mathematical notation. This includes things like sigma notation, summation notation, and product notation.
Get comfortable with the language of mathematics as it relates to logic and proofs.

Read Discrete Mathematics and Its Applications

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Provides a comprehensive overview of the core concepts and applications of discrete mathematics.

View Discrete Mathematics and Its Applications (in... on Amazon

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Read the chapter introductions to get an overview of the main topics covered.
Go through the examples and exercises to reinforce your understanding.
Solve the practice problems at the end of each chapter to test your knowledge.

Solve practice problems from Discrete Mathematics textbooks

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Provides opportunities to practice solving problems and apply the concepts learned in the course.

Browse courses on Problem Solving

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Choose a textbook with a good collection of practice problems.
Start with easier problems and gradually move on to more challenging ones.
Check your solutions against the answer key to identify any errors.
Review the solutions to understand the correct approach and reasoning.

Four other activities

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Follow online tutorials on Discrete Mathematics

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Provides structured guidance and explanations to supplement the course material.

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Search for reputable websites or platforms that offer video tutorials on Discrete Mathematics.
Choose tutorials that align with the topics covered in the course.
Watch the videos attentively and take notes on key concepts.
Pause the videos when needed to reflect and reinforce your understanding.
Complete any practice exercises or quizzes associated with the tutorials.

Create concept maps or mind maps for Discrete Mathematics topics

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Helps organize and visualize the relationships between different concepts in Discrete Mathematics.

Browse courses on Concept Mapping

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Start by identifying the main concepts in a particular topic.
Use branches or nodes to connect related concepts and ideas.
Add labels and annotations to explain the connections and relationships.
Review your concept map or mind map to reinforce your understanding.

Participate in online forums or discussion groups for Discrete Mathematics

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Provides opportunities to engage with peers, ask questions, and share insights.

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Find online forums or discussion groups dedicated to Discrete Mathematics.
Introduce yourself and ask questions related to the course material.
Respond to questions or comments from other participants.
Share your own insights and understanding to help others.

Organize and review course materials

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Helps students stay organized and keeps the course material fresh in their minds.

Browse courses on Organization

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Keep a dedicated notebook or binder for the course.
File lecture notes, handouts, and assignments in an organized manner.
Review your notes regularly to reinforce your understanding.
Create flashcards or summaries of key concepts for quick reference.

Career center

Learners who complete Discrete Mathematics will develop knowledge and skills that may be useful to these careers:

Data Scientist

Data Scientists are responsible for collecting, analyzing, and interpreting data to extract meaningful insights. Discrete Mathematics provides a strong foundation for this role, as it covers topics such as set theory, logic, number theory, and graph theory. These topics are essential for understanding the data structures and algorithms used in data science. Additionally, Discrete Mathematics helps develop the critical thinking and problem-solving skills necessary for success as a Data Scientist.

See salaries and explore the career path for Data Scientist

Software Engineer

Software Engineers design, develop, and maintain software applications. Discrete Mathematics is a valuable asset for Software Engineers, as it helps them understand the underlying principles of computer science. The course covers topics such as sets, logic, functions, relations, and graph theory, which are all essential for understanding the design and implementation of software systems. Additionally, Discrete Mathematics helps Software Engineers develop the analytical and problem-solving skills necessary for success in this field.

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Computer Programmer

Computer Programmers write and maintain the code that powers computer applications. Discrete Mathematics provides a strong foundation for this role, as it covers topics such as sets, logic, functions, and graph theory. These topics are essential for understanding the data structures and algorithms used in programming. Additionally, Discrete Mathematics helps Computer Programmers develop the critical thinking and problem-solving skills necessary for success in this field.

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Actuary

Actuaries use mathematical and statistical techniques to assess risk and uncertainty. Discrete Mathematics is a valuable asset for Actuaries, as it helps them understand the underlying principles of probability and statistics. The course covers topics such as sets, logic, number theory, and combinatorics, which are all essential for understanding the actuarial models used to assess risk. Additionally, Discrete Mathematics helps Actuaries develop the analytical and problem-solving skills necessary for success in this field.

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Statistician

Statisticians collect, analyze, and interpret data to extract meaningful insights. Discrete Mathematics provides a strong foundation for this role, as it covers topics such as sets, logic, number theory, and combinatorics. These topics are essential for understanding the statistical models used to analyze data. Additionally, Discrete Mathematics helps Statisticians develop the critical thinking and problem-solving skills necessary for success in this field.

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Operations Research Analyst

Operations Research Analysts use mathematical and analytical techniques to improve the efficiency of organizations. Discrete Mathematics is a valuable asset for Operations Research Analysts, as it helps them understand the underlying principles of optimization and decision-making. The course covers topics such as sets, logic, number theory, and graph theory, which are all essential for understanding the models used to optimize operations. Additionally, Discrete Mathematics helps Operations Research Analysts develop the analytical and problem-solving skills necessary for success in this field.

See salaries and explore the career path for Operations Research Analyst

Cryptographer

Cryptographers design and implement algorithms to protect information from unauthorized access. Discrete Mathematics is a valuable asset for Cryptographers, as it helps them understand the underlying principles of cryptography. The course covers topics such as sets, logic, number theory, and combinatorics, which are all essential for understanding the algorithms used to encrypt and decrypt data. Additionally, Discrete Mathematics helps Cryptographers develop the analytical and problem-solving skills necessary for success in this field.

See salaries and explore the career path for Cryptographer

Financial Analyst

Financial Analysts use mathematical and statistical techniques to analyze financial data and make investment recommendations. Discrete Mathematics provides a strong foundation for this role, as it covers topics such as sets, logic, number theory, and combinatorics. These topics are essential for understanding the financial models used to analyze investments. Additionally, Discrete Mathematics helps Financial Analysts develop the critical thinking and problem-solving skills necessary for success in this field.

See salaries and explore the career path for Financial Analyst

Data Analyst

Data Analysts collect, analyze, and interpret data to extract meaningful insights. Discrete Mathematics provides a strong foundation for this role, as it covers topics such as sets, logic, number theory, and combinatorics. These topics are essential for understanding the data structures and algorithms used in data analysis. Additionally, Discrete Mathematics helps Data Analysts develop the critical thinking and problem-solving skills necessary for success in this field.

See salaries and explore the career path for Data Analyst

Business Analyst

Business Analysts use mathematical and analytical techniques to improve the efficiency of businesses. Discrete Mathematics provides a strong foundation for this role, as it covers topics such as sets, logic, number theory, and combinatorics. These topics are essential for understanding the models used to analyze business processes. Additionally, Discrete Mathematics helps Business Analysts develop the critical thinking and problem-solving skills necessary for success in this field.

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Teacher

Teachers educate students in a variety of subjects. Discrete Mathematics may be useful for Teachers, as it can help them understand the underlying principles of mathematics. The course covers topics such as sets, logic, number theory, and graph theory, which are all essential for understanding the concepts taught in mathematics classes. Additionally, Discrete Mathematics can help Teachers develop the critical thinking and problem-solving skills necessary for success in this field.

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Economist

Economists use mathematical and statistical techniques to analyze economic data and make policy recommendations. Discrete Mathematics may be useful for Economists, as it can help them understand the underlying principles of economics. The course covers topics such as sets, logic, number theory, and combinatorics, which are all essential for understanding the models used to analyze economic data. Additionally, Discrete Mathematics can help Economists develop the critical thinking and problem-solving skills necessary for success in this field.

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Biostatistician

Biostatisticians use mathematical and statistical techniques to analyze biological data and make medical recommendations. Discrete Mathematics may be useful for Biostatisticians, as it can help them understand the underlying principles of statistics. The course covers topics such as sets, logic, number theory, and combinatorics, which are all essential for understanding the models used to analyze biological data. Additionally, Discrete Mathematics can help Biostatisticians develop the critical thinking and problem-solving skills necessary for success in this field.

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Market Researcher

Market Researchers use mathematical and statistical techniques to analyze market data and make marketing recommendations. Discrete Mathematics may be useful for Market Researchers, as it can help them understand the underlying principles of statistics. The course covers topics such as sets, logic, number theory, and combinatorics, which are all essential for understanding the models used to analyze market data. Additionally, Discrete Mathematics can help Market Researchers develop the critical thinking and problem-solving skills necessary for success in this field.

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Psychologist

Psychologists use mathematical and statistical techniques to analyze psychological data and make recommendations for treatment. Discrete Mathematics may be useful for Psychologists, as it can help them understand the underlying principles of statistics. The course covers topics such as sets, logic, number theory, and combinatorics, which are all essential for understanding the models used to analyze psychological data. Additionally, Discrete Mathematics can help Psychologists develop the critical thinking and problem-solving skills necessary for success in this field.

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