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Discrete Mathematics explores mathematical structures and relationships with distinct, separate values. It's fundamental for computer science, cryptography, algorithms, and decision-making in real-world scenarios.

£39.99 inc. VAT
Course Access

1 year

Last Updated

December 27, 2023

Students Enrolled

4

Course Duration

18 hours, 57 minutes

Course Instructor
Certification
The Discrete Mathematics course provides a foundational exploration of mathematical concepts crucial for computer science and various branches of discrete structures. The curriculum encompasses a diverse array of topics, including Sets, which lay the groundwork for understanding collections of objects, Logic, emphasizing the principles of reasoning and deduction, and Number Theory, exploring properties and relationships of integers. Students delve into Proofs, honing their skills in constructing logical arguments to validate mathematical statements. Functions and Relations are studied to comprehend mappings and connections between elements, while Graph Theory extends this understanding to analyse networks and relationships graphically. The course introduces Statistics to familiarise students with data analysis and probability. Combinatorics delves into counting and arrangement principles, and Sequence and Series explore ordered lists and summation. By addressing these fundamental areas, the Discrete Mathematics course equips students with the analytical and problem-solving tools essential for applications in computer science and various mathematical disciplines.

You will have the following skills after completing this course:

  • You will learn and develop the ability to think, read and write abstractly and Mathematically.
  • The fundamentals of Set Theory including set builder notation, and set operations and properties.
  • Tautologies, contradictions, De Morgan's Laws in Logic, logical equivalence, and formulating quantified statements.
  • Learn how to create truth tables and tell the falsehood and truthfulness of a compound statement.
  • 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.
  • How to find equivalence relations and equivalence classes.
  • Essential concepts in Statistics and Combinatorics.
  • Master arithmetic and geometric sequences, and partial sums.
  • You will learn the fundamental concepts in Graph Theory like incidence and adjacency matrices, walks, eccentricity, hamiltonian paths and circuits, connectedness, and Ore's Theorem.

Who will benefit from this course?

A Discrete Mathematics course is beneficial for a wide range of students and professionals from various fields. Here are some groups of people who can benefit from studying Discrete Mathematics:
  1. Computer Science Students:Discrete Mathematics forms the theoretical foundation for many computer science concepts, including algorithms, data structures, and computer networks. It is crucial for understanding topics such as graph theory, combinatorics, logic, and set theory, which are fundamental to computer science.
  2. Mathematics Students:Discrete Mathematics is a branch of mathematics, and students studying pure mathematics or applied mathematics can gain a deeper understanding of mathematical structures and reasoning through this course.
  3. Information Technology Professionals:Professionals working in the field of information technology, software development, and programming can benefit from Discrete Mathematics as it provides the theoretical background for efficient algorithm design and analysis.
  4. Engineering Students:Many engineering disciplines, especially those related to computer engineering, electrical engineering, and telecommunications, require a strong foundation in Discrete Mathematics.
  5. Data Scientists and Analysts:Understanding discrete structures and logic is essential for data scientists and analysts, especially when dealing with discrete data and algorithms for data manipulation.
  6. Cryptography and Security Professionals:Cryptography relies heavily on discrete mathematical concepts, and individuals working in the field of information security can benefit from a solid understanding of Discrete Mathematics.
  7. Business and Economics Students:Discrete Mathematics is used in optimisation problems and decision-making, making it relevant for students studying business, economics, and operations research.
  8. Educators and Researchers:Teachers, professors, and researchers in mathematics and computer science can use the knowledge gained from Discrete Mathematics to contribute to their respective fields and enhance their teaching methods.
  9. Anyone Interested in Logical Reasoning:The course helps develop strong logical reasoning skills, which are valuable in various aspects of life, including problem-solving and decision-making.
  10. Programming and Software Development Enthusiasts:Individuals interested in programming and software development can benefit from the course by gaining a deeper understanding of the theoretical underpinnings of algorithms and computational processes.
In summary, anyone with an interest in mathematics, computer science, information technology, engineering, data science, or related fields can find value in studying Discrete Mathematics. The concepts learned in this course provide a solid foundation for various areas of study and professional applications.

Why Should You Take This Online Course?

  • Expertly Designed and Delivered by Industry Experts: Developed and delivered by MIRAN FATTAH - B.S. in Mathematics & Geophysics
  • Immediate Recognition with an Instant E-Certificate: After finishing our online course, you will receive an instant E-certificate. This certification acknowledges your dedication and successful course completion, allowing you to demonstrate your newly gained knowledge and skills to potential employers, colleagues, or clients. The E-certificate validates your accomplishments immediately, raising your professional standing.
  • Convenient Online Learning Experience: Because our course is entirely online, you may learn at your own pace and convenience. The course materials are accessible from anywhere and anytime, making it ideal for people with hectic schedules. The curriculum is delivered via captivating videos and extensive reading materials, creating a dynamic and interactive learning experience.
  • Self-paced Learning for Maximum Progress: We recognise that everyone has various learning styles and time commitments. As a result, our online course provides self-paced study. You can work through the course materials independently, allowing for a more personalised learning experience. Our course supports your individual learning preferences, whether you like to immerse yourself in the information or take it step by step.
  • Laptop, tablet, and smartphone compatibility: Our online course is device-compatible to improve accessibility. Whether you choose a laptop, tablet, or smartphone, you may easily access and interact with the course contents. This adaptability allows you to learn on the go, incorporating your studies into your everyday routine and maximising your learning possibilities.

Career prospects after completing this course:

Completing a Discrete Mathematics course can open up a variety of career prospects, particularly in fields that require strong analytical and problem-solving skills. Here are some career paths where knowledge of Discrete Mathematics is highly valuable:
  1. Software Developer/Programmer:Discrete Mathematics is fundamental to algorithm design and analysis, making it crucial for software development. Understanding discrete structures helps in creating efficient and optimised algorithms.
  2. Computer Scientist/Computer Engineer:Professionals in these fields often work on designing and analysing algorithms, developing software systems, and working with computational structures, all of which benefit from a solid foundation in Discrete Mathematics.
  3. Data Scientist/Analyst:Discrete Mathematics is useful in data manipulation, combinatorics, and optimisation problems. Data scientists and analysts use these skills to analyse and derive insights from data.
  4. Network Engineer:Understanding graph theory, a branch of Discrete Mathematics, is essential for network engineers working on the design and optimisation of computer networks.
  5. Cryptographer/Security Analyst:Cryptography relies on mathematical concepts from Discrete Mathematics. Professionals in cybersecurity and cryptography use these principles to secure information and communications.
  6. Operations Research Analyst:Discrete Mathematics plays a key role in optimisation problems, which are often encountered in operations research. Professionals in this field use mathematical models to improve decision-making and resource allocation.
  7. Mathematician/Researcher:A strong background in Discrete Mathematics can lead to a career in pure mathematics or research. Mathematicians often study discrete structures and use them to solve theoretical problems.
  8. Educator/Teacher:Those with expertise in Discrete Mathematics can pursue a career in education, teaching the subject at the high school or college level.
  9. Business Analyst:Business analysts use mathematical modeling and logical reasoning, skills developed through Discrete Mathematics, to analyse business processes and make informed decisions.
  10. Artificial Intelligence/Machine Learning Engineer:Understanding algorithms and computational structures is essential for professionals working in AI and machine learning. Discrete Mathematics provides a strong foundation for these areas.
  11. Quality Assurance Analyst:Professionals in quality assurance and testing benefit from a strong logical and analytical mindset, which is cultivated through the study of Discrete Mathematics.
  12. Financial Analyst/Quantitative Analyst:Discrete Mathematics can be applied in finance for modeling and analysing discrete financial structures, making it relevant for individuals in financial analysis or quantitative analysis roles.
In summary, completing a Discrete Mathematics course enhances your analytical and problem-solving skills, making you well-suited for a variety of careers in technology, mathematics, research, education, and business. The versatility of the skills acquired in Discrete Mathematics opens doors to a wide range of professions where logical reasoning and mathematical modeling are valued.

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Course Content

    • Introduction 00:01:00
    • Definition of a Set 00:09:00
    • Number Sets 00:10:00
    • Set Equality 00:09:00
    • Set-Builder Notation 00:10:00
    • Types of Sets 00:12:00
    • Subsets 00:10:00
    • Power Set 00:05:00
    • Ordered Pairs 00:05:00
    • Cartesian Products 00:14:00
    • Cartesian Plane 00:04:00
    • Venn Diagrams 00:03:00
    • Set Operations (Union, Intersection) 00:15:00
    • Properties of Union and Intersection 00:12:00
    • Set Operations (Difference, Complement) 00:12:00
    • Properties of Difference and Complement 00:07:00
    • De Morgan’s Law 00:08:00
    • Partition of Sets 00:16:00
    • Introduction 00:01:00
    • Statements 00:07:00
    • Compound Statements 00:13:00
    • Truth Tables 00:09:00
    • Examples 00:13:00
    • Logical Equivalences 00:07:00
    • Tautologies and Contradictions 00:06:00
    • De Morgan’s Laws in Logic 00:12:00
    • Logical Equivalence Laws 00:03:00
    • Conditional Statements 00:13:00
    • Negation of Conditional Statements 00:10:00
    • Converse and Inverse 00:07:00
    • Biconditional Statements 00:09:00
    • Examples 00:12:00
    • Digital Logic Circuits 00:13:00
    • Black Boxes and Gates 00:15:00
    • Boolean Expressions 00:06:00
    • Truth Tables and Circuits 00:09:00
    • Equivalent Circuits 00:07:00
    • NAND and NOR Gates 00:07:00
    • Quantified Statements – ALL 00:08:00
    • Quantified Statements – THERE EXISTS 00:07:00
    • Negations of Quantified Statements 00:08:00
    • Introduction 00:01:00
    • Parity 00:13:00
    • Divisibility 00:11:00
    • Prime Numbers 00:08:00
    • Prime Factorization 00:09:00
    • GCD & LCM 00:17:00
    • Intro 00:06:00
    • Terminologies 00:08:00
    • Direct Proofs 00:09:00
    • Proofs by Contrapositive 00:11:00
    • Proofs by Contradiction 00:17:00
    • Exhaustion Proofs 00:14:00
    • Existence & Uniqueness Proofs 00:16:00
    • Proofs by Induction 00:12:00
    • Examples 00:19:00
    • Intro 00:01:00
    • Functions 00:15:00
    • Evaluating a Function 00:12:00
    • Domains 00:16:00
    • Range 00:05:00
    • Graphs 00:16:00
    • Graphing Calculator 00:06:00
    • Extracting Info from a Graph 00:12:00
    • Domain & Range from a Graph 00:08:00
    • Function Composition 00:10:00
    • Function Combination 00:09:00
    • Even and Odd Functions 00:08:00
    • One to One (Injective) Functions 00:09:00
    • Onto (Surjective) Functions 00:07:00
    • Inverse Functions 00:10:00
    • Long Division 00:16:00
    • Intro 00:01:00
    • The Language of Relations 00:10:00
    • Relations on Sets 00:13:00
    • The Inverse of a Relation 00:06:00
    • Reflexivity, Symmetry and Transitivity 00:13:00
    • Examples 00:08:00
    • Properties of Equality & Less Than 00:08:00
    • Equivalence Relation 00:07:00
    • Equivalence Class 00:07:00
    • Intro 00:01:00
    • Graphs 00:11:00
    • Subgraphs 00:09:00
    • Degree 00:10:00
    • Sum of Degrees of Vertices Theorem 00:23:00
    • Adjacency and Incidence 00:09:00
    • Adjacency Matrix 00:16:00
    • Incidence Matrix 00:08:00
    • Isomorphism 00:08:00
    • Walks, Trails, Paths, and Circuits 00:13:00
    • Examples 00:10:00
    • Eccentricity, Diameter, and Radius 00:07:00
    • Connectedness 00:20:00
    • Euler Trails and Circuits 00:18:00
    • Fleury’s Algorithm 00:10:00
    • Hamiltonian Paths and Circuits 00:06:00
    • Ore’s Theorem 00:14:00
    • The Shortest Path Problem 00:13:00
    • Intro 00:01:00
    • Terminologies 00:03:00
    • Mean 00:04:00
    • Median 00:03:00
    • Mode 00:03:00
    • Range 00:08:00
    • Outlier 00:04:00
    • Variance 00:09:00
    • Standard Deviation 00:04:00
    • Intro 00:03:00
    • Factorials 00:08:00
    • The Fundamental Counting Principle 00:13:00
    • Permutations 00:13:00
    • Combinations 00:12:00
    • Pigeonhole Principle 00:06:00
    • Pascal’s Triangle 00:08:00
    • Intro 00:01:00
    • Sequence 00:07:00
    • Arithmetic Sequences 00:12:00
    • Geometric Sequences 00:09:00
    • Partial Sums of Arithmetic Sequences 00:12:00
    • Partial Sums of Geometric Sequences 00:07:00
    • Series 00:13:00
    • Get Your Certificate & Transcript 00:00:00

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