A First Course in Abstract Algebra: Group Theory,Ring Theory

Name: A First Course in Abstract Algebra: Group Theory,Ring Theory
Rating: 3.3 (44 reviews)

(UPDATED) Modern Algebra for Group Theory, Linear Algebra, Discrete Mathematics, Cryptography, Complex Analysis Students

Created byMath Reddy

Last updated 9/2024

English

What you'll learn

[ Updated ( August - 2024) with new Video lectures ] Abstract Algebra - Group Theory and Ring Theory
Group theory with all types of groups, The Klein Four-Group, including Sub group, Commutative group, Cyclic Group, Permutation group
Ring theory with Zero Divisors, Commutative Ring, Ring with Zero Divisors, Division Ring or Skew Field, Field
What is Closure Property?
What is Associative Property?
What is Identity Property?
What is Inverse Property?
What is Commutative Property?
Function Definition,Domain, Co-domain and Range of function
Definition of group: When Set is called as Group?
Definition of Order of the group
What is Subgroup?
What does it mean by Commutative group?
All Theorems Statements on Cyclic Group
All Theorems Statements on Abilean Group
Fundamental theorem of Homomorphism
Quick revision by downloading Handwritten notes and Flash cards
What is Ring?
What does it mean by Ring with Unity?
What is Commutative Ring?
Definition of Ring with Zero Divisors
What is Division Ring or Skew Field?
Ring Theory : What is Field?

Course content

14 sections • 86 lectures • 6h 23m total length

30-Day Money-Back Guarantee and 3 more benefits1:04
Unlocking the Power of Abstract Algebra - Download PDF0:03
• Abstract algebra is a rich and powerful field of mathematics that explores abstract algebraic structures like groups and rings. • In this presentation, we'll dive into the key concepts and principles of abstract algebra, starting with an overview of the field and its modern applications. • We'll cover the fundamental definitions and properties of groups and rings, and explore how these abstract structures are used in various domains, including physics. • Understanding the core ideas of abstract algebra is crucial for many advanced areas of mathematics and its real-world applications. • This introductory slide sets the stage for the rest of the presentation, where we'll unpack the depth and versatility of this important branch of mathematics.
part 11:43
Explore the core ideas of abstract algebra by studying groups, rings, and fields, and see how these structures underpin modern algebra, computations, and applications in mathematics, computer science, and physics.
part 22:46
Part 32:11
Part 41:53
Explore normal subgroups, their invariance under conjugation, and factor (quotient) groups, and introduce rings as two binary operations, addition and multiplication, covering key properties like closure, associativity, identities, and inverses.
Part 51:50
Download PDF on What is Abstract Algebra and it's Applications0:02
Abstract Algebra : A to Z TOPICS - IN THIS COURSE0:42
Download PDF on topics Dihedral Groups (Group of Symmetries) and many more.0:02
We'll dive into specific algebraic structures like dihedral groups, general and special linear groups, and the additive group of integers modulo n.
We'll also cover the Klein four-group, group homomorphisms and isomorphisms, Lagrange's theorem, and the fundamental theorem of finite abelian groups
PDF : Download the Abstract Algebra PDF from the attached file in the Resource0:03
Download the New Resource0:01

What is Abstract Algebra?0:23
What is Abstract Algebra ?2:14
Explore abstract algebra's study of groups, rings, and fields, focusing on symmetries, dihedral groups, general and special linear groups, additive groups modulo n, and Klein four group.
Abstract Algebra: A Journey into the Foundations of Mathematics
Special Notations in Abstract Algebra0:32
what is Binary Operation in abstract algebra?0:09
What is Binary Operation in Abstract algebra7:39
2 Examples on Commutative Binary operation6:52
Dear students,
2 examples are solved in this video.
And you can download this video also.
Thank you
Choose the correct answer
Algebraic Structure of a Set
Closure Property in abstract algebra2:46
Basically,its operation like addition and subtraction on elements of a set
How to understand Closure Property in Group Theory?4:11
Explore the closure property in group theory, showing how a group operation keeps results inside the set, with numeric examples to illustrate when closure holds.
Associative Property1:35
Discover how the associative property makes addition and multiplication independent of grouping, with concrete examples like five plus six plus seven.
How to understand Associative Property in Group Theory?8:37
Explore how the associative property works in group theory by testing binary operations on numbers, showing addition is associative while subtraction is not.
Download Flash Card on Identity Property
Identity Property4:25
How to explain Identity Property in detail?8:46
The lecture clarifies the identity property in a binary operation, defines an identity element, and shows how to verify it for all elements in a set using concrete numeric examples.
What is Monoid?8:56
A monoid is a set with a binary operation that is closed, associative, and has an identity element.
Inverse Property3:52
How to explain Inverse Property in detail?8:15
Download Flash Card on Inverse Property
Commutative Property2:37
Discover the commutative property of addition and multiplication, where order does not affect results, as 6+7 = 7+6. See substitutions and fractional examples within abstract algebra.

What is Semi Group?0:04
What is Semi Group in Group theory of Abstract algebra13:50
When Set is called as Group?0:02
The definition of a group1:26
Special Linear Group, the Group C^n, and the additive Group of Integers Modulo2:31
How to explain Group in detail?6:01
Is (Z, +) Group or Not?11:10
Examples of Group - Part 1
Examples of Group in Abstract Algebra5:44
Examples of Group - Part 24:14
The Klein Four-Group2:16
Explore the Klein four group, an abelian group with four elements. Identify its identity, three involutions, subgroups, and isomorphisms in symmetry.
Sub Group1:16
Identify subgroups as subsets of a group that are closed under the same binary operation and form a group.
Order of the group1:57
Order of element in group theory4:25

Solved example problems on Even and Odd Permutations7:58
Functions0:05
Functions Part - 1 in Mathematics12:17
Functions Part - 2 in Mathematics14:42
Solved Problem 19:20
Solved Problem 28:17
Evaluate f(x) = x^2 + 5 by substituting at x = 1, 2, and 6 to reveal values such as 6, 9, and 41.
How to define Permutation Group?11:06
Learn how to define a permutation group by considering one-to-one mappings on a set and the way these permutations combine to form a group.
Solved Problem on How to find Product of two Permutations?4:40

What is Cyclic Group and Generator of Cyclic Group?0:53
What is Cyclic Group and Generator of Cyclic Group?3:09
How to find the Generator of a Cyclic group?8:37
Learn how to find a generator of a cyclic group, test whether a given element generates the entire group, and identify generators in small examples such as {0,1,2,3} under addition.
Solved Problem on finding Generator of Cyclic Group12:39
Download Notes on Important Statements

Requirements

Be able to understand Set definition
Be able to understand types of numbers

Description

UPDATED! Conquer Abstract Algebra: Master Groups & Rings with This Comprehensive Guide

Stay ahead of the curve: New lectures added in August - 2024, with more on the way!
Unlock the power of Abstract Algebra with this in-depth course, designed for mastery! Dive deep into Group & Ring Theory, conquering complex concepts like binary operations, subgroups, and homomorphisms with crystal-clear explanations and engaging video lectures.

Struggling with Abstract Algebra? Feel overwhelmed by Group Theory? Aiming to ace your exams? This course is your ultimate weapon.

Here's why you'll love it:

Master the fundamentals: Demystify key Group Theory concepts like subgroups, order, homomorphisms, and more. Grasp the intricacies of Ring Theory, mastering rings, fields, and division rings.
Learn at your own pace: Lifetime access allows you to progress comfortably, revisiting lectures and practicing at your convenience.
Interactive learning: Quizzes and downloadable resources boost your understanding and provide valuable self-assessment tools.
Unleash the power of mathematics: This course isn't just about formulas; it's about unlocking the language of mathematics, opening doors to advanced topics like Linear Algebra, Discrete Mathematics, and beyond.
Real-world applications: Apply your knowledge in diverse fields like engineering, physics, and computer science. Abstract Algebra isn't just theoretical; it's powerful and practical.
Udemy learning advantage: Gain the edge with lifetime access to course updates, fast and friendly support, and a prestigious Udemy Certificate of Completion to showcase your achievement.

Don't wait to conquer Abstract Algebra! Enroll today and transform your understanding of this fascinating branch of mathematics.

Bonus: Download a free Abstract Algebra PDF book to enhance your learning journey!

Instructor: Kishore Reddy, your dedicated guide to mastering Abstract Algebra.

Who this course is for:

Math majors
Beginners of Bachelors Degree Students
College Level Students
University Level Students
Anyone who want to learn higher level math
Any student who want to learn Abstract Algebra
Any student who want to learn Linear Algebra
Calculus Students
Algebra Students
And any Math student
Cryptography students
Logic
Ring Theory
Fields

A First Course in Abstract Algebra: Group Theory,Ring Theory

What you'll learn

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Course content