Basics of Group Theory

Duration: 4 min

This video lesson is available to enrolled students.

Return to /learn/ISRO/discrete-mathematics/group-theory/closure-algebraic-structure-associative-semigroup-identity-monoid/asset-basics-of-group-theory after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. General Aptitude & Reasoning: Number System, Percentage, Ratio and Proportion (Ratios), Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Speed Time and Distance, Mixture and Alligation, Data Interpretation, Algebra, Probability, Permutation and Combination, Venn Diagram, HCF LCM, Divisibility Rules, Age Problems, Pipe and Cistern, Partnership, Linear Algebra, Sequence and Series (Series), Statistics, Powers and Exponents (Surds and Indices), Arithmetic, Mensuration and Geometry, Calculus, Trigonometry, Vectors, Speed Mathematics and Basic Mathematics, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Analogy, Series (Number and Letter Series) (Numerical Relations and Reasoning), Puzzle Solving (Puzzles), Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Calendar, Seating Arrangements, Coding Decoding, Blood Relations, Directions (Direction Test), Clock, Analytical Reasoning (Counting Figures Reasoning), Ranking, Order and Sequence, Logical Sequence Of Words, Inequality, Data Sufficiency, Cubes & Dices
  3. Computer Networks & Cybersecurity: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware Basics, Network Security
  4. Programming, Data Structures & Algorithms: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, OOPS with C++, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  5. AI, Machine Learning, Big Data & Cloud: Emerging Tech Trends, Artificial Intelligence, Big Data Systems, Approaches to AI, Search Algorithms, Knowledge Representation, Cloud Computing
  6. Digital Logic & Computer Organization: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Register Transfer and Microoperations, Control Unit Design, Programming the Basic Computer
  7. TOC & Compiler: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory, Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment
  8. Discrete Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic
  9. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Unix OS, Linux OS, Distributed Systems
  10. Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, Object Oriented Technology, HTML Basics, JavaScript-Basics, Java, XML
  11. Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, Data Warehousing & Mining, Enhanced Data Models, NoSQL
  12. Other Recurring CS Topics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, Multimedia
  13. Live Classes: ISRO Live classes
  14. Full Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video introduces Group Theory through a visual puzzle and formal definitions. It starts with a 'Find the odd one in the group' exercise involving traffic lights, pumpkins, and leaves to illustrate pattern recognition. The lecture then defines Group Theory as a mathematical tool for estimating the strength of a set with respect to an operator, highlighting its application in research areas like soft computing and black hole physics. Finally, it sets the stage for studying basic set properties and number systems, specifically introducing the set of natural numbers. The instructor uses visual aids and equations to make abstract concepts accessible and relevant to real-world problems.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with an interactive visual puzzle labeled 'Find the odd one in the group.' The instructor analyzes six distinct rows of images to identify the outlier in each set. He points out a traffic light with a red light illuminated among green ones, a carved Jack-o'-lantern among plain pumpkins, a brown autumn leaf among green leaves, a dripping tap among those with blue streams, a trash can containing waste among empty ones, and an emoji with wide eyes among standard expressions. This segment serves as an engaging, intuitive introduction to the concept of identifying unique properties within a group, visually demonstrating how to distinguish elements based on specific attributes like color, state, or form.

  2. 2:00 – 3:50 02:00-03:50

    The content transitions to a formal lecture slide titled 'Group Theory.' The text defines Group Theory as a 'very important mathematical tool' used to 'estimate the strength of a set with respect to an operator.' The instructor writes '{ 3, * }' and 'A, *' on the screen to illustrate sets and operators. He explains the relevance of this theory in research, displaying complex equations related to black holes, including the Schwarzschild metric and gravitational force formulas. The section concludes by introducing the 'Set of all-Natural number(N),' defining it as 'N = {1,2,3, 4.... infinity}' and showing a hierarchical diagram of number systems ranging from complex numbers down to natural numbers, preparing students for the study of basic set properties.

The video provides a structured introduction to Group Theory, moving from concrete visual examples to abstract mathematical definitions. It begins by using a 'Find the odd one out' puzzle to demonstrate the fundamental concept of grouping elements based on shared characteristics, such as color, shape, or state. This intuitive approach prepares the viewer for the formal definition of Group Theory as a tool for analyzing sets and operators. The lecture highlights the practical application of these concepts in advanced research fields like soft computing and astrophysics, using black hole equations to illustrate complexity. Finally, it establishes the foundational context by defining the set of natural numbers and showing their place within the broader hierarchy of number systems, setting the stage for future lessons on set properties and algebraic structures in practical contexts.

Loading lesson…