Addition Modulo & Multiplication

Duration: 5 min

This video lesson is available to enrolled students.

Return to /learn/SSC-JE-IMD-SCIENTIFIC-ASSISTANT-COMPUTER-SCIENCE/engineering-mathematics/group-theory/classification-of-finite-and-infinite-groups/asset-addition-modulo-multiplication after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. General Intelligence & Reasoning: Analogy, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Logical Sequence Of Words, Syllogisms, Venn Diagram, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Data Sufficiency, Puzzle Solving (Puzzles), Data Arrangement, Cubes & Dices, Calendar, Clock, Arithmetic, Number System, HCF LCM, Verbal Analogy (Word Based Analogy), Visual Recognition and Figure Completion, Paper Folding and Cutting, Transformation of Shapes, Clocks and Calendars, Direction Sense, Cubes and Dice, Patterns in Two-Dimensional Figures, Seating Arrangements, Analogy and Classification, Logical Deduction and Induction, Alphabet and Word Tests, Mathematical Operations, Series Completion, Simplification and Approximation, Coding and Decoding, Numerical Reasoning, Assembling and Grouping of Shapes, Three-Dimensional Patterns and Visualization, Vocabulary, Number System, Averages, Mixtures and Alligation, Simple and Compound Interest, Percentages, Algebra, Speed, Time and Distance, Seating and Arrangement Puzzles, Traverse Surveying, Order, Ranking and Sequence, Constraint Puzzles, Syllogisms and Venn Diagrams, Reading Comprehension, Critical Reasoning, Permutations and Combinations, Narrative Sequencing, Project Monitoring, Resources and Safety, Profit, Loss and Discount, Ratio and Proportion, Time and Work, Mensuration, Data Interpretation, Powers, Surds and Logarithms, Sequences and Series, Articles and Determiners, Sentence Completion, Data Sufficiency, Blood Relations, Simple Interest and Compound Interest, Mixture and Alligation, Sequence and Series (Series), Speed Time and Distance, Algebra, Profit and Loss, Powers and Exponents (Surds and Indices), Permutation and Combination
  2. General Awareness: Physics, Chemistry, Biology, History, Geography, Polity, Indian Economy, Environment, Static General Knowledge, GK- Current Affairs, Artificial Intelligence, MS Office Applications, Terms & Abbreviations, Keyboard Shortcuts, Evolution of Indian Banking (Banking & Financial Awareness), Emerging Tech Trends
  3. Engineering Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Linear Algebra, Calculus, Probability, Statistics, Signal Space and Optimum Detection, Probability, Statistics
  4. Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep, Number Systems and Codes, Registers and Counters, Boolean Algebra and Logic Gates, Microprocessors and Microcontrollers, Logic Families and CMOS Logic, Microprocessors, Logic Gates and Boolean Algebra, Minimization of Boolean Functions, Timing, Hazards and Testing, Logic Families, Combinational Logic Design, Arithmetic Circuits, Waveform Generators and Timer Circuits, Semiconductor Memories and Programmable Logic Devices, Combinational Logic Circuits, Latches and Flip-Flops, Finite State Machines, Sequential Circuits and State Machines, Minimization of Boolean Functions, Arithmetic Circuits, Latches and Flip-Flops, Number Systems and Codes, Registers and Counters
  5. Computer Organisation & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer, Register Transfer and Microoperations, Semiconductor Memories and Programmable Logic, Processor Organization and Instructions, Memory Hierarchy and Input/Output, Registers and Counters
  6. Programming & Data Structures: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, HTML Basics, OOPS with C++, Java, Object Oriented Technology
  7. Databases: 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, Database Security & Authorization
  8. Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  9. Theory of Computation: 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
  10. Compiler Design: 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
  11. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Security, Windows OS, Distributed Systems, Unix OS, Linux OS
  12. Computer Networks: Introduction to CN, 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, Data Communication, Website, Browser & Services, Web Design & Development, Network Security, Cyber Threats and Malware Attacks, Cyber Safety and Security
  13. Full Length Mock Tests:
  14. Sectional Tests:
  15. Paper 2 - Full-length Mock Tests:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a detailed introduction to modular arithmetic, specifically focusing on addition and multiplication modulo operations. The instructor defines the binary operators +_m and *_m using conditional formulas based on the modulus m. Through the construction of Cayley tables, he demonstrates how these operations work on finite sets, showing how values wrap around when they exceed the modulus. The lecture covers the set {0, 1, 2, 3} for addition modulo 4 and the set {1, 2, 3, 4} for multiplication modulo 5, providing a clear visual guide to these algebraic structures.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The lecture starts with the definition of 'Addition modulo' on the slide, denoted by the symbol +_m. Two distinct rules are presented: a +_m b = a + b if the sum is less than m, and a +_m b = a + b - m if the sum is greater than or equal to m. The instructor sets up a Cayley table for the set {0, 1, 2, 3} with modulus m=4. He begins filling the table row by row. For the first row, he writes 0, 1, 2, 3. For the second row, he calculates 1+0=1, 1+1=2, 1+2=3, and then 1+3=4, which becomes 0 because 4 >= 4. He continues to the third row, calculating 2+0=2, 2+1=3, 2+2=4 (which becomes 0), and 2+3=5 (which becomes 1).

  2. 2:00 – 5:00 02:00-05:00

    The topic shifts to 'Multiplication modulo', denoted by *_m. The slide displays the rules: a *_m b = a * b if the product is less than m, and a *_m b = (a * b) % m if the product is greater than or equal to m. A new table is introduced for the set {1, 2, 3, 4} with modulus m=5. The instructor fills the first row with 1, 2, 3, 4. In the second row, he calculates 2*1=2, 2*2=4, 2*3=6 (which becomes 1), and 2*4=8 (which becomes 3). He proceeds to the third row, calculating 3*1=3, 3*2=6 (becomes 1), 3*3=9 (becomes 4), and 3*4=12 (becomes 2). Finally, he fills the fourth row: 4*1=4, 4*2=8 (becomes 3), 4*3=12 (becomes 2), and 4*4=16 (becomes 1). He circles the results that required the modulo operation to emphasize the wrapping effect.

  3. 5:00 – 5:14 05:00-05:14

    The video concludes with the fully completed multiplication modulo 5 table displayed on the screen. The instructor gestures towards the table, likely summarizing the properties of the operation or the group structure formed by these elements. The final table shows a symmetric pattern of results, illustrating the closure property of the operation within the set. The slide remains visible as the lecture ends.

The lesson systematically builds understanding of modular arithmetic by first defining addition modulo and then multiplication modulo. The instructor uses Cayley tables as a primary pedagogical tool to visualize how binary operators function within finite sets. By explicitly calculating each entry and highlighting cases where the modulus applies, the lecture clarifies the concept of 'wrapping around' values. This progression from definition to concrete example ensures students grasp both the theoretical rules and their practical application in algebraic structures.

Loading lesson…