Small Notations

Duration: 2 min

This video lesson is available to enrolled students.

Return to /learn/TPSC-ASSISTANT-TECHNICAL-OFFICER/algorithms/algorithm-analysis/asymptotic-notations/asset-small-notations after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. Paper 2 | Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep
  3. Paper 2 | Computer Organization And Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Control Unit Design, Instr Formats & Modes, Programming the Basic Computer
  4. Paper 2 | Analog And Digital Communication: Introduction to Communication Systems & Random Signals, Analog Communication Systems, Information Theory & Digital Communication Fundamentals, Digital Modulation & Detection Techniques, Error Control, Synchronization & Multiple Access Techniques
  5. Paper 2 | Programming in C: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  6. Paper 2 | Data Structures And Programming: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Java, OOPS with C++, Java Fundamentals, Array, String, IO & References
  7. Paper 2 | Algorithms: Algorithm Analysis, Sorting Algorithms, Time Complexity Analysis, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  8. Paper 2 | 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
  9. Paper 2 | 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
  10. Paper 2 | Databases: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Relational Calculus, File Organization & Indexing, Transaction Management, Concurrency Control
  11. Paper 2 | Information Systems and Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  12. Paper 2 | Computer Networks: 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
  13. Paper 2 | Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, HTML Basics, JavaScript-Basics, CSS, XML, HTML5
  14. Paper 2 | Cyber Security And Emerging Technologies: Emerging Tech Trends
  15. Paper 2 | Cloud Technology: Cloud Computing
  16. Paper 2 | Probability and statistics: Probability, Statistics
  17. Paper-1 English: Vocabulary, Preposition, Articles, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Cloze Test (Cloze Passage), Sentence Construction
  18. Paper 1 General Mental Ability & Logical reasoning: Ratio and Proportion (Ratios), Divisibility Rules, Data Interpretation, Mixture and Alligation, Permutation and Combination, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Percentage, Average, Powers and Exponents (Surds and Indices), Algebra, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Mensuration and Geometry, Mental Ability, Age Problems, Partnership, Arithmetic, Speed Mathematics and Basic Mathematics, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Selection Decision Table (Decision Making), Logical Sequence Of Words, Venn Diagram, Analogy
  19. Paper-1 General Knowledge & Current Affairs: State Wise GK, History, Geography, GK- Current Affairs, Static General Knowledge
  20. Full Length Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The lecture focuses on "Small notations" in asymptotic analysis, specifically distinguishing them from "Big notations" through the lens of real number inequalities. The instructor explains that while the logic is similar, small notations (little-o and little-omega) strictly exclude the equal case, unlike their Big counterparts. The lesson transitions into an analogy comparing function growth rates to real number comparisons (a vs b), mapping Big O to a <= b, Big Omega to a >= b, Theta to a = b, little-o to a < b, and little-omega to a > b. The instructor emphasizes that for small notations, the relationship must be strictly increasing or strictly decreasing, prohibiting equality. This visual analogy helps students grasp the strictness of the bounds.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video begins with a slide titled "Small notations" stating that everything is the same as big notations except the equal case is not allowed. The instructor underlines "strictly increasing or monotonically increasing case" to emphasize the strictness. The slide then changes to "Analogy of asymptomatic notation with real numbers", listing mappings like f(n) is O(g(n)) corresponding to a <= b. He writes f(n) and g(n) on the board, labeling them a and b respectively to set up the analogy. He explains that for small notations, we take the strictly increasing case, contrasting it with the inclusive nature of Big O.

  2. 2:00 – 2:28 02:00-02:28

    The instructor continues with the analogy slide. He writes a = b next to a <= b and a >= b to show that Big O and Big Omega include equality. Then, he circles a = b next to a < b (little-o) and asks "a=b?", highlighting that equality is forbidden for small notations. He reinforces that little-o corresponds strictly to a < b and little-omega to a > b, distinguishing them from the inclusive inequalities of Big O and Big Omega. This visual cue solidifies the concept that small o implies a strictly lower growth rate.

The lecture effectively bridges the gap between abstract asymptotic notation and familiar real number inequalities. By mapping f(n) to a and g(n) to b, the instructor clarifies that Big O/Omega are inclusive (<=, >=) while small o/omega are exclusive (<, >). This distinction is crucial for understanding algorithm complexity bounds, ensuring students recognize that little-o implies a strictly lower growth rate, never equal. The visual annotations on the slide serve as a powerful mnemonic for exam preparation.

Loading lesson…