Small Notations

Duration: 2 min

This video lesson is available to enrolled students.

Return to /learn/UP-POLICE-COMPUTER-OPERATOR/computer-science/algorithm-analysis/asymptotic-notations/asset-small-notations after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About the course: About the Course
  2. General Knowledge: Polity, Physics, Biology, State Wise GK, Chemistry, History, Geography, GK- Current Affairs, Indian Economy, Static General Knowledge, Environment, Evolution of Indian Banking (Banking & Financial Awareness)
  3. Mental Aptitude and Reasoning: Ratio and Proportion (Ratios), Divisibility Rules, Data Interpretation, Permutation and Combination, Number System, 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), Vocabulary, Profit and Loss, Arithmetic, Mental Ability, Percentage, Algebra, Mensuration and Geometry, Age Problems, Clock, Calendar, Verbal Analogy (Word Based Analogy), Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Analogy, Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Selection Decision Table (Decision Making), Cubes & Dices, Blood Relations, Venn Diagram, Logical Sequence Of Words, Inequality, Directions (Direction Test), Data Arrangement, Facts, Inference and Judgements, Syllogisms, Seating Arrangements, Ranking, Order and Sequence
  4. CS | Computer Fundamentals: Basics of COA, Number System, Number Representation, C Fundamentals, Algorithm Analysis, Input Output Organisation
  5. CS | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, SQL
  6. CS | Workplace productivity Tools: MS Office Applications, Keyboard Shortcuts
  7. CS | Computer Networks: Introduction to CN, Data Communication, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, Application Layer, Hardware Basics, Network Security
  8. CS | The Internet: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Web Publishing & Hosting, Server Side & Security, Emerging Technologies
  9. CS | Emerging Technologies: Artificial Intelligence, Emerging Tech Trends, Introduction to OS, Windows OS, Linux OS, Unix OS, JavaScript-Basics
  10. CS | Boolean algebra: Digital Systems & Boolean Basics, Boolean Expression, Boolean Minimization, Logic Gates & Hardware
  11. CS | Data Structures: Introduction to DS, Array, Stack, Queue
  12. CS | Cryptography: Society, Law & Ethics, Cyber Threats and Malware Attacks, Role of Internet and Web Services, Security in Mobile and Wireless Computing, Electronic Data Interchange and E-Commerce, Physical Security and Cryptography Basics, Intrusion Detection Systems (IDS), Cyber Safety and Security
  13. UP Police Previous Year Papers:
  14. UP Police Full Mock Tests:
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…