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Syllabus
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Syllabus
Lecture Notes- UNIT 1
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1.1 Relations and Types of Relations
1.2 Equivalence Relation
1.3 Matrix Relation
1.3 Adjacency Matrix
1.4 Introduction of functions
1.5 Composition of functions
1.6 Inverse Functions
UNIT 2
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Logic Connectives
Problems (Truth Table)
UNIT 3
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3.1 Probability- Introduction
3.2 Types of events
3.3 Problems 1
3.3 Problems
3.4 Conditional probability
3.5 Bayes Theorem
UNIT 4
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4.1 Test of Hypothesis- Introduction
4.2 Large Sample Test: Z test
4.3 Difference Population mean and sample means
4.4 Problems
4.4 Problems 1
UNIT 5
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5.1 Introduction
5.2 Test of Hypothesis – Small Sample Test – t test Problems and Solutions
Test of Hypothesis – Small Sample Test – t test Problems and Solutions 1
5.3 Test of Hypothesis – Small Sample Test – Chi square test Problems and Solutions
Test of Hypothesis – Small Sample Test – Chi Square test Problems and Solutions 1
Test of Hypothesis – Small Sample Test – Chi Square test Problems and Solutions 2
5.4 Test of Hypothesis – Small Sample Test – F test Problems and Solutions
QUESTION BANK
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QUESTION BANK
Puzzles
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Puzzle 1
Puzzle 2
Puzzle 3
Puzzle 4
Puzzle 5
Resource Links
1.https://www.geeksforgeeks.org/discrete-mathematics-relations/ 2.https://www.tutorialspoint.com/discrete_mathematics/discrete_mathematics_proposition al_logic.htm 3.Resource Link: https://www.khanacademy.org/math/statistics-probability/probability- library 4.Resource Link: https://stattrek.com/hypothesis-test/hypothesis-testing.aspx 5.Resource Link: https://statistics.laerd.com/statistical-guides/independent-t-test- statistical-guide.php
YouTube links
1.https://www.youtube.com/watch?v=KbB3PrF29Sg 2.https://www.youtube.com/watch?v=R_S-YVvAofM 3.https://www.youtube.com/watch?v=uzkc-qNVoOk 4.https://www.youtube.com/watch?v=VK-rnA3-41c 5.https://www.youtube.com/watch?v=pTmLQvMM-1M
NPTEL links
1.https://nptel.ac.in/courses/106106183 2.https://nptel.ac.in/courses/111103016 3.https://nptel.ac.in/courses/111105041 4.https://nptel.ac.in/courses/111105043 5.https://nptel.ac.in/courses/111104120
Assignments
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Assignment 1
Assignment 2
Assignment 3
Assignment 4
Assignment 5
25UCU302-Discrete Structures with Probability and Hypothesis Testing
UNIT 1
Relations and Functions

Relations – Types of Relations – Equivalence relations – Matrices of Relations – Functions – Types of function – Inverse function

UNIT 2
Logic Connectives

Logic – Introduction – Connectives – Equivalence formulas – Tautological implications -Normal forms – (PCNF &PDNF)

UNIT 3 
Probability

Introduction – Types of Events – Problems – Conditional Probability – Bayes theorem

UNIT 4
Test of Hypothesis

Null Hypothesis ᎓ Alternate Hypothesis ᎓ Degrees of freedom – Large Sample Test: Z test – Difference Population mean and sample means – Difference between sample means

UNIT 5
Small sample test

t test for single mean ᎓ difference between two means – chi square test – F test

Reference Book:

Kenneth H. Rosen , (2022), Discrete Mathematics and Its Applications, (8th Edition) McGraw-Hill Education Susanna S. Epp, (2022), Discrete Mathematics with Applications, (5th Edition) , Cengage Learning.

Text Book:

Oscar Levin. (2024). Discrete Mathematics: An Open Introduction, 4th Edition, Open Math Books Oscar Levin. (2024). Discrete Mathematics: An Open Introduction, 4th Edition, Open Math Books S.C. Gupta & V.K. Kapoor (2023). Fundamentals of Mathematical Statistics (12th Revised & Enlarged Edition). Sultan Chand & Sons

 

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