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DISCRETE MATHEMATICS & PROBABILITY
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GANPAT UNIVERSITY |
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FACULTY OF ENGINEERING & TECHNOLOGY |
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Programme |
Bachelor of Technology |
Branch/Spec. |
Computer Engineering/Information Technology/ Computer Engineering (Artificial Intelligence) |
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Semester |
III |
Version |
2.0.0.1 |
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Effective from Academic Year |
2023-24 |
Effective for the batch Admitted in |
July 2022 |
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Subject code |
2BS3102 |
Subject Name |
Discrete Mathematics & Probability |
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Teaching scheme |
Examination scheme (Marks) |
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(Per Week) |
Lecture (DT) |
Practical (Lab) |
Total |
CE |
SEE |
Total |
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L |
TU |
P |
TW |
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Credit |
3 |
1 |
0 |
0 |
4 |
Theory |
40 |
60 |
100 |
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Hours |
3 |
1 |
0 |
0 |
4 |
Practical |
0 |
0 |
0 |
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Pre-requisites: |
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Basic knowledge of Algebra, Function and Statistics |
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Course Outcome (COs): |
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CO |
Description |
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CO 1 |
Express physical phenomenon in Group theory and Graph theory. |
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Solve Correlation & Regression. |
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CO 3 |
Use basic knowledge of Probability distributions and their applications in Computer Engineering & Information Technology to cater various problems |
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Theory syllabus |
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Unit |
Content |
Hrs. |
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1 |
Algebraic Structures and Morphism Algebraic structures with one Binary Operation, Semi Groups, Monoids, Groups, Congruence Relation & Quotient Structures, Abelian Group, Cyclic Group, Subgroup, Permutation Groups, Coset Decomposition Of Groups, Normal Subgroups, Lagrange’s Theorem, Algebraic Structures with two Binary operation, Rings , Integral Domain and Fields & their examples. |
10 |
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2 |
Graphs and Trees Basic Concept of Graph and their properties, Degree, , Path, Cycle, Subgraphs, Isomorphism, Reachability and Connectedness, Matrix Representation Of Graphs, Eulerian & Hamiltonian Walks, Graph Colouring, Colouring Maps, Colouring Vertices, Colouring Edges, Trees, Routed trees and Sorting, Weighted trees and Prefixes codes. |
10 |
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3 |
Fuzzy Sets Basic Definitions of Fuzzy sets, Basic Operations on Fuzzy Sets, Image and Inverse Images, I-V Fuzzy Sets, Fuzzy Relations. |
03 |
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4 |
Correlation Definition of Correlation, Types of Correlation, Scatter Diagram Method, Karl Person’s Correlation Coefficients, Correlation Coefficients for Bivariate frequency distribution, Probable error for Correlation Coefficients, Rank Correlation Co- efficient. |
07 |
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5 |
Regression Definition of Regression, Regression lines, Regression Coefficients, Properties of regression Coefficients, Fitting of regression lines and estimation for Bivariate frequency distribution. |
06 |
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6 |
Probability Distributions Binomial Distribution Introduction, Probability mass function of Binomial distribution, Mean and Variance of Binomial distribution, Properties of Binomial Distribution, Uses of Binomial Distribution. Poisson Distribution Introduction, Probability mass function of Poisson distribution, Mean and Variance of Poisson distribution, Properties of Poisson Distribution, Applications of Poisson Distribution. Normal Distribution Introduction, Probability density function of Normal distribution, Properties of Normal distribution, Importance of Normal Distribution. |
09 |
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Practical content: |
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Assignments and tutorials are based on the above syllabus. |
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Text Books: |
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1. |
Discrete Mathematical Structures With Application To Computer Science By Tremblay, J.P. & Manohar, Mcgraw Hill - New Delhi Textbook of engineering mathematics By A.B.Mathur and V.P.Jaggi. |
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2. |
Discrete Mathematics and Its Applications By Rosen, Kenneth McGraw Hill - New Delhi |
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3 |
Fuzzy Sets and Fuzzy Logic. Theory and Applications By George J. Klir/Bo Yuan |
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4 |
Fundamental of Applied Statistics By S.C. Gupta & V.K. Kapoor, Sultan Chand Publication |
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Reference Books: |
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1. |
Discrete Mathematical Structures For Computer Science By Kolman, B& Busby R.C,Prentice Hall Of India Pvt Ltd., New Delhi |
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2. |
Applied Discrete Structures for Computer Science By Alan Doerr & Kenneth, Galgotia Pub. Pvt Ltd., New Delhi |
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3. |
An introduction to Probability theory and its Application By W Feller, Vol.1 3rd Ed. Wiley, 1968. |
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4. |
Probability, Statistics and Random Process By T Veerarajan, TMH |
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ICT/MOOCS: |
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1. |
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2. |
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3. |
https://nptel.ac.in/courses/102101056/11 |
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4. |
https://nptel.ac.in/courses/111105041/8 |
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Mapping of CO-PO and CO-PSO: |
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PO1 |
PO2 |
PO3 |
PO4 |
PO5 |
PO6 |
PO7 |
PO8 |
PO9 |
PO10 |
PO11 |
PO12 |
PSO1 |
PSO2 |
PSO3 |
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CO1 |
3 |
2 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
2 |
1 |
3 |
3 |
3 |
1 |
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CO2 |
2 |
1 |
2 |
1 |
2 |
1 |
3 |
0 |
2 |
1 |
1 |
2 |
3 |
3 |
1 |
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CO3 |
3 |
2 |
1 |
1 |
1 |
0 |
3 |
2 |
1 |
2 |
3 |
2 |
3 |
2 |
1 |
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