Prerequisites: Mathematics courses of first year of study. Course Objectives:
The Number Theory basic concepts useful for cryptography etc
The theory of Probability, and probability distributions of single and multiple random variables
The sampling theory and testing of hypothesis and making inferences
Stochastic process and Markov chains.
Course Outcomes: After learning the contents of this course, the student must be able to
Apply the number theory concepts to cryptography domain
Apply the concepts of probability and distributions to some case studies
Correlate the material of one unit to the material in other units
Resolve the potential misconceptions and hazards in each topic of study. UNIT – I
Greatest Common Divisors and Prime Factorization: Greatest common divisors, The Euclidean algorithm, The fundamental theorem of arithmetic, Factorization of integers and the Fermat numbers Congruences: Introduction to congruences, Linear congruences, The Chinese remainder theorem, Systems of linear congruences UNIT – II
Simple Linear Regression and Correlation: Introduction to Linear Regression, The Simple Linear Regression Model, Least Squares and the Fitted Model, Properties of the Least Squares Estimators,Inferences Concerning the Regression Coefficients, Prediction, Simple Linear Regression Case Study Random Variables and Probability Distributions: Concept of a Random Variable, Discrete Probability Distributions, Continuous Probability Distributions, Statistical Independence.Discrete Probability Distributions: Binomial Distribution, Poisson distribution. UNIT – III
Continuous Probability Distributions: Normal Distribution, Areas under the Normal Curve,Applications of the Normal Distribution, Normal Approximation to the Binomial Fundamental Sampling Distributions: Random Sampling, Sampling Distributions, Sampling Distribution of Means and the Central Limit Theorem, Sampling Distribution of S2, t–Distribution, FDistribution. UNIT – IV
Estimation & Tests of Hypotheses: Introduction, Statistical Inference, Classical Methods of Estimation. Estimating the Mean, Standard Error of a Point Estimate, Prediction Intervals, Tolerance Limits, Estimating the Variance, Estimating a Proportion for single mean , Difference between Two Means, between Two Proportions for Two Samples and Maximum Likelihood Estimation. UNIT – V
Stochastic Processes and Markov Chains: Introduction to Stochastic processes- Markov process.Transition Probability, Transition Probability Matrix, First order and Higher order Markov process,nstep transition probabilities, Markov chain, Steady state condition, Markov analysis
TEXT BOOKS:
1. Kenneth H. Rosen, Elementary number theory & its applications, sixth edition, Addison Wesley, ISBN 978 0-321-50031-1
2. Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, Keying Ye, Probability & Statistics for Engineers & Scientists, 9th Ed. Pearson Publishers.
3. S. D. Sharma, Operations Research, Kedarnath and Ramnath Publishers, Meerut, Delhi REFERENCE BOOK:
1. S C Gupta and V K Kapoor, Fundamentals of Mathematical statistics, Khanna publications
2. T.T. Soong, Fundamentals of Probability And Statistics For Engineers, John Wiley & Sons Ltd, 2004.
3. Sheldon M Ross, Probability and statistics for Engineers and scientists, Academic Press.
CSE-AIML
SEMESTER
SUBJECT CODE
SUBJECT
Lession Plan Lecturer Notes & Question Bank
SYLLABUS
I
MA101BS
Mathematics – I
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I
AP102BS
Applied Physics
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I
CS103ES
Programming for Problem Solving
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I
ME104ES
Engineering Graphics
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I
AP105BS
Applied Physics Lab
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I
CS106ES
Programming for Problem Solving Lab
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I
MC109ES
Environmental Science
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II
MA201BS
Mathematics – II
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II
CH202BS
Chemistry
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II
EE203ES
Basic Electrical Engineering
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II
ME205ES
Engineering Workshop
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II
EN205HS
English
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II
CH206BS
Engineering Chemistry Lab
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II
EN207HS
English Language and Communication Skills Lab
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II
EE208ES
Basic Electrical Engineering Lab
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II-I
CS310PC
Discrete Mathematics
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II-I
CS302PC
Data Structures
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II-I
MA313BS
Mathematical and Statistical Foundations
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II-I
CS304PC
Computer Organization and Architecture
II-I
CS311PC
Python Programming
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II-I
SM306MS
Business Economics & Financial Analysis
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II-I
CS307PC
Data Structures Lab
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II-I
CS312PC
Python Programming Lab
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II-I
MC309
Gender Sensitization Lab
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II-II
CS416PC
Formal Language and Automata Theory
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II-II
CS417PC
Software Engineering
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II-II
CS403PC
Operating Systems
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II-II
CS404PC
Database Management Systems
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II-II
CS412PC
Object Oriented Programming using Java
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II-II
CS406PC
Operating Systems Lab
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II-II
CS407PC
Database Management Systems Lab
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II-II
CS408PC
Java Programming Lab
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II-II
MC409
Constitution of India
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III-I
Design and Analysis of Algorithms
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III-I
Machine Learning
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III-I
Computer Networks
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III-I
Compiler Design
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III-I
Graph Theory (PE1)
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III-I
Introduction to Data Science(PE1)
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III-I
Web Programming(PE1)
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III-I
Image Processing(PE1)
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III-I
Computer Graphics(PE1)
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III-I
Software Testing Methodologies(PE2)
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III-I
Information Retrieval Systems(PE2)
III-I
Pattern Recognition(PE2)
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III-I
Computer Vision and Robotics(PE2)
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III-I
Data Warehousing and Business Intelligence(PE2)
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III-I
Machine Learning Lab
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III-I
Computer Networks Lab
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III-I
Advanced Communication Skills Lab
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III-I
Intellectual Property Rights
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III-II
Artificial Intelligence
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III-II
DevOps
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III-II
Natural Language Processing
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III-II
Internet of Things(PE3)
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III-II
Data Mining(PE3)
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III-II
Scripting Languages(PE3)
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III-II
Mobile Application Development(PE3)
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III-II
Cryptography and Network Security(PE3)
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III-II
Artificial Intelligence and Natural Language
Processing Lab
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