Rashtrasant Tukadoji Maharaj Nagpur University, Maharashtra, Artificial Intelligence Semester 4, Mathematical Foundations for Artificial Intelligence Syllabus

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Unit - 1 Numerical Analysis

Unit 1

Numerical analysis

1.1 Solution of algebraic and transcendental Equations Newton–Raphson method

1.2 Method of false position

1.3 Solution of simultaneous linear equations using GaussSeidal method and Crout’s method LU decomposition

1.4 Numerical solution of ordinary differential equations Taylors series method

1.5 Euler’s modified method

1.6 RungeKutta fourth order method

1.7 Milne’s predictor corrector method

Unit - 2 Linear Algebra

Unit 2

Linear algebra

2.1 Introduction and examples of vector spaces

2.2 Linear dependence and independence of vectors

2.3 Linear spans Spanning sets

2.4 Eigen values and Eigen vectors Reduction to diagonal form

2.5 Singular value decomposition Sylvester’s theorem Statement only

2.6 Largest Eigen value and its corresponding Eigen vector by iteration method

Linear algebra

Unit 2

Linear algebra

2.1 Introduction and examples of vector spaces

2.2 Linear dependence and independence of vectors

2.3 Linear spans Spanning sets

Unit 2

Linear algebra

Unit 2

Linear algebra

2.1 Introduction and examples of vector spaces

2.2 Linear dependence and independence of vectors

2.3 Linear spans Spanning sets

2.4 Eigen values and Eigen vectors Reduction to diagonal form

2.5 Singular value decomposition Sylvester’s theorem Statement only

2.6 Largest Eigen value and its corresponding Eigen vector by iteration method

Unit - 3 Mathematical Expectation And Probability Distributions

Unit 3

Mathematical expectations and probability distributions

3.1 Discrete Random Variable Review of discrete random variable

3.2 Probability function and Distribution function

3.3 Mathematical expectation

3.4 Variance and Standard deviation

3.5 Moments Moment generating function

3.6 Probability Distributions Binomial distribution

3.7 Poisson distribution

3.8 Normal distribution

3.9 Exponential distribution

Unit 3

Mathematical expectations and probability distributions

3.1 Discrete Random Variable Review of discrete random variable

3.2 Probability function and Distribution function

3.3 Mathematical expectation

3.4 Variance and Standard deviation

3.5 Moments Moment generating function

3.6 Probability Distributions Binomial distribution

3.7 Poisson distribution

3.8 Normal distribution

3.9 Exponential distribution

Unit - 4 Statistical Techniques

Unit 4

Statistical techniques

4.1 Statistics Introduction to correlation and regression Multiple correlation and its properties Multiple regression analysis Regression equation of three variables

4.2 Measures of central tendency and dispersion Mean Median Quartile Decile Percentile Mode Mean deviation Standard deviation

4.3 Skewness Test and uses of skewness and types of distributions Measure of skewness Karl Pearson’s coefficient of skewness Measure of skewness based on moments.

Unit - 5 Stochastic Process And Sampling Techniques

Unit 5

Stochastic process and sampling techniques

5.1 Stochastic Process Introduction of stochastic process

5.2 Classification of random process Stationary and nonstationary random process Stochastic matrix

5.3 Markov Chain Classification of states Classification of chains Random walk and Gambler ruin

5.4 Sampling Population Universe Sampling types and distribution Sampling of mean and variance

5.5 Testing a hypothesis Null and Alternative Hypothesis Onetail and twotails testsOnly introduction

5.6 t test and F test Only introduction Chisquare test

Unit 5

Stochastic process and sampling techniques

5.1 Stochastic Process Introduction of stochastic process

5.2 Classification of random process Stationary and nonstationary random process Stochastic matrix

5.3 Markov Chain Classification of states Classification of chains Random walk and Gambler ruin

5.4 Sampling Population Universe Sampling types and distribution Sampling of mean and variance

5.5 Testing a hypothesis Null and Alternative Hypothesis Onetail and twotails testsOnly introduction

5.6 t test and F test Only introduction Chisquare test

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Other Subjects of Semester-4
Theory of computation
Database management system
Microcontroller and embedded systems
Object oriented programming using java
Introduction to artificial intelligence
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