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AKTU Mathematical Foundation AI , ML and Data Science (BAI051) Syllabus PDF – B.Tech 3rd Year
Mathematical Foundation AI , ML and Data Science BAI051
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Official AKTU syllabus of Mathematical Foundation AI , ML and Data Science (BAI051) for B.Tech 3rd Year – 3 credits, L-T-P 3-0-0. Read the unit-wise course content, course outcomes, evaluation pattern and recommended books online, or download the PDF.
Syllabus — Mathematical Foundation AI , ML and Data Science
Download PDFBAI051 · 3 credits · L-T-P 3-0-0
Course Outcomes
At the end of course , the student will be able to:
| CO 1 | Understand and apply the probability distributions, random number generation and density estimations to perform analysis of various kinds of data | K2, K , K 4 6 |
| CO 2 | Understand and manipulate data, design and perform simple Monte Carlo experiments, and be able to use resampling methods | K , K 5 6 |
| CO 3 | Perform statistical analysis on variety of data | K , K 2 5 |
| CO 4 | Perform appropriate statistical tests using R and visualize the outcome | K , K 2 4 |
| CO 5 | Discuss the results obtained from their analyses after creating customized graphical and numerical summaries | K , K 2 3 |
Course Content
L-T-P: 3-0-0
| Unit | Topic | Proposed Lecture |
|---|---|---|
| I | Descriptive Statistics: Diagrammatic representation of data, measures of central tendency, measures of dispersion, measures of skewness and kurtosis, correlation, inference procedure for correlation coefficient, bivariate correlation, multiple correlations, linear regression and its inference procedure, multiple regression. Probability: Measures of probability, conditional probability, independent event, Bayes’ theorem, random variable, discrete and continuous probability distributions, expectation and variance, markov inequality, chebyshev’s inequality, central limit theorem. | 08 |
| II | Inferential Statistics: Sampling & Confidence Interval, Inference & Significance. Estimation and Hypothesis Testing, Goodness of fit, Test of Independence, Permutations and Randomization Test, t-test/z-test (one sample, independent, paired), ANOVA, chi-square. Linear Methods for Regression Analysis: multiple regression analysis, orthogonalization by Householder transformations (QR); singular value decomposition (SVD); linear dimension reduction using principal component analysis (PCA). | 08 |
| III | Pseudo-Random Numbers: Random number generation, Inverse-transform, acceptance-rejection, transformations, multivariate probability calculations. Monte Carlo Integration: Simulation and Monte Carlo integration, variance reduction, Monte Carlo hypothesis testing, antithetic variables/control variates, importance sampling, stratified sampling Markov chain Monte Carlo (McMC): Markov chains; Metropolis-Hastings algorithm; Gibbs sampling; convergence | 08 |
| IV | Vector Spaces- Vector Space, Subspace , Linear Combination, Linear Independence, Basis, Dimension, Finding a Basis of a Vector Space , Coordinates, Change of Basis Inner Product Spaces- Inner Product, Length, Orthogonal Vectors, Triangle Inequality, Cauchy- Schwarz Inequality, Orthonormal (Orthogonal) Basis, Gram-Schmidt Process | 08 |
| V | Linear Transformations- Linear Transformations and Matrices for Linear Transformation, Kernel and Range of a Linear Transformations, Change of Basis Eigenvalues and Eigenvectors- Definition of Eigenvalue and Eigenvector, Diagonalization , Symmetric Matrices and Orthogonal Diagonalization | 08 |
Reference Books
- S.C. Gupta & V.K. Kapoor, “Fundamentals of Mathematical Statistics”, Sultan Chand & Sons
- Sheldon M. Ross, “Introduction to Probability and Statistics for Engineers and Scientists”, Academic Press.
- Dudewicz, E.J., Mishra, S.N., “Modern Mathematical Statistics”, Willy
- Purohit S. G., Gore S. D., Deshmukh S. K., “Statistics using R, Narosa
- Rizzo, M. L., “Statistical Computing with R”, Boca Raton, FL: Chapman & Hall/CRC Press
- Normal Maltoff, The Art of R programming, William
- Dalgaard, Peter, “Introductory statistics with R”, Springer Science & Business Media
- M. D. Ugarte, A. F. Militino, A. T. Arnholt, “Probability and Statistics with R”, CRC Press
- Kundu, D. and Basu, A., “Statistical computing – existing methods and recent developments”, Narosa
- Gentle, James E., Härdle, Wolfgang Karl, Mori, Yuich, “Handbook of Computational Statistics”, Springer
- Givens and Hoeting, “Computational Statistics”, Wiley Series in Prob. and Statistics
- Elementary Linear Algebra by Ron Larson, 8th edition, Cengage Learning, 2017
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