BCAI051 Mathematical Foundation AI, ML and Data Science Syllabus
AKTU B.Tech · 3rd Year · Unit-wise syllabus (effective 2024-25)
BCAI051 Mathematical Foundation AI, ML and Data Science (also written as KCAI051) is a subject in the 3rd year of the AKTU B.Tech programme, prescribed by Dr. A.P.J. Abdul Kalam Technical University. The syllabus is divided into 5 units: Descriptive Statistics and Probability, Inferential Statistics and Linear Methods for Regression Analysis, Pseudo-Random Numbers and Monte Carlo Integration. The complete unit-wise topic list, course outcomes and reference books are given below, taken from the official AKTU syllabus effective from 2024-25.
BCAI051 Subject Details
| Subject Code | BCAI051 / KCAI051 |
|---|---|
| Subject Name | Mathematical Foundation AI, ML and Data Science |
| University | Dr. A.P.J. Abdul Kalam Technical University (AKTU) |
| Course | B.Tech (Bachelor of Technology) |
| Year / Semester | 3rd Year |
| Total Units | 5 |
| Scheme Effective From | 2024-25 |
| Last Verified | 2026-08-19 |
BCAI051 Mathematical Foundation AI, ML and Data Science Unit-Wise Syllabus
Official AKTU syllabus (effective 2024-25) — 5 units.
Unit 1: Descriptive Statistics · Probability
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.
Unit 2: Inferential Statistics · Linear Methods for Regression Analysis
Inferential Statistics: Sampling & Confidence Interval, Inference & Significance. Estimation and Hypothesis Testing, Goodness of fit, Test of Independence, Permutations and Randomization Test, ttest/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).
Unit 3: Pseudo-Random Numbers · Monte Carlo Integration
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
Unit 4
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
Unit 5
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
BCAI051 Course Outcomes
- At the end of course, the student will be able to:
- Understand and apply the probability distributions, random number generation and density K2, K4, K6
- estimations to perform analysis of various kinds of data
- Understand and manipulate data, design and perform simple Monte Carlo experiments, and be K5, K6
- able to use resampling methods
- CO 3 Perform statistical analysis on variety of data K2, K5
- CO 4 K2, K4
- Perform appropriate statistical tests using R and visualize the outcome K2, K3
- Discuss the results obtained from their analyses after creating customized graphical and
- numerical summaries
- DETAILED SYLLABUS 3-0-0
BCAI051 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
Frequently Asked Questions about BCAI051
What is the syllabus of BCAI051 Mathematical Foundation AI, ML and Data Science?
The AKTU BCAI051 Mathematical Foundation AI, ML and Data Science syllabus is divided into 5 units: Descriptive Statistics and Probability; Inferential Statistics and Linear Methods for Regression Analysis; Pseudo-Random Numbers and Monte Carlo Integration. The complete topic list for each unit is published on this page, taken from the official Dr. A.P.J. Abdul Kalam Technical University syllabus effective from 2024-25.
How many units are there in BCAI051?
BCAI051 Mathematical Foundation AI, ML and Data Science has 5 units in the AKTU syllabus.
Is BCAI051 the same subject as KCAI051?
Yes. AKTU renumbered its B.Tech subject codes from the 2022-23 session onwards, so the same subject appears as BCAI051 and KCAI051 depending on the scheme year. The syllabus content is the same.
Where can I download BCAI051 previous year question papers?
AKTU B.Tech previous year question papers for every semester are available to download free on Ryzenstudy, with no login or registration required.
Is this the official AKTU syllabus for BCAI051?
Yes. Every topic on this page is taken from the official Dr. A.P.J. Abdul Kalam Technical University syllabus document (AKTU B.Tech 3rd Year Computer Science and Engineering (Data Science) Syllabus), effective from 2024-25. A direct link to the original AKTU PDF is provided at the top of this page. Last verified on 2026-08-19.
Related AKTU Syllabus
Source: Dr. A.P.J. Abdul Kalam Technical University official syllabus — AKTU B.Tech 3rd Year Computer Science and Engineering (Data Science) Syllabus, effective from 2024-25. Ryzenstudy is not affiliated with AKTU. Content last verified on 2026-08-19.