Course Course Course L T P C

21MAC505T LINEAR ALGEBRA AND STATISTICAL METHODS C PROFESSIONAL CORE

Code Name Category 3 1 0 4

Pre-requisite Co- requisite Progressive

Nil Nil Nil
Courses Courses Courses
Course Offering Department Mathematics Data Book / Codes / Standards Statistical Tables

Course Learning
The purpose of learning this course is to:
Rationale (CLR):
CLR-1: define and apply basic concepts of linear algebra, including vectors, matrices, vector spaces, and linear transformations.
CLR-2: demonstrate foundational knowledge of probability theory and statistical concepts.
CLR-3: apply concepts from gradient calculus to analyze and optimize learning models.
CLR-4: explain the principles of non-parametric statistics and its uses
CLR-5: utilize statistical tools and techniques for analyzing complex and high-dimensional datasets.

Programme Outcomes
Course Outcomes
At the end of this course, learners will be able to: (PO)
(CO):
1 2 3
CO-1: explain the concepts of linear algebra, vectors, projections, principal component analysis and generative models 3 3
CO-2: demonstrate the mathematics knowledge with respect to matrices, gradient calculus, optimization models. 3 3
CO-3: familiarize the mathematics knowledge with respect to probability, statistics. 3 3
CO-4: explain the concepts of non-parametric statistics 3 3
CO-5: apply the concepts of statistics to complex datasets 3 3

Module-1 - Linear Algebra 12 Hour

Systems of Linear Equations - Machine learning motivation - A geometric notion of singularity - Singular vs non-singular matrices - Linear dependence and independence - Matrix row-reduction - Row operations
that preserve singularity - The rank of a matrix - Row echelon form - Reduced row echelon form- LU decomposition- Solving Systems of Linear Equations - Machine learning motivation - Solving non- singular
systems of linear equations - Solving singular systems of linear equations - Solving systems of equations with more variables - Gaussian elimination.
Module-2 - Probability and Statistics 12 Hour
Introduction to probability - Concept of probability: repeated random trials - Conditional probability and independence - Random variables - Cumulative distribution function - Discrete random variables: Binomial
distribution - Probability mass function - Continuous random variables: Uniform distribution - Continuous random variables: Gaussian distribution -Joint distributions - Marginal and conditional distributions -
Independence - covariance - Multivariate normal distribution - Sampling and point estimates - Interval estimation -Confidence intervals – Confidence Interval for mean of population - Biased vs Unbiased estimates-
Maximum likelihood estimation - Intuition behind maximum likelihood estimation - Hypothesis testing - Describing samples: sample proportion and sample mean - Two types of errors - Test for proportion and
means - Two sample inference for difference between groups.
Module-3 - Bayesian Statistics and its applications in various fields 12 Hour
Bayesian statistics and its applications in various fields - Bayesian Learning: Bayes theorem - maximum likelihood and least squared error hypotheses – Naïve Bayes classifier- Bayesian belief networks- gradient
ascent training of Bayesian networks- learning the structure of Bayesian networks- the EM algorithm- mixture of models- Markov models- hidden Markov models - Time series analysis and forecasting techniques -
Basic Properties of time-series data: Distribution and moments- Stationarity- Autocorrelation- Heteroscedasticity- Normality- Survival Analysis.
Module-4 - Non-Parametric Statistics 12 Hour
Non-parametric Statistics - Chi square test- Sign test -Wilcoxon signed rank test - Mann Whitney test - Run test - Kolmogorov Smirnov test - Spearmann and Kendall’s test - Tolerance region.
Module-5 - Multivariate Statistical Methods for Analyzing Complex Datasets 12 Hour
Multivariate statistical methods for analysing complex datasets - Factor Analysis - Cluster Analysis- Regression Analysis - Discriminant Analysis.

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M.Tech Programmes-Regulations 2021-Volume-23-School of Computing Syllabi-Control Copy
 1. James D. Miller, Statistics for Data Science, Packt Publishing (2017) 4. Nonparametric Statistical Methods, Myles Hollander, Douglas A. Wolfe, Eric
Learning 2. IND James D. Hamilton, Time Series Analysis, Levant Books (2012) Chicken, Wiley (2013)
Resources 3. Bayesian Statistics for Beginners: a step-by-step approach, Therese M. Donovan, 5. Introduction to Probability, Benedek Valkó, David F. Anderson, Cambridge (2017)
Ruth M. Mickey (2019) 6. Introduction to Linear Algebra, 5th Edition, Gilbert Strang, Wellesley (2016)

Learning Assessment
Continuous Learning Assessment (CLA)
Summative
Formative Life-Long Learning
Bloom’s Final Examination
CLA-1 Average of unit test CLA-2
Level of Thinking (40% weightage)
(50%) (10%)
Theory Practice Theory Practice Theory Practice
Level 1 Remember 15% - 15% - 15% -
Level 2 Understand 25% - 25% - 25% -
Level 3 Apply 30% - 30% - 30% -
Level 4 Analyze 30% - 30% - 30% -
Level 5 Evaluate - - - - - -
Level 6 Create - - - - - -
Total 100 % 100 % 100 %

Course Designers
Experts from Industry Experts from Higher Technical Institutions Internal Experts
1. Mr. Madhan Shanmugasundaram, Infosys Technologies 1. Prof. Y.V.S.S. Sanyasiraju, IIT Madras, sryedida@iitm.ac.in 1. Dr. V. Subburayan, SRMIST
2. Prof. K.C. Sivakumar, IIT Madras, kcskumar@iitm.ac.in 2. Dr. P. Sambath. SRM IST
3. Dr. M. Sivaji, SRMIST

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M.Tech Programmes-Regulations 2021-Volume-23-School of Computing Syllabi-Control Copy