Vectors Spaces, Basis and Dimensions – Change of Basis, Orthogonality and Gram Schmidt Process – Four Fundamental Spaces: Column Space, Null Space, Row Space and Left Null Space

– Projection, Least Squares and Linear Regression – Eigen Value Decomposition and Diagonalization – Special Matrices, Similarity and Algorithms – Singular Value Decomposition.

Probability models and axioms, Bayes’ rule, Conditional Probability, Independence – Discrete random variables: probability mass functions(PMF), expectations, multiple discrete random variables: joint PMFs – Continuous random variables: probability density functions (PDF), expectations, multiple continuous random variables, continuous Bayes rule – Binomial, Poisson, Geometric, Exponential, Uniform and Normal Distributions – Derived distributions; convolution; covariance and correlation – Weak law of large numbers, central limit theorem.

Parameter Estimation – Hypothesis Testing – Application of Hypothesis Testing in Statistics: case studies- Regression – Analysis of Variance – Non parametric Hypothesis Tests – Experiment Design

Pre-Requisite(s): Basics of Linear Algebra
Course Type: Theory

Course Objectives

• This course aims to provide solid mathematical foundations to understand, formulate and solve important problems in real-life context in the field of Computer Science and Engineering.
• The foundational knowledge offered in this course will also provide necessary skills to quantify and analyze the existing computational systems thus developing an in-depth understanding of such systems.

Course Outcomes

1. CO1: Understand and Apply the basic concepts of vector spaces, subspaces, linear independence, span, basis and dimension and analyze such properties on the given set.
2. CO2: Understand and Apply the concept of inner products and apply it to define the notion of length, distance, angle, orthogonality, orthogonal complement, orthogonal projection, orthonormalization and apply these ideas to obtain least square solution.
3. CO3: Understand the theory of random variable and distributions to analyze the data
4. CO4: Understand the theory of two random variables and analyze the relationship in data analytics
5. CO5: Understand the statistical procedure of hypothesis testing and use it to analyze the data

CO-PO Mapping

Evaluation Pattern: 60/40

Note: Continuous assessments can include quizzes, tutorials, lab assessments, case study and project reviews. Midterm and End semester exams can be a theory exam or lab integrated exam for two hours.

1. Gilbert Strang, Linear algebra for everyone, Wellesley-Cambridge Press, 2020.
2. Axler Sheldon, Linear algebra done right, Springer Nature, 2024.
3. Howard Anton and Chris Rorrers,” Elementary Linear Algebra”, Tenth Edition, 2010 John Wiley & Sons, Inc.
4. David Forsyth, “Probability and Statistics for Computer Science”, Springer international publishing, 2018
5. Ernest Davis, “Linear Algebra and Probability for Computer Science Applications”, CRC Press, 2012