JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Pre-Requisites

UG level course in Mathematics

Course Objectives:

The student should be able to choose appropriate data structures, understand the ADT/libraries, and use it to design algorithms for a specific problem. Students should be able to understand the necessary mathematical abstraction to solve problems. To familiarize students with advanced paradigms and data structure used to solve algorithmic problems. Student should be able to come up with analysis of efficiency and proofs of correctness.

Course Outcomes

After completion of course, students would be able to:

Understand the implementation of symbol table using hashing techniques. Understand the implementation of symbol table using hashing techniques. Develop algorithms for text processing applications. Identify suitable data structures and develop algorithms for computational geometry problems.

UNIT - I

Basics of Data Science: Introduction; Typology of problems; Importance of linear algebra, statistics and optimization from a data science perspective; Structured thinking for solving data science problems.

UNIT - II

Probability spaces, conditional probability, independence; Random variables, distribution functions, probability mass and density functions, functions of random variables, standard univariate discrete and continuous distributions;

UNIT - III

Mathematical expectations, moments, moment generating functions, inequalities; Random vectors, joint, marginal and conditional distributions, conditional expectations, independence, covariance, correlation,

UNIT - IV

Standard multivariate distributions, functions of random vectors; Law of large numbers, central limit theorem. Sampling distributions; Point estimation - estimators, minimum variance unbiased estimation, maximum likelihood estimation, method of moments, consistency; Interval estimation;

UNIT - V

Testing of hypotheses - tests and critical regions, likelihood ratio tests; Linear regression.

Text Books:

G. Strang (2016). Introduction to Linear Algebra, Wellesley-Cambridge Press, Fifth edition, USA. B. L. S. Prakasa Rao, A First Course in Probability and Statistics, World Scientific/Cambridge University Press India, 2009.

Reference Book:

R. V. Hogg, J. W. McKean and A. Craig, Introduction to Mathematical Statistics, 6th Ed., Pearson Education India, 2006. M.Tech. (Data Science) I Year I Semester