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Course: Elements of Mathematics and Statistics
Level: Postgraduate
Time: Currently not offered
Syllabus
Past Exams


Syllabus:
Module 1: Elements of Mathematics
Unit 01: Set theory: Sets and their representation; Universal Set; Empty Set; Subsets; Power Set’ Venn Diagrams; Union and Intersection of Sets; Difference of Sets; Complements of Sets
Unit 02: Relations and Functions: Ordered pairs, Definition of a relation, domain and range of a relation; Functions as a special kind of relation from one set to another, domain and range of a function, real valued functions of the real variable, graphs of standard functions One to one and onto functions, inverse of a function, composite functions

Module 2: Introduction to Statistics
Unit 03: Introduction to Statistics
Unit 04: Statistical Applications, Challenges

Module 3: Data Collection and Presentation
Unit 05: Methods of data collection; Scales of measurement
Unit 06: Data Pre-processing: Coding, Classification, Tabulation etc
Unit 07: Data Visualisation - graphical and tabular; Frequency tables and curves, histogram, Frequency Polygon, Ogive etc

Module 4: Descriptive Statistics
Unit 08: Measures of central tendency
Unit 09: Measures of Dispersion
Unit 10: Measures of Asymmetry
Unit 11: Measures of Relationship
Unit 12: Simple Regression, Regression Vs Correlation
Unit 13: Index and Time Series

Module 5: Basics of Probability
Unit 14: Probability: Concepts: Classical and axiomatic,
Unit 15: properties of a probability measure; conditional probability, etc

Module 6: Independent events and Random variable
Unit 16: Independent events, random variable, discrete and continuous random variable
Unit 17: Distribution function, probability density functions
Unit 18: Probability Distributions such as Normal, Exponential, Binomial, Poisson, Geometric, Negative binomial distributions

Module 7: Statistical Test, Analysis of Variance and Regression analysis
Unit 19: Confidence intervals
Unit 20: Estimatiend Parameters
Unit 21: T-Test
Unit 22: Z-Test
Unit 23: Chi - Square tests, Goodness-of-fit test
Unit 24: Analysis of Variance (ANOVA) and
Unit 25: Analysis of Covariance (ANCOVA)
Unit 26: Regression analysis; Curve fitting

Module 8: Practicals
Unit 27-29: Statistical tests and regression analysis
Unit 30-32: Introduction to statistical analysis tool (such as R)

Reference Texts:
1. David M. Dietz, Christopher D. Barr, and Mine Cetinkaya-Rundel (2015). OpenIntro Statistics, American Institute for Mathematics.
2. Mathematics Class 11th textbook. NCERT.
3. Nicholas J. Horton, Daniel T. Kaplan, and Randall Pruim (2015). A Student’s Guide to R.
4. Freedman, David, Robert Pisani, & Roger Pervis (2007). Statistics. New York: W. W. Norton.
5. James, Gareth, Daniela Witten, Trevor Hastie, & Robert Tibshirani (2013). An Introduction to Statistical Learning: With Applications in R. New York: Springer.
6. Kabacoff, Robert (2015). R In Action: Data Analysis and Graphics with R. Shelter Island, NY: Manning Publications Co.



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Past Exams
Midterm
22.pdf 23.pdf
Semestral
22.pdf 23.pdf
Supplementary and Back Paper
23.pdf

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[Indian Statistical Institute]