Fundamentals of Logic
Basic connectives and truth tables,logical equivalence, laws oflogic, logical implication rules of inference. Quantifiers Propositional logic, equivalences, predicates and quantifiers, rules of inference, introduction to proofs, proof methods.
Sets Theory and Probability
Sets and subsets, set operations, laws of set theory, counting and venn diagrams. A first word on probability, axioms of probability, conditional probability, Bayes' theorem.
Fundamentals of Counting and Properties of Integers
The rules of Sum and Product, Permutations and Combinations, The Binomial theorem, Mathematical Induction, Recursive definitions: Fibonacci and Lucas numbers
Fundamentals of Counting and Properties of Integers
The rules of Sum and Product, Permutations and Combinations, The Binomial theorem, Mathematical Induction, Recursive definitions: Fibonacci and Lucas numbers
Random variables and Probability Distributions
Concept of a random variable Discrete probability distributions, Continuous probability distributions, Mean, Variance and Covariance of random variables. Binomial and Poisson distributions, Exponential and Normal distributions with mean, variables and problems.
Statistical methods and Curve Fitting
Correlation, coefficient of correlations, lines of regression-principle ofleast square. Rank correlation. Curve Fitting- Graphical method, Principle ofleast square- to fit a straight line and parabola. Fitting of other curves ofthe form y= axb y= ae y"= b
Question paper pattern:
• The question paper will have ten questions.
• Each full question will be for 20 marks.
• There will be 2 full questions (with a maximum of four sub questions) from each Module.
• Each full question will have sub questions covering all the topics under a Module.
• The students will have to answer 5 full questions, selecting one full question from each MODULE
Textbooks:
1. Discrete and Combinatorial Mathematics by Ralph P. Grimaldi andB VRamana, 5thedition,Pearson, 2011. (Chapters: 1.1to 1.34.1, 4.2,2.1 to 2.5, 3.1to 3.6)
2. Probability and Statistics for Engineers and Scientists by Walpole Myers Ye Pearson Education, Eighth edition. (Chapters: 3.1-3.3, 4.1to 4.4, 5.3, 5.6, 6.2to 6.4, 6.6, 6.7)
3. Higher Engineering Mathematics by Dr. B.S. Grewal, Khanna publishers, 40th edition (Chapters: 25.12 to25.16,24.1 to24.6)
Reference Books:
1. Discrete Mathematics and its Applications by Kenneth H Rosen, 7th edition, (Indian adaptation by Kamala Krithivasan), Tata McGraw Hill, 2011.
2. Discrete Mathematical Structures with Applications to Computer Science by J.P. Tremblay and R.Manohar, McGrawHill.
3. Probability and Statistics for Engineers by Richard A. Johnson and C. B. Gupta, Pearson Education.
4. Discrete Mathematics by J. K.. Sharma, Macmillan Publishers India Ltd. 3rd edition 2011.