06CS34 - Discrete Mathematical Structures Regulation 2006 - 2007 |
PART A |
UNIT – I |
Set Theory: Sets and Subsets, Set Operations and the Laws of Set
Theory, Counting and Venn Diagrams, A First Word on Probability,
Countable and Uncountable Sets. |
UNIT – II |
Fundamentals of Logic: Basic Connectives and Truth Tables, Logic
Equivalence The Laws of Logic, Logical Implication Rules of
Inference |
UNIT – III |
Fundamentals of Logic contd.: The Use of Quantifiers, Quantifiers,
Definitions and the Proofs of Theorems |
UNIT – IV |
Properties of the Integers: Mathematical Induction, The Well
Ordering Principle Mathematical Induction, Recursive Definitions |
PART B |
UNIT – V |
Relations and Functions: Cartesian Products and Relations,
Functions Plain and One-to-One, Onto Functions Stirling
Numbers of the Second Kind, Special Functions, The Pigeon-hole
Principle, Function Composition and Inverse Functions |
UNIT – VI |
Relations contd.: Properties of Relations, Computer Recognition
Zero-One Matrices and Directed Graphs, Partial Orders Hasse
Diagrams, Equivalence Relations and Partitions |
UNIT – VII |
Groups: Definitions, Examples, and Elementary Properties,
Homomorphisms, Isomorphisms, and Cyclic Groups, Cosets, and
Lagranges Theorem
Coding Theory and Rings: Elements of Coding Theory, The
Hamming Metric, The Parity Check, and Generator Matrices |
UNIT – VIII |
Group Codes: Decoding with Coset Leaders, Hamming Matrices
Rings and Modular Arithmetic: The Ring Structure Definition and
Examples, Ring Properties and Substructures, The Integers Modulo
n |
REFERENCE |
TEXT BOOKS: |
Discrete and Combinatorial Mathematics, Ralph P. Grimaldi, 5th
Edition, PHI/Pearson Education, 2004.
(Chapter 3.1, 3.2, 3.3, 3.4, Appendix 3, Chapter 2, Chapter 4.1, 4.2,
Chapter 5.1 to 5.6, Chapter 7.1 to 7.4, Chapter 16.1, 16.2, 16.3, 16.5
to 16.9, and Chapter 14.1, 14.2, 14.3).
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Reference Books |
1. Discrete Mathematics and its Applications, Kenneth H. Rosen, 6th
Edition, McGraw Hill, 2007.
2. Discrete Mathematical Structures: Theory and Applications,
D.S. Malik and M.K. Sen, Thomson, 2004.
3. Discrete Mathematics with Applications, Thomas Koshy,
Elsevier, 2005.
4. A Treatise on Discrete Mathematical Structures, Jayant Ganguly,
Sanguine Technical Publishers, 2006.
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