Discrete Structure is a main course for bs four year program specially for math students.This course is purely on math and logic based.
Things you will cover in this course:
- Mathematical reasoning: introduction to logic,
- propositional and predicate
- calculus; negation disjunction and conjunction;
- implication and equivalence;
- truth tables;
- predicates;
- quantifiers;
- natural deduction;
- rules of Inference;
- methods of proofs;
- use in program proving;
- resolution principle; Set theory:
- Paradoxes in set theory;
- inductive definition of sets and proof by induction;
- Relations,
- representation of relations by graphs;
- properties of relations,
- equivalence relations and partitions;
- Partial orderings; Linear and wellordered
- sets; Functions: mappings, injection and surjection,
- composition of
- functions; inverse functions; special functions; Peano postulates; Recursive 20
- function theory; Elementary combinatorics; counting techniques; recurrence
- relation; generating functions.
- Graph Theory: elements of graph theory, Planar Graphs, Graph Colouring,
- Euler graph, Hamiltonian path, trees and their applications.
Reference material:
1. Discrete Mathematical Structure with Application to Computer Science, J.P. Temblay and B Manohar, McGraw-Hill, 2nd Edition.2. Discrete Mathematics, 7th edition, Richard Johnson Baugh, 2008,Prentice Hall Publishers.
3. Discrete Mathematics and Its Applications, 6th edition, Kenneth H. Rosen,2006, McGraw-Hill Book Co.
4. Discrete Mathematical Structures, 4th edition, Kolman, Busby & Ross,2000, Prentice-Hall Publishers.
5. Discrete and Combinatorial Mathematics: An Applied Introduction, Ralph P. Grimaldi, Addison-Wesley Pub. Co., 1985.
6. Logic and Discrete Mathematics: A Computer Science Perspective byWinifred Grassman, Jean-Paul Tremblay, Winifred Grassman, Prentice Hall, 1995
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