Logic, Discrete Mathematical Structures

A subject to be done very carefully! Yes, this subject requires constant and day-2-day practice. What do we have in this subject? Sets,Relations and Fuctions, LOGIC, one that was done in XIIth Standard, Counting Principles, this one includes Permutation, Combination, Pigeonhole Principle, Relations and Digraphs, Groups and Semigroups etc. All the techniques thought in this are very essential part of programming. Sums should be solved daily and contents must be revised.


Fundamentals - Sets and subsets, Operations on sets, Sequences, Division in the integers, Mathematical structures
Logic " Propositions and Logical operations, Conditional Statements, Methods of proof, mathematical induction
Counting " Permutations, Combinations, The pigeon hole principle, elements of probability, recurrence relations
Relations and Digraphs " Product sets and partitions, relations and digraphs, paths in relations and digraphs, properties of relations, equivalence relations, computer representation of relations and digraphs, manipulation of relations, Transitive closure and Warshall;s algorithm
Functions " Functions for computer science, permutation functions, growth of functions
Graph theory " Graphs, Euler paths and circuits, Hamiltonian paths and circuits, coloring graphs
Order relations and structures " Partially ordered sets, External elements of partially ordered sets, Lattices, Finite Boolean algebra, Functions on Boolean algebra, Boolean functions as Boolean polynomials
Trees " labeled trees, tree searching, Undirected trees, Minimal spanning trees
Semigroups and groups " Binary operations, semigroups, products and quotients of semigroups, groups, Products and quotients of groups
Languages and finite state machines " Languages, representation of special languages and grammars, Finite state machines, Semi groups , machines and languages, machines and regular languages
Groups and coding " Coding of binary information and error detection Decoding and error correction

Discrete Mathematical Structures by "Kolman"
Discrete structures by Liu


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