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The Best Books for Discrete Mathematics/Discrete Structures/Combinatorics

Discrete Mathematics/Discrete Structures/Combinatorics

This is typically a compulsory course in many undergrad CS programs. While most traditional engineering branches are based on ideas of continuous domain mathematics and involve calculus; much of Computer Science is based on Discrete Mathematics. A course in Discrete Mathematics typically covers sets, relations, recurrence relations, number theory, groups, fields, permutations and combinations, complexity etc.  Here's a quick look at some of the topics often covered in a Discrete Mathematics course.

Propositional logic: Syntax and semantics, valid, satisfiable and unsatisfiable formulas, the validity of some logical arguments.Proof TechniquesForward proof, proof by contradiction, contrapositive proofs, proof of necessity and sufficiency.Sets, relations and functions: Operations on sets, relations and functions, binary relations, partial ordering relations, equivalence relations, principles of mathematical induction. Size of a set: Finite and infinite sets, countable and uncountable sets, Cantor's diagonal argument and the power set theorem, Schröder-Bernstein theorem. Combinatorics: Basic counting techniques: inclusion and exclusion, pigeon-hole principle, permutation, combination, summations. Introduction to recurrence relations and generating functions. Algebraic structures and morphisms : Algebraic structures with one binary operation - semigroups, monoids and groups, congruence relation and quotient structures. Free and cyclic monoids and groups, permutation groups, substructures, normal subgroups. Algebraic structures with two binary operations - rings, integral domains and fields. Boolean algebra and Boolean ring. Graphs and trees: degree, path, cycle, subgraphs, isomorphism, Eulerian and Hamiltonian walks, graph coloring, planar graphs, trees.

Here are some recommended books for studying Discrete Mathematics, in case you'd like to take a look at them on Amazon.

Discrete Mathematics

 


Discrete Mathematics with Applications
 


Discrete Mathematics 
 


Discrete Mathematics 
 


Discrete Mathematics and Its Applications 
 


Discrete Mathematics 
 


Schaum's Outline of Discrete Mathematics, Revised Third Edition (Schaum's Outline Series) 
 

Discrete Mathematics (7th Edition)
 

Discrete Mathematics
 

Concrete Mathematics: A Foundation for Computer Science (2nd Edition) 
 

2000 Solved Problems in Discrete Mathematics
 

Discrete Mathematics DeMYSTiFied 
 

Discrete Mathematics with Ducks 
 
Discrete Mathematics and Its Applications
 

Discrete Mathematics: Introduction to Mathematical Reasoning
 

Discrete Mathematics With Applications
 

Discrete Mathematics (5th Edition)
 
 
Schaum's Outline of Discrete Mathematics, 3rd Ed. (Schaum's Outline Series) 
 

Discrete Mathematics (5th Edition)
 Discrete Mathematics with Graph Theory (3rd Edition)