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  #2  
5th December 2015, 12:42 PM
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Re: DSF notes for Mumbai University

Hello, I want the details of the DSF notes of Mumbai University and I want to know some of the reference books please provide me.
  #3  
5th December 2015, 12:42 PM
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Join Date: Aug 2012
Re: DSF notes for Mumbai University

Hello, herte I am providing you the reference books for the DSF of Mumbai University as under:

Text books

1. Ralph P. Grimaldi, B. V. Ramana, “ Discrete and Combinatorial Mathematics” Fifth Edision, Pearson Education.
2. Bernard Kolman, Robert C. Busby ,Sharon Cutler Ross, Nadeem-ur-Rehman, “ Discrete Mathematical Structures” Pearson Education.
3. D. S. Malik and M. K. Sen , “Discrete Mathematical Structures”, Thomson

Reference Books
1. Kenneth H. Rosen, “Discrete Mathematics and its Applications”, Tata McGraw- Hill.
2. Garry Haggard, John Schlipf, Sue Whitesides. “Discrete Mathematics For Computer Science”, Thomson.
3. Joe Mott, Abraham Kandel and Theodore Baker, “ Discrete Mathematics for Computer Scientist and Mathematicians”, Second Edition PHI
4. Richard Johnsonbaugh, “ Discrete Mathematics “ Pearson Education
5. C. L. Liu, “ Elements of Discrete Mathematics” Tata McGRAW-Hill

Syllabus:
Discrete Structure and Graph Theory (DSGT)

Detailed syllabus

01.
Set Theory
Sets , Venn diagrams, Operations on sets
Laws of set theory, Power set and products
Partitions of sets, The Principle of Inclusion-Exclusion 3

02.
Logic
Propositions and logical operations, Truth tables
Equivalence, Implications
Laws of logic, Normal Forms
Predicates and Quantifiers
Mathematical Induction

03.
Relations, Diagraph and Lattices
Relations, paths and digraphs;
Properties and types of binary relations;
Manipulation of relations, closures, Warshall's algorithm
Equivalence and Partial ordered relations;
Posets and Hasse diagram;
Lattice.

04.
Functions and Pigeon Hole Principle:
Definition and types of functions : injective, surjective and bijective;
Composition, identity and inverse;
Pigeon-hole principle.

05.
Graphs
Definition;
Paths and circuits : Eulerian, Hamiltonian;
Planer graphs, Graph coloring
Isomorphism Of Graphs
Traveling salesperson problem

06.
Trees
Trees, Rooted tree and path length in rooted tree
Spanning tree and minimum spanning tree
Isomorphism of trees
Weighted Trees and Prefix Codes

07.
Algebraic Structures
Algebraic structures with one binary operation - semigroups, monoids and groups.
Product and quotient of algebraic structures
Isomorphism, homomorphism, automorphism;
Cyclic Groups, Normal subgroup, Codes and group codes
Algebraic structures with two binary operations - rings, integral domains and fields.
Ring Homomorphisms and Isomorphisms

08.
Generating Functions and Recurrence Relations.
Series and Sequences;
Generating functions;
Recurrence relations;
Applications: Solving Differential equations, Fibonacci


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