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  #2  
3rd December 2015, 08:06 AM
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Re: DSGT Question Papers Mumbai University

Hello, I am studying computers at the Mumbai University and I want the papers of the DSGT of the university.
  #3  
3rd December 2015, 08:12 AM
Super Moderator
 
Join Date: Aug 2012
Re: DSGT Question Papers Mumbai University

Hello, here I am providing you the course details with the reference books and the papers as under:

Discrete Structure and Graph Theory (DSGT)
Detailed syllabus

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

Logic

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

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.

Functions and Pigeon Hole Principle:

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

Graphs

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

Trees

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

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

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

Reference Books:

1 Elements of Applied mathematics, P N & J N Wartikar, Pune Vidarthi Gruha Prakashan
2 Advanced Engineering Mathematics, E Kreyszing, Wiley Eastern Limited
3 Advanced Modern Engineering Mathematics, Glyn James
4 Fourier Transform, Schuam Series
5 Higher Engineering Mathematics, B. V. Ramanna, Tata McGraw Hill

Here I am providing you some papers as under:
DSGT Question Papers Mumbai University





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