BE Computer Engineering Semester 3 (SE Second Year)University of Mumbai
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# Discrete Structures Semester 3 (SE Second Year) BE Computer Engineering University of Mumbai Topics and Syllabus

SubjectDiscrete Structures
CBCGS [2017 - current]
CBGS [2013 - 2016]
Old [2000 - 2012]

## Topics with syllabus and resources

100.00 Set Theory
• Sets, Venn diagrams, Operations on Sets
• Laws of set theory, Power set and Products
• Partitions of sets, The Principle of Inclusion and Exclusion
200.00 Logic
• Propositions and logical operations, Truth tables
• Equivalence, Implications
• Laws of logic, Normal Forms
• Predicates and Quantifiers
• Mathematical Induction
300.00 Relations, Digraphs 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
400.00 Functions and Pigeon Hole Principle
• Definition and types of functions:- Injective, Surjective and Bijective
• Composition, Identity and Inverse
• Pigeon-hole principle
500.00 Generating Functions and Recurrence Relations
• Series and Sequences
• Generating functions
• Recurrence relations
• Recursive Functions:- Applications of recurrence relations e,g, Factorial, Fibonacci, Binary search, Quick Sort etc.
600.00 Graphs and Subgraphs
• Definitions, Paths and circuits:- Eulerian and Hamiltonian
• Planer graphs, Graph coloring
• Isomorphism of graphs
• Subgraphs and Subgraph isomorphism
700.00 Trees
• Trees and weighted trees
• Spanning trees and minimum spanning tree
• Isomorphism of trees and sub trees
• Prefix codes
800.00 Algebraic Structures
• Algebraic structures with one binary operation:- semigroup, monoids and groups
• Product and quotient of algebraic structures
• Isomorphism, Homomorphism and Automorphism
• Cyclic groups, Normal subgroups
• Codes and group codes
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