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SYLLABUS
UNIT-I
The foundations: logic and proofs Propositional Logic - Applications of Propositional Logic - Propositional Equivalence - Predicates and Quantifiers - Nested Quantifiers - Rules of Inference - Introduction to Proofs - Proof Methods and Strategy.
UNIT-II
Basic structures, sets, functions, sequences, sums matrices and relations sets Functions - Sequences & Summations - Cardinality of Sets and Matrices Relations - Relations and Their Properties - n-ary Relations and Their Applications - Representing Relations - Closures of Relations - Equivalence Relations - Partial Orderings.
UNIT-III
Algorithms, induction and recursion Algorithms - The Growth of Functions - Complexity of Algorithms, Induction and Recursion: Mathematical Induction - Strong Induction and Well-Ordering - Recursive Definitions and Structural Induction - Recursive Algorithms - Program Correctness
UNIT-IV
Discrete probability and advanced counting techniques An Introduction to Discrete Probability - Probability Theory - Bayes’ Theorem - Expected Value and Variance. Advanced Counting Techniques: Recurrence Relations - Solving Linear Recurrence Relations - Divide-and-Conquer Algorithms and Recurrence Relations - Generating Functions - Inclusion- Exclusion - Applications of Inclusion-Exclusion
UNIT-V
Graphs and trees Graphs: Graphs and Graph Models - Graph Terminology and Special Types of Graphs - Representing Graphs and Graph Isomorphism - Connectivity - Euler and Hamilton Paths - Shortest-Path Problems - Planar Graphs - Graph Coloring. Trees: Introduction to Trees - Applications of Trees - Tree Traversal - Spanning Trees - Minimum Spanning Trees
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CategoriesEngineering
Format EPUB
TypeeBook