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| | Key Concepts Covered | |-----------|--------------------------| | Set Theory | Basic set operations, Venn diagrams, power sets, Cartesian products | | Number Theory | Divisibility, prime numbers, modular arithmetic, Euclidean algorithm | | Relations and Digraphs | Properties of relations, equivalence relations, partial orders, directed graphs | | Functions | Injective, surjective, bijective functions; composition and inverse functions | | Mathematical Induction | Principle of mathematical induction, strong induction, well-ordering | | Combinatorics | Permutations, combinations, binomial theorem, pigeonhole principle | | Fundamentals of Probability | Basic probability concepts, conditional probability, Bayes' theorem | | Recurrence Relations and Generating Functions | Solving recurrences, generating functions, Fibonacci sequences | | Graph Theory | Graphs, paths, cycles, Eulerian and Hamiltonian graphs, graph coloring | | Trees | Properties of trees, spanning trees, binary trees, tree traversal algorithms | | Algebraic Structures | Groups, rings, fields, homomorphisms, isomorphisms | | Mathematical Logic | Propositional logic, predicate logic, logical equivalence, quantifiers | | Boolean Algebra | Boolean functions, logic gates, Karnaugh maps, simplification | | Lattices | Partial orders as lattices, distributive and modular lattices | | Language, Grammar and Automata | Formal languages, regular expressions, finite automata, context-free grammars | discrete mathematics by j k sharma pdf free download free
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