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Discrete Mathematics screenshot
Discrete Mathematics screenshot
Discrete Mathematics screenshot
Discrete Mathematics screenshot
Discrete Mathematics screenshot
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128
Sub Topics
246
MCQs
104
MCOs
174
True/False
102
Fill Blanks
28
Rearrange
95
Matching
43
Comprehensions
90
Flashcard Decks
Curriculum

What You'll Learn

01 Fundamentals of Logic
2 topics
1 Propositions and Logical Operations
  • Propositional Logic
  • Truth Tables
  • Logical Equivalence
  • Predicates and Quantifiers
2 Logical Inference and Proofs
  • Rules of Inference
  • Direct Proofs
  • Proof by Contradiction
  • Mathematical Induction
  • Strong Induction
  • The Well-Ordering Principle
02 Set Theory
3 topics
1 Basic Set Concepts
  • Set Notation and Operations
  • Venn Diagrams
  • Set Identities
  • Power Sets
2 Relations Between Sets
  • Cartesian Products
  • Set Cardinality
  • Countable and Uncountable Sets
  • Cantor's Diagonal Argument
3 Multisets and Fuzzy Sets
  • Multiset Operations
  • Fuzzy Set Theory
  • Applications
03 Functions and Relations
3 topics
1 Functions
  • Domain and Range
  • Types of Functions (Injective, Surjective, Bijective)
  • Function Composition
  • Inverse Functions
2 Relations
  • Properties of Relations
  • Equivalence Relations
  • Partial Orders
  • Total Orders
3 Closures of Relations
  • Reflexive Closure
  • Symmetric Closure
  • Transitive Closure
04 Combinatorics
3 topics
1 Counting Principles
  • Sum and Product Rules
  • Permutations
  • Combinations
  • The Pigeonhole Principle
2 Advanced Counting Techniques
  • Inclusion-Exclusion Principle
  • Recurrence Relations
  • Generating Functions
  • Catalan Numbers
3 Binomial Coefficients
  • Pascal's Triangle
  • Binomial Theorem
  • Multinomial Coefficients
05 Number Theory
4 topics
1 Divisibility and Modular Arithmetic
  • Division Algorithm
  • Prime Numbers
  • Greatest Common Divisors
  • Least Common Multiples
2 Modular Arithmetic
  • Congruence Relations
  • Modular Exponentiation
  • Solving Modular Equations
3 Number-Theoretic Functions
  • Euler's Phi Function
  • Perfect Numbers
  • Fermat's Little Theorem
  • Euler's Theorem
4 Applications in Cryptography
  • RSA Algorithm
  • Primality Testing
  • Factorization Algorithms
06 Graph Theory
5 topics
1 Basic Graph Concepts
  • Vertices and Edges
  • Types of Graphs (Simple, Directed, Weighted)
  • Graph Representations (Adjacency Matrix, Adjacency List)
  • Graph Isomorphism
2 Graph Connectivity
  • Paths and Cycles
  • Eulerian and Hamiltonian Paths
  • Connectedness
  • Strong Connectivity in Directed Graphs
3 Trees
  • Properties of Trees
  • Spanning Trees
  • Minimum Spanning Trees
  • Rooted Trees
4 Graph Coloring
  • Vertex Coloring
  • Edge Coloring
  • Chromatic Number
  • Four-Color Theorem
5 Planar Graphs
  • Euler's Formula
  • Kuratowski's Theorem
  • Dual Graphs
07 Algebraic Structures
3 topics
1 Groups
  • Group Properties
  • Subgroups
  • Cyclic Groups
  • Permutation Groups
2 Rings and Fields
  • Ring Properties
  • Integral Domains
  • Field Properties
  • Finite Fields
3 Boolean Algebra
  • Boolean Functions
  • Logic Gates
  • Minimization of Boolean Functions
  • Karnaugh Maps
08 Algorithms and Complexity
4 topics
1 Algorithm Analysis
  • Time Complexity
  • Space Complexity
  • Asymptotic Notation (Big-O, Big-Omega, Big-Theta)
2 Recursive Algorithms
  • Divide and Conquer
  • Master Theorem
  • Recurrence Relations
3 Graph Algorithms
  • Breadth-First Search
  • Depth-First Search
  • Shortest Path Algorithms (Dijkstra's, Bellman-Ford)
  • Topological Sorting
4 Computational Complexity
  • P and NP Classes
  • NP-Completeness
  • Cook's Theorem
  • Reducibility
09 Formal Languages and Automata
4 topics
1 Languages and Grammars
  • Alphabet and Strings
  • Formal Grammars
  • Chomsky Hierarchy
2 Finite Automata
  • Deterministic Finite Automata (DFA)
  • Nondeterministic Finite Automata (NFA)
  • Regular Expressions
  • Regular Languages
3 Context-Free Languages
  • Context-Free Grammars
  • Pushdown Automata
  • Parsing Techniques
4 Turing Machines
  • Definition and Examples
  • Computational Models
  • Decidability and the Halting Problem
  • Church-Turing Thesis
10 Discrete Probability
3 topics
1 Probability Spaces
  • Sample Spaces and Events
  • Probability Functions
  • Conditional Probability
  • Bayes' Theorem
2 Random Variables
  • Discrete Random Variables
  • Probability Mass Functions
  • Expected Value and Variance
  • Joint Distributions
3 Probabilistic Methods in Computer Science
  • Randomized Algorithms
  • Markov Chains
  • Information Theory Basics
  • Error-Correcting Codes

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