"excellent"
"hi, thank you for your app. I love the way you teach, and the support messages through answering questions are very warm. im giving five stars, but I do also want to mention there are text mistakes and one question on contingency seemed to have all wrong answers. thank you"
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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Discrete Mathematics
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