Mathematics

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Discrete Mathematics Propositional and First Order Logic Set Theory Combinatorics Probability Graph Theory Engineering Mathematics : Linear Algebra Calculus Statistics and Numerical Methods Quick Links Discrete Mathematics

Propositional and First Order Logic Introduction to Propositional Logic Propositional Equivalences Predicates and Quantifiers Some theorems on Nested Quantifiers Rules of Inference PDNF and PCNF in Discrete Mathematics

Set Theory Introduction Set Operations Inclusion-Exclusion and its various Applications Power Set and its Properties Partial Orders and Lattices Groups Introduction and types of Relations Discrete Mathematics | Representing Relations Relations | Representations in Matrices and Graphs Closure of Relations and Equivalence Relations Number of possible Equivalence Relations on a finite set Classes (Injective, surjective, Bijective) of Functions Total number of possible functions Generating Functions | Introduction and Prerequisites Sequence, Series and Summations Independent Sets, Covering and Matching Introduction to Proofs Hasse Diagrams Introduction to Mojette transform Rings, Integral domains and Fields

Combinatorics Pigeon Hole Principle Combinatorics Basics PnC and Binomial Coefficients Generalized PnC Set Corollaries of Binomial Theorem Number of triangles in a plane if no more than two points are collinear Sum of squares of even and odd natural numbers Finding nth term of any Polynomial Sequence Discrete Mathematics | Types of Recurrence Relations

Probability Mathematics | Probability Conditional Probability Bayes’s Formula for Conditional probability Prosecutor’s Fallacy Random Variables

Graph Theory Graph Theory Basics Graph Types and Applications Euler and Hamiltonian Paths Planar Graphs and Graph Coloring Graph Isomorphisms and Connectivity Matching (graph theory) Betweenness Centrality (Centrality Measure) Mathematics | Walks, Trails, Paths, Cycles and Circuits in Graph Graph measurements: length, distance, diameter, eccentricity, radius, center Relationship between number of nodes and height of binary tree

Linear Algebra Matrix Introduction Different Operations on Matrices Representations of Matrices and Graphs in Relations Eigen Values and Eigen Vectors System of Linear Equations LU Decomposition of a System of Linear Equations Doolittle Algorithm : LU Decomposition

Calculus Limits, Continuity and Differentiability Cauchy’s Mean Value Theorem Lagrange’s Mean Value Theorem Rolle’s Mean Value Theorem Unimodal functions and Bimodal functions Surface Area and Volume of Hexagonal Prism Inverse functions and composition of functions Indefinite Integrals

Statistics and Numerical Methods Mean, Variance and Standard Deviation Newton’s Divided Difference Interpolation Formula Law of total probability Probability Distributions Set 1 (Uniform Distribution) Probability Distributions Set 2 (Exponential Distribution) Probability Distributions Set 3 (Normal Distribution) Probability Distributions Set 4 (Binomial Distribution) Probability Distributions Set 5 (Poisson Distribution) Homogeneous Poisson Process Nonhomogeneous Poisson Processes Renewal processes in probability Mathematics | Covariance and Correlation Scales of Measurement Univariate, Bivariate and Multivariate data and its analysis Hypergeometric Distribution model