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Engineering Mathematics Tutorials

Last Updated : 12 Jun, 2024
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Table of Content

Discrete Mathematics

Propositional and First Order Logic :

  1. Introduction to Propositional Logic
  2. Introduction to Propositional Logic | Set 2
  3. Propositional Equivalences
  4. Predicates and Quantifiers
  5. Predicates and Quantifiers | Set 2
  6. Some theorems on Nested Quantifiers
  7. Rules of Inference
  8. PDNF and PCNF in Discrete Mathematics

Set Theory :

  1. Introduction
  2. Set Operations
  3. Inclusion-Exclusion and its various Applications
  4. Power Set and its Properties
  5. Partial Orders and Lattices
  6. Groups
  7. Introduction and types of Relations
  8. Discrete Mathematics | Representing Relations
  9. Relations | Representations in Matrices and Graphs
  10. Closure of Relations and Equivalence Relations
  11. Number of possible Equivalence Relations on a finite set
  12. Classes (Injective, surjective, Bijective) of Functions
  13. Total number of possible functions
  14. Generating Functions | Introduction and Prerequisites
  15. Generating Functions – Set 2
  16. Sequence, Series and Summations
  17. Independent Sets, Covering and Matching
  18. Introduction to Proofs
  19. Hasse Diagrams
  20. Introduction to Mojette transform
  21. Rings, Integral domains and Fields

>> Quiz on Set Theory and Algebra

Combinatorics :

  1. Pigeon Hole Principle
  2. Combinatorics Basics
  3. PnC and Binomial Coefficients
  4. Generalized PnC Set 1
  5. Generalized PnC Set 2
  6. Corollaries of Binomial Theorem
  7. Number of triangles in a plane if no more than two points are collinear
  8. Sum of squares of even and odd natural numbers
  9. Finding nth term of any Polynomial Sequence
  10. Discrete Mathematics | Types of Recurrence Relations – Set 2

>> Combination and Permutation Practice Questions | Set 1
>> Problem on permutations and combinations | Set 2

Probability :

  1. Mathematics | Probability
  2. Conditional Probability
  3. Bayes’s Formula for Conditional probability
  4. Prosecutor’s Fallacy
  5. Random Variables

Graph Theory :

  1. Graph Theory Basics – Set 1
  2. Graph Theory Basics – Set 2
  3. Graph Types and Applications
  4. Euler and Hamiltonian Paths
  5. Planar Graphs and Graph Coloring
  6. Graph Isomorphisms and Connectivity
  7. Matching (graph theory)
  8. Betweenness Centrality (Centrality Measure)
  9. Mathematics | Walks, Trails, Paths, Cycles and Circuits in Graph
  10. Graph measurements: length, distance, diameter, eccentricity, radius, center
  11. Relationship between number of nodes and height of binary tree

>> Graph theory practice questions

Engineering Mathematics

Linear Algebra :

  1. Matrix Introduction
  2. Different Operations on Matrices
  3. Representations of Matrices and Graphs in Relations
  4. Eigen Values and Eigen Vectors
  5. System of Linear Equations
  6. LU Decomposition of a System of Linear Equations
  7. Doolittle Algorithm : LU Decomposition

>> Quiz on Linear Algebra

Calculus :

  1. Limits, Continuity and Differentiability
  2. Cauchy’s Mean Value Theorem
  3. Lagrange’s Mean Value Theorem
  4. Rolle’s Mean Value Theorem
  5. Unimodal functions and Bimodal functions
  6. Surface Area and Volume of Hexagonal Prism
  7. Inverse functions and composition of functions
  8. Indefinite Integrals

Statistics and Numerical Methods :

  1. Mean, Variance and Standard Deviation
  2. Newton’s Divided Difference Interpolation Formula
  3. Law of total probability
  4. Probability Distributions Set 1 (Uniform Distribution)
  5. Probability Distributions Set 2 (Exponential Distribution)
  6. Probability Distributions Set 3 (Normal Distribution)
  7. Probability Distributions Set 4 (Binomial Distribution)
  8. Probability Distributions Set 5 (Poisson Distribution)
  9. Homogeneous Poisson Process
  10. Nonhomogeneous Poisson Processes
  11. Renewal processes in probability
  12. Mathematics | Covariance and Correlation
  13. Scales of Measurement
  14. Univariate, Bivariate and Multivariate data and its analysis
  15. Hypergeometric Distribution model

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