Lesson 135 LAST LESSON: END OF COURSE - Final Words | Discrete Mathematics COURSE OUTCOMES

~Kindly support via Super Chat & Super Stickers in[Comments]. ___________________________________________________________ Udemy R with Complete data science Course: https://www.udemy.com/course/r-progra... For Code, Slides and Notes https://fahadhussaincs.blogspot.com/ Do Subscribe, likes and Shares to others. Chapter 1 The Foundations: Logic and Proofs 1.1 Propositional Logic 1.2 Applications of Propositional Logic 1.3 Propositional Equivalences 1.4 Predicates and Quantifiers 1.5 Nested Quantifiers 1.6 Rules of Inference 1.7 Introduction to Proofs 1.8 Proof Methods and Strategy Chapter 2 Basic Structures: Sets, Functions, Sequences, Sums, and Matrices 2.1 Sets 2.2 Set Operations 2.3 Functions 2.4 Sequences and Summations 2.5 Cardinality of Sets 2.6 Matrices Chapter 3 Algorithms 3.1 Algorithms 3.2 The Growth of Functions 3.3 Complexity of Algorithms Chapter 4 Number Theory and Cryptography 4.1 Divisibility and Modular Arithmetic 4.2 Integer Representations and Algorithms 4.3 Primes and Greatest Common Divisors 4.4 Solving Congruences 4.5 Applications of Congruences 4.6 Cryptography Chapter 5 Induction and Recursion 5.1 Mathematical Induction 5.2 Strong Induction and Well-Ordering 5.3 Recursive Definitions and Structural Induction 5.4 Recursive Algorithms 5.5 Program Correctness Chapter 6 Counting 6.1 The Basics of Counting 6.2 The Pigeonhole Principle 6.3 Permutations and Combinations 6.4 Binomial Coefficients and Identities 6.5 Generalized Permutations and Combinations 6.6 Generating Permutations and Combinations Chapter 7 Discrete Probability 7.1 An Introduction to Discrete Probability 7.2 Probability Theory 7.3 Bayes’ Theorem 7.4 Expected Value and Variance Chapter 8 Advanced Counting Techniques 8.1 Applications of Recurrence Relations 8.2 Solving Linear Recurrence Relations 8.3 Divide-and-Conquer Algorithms and Recurrence Relations 8.4 Generating Functions 8.5 Inclusion–Exclusion 8.6 Applications of Inclusion–Exclusion Chapter 9 Relations 9.1 Relations and Their Properties 9.2 n-ary Relations and Their Applications 9.3 Representing Relations 9.4 Closures of Relations 9.5 Equivalence Relations 9.6 Partial Orderings Chapter 10 Graphs 10.1 Graphs and Graph Models 10.2 Graph Terminology and Special Types of Graphs 10.3 Representing Graphs and Graph Isomorphism 10.4 Connectivity 10.5 Euler and Hamilton Paths 10.6 Shortest-Path Problems 10.7 Planar Graphs 10.8 Graph Coloring Chapter 11 Trees 11.1 Introduction to Tree 11.2 Applications of Trees 11.3 Tree Traversal 11.4 Spanning Trees 11.5 Minimum Spanning Trees Chapter 12 Boolean Algebra 12.1 Boolean Functions 12.2 Representing Boolean Functions 12.3 Logic Gates 12.4 Minimization of Circuits Chapter 13 Modeling Computation 13.1 Languages and Grammars 13.2 Finite-State Machines with Output 13.3 Finite-State Machines with No Output 13.4 Language Recognition 13.5 Turing Machines Discrete Mathematics or Discrete Structures in Urdu/Hindi by Fahad Hussain.    / @fahadhussaintutorial   Discrete mathematics is the study of mathematical structures that are countable or otherwise distinct and separable which is used in the Data Science and Machine Learning including Examples of structures that are discrete are combinations, graphs, and logical statements. Discrete structures can be finite or infinite. For Complete course Playlist's YouTube Channel:    / fahadhussai.  . For Complete course Playlist's YouTube Channel:    / @fahadhussaintutorial   For Complete course of Android    • The complete Android Application Developme...   For Complete course of C Language:    • C language tutorial for beginners Urdu/Hindi   For Complete course of C# (Sharp) Language:    • C# Tutorial For Beginners in Hindi/Urdu   For Complete course of Deep Learning:    • Deep learning from Scratch | Deep learning...   For Complete course of Machine Learning:    • Machine Learning using Python 2021 in Urdu...   For Complete course of Python:    • Python tutorial for beginners   For Complete course of Swift:    • Swift Programming For IOS From Scratch | S...   For Complete course of iOS:    • IOS Mobile App Development Tutorial for be...   For Complete course of NLP:    • Natural Language Processing (NLP) with Dee...   #datascience #discretemathematics #discretemaths #set #graph #graphtheory #trees #predicate #quantifier #datascience #propositions #datascience #propositionallogic #proof #discrete_mathematics #directproof #indirectproof #discrete #mathematicalinduction #fahad #fahadhussain #fahadhussaincs #function #relation #ai #NumberTheory #Cryptography #BooleanFunctions #Booleanalgebra #counting #induction #recursion