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تحميل Discrete Mathematics basics

Mathematics 2024-01-20

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عدد الدروس 44

قسم Mathematics

Discrete Mathematics

Lec 1 Boolean Functions

Lec 2 Propositional Calculus Introduction

Lec 3 First Order Logic Introduction

Lec 4 First Order Logic Introduction Cont d

Lec 5 Proof System for Propcal

Lec 6 First Order Logic wffs interpretations models

Lec 7 Soundness and Completeness of the First Order Proof System

Lec 8 Sets Relations Functions

Lec 9 Functions Embedding of the theories of naturals numbers and integers in Set Theory

Lec 10 Embedding of the theories of integers and rational numbers in Set Theory Countable Sets

Lec 11 Introduction to graph theory

Lec 12 Trees Cycles Graph coloring

Lec 13 Bipartitie Graphs

Lec 14 Bipartitie Graphs Edge Coloring and Matching

Lec 15 Planar Graphs

Lec 16 Graph Searching BFS and DFS

Lec 17 Network Flows

Lec 18 Counting Spanning Trees in Complete Graphs

Lec 19 Embedding of the theory of ral numbers in Set Theory Paradoxes

Lec 20 ZF Axiomatization of Set Theory

Lec 21 Partially ordering relations

Lec 22 Natural numbers divisors

Lec 23 Lattices

Lec 24 GCD Euclid s Algorithm

Lec 25 Prime numbers

Lec 26 Congruences

Lec 27 Pigeon Hole Principle

Lec 28 Stirling Numbers Bell Numbers

Lec 29 Generating Functions

Lec 30 Product of Generating Functions

Lec 31 Composition of Generating Function

Lec 32 Principle of Inclusion Exclusion

Lec 33 Rook placement problem

Lec 34 Solution of Congruences

Lec 35 Chinese Remainder Theorem

Lec 36 Totient Congruences Floor and Ceiling Functions

Lec 37 Introduction to Groups

Lec 38 Modular Arithmetic and Groups

Lec 39 Dihedral Groups Isomorhphisms

Lec 40 Cyclic groups Direct Products Subgroups

Lec 41 Cosets Lagrange s theorem

Lec 42 Rings and Fields

Lec 43 Construction of Finite Fields

Mathematics
2024-01-20