MATH 204 • Discrete Mathematics • Final
Number Theory
Definition of Divisibility
Example 1
Example 2
Example 3
Division Algorithm
Definition of Modular Arithmetic
Example 1
Properties of Modular Arithmetic
Example 1
Example 2
Prime Numbers
Example 1
Example 2
Example 3
GCD Greatest Common Divisor
LCM Least Commun Multiple
Example 1
Euclidian Algorithm
Example 1
Bézout Identity
Example 1
Example 2
Example 3
Inverse of a Number in Modular Arithmetic
Primitive Root
Discrete Logarithm
Fermat's Little Theorem
Solving Linear Congruences
Example 1
Example 2
Algortithm and Complexity
Big-O Notation
Example 1
Example 2
Example 3
Example 4
Sum Property of Big-O Notation
Multiplication Property of Big-O Notation
Example 1
Example 2
Big-Omega Notation
Big-Theta Notation
Example 1
Example 2
Linear Search Algorithm
Binary Search Algorithm
Bubble Sort Algorithm
Counting Part 1
Introduction to Counting
Exam like Question 6
Exam like Question 7
Combination & Permutation: Intuition
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Combination
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Permutation 1
Permutation 2
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Exam like Question 16
Counting Part 2
Binomial Theorem
Example 1
Example 3
Example 2
Pascal Identity
Vandermonde's Identity
Example 1
Combinatorial Proof
Example 1
Principle Inclusion-Exclusion
Example 1
Example 2
Distributing Objects into Boxes
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Pigeonhole Principle
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Recurrence Relations
Introduction
Homogenous Recurrence Relations
Example 1
Example 2
Example 3
Example 4
Non Homogenous Recurrence Relations
Example5
Example 6
Creating Recurrence Relations
Example 7
Example 8
Example 9
Generating Functions
Definition
Example 1
Example 2
Example 3
Example 4
Example 5
Extended Binomial Theorem
Counting Problems with Generating Functions
Example 6
Example 7
Example 8
Example 9
Example 10
Graph Theory
Introduction
Example 1
Graph Terminology
Example 2
Handshaking Theorem
Example 3
Example 4
Special Graphs
Example 5
Example 6
Bipartite Graphs
Example 7
Example 8
Complete Bipartite Graph
Matching
Example 9
Subgraph
Example 10
Subgraph Induced
Edge Contraction
Example 11
Complementary Graph
Example 12
Example 13
Example 14
Adjacency Matrices - Undirected Graphs
Adjacency Matrices - Directed Graphs
Example 15
Example 16
Incidence Matrices
Example 17
Isomorphism of Graphs
Example 18
Example 19
Example 20
Example 21
Definition of Paths and Circuits
Connected Graphs
Euler Paths and Circuits
Example 22
Hamilton Paths and Circuits
Example 23
Example 24
Sample Final Problems
Exam like Question 1
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Exam like Question 6
Exam like Question 7
Exam like Question 8
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Exam like Question 11
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Exam like Question 15
Exam like Question 16
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Eğitmen
Eğitmen
2007 yılında Galatasaray Üniversitesi Bilgisayar Mühendisliği bölümünden birincilikle mezun olduktan sonra Fransa'da Kriptoloji üzerine Fransa hükümeti tarafından verilen bursla yüksek lisans yaptım. Devamında ikinci kez sınava girerek Boğaziçi Matematik bölümünü de bitirdim. Yaklaşık 15 yıldır üniversite öğrencilerine dersler vermekteyim.
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