فصل 1: منطق و مجموعه ها
فصل 2: ​​رابطه و توابع
فصل 3: اعداد طبیعی
فصل 4 :بخش پذیری و تجزیه به عامل های اول
فصل 5 : languages
فصل 6 : دستگاه های کراندار
فصل 7 :نظریه ماشین ها
فصل 8: ماشین های تورینگ
فصل 9: گروه ها و حساب پیمانه
فصل 10: مقدمه ای بر نظریه کدگذاری
فصل 11: کدهای GROUP
فصل 12: کلید عمومی رمزنگاری
فصل 13: اصل شمول و عدم شمول
فصل 14 : توابع مولد :
فصل15 : معادلات گوناگون
فصل 16 : روابط بازگشتی
فصل 17 : گراف ها
فصل 18 : وزن گراف ها
فصل 19 : الگوریتم های جست و جو
فصل 20 : گراف جهت دار یا direct graph

نام کتاب:Discrete Mathematics
نویسندگان : W W L Chen
انتشار : Macquarie University 2008
فرمت فایل:PDF
زبان کتاب : انگلیسی

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SECTION A --- BASIC MATERIAL

Chapter 1: LOGIC AND SETS

• Sentences
• Tautologies and Logical Equivalence
• Sentential Functions and Sets
• Set Functions
• Quantifier Logic
• Negation

Chapter 2: RELATIONS AND FUNCTIONS

• Relations
• Equivalence Relations
• Equivalence Classes
• Functions

Chapter 3: THE NATURAL NUMBERS

• Introduction
• Induction

Chapter 4: DIVISION AND FACTORIZATION

• Division
• Factorization
• Greatest Common Divisor
• An Elementary Property of Primes

SECTION B --- COMPUTATIONAL ASPECTS

Chapter 5: LANGUAGES

• Introduction
• Regular Languages

Chapter 6: FINITE STATE MACHINES

• Introduction
• Pattern Recognition Machines
• An Optimistic Approach
• Delay Machines
• Equivalence of States
• The Minimization Process
• Unreachable States

Chapter 7: FINITE STATE AUTOMATA

• Deterministic Finite State Automata
• Equivalence of States and Minimization
• Non-Deterministic Finite State Automata
• Regular Languages
• Conversion to Deterministic Finite State Automata
• A Complete Example

Chapter 8: TURING MACHINES

• Introduction
• Design of Turing Machines
• Combining Turing Machines
• The Busy Beaver Problem
• The Halting Problem

Chapter 9: GROUPS AND MODULO ARITHMETIC

• Addition Groups of Integers
• Multiplication Groups of Integers
• Group Homomorphism

Chapter 10: INTRODUCTION TO CODING THEORY

• Introduction
• Improvement to Accuracy
• The Hamming Metric

Chapter 11: GROUP CODES

• Introduction
• Matrix Codes --- An Example
• Matrix Codes --- The General Case
• Hamming Codes
• Polynomials in Z2[X]
• Polynomial Codes

Chapter 12: PUBLIC KEY CRYPTOGRAPHY

• Basic Number Theory
• The RSA Code

SECTION C --- MATHEMATICAL ASPECTS

Chapter 13: PRINCIPLE OF INCLUSION-EXCLUSION

• Introduction
• The General Case
• Two Further Examples

Chapter 14: GENERATING FUNCTIONS

• Introduction
• Some Simple Observations
• The Extended Binomial Theorem

Chapter 15: NUMBER OF SOLUTIONS OF A LINEAR EQUATION

• Introduction
• Case A --- The Simplest Case
• Case B --- Inclusion-Exclusion
• Case C --- A Minor Irritation
• Case Z --- A Major Irritation
• The Generating Function Method

Chapter 16: RECURRENCE RELATIONS

• Introduction
• How Recurrence Relations Arise
• Linear Recurrence Relations
• The Homogeneous Case
• The Non-Homogeneous Case
• The Method of Undetermined Coefficients
• Lifting the Trial Functions
• Initial Conditions
• The Generating Function Method

Chapter 17: GRAPHS

• Introduction
• Valency
• Walks, Paths and Cycles
• Hamiltonian Cycles and Eulerian Walks
• Trees
• Spanning Tree of a Connected Graph

Chapter 18: WEIGHTED GRAPHS

• Introduction
• Minimal Spanning Tree

Chapter 19: SEARCH ALGORITHMS

• Depth-First Search
• Breadth-First Search
• The Shortest Path Problem

Chapter 20: DIGRAPHS

• Introduction
• Networks and Flows
• The Max-Flow-Min-Cut Theorem