Fundamentals of Advanced Mathematics

Cover
Title Page
Copyright
ABOUT THE AUTHOR
TABLE OF CONTENTS
List of Figures
List of Tables
List of Abbreviations
Preface
Chapter 1 Fundamentals of Mathematics
	1.1. Introduction
	1.2. Proof And Mathematical Argument
	1.3. Sets, Relations, And Functions
	1.4. Construction And Properties Of Number Systems
	1.5. Some Number Theory
	1.6. Case Study: Analysis On Mathematics Fundamental Knowledge For Mathematics Engineering Courses Based on A Comparative Study Of Students’ Entry Performance
	References
Chapter 2 Algebra And Basic Math
	2.1. Fundamentals Of Algebra
	2.2. Operations On Monomials and Polynomials
	2.3. Linear Equations In One Variable
	2.4. Problems To Solve
	References
Chapter 3 Number Theory And Number System
	3.1. Introduction
	3.2. Number Theory
	3.3. Facts About Number Theory
	3.4. Number Systems, Base Conversions, And Computer Data Representation
	3.5. Conversions
	3.6. Number Systems
	3.7. Conclusion
	References
Chapter 4 Relations And Functions
	4.1. Introduction
	4.2. Binary Relations
	4.3. Functions
	4.4. Case Study: A Mathematical-Algorithmic Approach To Sets
	References
Chapter 5 Propositional Logic
	5.1. Propositional Logic
	5.2. Introduction
	5.3. Connectives
	5.4. Tautologies
	5.5. Contradictions
	5.6. Contingency
	5.7. Propositional Equivalences
	5.8. Inverse, Converse, And Contra-Positive
	5.9. Duality Principle
	5.10. Predicate Logic
	5.11. Well-Formed Formula
	5.12. Quantifiers
	5.13. Nested Quantifiers
	5.14. Rules Of Inference
	5.15. Operators And Postulates
	5.16. Semigroup
	5.17. Group
	5.18. Abelian Group
	5.19. Cyclic Group And Subgroup
	5.20. Partially Ordered Set (Poset)
	5.21. Hasse Diagram
	5.22. Linearly Ordered Set
	5.23. Lattice
	5.24. Case Study 1: The Pragmatics Of Telling The Truth
	References
Chapter 6 Graph Theory
	6.1. Introduction
	6.2. Links And Their Structures
	6.3. Basic Structural Properties
	6.4. Graph Theory Trees
	6.5. Graph Theory Application
	6.6. A Graph—Theoretic Data Model For Genome Mapping Databases
	6.7. Case Study: Applying Graph Theory To Interaction Design
	References
Chapter 7 Mathematical Induction And Recursion
	7.1. Introduction
	7.2. The Principle Of Mathematical Induction
	7.3. Proof By Induction: Introduction
	7.4. Induction And Recursion
	7.5. Strong Induction
	7.6. Case Study: The Flipping Glasses Puzzle
	References
Chapter 8 Cardinality
	8.1. Introduction
	8.2. What Is Cardinality
	8.3. Types Of Cardinality
	8.4. Types Of Sets
	8.5. Subsets
	8.6. Sets With The Same Cardinality
	8.7. Set Theory Symbols
	8.8. Boolean Algebra
	8.9. Values Of Cardinality
	8.10. Elementary Theorems
	8.11. Advanced Theorems
	8.12. Cardinality Of The Continuum
	8.13. Controversies
	8.14. Conclusion
	References
Index
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