Fundamentals of Advanced Mathematics

Fundamentals of Advanced Mathematics explains the basic fundamentals of mathematics by introducing it to the readers. It further goes on to explain algebra and the basic math related to it and elaborate on the number theory and number system. Also discussed in the book are the relations and functions, the use of proportional logic, the graph theory and the mathematical induction and recursion and the various theorems and logics related to it. The book also delves upon the cardinal system. It gives some solved examples and the questions to be practiced in the later halves of the chapters. 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 Back Cover