http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
The Math Thought Mindset: Logic, Reasoning, and Proofs prioritizes the understanding of how things work, which is crucial for mastering mathematics. This mindset is central in computer science, economics, artificial intelligence, data science, machine learning, and engineering, where analytical reasoning determines success. Mathematics is a language of reasoning that reveals deeper truths about our world.This book embraces the Math Thought Mindset as a bridge between computational problem-solving and abstract mathematical reasoning. This text aims to develop mathematical intuition by guiding students to construct logical arguments, recognize patterns, and confidently write proofs.This subtle shift in thinking distinguishes students who excel in mathematics from those who merely pass by memorizing steps. Many students struggle with mathematics because of how they were trained to rely on rote memorization. Students struggle because they have learned to focus on getting the right answer rather than understanding why an answer is correct, believing that mastering procedures is the same as mastering mathematical concepts.This book challenges that notion. Readers will learn to construct arguments, recognize patterns, and think critically. Whether the reader is encountering formal proofs for the first time or needs to refine a skill set, this text is designed to guide the student of mathematics forward. By the end of this text, readers will improve problem-solving and foster a deeper mathematical understanding.Step-by-step explanations and examples are presented through each section, aiming to bridge the gap between computational mathematics and abstract reasoning. Exercise sets contain a mix of problems requiring little background in proof-based mathematics and challenging problems for those seeking deeper engagement with the material.
Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Dedication -- Contents -- About the Author -- Acknowledgments -- Introduction -- 1. Logic Basics -- 1.1. Introduction -- 1.2. Basic Logical Operators -- 1.3. Logical Equivalences -- 1.4. Conditional Statements -- 1.5. Universal and Existential Quantifiers -- 1.6. Negating Quantifiers -- 2. Deductive Reasoning -- 2.1. Introduction -- 2.2. Valid Argument -- 2.3. Rules of Inference -- 2.4. Quantified Rules of Inference -- 2.5. Heuristic Diagrams -- 3. Elementary Set Theory -- 3.1. Introduction -- 3.2. Set Fundamentals
3.3. Set Operations -- 3.4. Element Chasing -- 3.5. Set Identities and Laws -- 3.6. The Pigeonhole Principle -- 4. Proof Methods -- 4.1. Introduction -- 4.2. Grammar and Fundamentals -- 4.3. Quantified Statements -- 4.4. Direct Proofs -- 4.5. Indirect Proofs: Contradictions -- 4.6. Indirect Proofs: Contrapositive -- 4.7. Mathematical Induction -- 4.8. Strong Mathematical Induction -- 4.9. Other Proof Methods -- 4.10. Developing Conjectures -- 5. Boolean Algebra -- 5.1. Introduction -- 5.2. Boolean Algebra -- 5.3. Canonical Forms: SOP and POS -- 5.4. Karnaugh Maps -- 5.5. Digital Circuits
5.6. Universal Gates -- A. Appendix -- A.1. Rules of Inferences -- A.2. Quantified Rules of Inferences -- A.3. Logic and Venn Diagrams -- A.4. Well-Ordering Principle -- A.5. List of Commonly Used Symbols -- Index