Title
Proofs: A Longform Mathematics Textbook (The Longform Math Textbook Series)-used
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This Textbook Is Designed For Students. Rather Than The Typical Definitiontheoremproofrepeat Style, This Text Includes Much More Commentary, Motivation And Explanation. The Proofs Are Not Terse, And Aim For Understanding Over Economy. Furthermore, Dozens Of Proofs Are Preceded By 'Scratch Work' Or A Proof Sketch To Give Students A Bigpicture View And An Explanation Of How They Would Come Up With It On Their Own.This Book Covers Intuitive Proofs, Direct Proofs, Sets, Induction, Logic, The Contrapositive, Contradiction, Functions And Relations. The Text Aims To Make The Ideas Visible, And Contains Over 200 Illustrations. The Writing Is Relaxed And Conversational, And Includes Periodic Attempts At Humor.This Text Is Also An Introduction To Higher Mathematics. This Is Done Inpart Through The Chosen Examples And Theorems. Furthermore, Following Every Chapter Is An Introduction To An Area Of Math. These Include Ramsey Theory, Number Theory, Topology, Sequences, Real Analysis, Big Data, Game Theory, Cardinality And Group Theory.After Every Chapter Are 'Protips,' Which Are Short Thoughts On Things I Wish I Had Known When I Took My Introtoproofs Class. They Include Finer Comments On The Material, Study Tips, Historical Notes, Comments On Mathematical Culture, And More. Also, After Each Chapters Exercises Is An Introduction To An Unsolved Problem In Mathematics.In The First Appendix We Discuss Some Further Proof Methods, The Second Appendix Is A Collection Of Particularly Beautiful Proofs, And The Third Is Some Writing Advice.
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- Q: How many pages does this textbook have? A: This textbook has five hundred eleven pages. It covers a wide range of topics in mathematics.
- Q: What is the binding type of the book? A: The book is available in paperback binding. This makes it lightweight and easy to handle.
- Q: What are the dimensions of the textbook? A: The textbook measures eight and a half inches in length, one point sixteen inches in width, and eleven inches in height. These dimensions make it a manageable size for readers.
- Q: Is this textbook suitable for beginners? A: Yes, this textbook is designed for students, including beginners. It emphasizes understanding concepts over mere memorization.
- Q: What topics are covered in the textbook? A: The textbook covers intuitive proofs, sets, induction, logic, functions, relations, and more. It also introduces higher mathematics through selected examples.
- Q: How does the book help with understanding proofs? A: The textbook includes extensive commentary and motivation throughout. It prioritizes understanding and provides 'scratch work' before many proofs.
- Q: Are there tips for studying included in the book? A: Yes, each chapter includes 'pro-tips' that provide study advice and insights from the author's experiences. These tips enhance the learning process.
- Q: Does the book include illustrations? A: Yes, the textbook contains over two hundred illustrations. These visuals aid in making complex ideas more accessible.
- Q: What kind of exercises does the book have? A: The textbook includes exercises at the end of each chapter. Additionally, it introduces unsolved problems in mathematics following these exercises.
- Q: Are there appendices in the textbook? A: Yes, the textbook includes three appendices. They cover further proof methods, beautiful proofs, and writing advice.
- Q: Who is the author of this textbook? A: The author of the textbook is Jay Cummings. He aims to make mathematics engaging and relatable.
- Q: Is the writing style of the book formal or conversational? A: The writing style is relaxed and conversational, making it easier for students to engage with the material.
- Q: What is the primary audience for this textbook? A: The primary audience is students who are learning higher mathematics. It is particularly beneficial for those in introductory proof courses.
- Q: Can this book be used for self-study? A: Yes, the book is suitable for self-study. Its clear explanations and structured layout make it effective for independent learners.
- Q: What makes this textbook different from others? A: This textbook stands out due to its emphasis on understanding, extensive commentary, and inclusion of humor. It also provides a broader view of mathematics.
- Q: Is there humor included in the writing? A: Yes, the writing includes periodic attempts at humor. This helps to create a more enjoyable learning experience.