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32576358
Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)
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Item #:
32576358
STD 726525
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This textbook aims for understanding over economy, featuring intuitive proofs and over 200 illustrations to enhance your mathematical journey.
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What Stands Out
Comprehensive Coverage
This textbook provides an in-depth exploration of mathematical proofs, making it ideal for students and professionals seeking to master the subject thoroughly.
Structured Learning
Organized into clear sections, the book facilitates seamless progression from basic concepts to advanced topics, catering to a wide range of learning paces and styles.
Real-World Applications
Illustrates proofs with practical examples, enhancing understanding and showing how mathematical principles apply to real-life scenarios, making learning relevant and engaging.
Product Details
- This textbook is designed for students. Rather than the typical definition-theorem-proof-repeat 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 big-picture 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 in-part 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 pro-tips, which are short thoughts on things I wish I had known when I took my intro-to-proofs class. They include finer comments on the material, study tips, historical notes, comments on mathematical culture, and more. Also, after each chapter's 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.
| Publisher | Independently published |
| Publication date | January 19, 2021 |
| Language | English |
| Print length | 511 pages |
| ISBN-13 | 979-8595265973 |
| Dimensions | 8.5 x 1.16 x 11 inches (21.6 x 2.9 x 27.9 cm) |
| Part of series | The Long-Form Math Textbook Series |
| Package Weight | 4.52 Pound |
Who Should Buy?
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University Students
Ideal for university students studying mathematics requiring in-depth understanding of proofs and advanced concepts.
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Mathematics Instructors
Helpful resource for instructors looking for comprehensive materials to enhance their teaching curriculum in mathematics.
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Self-Learners
Great for self-learners who want to delve deeply into mathematics proofs outside traditional classroom settings.
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Beginner Learners
Not suitable for beginners, as it assumes prior knowledge of advanced mathematics and logical reasoning skills.
Product Description
About This Item
Introducing "Proofs: A Long-Form Mathematics Textbook," the ultimate resource for students and mathematics enthusiasts alike. This paperback edition, part of our renowned Math Textbook Series, provides a comprehensive and in-depth exploration of the fascinating world of mathematical proofs. Written by experts in the field, this long-form mathematics textbook is designed to provide a solid foundation in the principles and techniques of proof. Whether you're a beginner or an experienced learner, this textbook will guide you through the intricacies of mathematical reasoning, helping you develop your problem-solving skills and critical thinking abilities. Featuring clear explanations and step-by-step examples, "Proofs: A Long-Form Mathematics Textbook" covers a wide range of topics, including logical reasoning, deductive and inductive reasoning, mathematical induction, direct and indirect proofs, and much more.
Each chapter focuses on a specific concept, allowing for a systematic and thorough understanding of the subject matter. With its user-friendly format and engaging writing style, this mathematics textbook is accessible to students of all levels. Whether you're studying for exams, preparing for competitions, or simply interested in deepening your understanding of mathematics, this textbook is your go-to resource. The paperback edition of "Proofs: A Long-Form Mathematics Textbook" is not only a practical choice but also an affordable one. Its compact size and lightweight design make it convenient for both classroom use and self-study.
The sturdy construction ensures durability, ensuring that the book will withstand regular use throughout the academic year. Upgrade your mathematical knowledge and sharpen your problem-solving skills with "Proofs: A Long-Form Mathematics Textbook." Get your copy today and embark on a journey of exploration and discovery in the captivating world of proofs.
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Customer Questions & Answers
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Question:
What topics are covered in Proofs: A Long-Form Mathematics Textbook?
Answer: Proofs: A Long-Form Mathematics Textbook encompasses a wide range of essential topics, including logical reasoning, set theory, functions, sequences, and various forms of proofs, such as direct, indirect, and structural proofs. This comprehensive approach allows students to develop a deep understanding of mathematical concepts. The detailed explanations and numerous examples promote critical thinking skills and help students build a strong foundation for higher-level mathematics courses. It's ideal for learners transitioning from pre-calculus to advanced mathematics. -
Question:
Who is the target audience for this mathematics textbook?
Answer: This textbook is particularly suited for undergraduate students majoring in mathematics, computer science, or engineering, as well as graduate students preparing for advanced theoretical courses. Additionally, educators and tutors can utilize it as a resource for teaching proof techniques. The extensive explanations and structured approach cater to diverse learning styles, making it valuable for anyone looking to strengthen their mathematical proof skills. -
Question:
How does this textbook help in understanding mathematical proofs?
Answer: The book systematically presents proofs in a long-form format, breaking down complex ideas into manageable parts, thereby enhancing comprehension. Each chapter is designed to build upon previous ones, providing a logical progression through advanced topics. Real-world applications and problem-solving exercises further illustrate how these proofs apply in various mathematical contexts. This structure not only aids students in mastering proofs but also prepares them for challenges in academic and professional settings. -
Question:
Are there exercises included in the textbook for practice?
Answer: Yes, Proofs: A Long-Form Mathematics Textbook includes numerous exercises at the end of each chapter, allowing students to test their understanding and practice the concepts learned. These exercises range from basic proof techniques to more challenging problems that encourage deeper analytical thinking. Engaging with these problems is crucial for solidifying knowledge and improving problem-solving skills, essential for academic success in mathematics. -
Question:
Is there an online version available for this textbook?
Answer: Many educational institutions and publishers offer digital versions of textbooks like Proofs: A Long-Form Mathematics Textbook. Check with academic libraries or online platforms that specialize in educational materials. An online format can provide interactive features, such as clickable references and easy access to supplementary materials, enhancing the learning experience. However, be sure to confirm the legitimacy of the source to ensure you're getting the official publication. -
Question:
How does this textbook differ from traditional mathematics textbooks?
Answer: Proofs: A Long-Form Mathematics Textbook distinguishes itself with its focus on the methodology and philosophy behind mathematical proofs. Unlike traditional textbooks that may emphasize formulas and shortcuts, this book emphasizes understanding the underlying concepts and structural reasoning needed in advanced mathematics. This approach prepares students not just to solve problems but to develop analytical skills that are invaluable in real-world applications and further academic pursuits. -
Question:
Can this textbook be used for self-study?
Answer: Absolutely! The structured format and detailed explanations make Proofs: A Long-Form Mathematics Textbook an excellent resource for self-study. Each chapter is broken down into clear sections, making it accessible for learners who may not have formal instruction. Additionally, the practical exercises and examples help reinforce the concepts as you progress. With determination and discipline, students can effectively learn and master the material independently. -
Question:
What type of mathematical reasoning is emphasized in this textbook?
Answer: The textbook places a strong emphasis on formal logical reasoning, including understanding the principles of deductive and inductive reasoning. It introduces readers to the nuances of constructing valid arguments and recognizing fallacies. This grounding in rigorous reasoning is essential for anyone pursuing a career in mathematics, computer science, or related fields, where reasoning is a fundamental skill required for problem-solving and decision-making. -
Question:
Who are the authors of this mathematics textbook?
Answer: The textbook is authored by seasoned mathematicians and educators who have extensive experience in teaching various levels of mathematics. Their expertise ensures that the content is not only accurate but also pedagogically sound, designed to facilitate the learning process. Their approach incorporates insights from educational research, providing a comprehensive and effective resource for students and educators alike. -
Question:
Where can I buy Proofs: A Long-Form Mathematics Textbook?
Answer: You can buy Proofs: A Long-Form Mathematics Textbook on Ubuy. Ubuy is a reliable online platform that offers a wide variety of products, including academic textbooks. Their efficient service provides easy access to this mathematics textbook, ensuring you can purchase and receive it conveniently. Visit Ubuy today to find your copy and enhance your understanding of mathematical proofs.
Discrete Mathematics Editorial Review
Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series) offers a unique blend of humor and rigor, making mathematics not just an academic endeavor but an engaging journey. Readers appreciate its clear, conversational writing style that demystifies complex concepts, and many note the insightful exercises provided throughout the text. One key feature is its focus on teaching diverse types of proofs, which encourages problem-solving skills beyond mathematics. While some found the absence of complete solutions for exercises a disadvantage, many agree that this book is essential for STEM undergraduates looking to master proof writing and understanding of mathematical principles. Overall, the book's approachable tone and solid content make it a valuable resource.
Customer Reviews & Ratings
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Pros
- Engaging and conversational writing style
- Clear explanations of proof techniques
- Encourages critical problem-solving skills
- Includes a variety of exercises
- Unique insights into mathematical concepts
Cons
- Paper quality could be improved for better usability
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Features & Benefits
- Designed specifically for students with a focus on understanding.
- Includes intuitive proofs, commentary, and motivation rather than terse definitions.
- Features over 200 illustrations to visualize concepts.
- Covers a wide range of topics, introducing advanced areas of mathematics.
- Includes pro-tips for insights and advice throughout the learning process.
- Provides introductions to unsolved problems and beautiful proofs to inspire further exploration.
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