Title
The Foundations of Mathematics,New
Delivery time: 8-12 business days (International)
The transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory.The authors have many years' experience of the potential difficulties involved, through teaching firstyear undergraduates and researching the ways in which students and mathematicians think. The book explains the motivation behind abstract foundational material based on students' experiences of school mathematics, and explicitly suggests ways students can make sense of formal ideas.This second edition takes a significant step forward by not only making the transition from intuitive to formal methods, but also by reversing the process using structure theorems to prove that formal systems have visual and symbolic interpretations that enhance mathematical thinking. This is exemplified by a new chapter on the theory of groups.While the first edition extended counting to infinite cardinal numbers, the second also extends the real numbers rigorously to larger ordered fields. This links intuitive ideas in calculus to the formal epsilondelta methods of analysis. The approach here is not the conventional one of 'nonstandard analysis', but a simpler, graphically based treatment which makes the notion of an infinitesimal natural and straightforward.This allows a further vision of the wider world of mathematical thinking in which formal definitions and proof lead to amazing new ways of defining, proving, visualising and symbolising mathematics beyond previous expectations.
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Shipping & Returns
Shipping
We ship your order within 2–3 business days for USA deliveries and 5–8 business days for international shipments. Once your package has been dispatched from our warehouse, you'll receive an email confirmation with a tracking number, allowing you to track the status of your delivery.
Returns
To facilitate a smooth return process, a Return Authorization (RA) Number is required for all returns. Returns without a valid RA number will be declined and may incur additional fees. You can request an RA number within 15 days of the original delivery date. For more details, please refer to our Return & Refund Policy page.
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Warranty
We provide a 2-year limited warranty, from the date of purchase for all our products.
If you believe you have received a defective product, or are experiencing any problems with your product, please contact us.
This warranty strictly does not cover damages that arose from negligence, misuse, wear and tear, or not in accordance with product instructions (dropping the product, etc.).
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Frequently Asked Questions
- Q: What is the main focus of 'The Foundations of Mathematics'? A: 'The Foundations of Mathematics' mainly focuses on bridging the gap between school mathematics and university-level mathematics, emphasizing proof, logic, and abstract concepts.
- Q: Who is the author of this book? A: The author of 'The Foundations of Mathematics' is Ian Stewart, who has extensive experience in teaching first-year undergraduates.
- Q: How does this book help students transition from intuitive to formal mathematics? A: This book provides explanations and methods to help students transition from intuitive mathematical concepts to formal methods, including structure theorems and visual interpretations.
- Q: What is new in the second edition of this book? A: The second edition includes a new chapter on the theory of groups and extends the real numbers to larger ordered fields, enhancing the link between calculus and formal analysis.
- Q: Is this book suitable for beginners in mathematics? A: While 'The Foundations of Mathematics' is designed for students transitioning to higher mathematics, it may be more suitable for those with some background in mathematical concepts.
- Q: What topics are covered in this book? A: This book covers a variety of topics, including set theory, proof techniques, abstract mathematical concepts, and the theory of groups.
- Q: What is the binding type of this book? A: 'The Foundations of Mathematics' is available in paperback binding, making it accessible and easy to handle.
- Q: How many pages does this book have? A: The book contains 432 pages, providing comprehensive coverage of its topics.
- Q: When was 'The Foundations of Mathematics' published? A: 'The Foundations of Mathematics' was published on May 1, 2015.
- Q: What is the condition of the book being sold? A: The book is in new condition, ensuring that it is free from wear and tear.