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Mathematical Structures: From Linear Algebra Over Rings to Geometry with Sheaves - Paperback
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by Joachim Hilgert (Author)
This textbook is intended to be accessible to any second-year undergraduate in mathematics who has attended courses on basic real analysis and linear algebra. It is meant to help students to appreciate the diverse specialized mathematics courses offered at their universities. Special emphasis is on similarities between mathematical fields and ways to compare them. The organizing principle is the concept of a mathematical structure which plays an important role in all areas of mathematics.
The mathematical content used to explain the structural ideas covers in particular material that is typically taught in algebra and geometry courses. The discussion of ways to compare mathematical fields also provides introductions to categories and sheaves, whose ever-increasing role in modern mathematics suggests a more prominent role in teaching.
The book is the English translation of the second edition of "Mathematische Strukturen" (Springer, 2024) written in German. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.
Back Jacket
This textbook is intended to be accessible to any second-year undergraduate in mathematics who has attended courses on basic real analysis and linear algebra. It is meant to help students to appreciate the diverse specialized mathematics courses offered at their universities. Special emphasis is on similarities between mathematical fields and ways to compare them. The organizing principle is the concept of a mathematical structure which plays an important role in all areas of mathematics.
The mathematical content used to explain the structural ideas covers in particular material that is typically taught in algebra and geometry courses. The discussion of ways to compare mathematical fields also provides introductions to categories and sheaves, whose ever-increasing role in modern mathematics suggests a more prominent role in teaching.
The Author
Joachim Hilgert is a retired professor of mathematics at the University of Paderborn.
The book is the English translation of the second edition of "Mathematische Strukturen" (Springer, 2024) written in German. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.
Author Biography
Joachim Hilgert is a retired professor of mathematics at the University of Paderborn.
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Standard U.S. returns are accepted for eligible new, unopened items within 30 days of carrier delivery. Returns are by mail. Customers are responsible for standard return shipping, there is no restocking fee, and standard exchanges are not offered. Once an approved return is received and inspected, the refund is issued to the original payment method within 5 business days. Damaged, defective, or incorrect items are handled at no return-shipping cost to the customer.
Return eligibility is subject to the full policy. Opened, read, or unsealed books with broken seals or visible wear are final sale. Digital downloads, gift cards, and personalized products are non-refundable. Original shipping charges are not refunded for standard returns. Contact us within 7 days of delivery about damaged, defective, or incorrect items.
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