Mathematical Structures: From Linear Algebra Over Rings to Geometry with Sheaves
暫譯: 數學結構:從環上的線性代數到帶有層的幾何學
Hilgert, Joachim
- 出版商: Springer
- 出版日期: 2024-08-07
- 售價: $2,610
- 貴賓價: 9.5 折 $2,480
- 語言: 英文
- 頁數: 333
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3662694115
- ISBN-13: 9783662694114
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相關分類:
線性代數 Linear-algebra
海外代購書籍(需單獨結帳)
商品描述
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.
商品描述(中文翻譯)
這本教科書旨在讓任何修習過基礎實分析和線性代數課程的二年級數學本科生都能輕鬆理解。它的目的是幫助學生欣賞他們大學所提供的各種專業數學課程。特別強調數學領域之間的相似性以及比較它們的方法。組織原則是數學結構的概念,這在數學的所有領域中都扮演著重要角色。
用來解釋結構思想的數學內容特別涵蓋了通常在代數和幾何課程中教授的材料。討論比較數學領域的方法也提供了對類別和層的介紹,這些在現代數學中日益增長的角色暗示了在教學中更突出的地位。
這本書是《Mathematische Strukturen》(Springer, 2024)第二版的英文翻譯,原著是德文。翻譯是借助人工智慧完成的,隨後進行了主要針對內容的人為修訂。
作者簡介
Joachim Hilgert is a retired professor of mathematics at the University of Paderborn.
作者簡介(中文翻譯)
喬阿基姆·希爾格特(Joachim Hilgert)是帕德博恩大學(University of Paderborn)退休的數學教授。