Introduction to Advanced Mathematics, 2/e (IE-Paperback)
暫譯: 高等數學導論，第二版 (IE-平裝本)

William Barnier / Norman Feldman

Introduction to Advanced Mathematics, 2/e (IE-Paperback)

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商品描述

Description:

For a one-quarter/semester, sophomore-level transitional (“bridge”) course that supplies background for students going from calculus to the more abstract, upper-division mathematics courses. Also appropriate as a supplement for junior-level courses such as abstract algebra or real analysis.

Focused on “What Every Mathematician Needs to Know,” this text provides material necessary for students to succeed in upper-division mathematics courses, and more importantly, the analytical tools necessary for thinking like a mathematician. It begins with a natural progression from elementary logic, methods of proof, and set theory, to relations and functions; then provides application examples, theorems, and student projects.

 

Table of Contents:

1. Introduction to Logic.

2. Methods of Proof.

3. Set Theory.

4. Cartesian Products and Functions.

5. Relations.

6. Cardinality.

7. Number Theory.

8. Rings and Integral Domains.

9. Limits and the Real Numbers.

商品描述(中文翻譯)

描述：

這是一門為期一學期的二年級過渡（“橋樑”）課程，旨在為學生從微積分過渡到更抽象的高年級數學課程提供背景知識。此課程也適合作為抽象代數或實分析等三年級課程的補充。

本書專注於“每位數學家需要知道的內容”，提供學生在高年級數學課程中成功所需的材料，更重要的是，提供思考如數學家的分析工具。內容從基本邏輯、證明方法和集合論開始，然後進入關係和函數，接著提供應用範例、定理和學生專案。

目錄：

1. 邏輯入門。



2. 證明方法。



3. 集合論。



4. 笛卡爾積和函數。



5. 關係。



6. 基數。



7. 數論。



8. 環和整數域。



9. 極限與實數。

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