公理化幾何學 (英文) 約翰.李 9787040612561 【台灣高等教育出版社】
圖書均為代購，正常情形下，訂後約兩周可抵台。
物品所在地：中國大陸
原出版社：高等教育
物品所在地：中國大陸
原出版社：高等教育
NT$1,266
商品編號:
供貨狀況:
尚有庫存
加入最愛
此商品 「 最高 」可以折抵紅利
0
點
(約等於 NT$0 )
商品介紹
| *完成訂單後正常情形下約兩周可抵台。 *本賣場提供之資訊僅供參考，以到貨標的為正確資訊。 印行年月：202402*若逾兩年請先於私訊洽詢存貨情況，謝謝。 台灣(台北市)在地出版社，每筆交易均開具統一發票，祝您中獎最高1000萬元。 書名：公理化幾何學 (英文) ISBN：9787040612561 出版社：高等教育 著編譯者：約翰.李 頁數：469 所在地：中國大陸 *此為代購商品 書號：1625184 可大量預訂，請先連絡。 內容簡介 幾何學的故事就是數學本身的故事：歐幾里得幾何學是第一個被系統研究並建立在堅實邏輯基礎上的數學分支，它是現代數學基礎上公理化方法的原型。作為一種邏輯思維模式，它已經被教授給學生兩千多年了。 本書講述了公理化方法如何從歐幾里得時代發展到現在，以幫助我們理解數學是什麼，如何閱讀和評估數學論證，以及為什麼數學已經達到了如此高的確定性水平。它主要面向計劃教授中學幾何的高年級本科生，但也適合任何希望更好地了解幾何和公理化方法的人。它引入了現代、嚴謹的歐幾里得和（較少程度上的）非歐幾里得幾何的公理化處理，為學生提供了充足的機會來練習閱讀和書寫證明，同時發展了中學教師在課堂上需要了解的大部分具體的幾何關係。目錄 PrefaceChapter 1 Euclid Reading Euclid After Euclid The Discovery of Non-Euclidean Geometry Gaps in Euclid's Arguments Modem Axiom Systems Exercises Chapter 2 Incidence Geometry Axiomatic Systems The Axioms of Incidence Geometry Interpretations and Models of Incidence Geometry Some Nonmodels Consistency and Independence Some Infinite Models Parallel Postulates Theorems in Incidence Geometry Exercises Chapter 3 Axioms for Plane Geometry Points and Lines Distance Segments Rays Plane Separation Convex Sets Exercises Chapter 4 Angles Angles Betweenness of Rays The Interior of an Angle Exercises Chapter 5 Triangles Definitions Intersections of Lines and Triangles Congruent Triangles Inequalities More Congruence Theorems Exercises Chapter 6 Models of Neutral Geometry The Cartesian Model The Poincare Disk Model Some Nonmodels Independence of the Neutral Geometry Postulates Exercises Chapter 7 Perpendicular and Parallel Lines Perpendicular Lines Parallel Lines Exercises Chapter 8 Polygons Polygons Convex Polygons Nonconvex Polygons Exercises Chapter 9 Quadrilaterals Convex Quadrilaterals Parallelograms Exercises Chapter 10 The Euclidean Parallel Po stulate Angle-Sum Theorems Quadrilaterals in Euclidean Geometry Exercises Chapter 11 Area Polygonal Regions Admissible Decompositions Area Formulas Is the Area Postulate Independent of the Others? Exercises Chapter 12 Similarity Definitions The Side-Splitter Theorem Triangle Similarity Theorems Proportion Theorems Collinearity and Concurrence Theorems The Golden Ratio Perimeters and Areas of Similar Figures Exercises Chapter 13 Right Triangles The Pythagorean Theorem Applications of the Pythagorean Theorem Similarity Relations in Right Triangles Trigonometry Categoricity of the Euclidean Postulates Exercises Chapter 14 Circles Definitions Circles and Lines Intersections between Circles Arcs and Inscribed Angles Inscribed and Circumscribed Polygons Regular Polygons and Circles Exercises Chapter 15 Circumference and Circular Area Circumference Approximations by Regular Polygons The Definition of Pi Area of a Circular Region Generalizations Exercises Chapter 16 Compass and Straightedge Constructions Basic Constructions Constructing Regular Polygons Impossible Constructions Exercises Chapter 17 The Parallel Postulate Revisited Postulates Equivalent to the Euclidean Parallel Postulate Angle Sums and Defects Clairaut's Postulate It's All or Nothing Exercises Chapter 18 Introduction to Hyperbolic Geometry The Hyperbolic Parallel Postulate Saccheri and Lambert Quadrilaterals Asymptotic Rays Asymptotic Triangles Exercises Chapter 19 Parallel Lines in Hyperbolic Geometry Parallel Lines and Angles Parallel Lines and Common Perpendiculars Distances between Parallel Lines Exercises Chapter 20 Epilogue: Where Do We Go from Here? Appendix A Hilbert's Axioms Appendix B Birkhoff's Postulates Appendix C The SMSG Postulates Appendix D The Postulates Used in This Book Postulates of Neutral Geometry Postulates of Euclidean Geometry Postulates of Hyperbolic Geometry Appendix E The Language of Mathematics Simple Statements Logical Connectives Conditional Statements Quantifiers Mathematical Definitions Exercises Appendix F Proofs The Structure of Mathematical Proofs Direct Proofs Indirect Proofs Existence Proofs Proof by Mathematical Induction Appendix G Sets and Functions Basic Concepts Ordered Pairs and Cartesian Products Functions Exercises Appendix H Properties of the Real Numbers Primitive Terms Definitions Properties Appendix I Rigid Motions: Another Approach Reflection Implies SAS SAS Implies Reflection 詳細資料或其他書籍請至台灣高等教育出版社查詢，查後請於PChome商店街私訊告知ISBN或書號，我們即儘速上架。 |
