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Grundlagen der Mathematik von Bernd S. W. Schröder: Neu-
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eBay-Artikelnr.:402983406533
Artikelmerkmale
- Artikelzustand
- Book Title
- Fundamentals of Mathematics
- Publication Date
- 2010-08-16
- Pages
- 348
- ISBN
- 9780470551387
Über dieses Produkt
Product Identifiers
Publisher
Wiley & Sons, Incorporated, John
ISBN-10
0470551380
ISBN-13
9780470551387
eBay Product ID (ePID)
84534390
Product Key Features
Number of Pages
348 Pages
Language
English
Publication Name
Fundamentals of Mathematics : an Introduction to Proofs, Logic, Sets, and Numbers
Publication Year
2010
Subject
Set Theory, Logic
Type
Textbook
Subject Area
Mathematics
Format
Hardcover
Dimensions
Item Height
1 in
Item Weight
23.2 Oz
Item Length
9.7 in
Item Width
6.7 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
2010-010589
Reviews
"This is a lovely introduction to mathematics. The book gives an elegant construction of the familiar number systems while at the same time introducing the student to mathematical logic, set theory and rigorous mathematical proof." (Zentralblatt MATH, 2011)
Dewey Edition
22
Illustrated
Yes
Dewey Decimal
510
Table Of Content
Preface. Questions. 1 Logic. 1.1 Statements. 1.2 Implications. 1.3 Conjunction, Disjunction and Negation. 1.4 Special Focus on Negation. 1.5 Variables and Quantifiers. 1.6 Proofs. 1.7 Using Tautologies to Analyze Arguments. 1.8 Russell's Paradox. 2 Set Theory. 2.1 Sets and Objects. 2.2 The Axiom of Specification. 2.3 The Axiom of Extension. 2.4 The Axiom of Unions. 2.5 The Axiom of Powers, Relations and Functions. 2.6 The Axiom of Infinity and the Natural Numbers. 3 Number Systems I: Natural Numbers. 3.1 Arithmetic With Natural Numbers. 3.2 Ordering the Natural Numbers. 3.3 A More Abstract Viewpoint: Binary Operations. 3.4 Induction. 3.5 Sums and Products. 3.6 Divisibility. 3.7 Equivalence Relations. 3.8 Arithmetic Modulo m. 3.9 Public Key Encryption. 4 Number Systems II: Integers. 4.1 Arithmetic With Integers. 4.2 Groups and Rings. 4.3 Finding the Natural Numbers in the Integers. 4.4 Ordered Rings. 4.5 Division in Rings. 4.6 Countable Sets. 5 Number Systems III: Fields. 5.1 Arithmetic With Rational Numbers. 5.2 Fields. 5.3 Ordered Fields. 5.4 A Problem With the Rational Numbers. 5.5 The Real Numbers. 5.6 Uncountable Sets. 5.7 The Complex Numbers. 5.8 Solving Polynomial Equations. 5.9 Beyond Fields: Vector Spaces and Algebras. 6 Unsolvability of the Quintic by Radicals. 6.1 Irreducible Polynomials. 6.2 Field Extensions and Splitting Fields. 6.3 Uniqueness of the Splitting Field. 6.4 Field Automorphisms and Galois Groups. 6.5 Normal Field Extensions. 6.6 The Groups Sn 6.7 The Fundamental Theorem of Galois Theory and Normal Subgroups. 6.8 Consequences of Solvability by Radicals. 6.9 Abel's Theorem. 7 More Axioms. 7.1 The Axiom of Choice, Zorn's Lemma and the Well-Ordering Theorem. 7.2 Ordinal Numbers and the Axiom of Replacement. 7.3 Cardinal Numbers and the Continuum Hypothesis. A Historical Overview and Commentary. A.1 Ancient Times: Greece and Rome. A.2 The Dark Ages and First New Developments. A.3 There is No Quintic Formula: Abel and Galois. A.4 Understanding Irrational Numbers: Set Theory. Conclusion and Outlook. Bibliography. Index.
Synopsis
Enforces the fundamental rule that you are not allowed to use any results that you have not proved yet, and consequently starts with an axiomatic system and builds from there Introduces proof methods in a separate section of the Logic chapter to facilitate the development of proof writing skills., An accessible introduction to abstract mathematics with an emphasis on proof writing Addressing the importance of constructing and understanding mathematical proofs, Fundamentals of Mathematics: An Introduction to Proofs, Logic, Sets, and Numbers introduces key concepts from logic and set theory as well as the fundamental definitions of algebra to prepare readers for further study in the field of mathematics. The author supplies a seamless, hands-on presentation of number systems, utilizing key elements of logic and set theory and encouraging readers to abide by the fundamental rule that you are not allowed to use any results that you have not proved yet. The book begins with a focus on the elements of logic used in everyday mathematical language, exposing readers to standard proof methods and Russell's Paradox. Once this foundation is established, subsequent chapters explore more rigorous mathematical exposition that outlines the requisite elements of Zermelo-Fraenkel set theory and constructs the natural numbers and integers as well as rational, real, and complex numbers in a rigorous, yet accessible manner. Abstraction is introduced as a tool, and special focus is dedicated to concrete, accessible applications, such as public key encryption, that are made possible by abstract ideas. The book concludes with a self-contained proof of Abel's Theorem and an investigation of deeper set theory by introducing the Axiom of Choice, ordinal numbers, and cardinal numbers. Throughout each chapter, proofs are written in much detail with explicit indications that emphasize the main ideas and techniques of proof writing. Exercises at varied levels of mathematical development allow readers to test their understanding of the material, and a related Web site features video presentations for each topic, which can be used along with the book or independently for self-study. Classroom-tested to ensure a fluid and accessible presentation, Fundamentals of Mathematics is an excellent book for mathematics courses on proofs, logic, and set theory at the upper-undergraduate level as well as a supplement for transition courses that prepare students for the rigorous mathematical reasoning of advanced calculus, real analysis, and modern algebra. The book is also a suitable reference for professionals in all areas of mathematics education who are interested in mathematical proofs and the foundation upon which all mathematics is built., An accessible introduction to abstract mathematics with an emphasis on proof writing Addressing the importance of constructing and understanding mathematical proofs, Fundamentals of Mathematics: An Introduction to Proofs, Logic, Sets, and Numbers introduces key concepts from logic and set theory as well as the fundamental definitions of algebra to prepare readers for further study in the field of mathematics. The author supplies a seamless, hands-on presentation of number systems, utilizing key elements of logic and set theory and encouraging readers to abide by the fundamental rule that you are not allowed to use any results that you have not proved yet. The book begins with a focus on the elements of logic used in everyday mathematical language, exposing readers to standard proof methods and Russells Paradox. Once this foundation is established, subsequent chapters explore more rigorous mathematical exposition that outlines the requisite elements of Zermelo-Fraenkel set theory and constructs the natural numbers and integers as well as rational, real, and complex numbers in a rigorous, yet accessible manner. Abstraction is introduced as a tool, and special focus is dedicated to concrete, accessible applications, such as public key encryption, that are made possible by abstract ideas. The book concludes with a self-contained proof of Abels Theorem and an investigation of deeper set theory by introducing the Axiom of Choice, ordinal numbers, and cardinal numbers. Throughout each chapter, proofs are written in much detail with explicit indications that emphasize the main ideas and techniques of proof writing. Exercises at varied levels of mathematical development allow readers to test their understanding of the material, and a related Web site features video presentations for each topic, which can be used along with the book or independently for self-study. Classroom-tested to ensure a fluid and accessible presentation, Fundamentals of Mathematics is an excellent book for mathematics courses on proofs, logic, and set theory at the upper-undergraduate level as well as a supplement for transition courses that prepare students for the rigorous mathematical reasoning of advanced calculus, real analysis, and modern algebra. The book is also a suitable reference for professionals in all areas of mathematics education who are interested in mathematical proofs and the foundation upon which all mathematics is built.
LC Classification Number
QA248.S358 2010
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- m***m (2305)- Bewertung vom Käufer.Letzte 6 MonateBestätigter KaufI’m thrilled with my recent purchase . The website was user-friendly, and the product descriptions were accurate. Customer service was prompt and helpful, answering all my questions. My order arrived quickly, well-packaged, and the product exceeded my expectations in quality. I’m impressed with the attention to detail and the overall experience. I’ll definitely shop here again and highly recommend from this seller to others. Thank you for a fantastic experience!
- a***n (45)- Bewertung vom Käufer.Letzte 6 MonateBestätigter KaufMistakenly ordered a paperback that I thought was a hardcover, not sellers fault; it was described properly on the listing. Seller still processed a refund the day I went to return the item and let me keep the item anyway. A+++ service. Book arrived quickly in great condition and for a great price. Thank you so much! Amazing seller!
- n***c (95)- Bewertung vom Käufer.Letzte 6 MonateBestätigter Kaufseller was communicative about my shipment, media mail took a while and tracking wasn't updated frequently, but seller communicated to me very quickly on status. the item came new and wrapped as described, though the packaging in it was packed wasn't sturdy and falling apart when it got to me.
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AlibrisBooks
98,6% positive Bewertungen•1,9 Mio. Artikel verkauft
Angemeldet als gewerblicher Verkäufer
Verkäuferbewertungen (514.464)
- m***m (2305)- Bewertung vom Käufer.Letzte 6 MonateBestätigter KaufI’m thrilled with my recent purchase . The website was user-friendly, and the product descriptions were accurate. Customer service was prompt and helpful, answering all my questions. My order arrived quickly, well-packaged, and the product exceeded my expectations in quality. I’m impressed with the attention to detail and the overall experience. I’ll definitely shop here again and highly recommend from this seller to others. Thank you for a fantastic experience!
- a***n (45)- Bewertung vom Käufer.Letzte 6 MonateBestätigter KaufMistakenly ordered a paperback that I thought was a hardcover, not sellers fault; it was described properly on the listing. Seller still processed a refund the day I went to return the item and let me keep the item anyway. A+++ service. Book arrived quickly in great condition and for a great price. Thank you so much! Amazing seller!
- n***c (95)- Bewertung vom Käufer.Letzte 6 MonateBestätigter Kaufseller was communicative about my shipment, media mail took a while and tracking wasn't updated frequently, but seller communicated to me very quickly on status. the item came new and wrapped as described, though the packaging in it was packed wasn't sturdy and falling apart when it got to me.