Del i serien Problem Books in Mathematics

Excursion through Elementary Mathematics, Volume I

Real Numbers and Functions

Inbunden, Engelska, 2017

AvAntonio Caminha Muniz Neto

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Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level. The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as well as many essential theorems related to the content.

Produktinformation

Utgivningsdatum2017-04-10
Mått155 x 235 x 48 mm
Vikt1 138 g
FormatInbunden
SpråkEngelska
SerieProblem Books in Mathematics
Antal sidor652
FörlagSpringer International Publishing AG
ISBN9783319538709
OriginaltitelTópicos de Matemática Elementar

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Antonio Caminha M. Neto received his PhD from the Federal University of Ceará, Brazil in 2004. In the same year he joined the University as a Professor of Mathematics, where he is now a member of the Differential Geometry Research Group. The author of several research papers, Caminha is distinguished by a CNPq Research Grant on Differential Geometry. He is also an Affiliate Member of the Brazilian Academy of Sciences. Prior to his academic career, Caminha was himself an Olympic competitor, who has placed 4th in the 1990 Brazilian Mathematical Olympiad. Subsequently, as a high school teacher in the 1990s, he coached Brazilian students in preparation for various mathematical competitions, from regional meets to the Iberoamerican Mathematical Olympiad and the International Mathematical Olympiad, where several of them were medalists. He was also a Leader of the Brazilian Team at the 1996 and 1999 South Cone Mathematical Olympiad, and Deputy Leader of the Brazilian Team at the 1995 and 2001International Mathematical Olympiads. In 2012, Caminha published a six-volume book collection entitled Topics in Elementary Mathematics with the Brazilian Mathematical Society, which gave rise to this book.

Chapter 1 The Set of Real Numbers.- Chapter 2 Algebraic Identities, Equations and Systems.- Chapter 3 Elementary Sequences.- Chapter 4 Induction and the Binomial Formula.- Chapter 5 Elementary Inequalities.- Chapter 6 The Concept of Function.- Chapter 7 More on Real Numbers.- Chapter 8 Continuous Functions.- Chapter 9 Limits and Derivatives.- Chapter 10 Riemann’s Integral.- Chapter 11 Series of Functions.- Bibliography.- Appendix A Glossary.- Appendix B Hints and Solutions.

“This book develops several basic concepts in elementary mathematics and which are needed in the preparation of mathematical Olympiads around the world. … Throughout the book, the author puts great emphasis on explaining the issues discussed. … The presentation is pedagogical and coherent throughout with emphasis on concepts and underlying ideas … . The author has succeeded in crafting a comprehensive book to give a well-rounded picture of the role of real numbers and functions in elementary mathematics.” (Teodora Liliana Rădulescu, zbMATH 1371.97002, 2017)