Excursions in classical analysis : pathways to advanced problem solving and undergraduate research
 Responsibility
 Hongwei Chen.
 Language
 English.
 Imprint
 Washington, D.C. : Mathematical Association of America, c2010.
 Physical description
 xiii, 301 p. : ill. ; 26 cm.
 Series
 Classroom resource materials.
Access
Creators/Contributors
 Author/Creator
 Chen, Hongwei.
 Contributor
 Mathematical Association of America.
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Preface 1. Two classical inequalities 2. A new approach for proving inequalities 3. Means generated by an integral 4. The L'Hopital monotone rule 5. Trigonometric identities via complex numbers 6. Special numbers 7. On a sum of cosecants 8. The gamma products in simple closed forms 9. On the telescoping sums 10. Summation of subseries in closed form 11. Generating functions for powers of Fibonacci numbers 12. Identities for the Fibonacci powers 13. Bernoulli numbers via determinants 14. On some finite trigonometric power sums 15. Power series 16. Six ways to sum zeta(2) 17. Evaluations of some variant Euler sums 18. Interesting series involving binomial coefficients 19. Parametric differentiation and integration 20. Four ways to evaluate the Poisson integral 21. Some irresistible integrals Solutions to selected problems.
 (source: Nielsen Book Data)
 Publisher's Summary
 Excursions in Classical Analysis introduces undergraduate students to advanced problem solving and undergraduate research in two ways. Firstly, it provides a colourful tour of classical analysis which places a wide variety of problems in their historical context. Secondly, it helps students gain an understanding of mathematical discovery and proof. In demonstrating a variety of possible solutions to the same sample exercise, the reader will come to see how the connections between apparently inapplicable areas of mathematics can be exploited in problemsolving. This book will serve as excellent preparation for participation in mathematics competitions, as a valuable resource for undergraduate mathematics reading courses and seminars and as a supplement text in a course on analysis. It can also be used in independent study, since the chapters are freestanding.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2010
 Series
 Classroom resource materials series
 ISBN
 9780883857687 (hbk.)
 0883857685 (hbk.)
 9780883859353 (eISBN)
 0883859351 (eISBN)