Hardcover ISBN:  9780883857687 
Product Code:  CLRM/35 
List Price:  $59.00 
MAA Member Price:  $44.25 
AMS Member Price:  $44.25 
eBook ISBN:  9780883859353 
Product Code:  CLRM/35.E 
List Price:  $55.00 
MAA Member Price:  $41.25 
AMS Member Price:  $41.25 
Hardcover ISBN:  9780883857687 
eBook: ISBN:  9780883859353 
Product Code:  CLRM/35.B 
List Price:  $114.00 $86.50 
MAA Member Price:  $85.50 $64.88 
AMS Member Price:  $85.50 $64.88 
Hardcover ISBN:  9780883857687 
Product Code:  CLRM/35 
List Price:  $59.00 
MAA Member Price:  $44.25 
AMS Member Price:  $44.25 
eBook ISBN:  9780883859353 
Product Code:  CLRM/35.E 
List Price:  $55.00 
MAA Member Price:  $41.25 
AMS Member Price:  $41.25 
Hardcover ISBN:  9780883857687 
eBook ISBN:  9780883859353 
Product Code:  CLRM/35.B 
List Price:  $114.00 $86.50 
MAA Member Price:  $85.50 $64.88 
AMS Member Price:  $85.50 $64.88 

Book DetailsClassroom Resource MaterialsVolume: 35; 2010; 301 pp
Excursions in Classical Analysis will introduce students to advanced problem solving and undergraduate research in two ways: it will provide a tour of classical analysis, showcasing a wide variety of problems that are placed in historical context, and it will help students gain mastery of mathematical discovery and proof.
The author presents a variety of solutions for the problems in the book. Some solutions reach back to the work of mathematicians like Leonhard Euler while others connect to other beautiful parts of mathematics. Readers will frequently see problems solved by using an idea that, at first glance, might not even seem to apply to that problem. Other solutions employ a specific technique that can be used to solve many different kinds of problems. Excursions emphasizes the rich and elegant interplay between continuous and discrete mathematics by applying induction, recursion, and combinatorics to traditional problems in classical analysis.
The book will be useful in students' preparations for mathematics competitions, in undergraduate reading courses and seminars, and in analysis courses as a supplement. The book is also ideal for self study, since the chapters are independent of one another and may be read in any order.

Table of Contents

Chapters

1. Two Classical Inequalities

2. A New Approach for Proving Inequalities

3. Means Generated by an Integral

4. The L’Hôpital 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 of $(\mathrm {arcsin}\; x)^2$

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


Additional Material

Reviews

... Based on his obviously very rich and farreaching experience in this didactic realm, the author offers a colorful panorama of various topics in calculus, both elementary and advanced, as well as a wide variety of typical problems placed in their respective historical contexts. ... No doubt, this fine book will be of great use and value for students preparing for mathematics competitions, participating in undergraduate analysis courses, seminars, and research projects, or conducting any kind of selfstudy in the field.
Zentrallblatt Math 
Chen (Christopher Newport Univ) offers many enjoyable trips through classical analysis, providing wonderful insights and remarkable connections. The focus is problem solving, while modeling various aspects of discovery, proof, and multiple solutions. ...
CHOICE Magazine 
Chen's book is a wonderful tour of classical analysis and would serve as an excellent source of undergraduate enrichment/research problems. It recalls the type of gems in classical analysis, number theory, and combinatorics I first encountered in the books of Polya and Szegő as an undergraduate many years ago. Peruse the table of contents and see if some of the topics and subtopics don't grab you.
Henry Ricardo, MAA Reviews


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 Book Details
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Excursions in Classical Analysis will introduce students to advanced problem solving and undergraduate research in two ways: it will provide a tour of classical analysis, showcasing a wide variety of problems that are placed in historical context, and it will help students gain mastery of mathematical discovery and proof.
The author presents a variety of solutions for the problems in the book. Some solutions reach back to the work of mathematicians like Leonhard Euler while others connect to other beautiful parts of mathematics. Readers will frequently see problems solved by using an idea that, at first glance, might not even seem to apply to that problem. Other solutions employ a specific technique that can be used to solve many different kinds of problems. Excursions emphasizes the rich and elegant interplay between continuous and discrete mathematics by applying induction, recursion, and combinatorics to traditional problems in classical analysis.
The book will be useful in students' preparations for mathematics competitions, in undergraduate reading courses and seminars, and in analysis courses as a supplement. The book is also ideal for self study, since the chapters are independent of one another and may be read in any order.

Chapters

1. Two Classical Inequalities

2. A New Approach for Proving Inequalities

3. Means Generated by an Integral

4. The L’Hôpital 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 of $(\mathrm {arcsin}\; x)^2$

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

... Based on his obviously very rich and farreaching experience in this didactic realm, the author offers a colorful panorama of various topics in calculus, both elementary and advanced, as well as a wide variety of typical problems placed in their respective historical contexts. ... No doubt, this fine book will be of great use and value for students preparing for mathematics competitions, participating in undergraduate analysis courses, seminars, and research projects, or conducting any kind of selfstudy in the field.
Zentrallblatt Math 
Chen (Christopher Newport Univ) offers many enjoyable trips through classical analysis, providing wonderful insights and remarkable connections. The focus is problem solving, while modeling various aspects of discovery, proof, and multiple solutions. ...
CHOICE Magazine 
Chen's book is a wonderful tour of classical analysis and would serve as an excellent source of undergraduate enrichment/research problems. It recalls the type of gems in classical analysis, number theory, and combinatorics I first encountered in the books of Polya and Szegő as an undergraduate many years ago. Peruse the table of contents and see if some of the topics and subtopics don't grab you.
Henry Ricardo, MAA Reviews