| Hardcover ISBN: | 978-0-88385-768-7 |
| Product Code: | CLRM/35 |
| List Price: | $59.00 |
| MAA Member Price: | $44.25 |
| AMS Member Price: | $44.25 |
| eBook ISBN: | 978-0-88385-935-3 |
| Product Code: | CLRM/35.E |
| List Price: | $55.00 |
| MAA Member Price: | $41.25 |
| AMS Member Price: | $41.25 |
| Hardcover ISBN: | 978-0-88385-768-7 |
| eBook: ISBN: | 978-0-88385-935-3 |
| 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: | 978-0-88385-768-7 |
| Product Code: | CLRM/35 |
| List Price: | $59.00 |
| MAA Member Price: | $44.25 |
| AMS Member Price: | $44.25 |
| eBook ISBN: | 978-0-88385-935-3 |
| Product Code: | CLRM/35.E |
| List Price: | $55.00 |
| MAA Member Price: | $41.25 |
| AMS Member Price: | $41.25 |
| Hardcover ISBN: | 978-0-88385-768-7 |
| eBook ISBN: | 978-0-88385-935-3 |
| 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 |
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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.
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Table of Contents
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Chapters
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1. Two Classical Inequalities
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2. A New Approach for Proving Inequalities
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3. Means Generated by an Integral
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4. The L’Hôpital Monotone Rule
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5. Trigonometric Identities via Complex Numbers
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6. Special Numbers
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7. On a Sum of Cosecants
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8. The Gamma Products in Simple Closed Forms
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9. On the Telescoping Sums
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10. Summation of Subseries in Closed Form
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11. Generating Functions for Powers of Fibonacci Numbers
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12. Identities for the Fibonacci Powers
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13. Bernoulli Numbers via Determinants
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14. On Some Finite Trigonometric Power Sums
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15. Power Series of $(\mathrm {arcsin}\; x)^2$
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16. Six Ways to Sum $\zeta (2)$
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17. Evaluations of Some Variant Euler Sums
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18. Interesting Series Involving Binomial Coefficients
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19. Parametric Differentiation and Integration
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20. Four Ways to Evaluate the Poisson Integral
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21. Some Irresistible Integrals
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Additional Material
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Reviews
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... Based on his obviously very rich and far-reaching 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 self-study 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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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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 far-reaching 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 self-study 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
