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Numbers and Functions: From a Classical-Experimental Mathematician's Point of View (Student Mathematical Library) epub

by Victor H. Moll


Numbers and Functions: From a Classical-Experimental Mathematician's Point of View (Student Mathematical Library) epub

ISBN: 0821887955

ISBN13: 978-0821887950

Author: Victor H. Moll

Category: Other

Subcategory: Science & Mathematics

Language: English

Publisher: American Mathematical Society (September 27, 2012)

Pages: 504 pages

ePUB book: 1686 kb

FB2 book: 1343 kb

Rating: 4.8

Votes: 195

Other Formats: lit doc rtf mbr





It is not for everyone-nothing is universal

It is not for everyone-nothing is universal. But if you are interested in classical analysis, special functions, integration, number theory, symbolic computing, and some other deep topics like the AGM, this will grab you by the collar and put you to work.

New mathematics often comes about by probing what is already known

New mathematics often comes about by probing what is already known. Mathematicians will change the parameters in a familiar calculation or explore the essential ingredients of a classic proof. Almost magically, new ideas emerge from this process. This book examines elementary functions, such as those encountered in calculus courses, from this point of view of experimental mathematics. The focus is on exploring the connections between these functions and topics in number theory and combinatorics.

New mathematics often comes about by probing what is already known.

The book covers an extensive swath of college mathematics: number systems and number theory . Now I wish to address the second part of the book’s title, From a al mathematician’s point of view.

The book covers an extensive swath of college mathematics: number systems and number theory, special families of numbers (Fibonacci, Catalan, Stirling, Bernoulli), combinatorics, calculus and analysis, polynomials and special families of polynomials (Bernoulli, Chebyshev, Legendre, Hermite), Landen transformations, and special functions ((Gamma), (psi), (zeta)). The book is by no means linear, with many references to later chapters which, I must say, does not at all hinder the reading but rather binds the material into coherent whole.

Электронная книга "Numbers and Functions: From a al Mathematician's . New mathematics often comes about by probing what is already known.

Электронная книга "Numbers and Functions: From a al Mathematician's Point of View", Victor H. Moll.

The focus is on exploring the connections between these functions and topics in number theory and combinatorics.

Download Numbers and Functions: From a al Mathematicians Point of View or any other file from Books category. Numbers and Functions: From a al Mathematician's Point of View By Victor H. Moll 2012 504 Pages ISBN: 0821887955 PDF 11 MB.

Numbers and Functions book. Published November 1st 2012 by American Mathematical Society (first published September 1st 2012).

Experimental and computational mathematics: Selected writings. The Computer as Crucible: An Introduction to Experimental Mathematics

Experimental and computational mathematics: Selected writings. A quiet revolution in mathematical computing and scientific visualization took place in the latter half of the 20th century. These developments have dramatically enhanced modes of mathematical insight and opportunities for "exploratory" computational experimentation. The Computer as Crucible: An Introduction to Experimental Mathematics. Keith Devlin and Jonathan Borwein, two well-known mathematicians with expertise in different mathematical specialties but with a common interest in experimentation in mathematics, have joined forces to create this introduction to experimental mathematics.

It contains very elementary but also some more sophisticated themes. I once also wrote an elementary book "Grundideen der Mathematik", . Wissenschaftsverlag 1992. But it is out of print and in German, thus probably does not count. answered Apr 25 '17 at 14:55.

Numbers and Functions From a al Mathematician's Point of View. Student mathematical library.

New mathematics often comes about by probing what is already known. Mathematicians will change the parameters in a familiar calculation or explore the essential ingredients of a classic proof. Almost magically, new ideas emerge from this process. This book examines elementary functions, such as those encountered in calculus courses, from this point of view of experimental mathematics. The focus is on exploring the connections between these functions and topics in number theory and combinatorics. There is also an emphasis throughout the book on how current mathematical software can be used to discover and prove interesting properties of these functions. The book provides a transition between elementary mathematics and more advanced topics, trying to make this transition as smooth as possible. Many topics occur in the book, but they are all part of a bigger picture of mathematics. By delving into a variety of them, the reader will develop this broad view. The large collection of problems is an essential part of the book. The problems vary from routine verifications of facts used in the text to the exploration of open questions.
Victor Moll, one of the greatest experimental mathematics researchers of our time, is also a very gifted teacher.
Luckily, he wrote up the lecture notes for his innovative classes in experimental mathematics, so that
undergraduate math (and science!) majors can get a glimpse of mathematics that is so much more fun
than the same old lemma/theorem/proof/corollary drivel that turned off so many talented people away from
mathematics, not because they were not capable of mastering it, but because it was no fun.

Exploring mathematics the way Moll does, by experiment, has the potential to attract to math all these
very talented young minds. For the math prof, it should be a case study, and paradigm, of how
to teach math the fun way!
Mathematical texts serve a variety of aims. A text like Rudin's Analysis is held together by a narrative that is essentially singular: you learn the theory of Analysis from the author's vantage, starting at the beginning. You may do some applications here and there, but it is a long work dedicated to justifying the standard tools. So you get the rudiments of a theory that requires laying a lot of brick. Numbers and Functions is not a text like this. Instead, each chapter breaks into a topic, highlights results and problems, and lays everything out very clearly, before moving to another topic. These topics are all related, but in a manner that is non-trivial. I find the style succinct and exciting. Anyway, to start from first principles and then arrive at all these topics would require thousands of pages, so the reader should come with some background. I love this book. It is not for everyone--nothing is universal. But if you are interested in classical analysis, special functions, integration, number theory, symbolic computing, and some other deep topics like the AGM, this will grab you by the collar and put you to work. Very well done.
There is no coherence to this book. The helter skelter style veers from one
subject to the next with no central goal or underlying plan. No sooner is a
topic picked up than it is discarded and it's on to something completely
different. There are no solutions to the exercises and no reasons to
own a copy of this book.