Numbers

(Graduate Texts in Mathematics / Readings in Mathematics) (v. 123)
Heinz-Dieter Ebbinghaus, Hans Hermes, Friedrich Hirzebruch, Max Koecher, Klaus Mainzer, Jürgen Neukirch, Alexander Prestel, Reinhold Remmert

Springer | 1996 | 395 páginas | rar -pdf | 9,5 Mb

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Descrição: This is a book about numbers - all kinds of numbers, from integers to p-adics, from rationals to octonions, from reals to infinitesimals. Who first used the standard notation for ¦? Why was Hamilton obsessed with quaternions? What was the prospect for "quaternionic analysis" in the 19th century? This is the story about one of the major threads of mathematics over thousands of years. It is a story that will give the reader both a glimpse of the mystery surrounding imaginary numbers in the 17th century and also a view of some major developments in the 20th.

Letters to a Young Mathematician

Ian Stewart

Basic Books | 2006 | 224 páginas | rar - pdf | 469 kb

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Descrição: From the renowned mathematician and writer Ian Stewart, an insightful and lively exploration of why mathematics matters The first scientific entry in the acclaimed Art of Mentoring series from Basic Books, Letters to a Young Mathematician tells readers what Ian Stewart wishes he had known when he was a student and young faculty member. Subjects ranging from the philosophical to the practical--what mathematics is and why it's worth doing, the relationship between logic and proof, the role of beauty in mathematical thinking, the future of mathematics, how to deal with the peculiarities of the mathematical community, and many others--are dealt with in Stewart's much-admired style, which combines subtle, easygoing humor with a talent for cutting to the heart of the matter. In the tradition of G.H. Hardy's classic A Mathematician's Apology, this book is sure to be a perennial favorite with students at all levels, as well as with other readers who are curious about the frequently incomprehensible world of mathematics.

Contents
Preface ix
1 Why Do Math? 1
2 How I Almost Became a Lawyer 11
3 The Breadth of Mathematics 18
4 Hasn’t It All Been Done? 33
5 Surrounded by Math 45
6 How Mathematicians Think 53
7 How to Learn Math 62
8 Fear of Proofs 71
9 Can’t Computers Solve Everything? 82
10 Mathematical Storytelling 87
11 Going for the Jugular 95
12 Blockbusters 103
13 Impossible Problems 110
14 The Career Ladder 122
15 Pure or Applied? 131
16 Where Do You Get Those Crazy Ideas? 147
17 How to Teach Math 157
18 The Mathematical Community 168
19 Pigs and Pickup Trucks 178
20 Pleasures and Perils of Collaboration 188
21 Is God a Mathematician? 196

Worlds Out of Nothing: A Course in the History of Geometry in the 19th Century

Jeremy Gray

Springer | 2011 | 410 páginas | PDF  | 3 Mb

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Based on the latest historical research, Worlds Out of Nothing is the first book to provide a course on the history of geometry in the 19th century. Topics covered in the first part of the book are projective geometry, especially the concept of duality, and non-Euclidean geometry. The book then moves on to the study of the singular points of algebraic curves (Plücker’s equations) and their role in resolving a paradox in the theory of duality; to Riemann’s work on differential geometry; and to Beltrami’s role in successfully establishing non-Euclidean geometry as a rigorous mathematical subject. The final part of the book considers how projective geometry rose to prominence, and looks at Poincaré’s ideas about non-Euclidean geometry and their physical and philosophical significance.

Three chapters are devoted to writing and assessing work in the history of mathematics, with examples of sample questions in the subject, advice on how to write essays, and comments on what instructors should be looking for

From China to Paris: 2000 Years Transmission of Mathematical Ideas

(Boethius. Texte und Abhandlungen zur Geschichte der Mathematik und der Naturwissenschaften)
Benno van Dalen, Joseph W. Dauben, Yvonne Dold-Samplonius, Menso Folkerts
Franz Steiner Verlag | 2002 | 470 páginas | PDF | 14,41 Mb

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Contents:
K. Vogel: A Surveying Problem Travels from China to Paris
J. Hoyrup: Seleucid Innovations in the Babylonian o Algebraico Tradition and their Kin Abroad
J. L. Berggren: Some Ancient and Medieval Approximations to Irrational Numbers and Their Transmission
J. Sesiano: A Reconstruction of Greek Multiplication Tables for Integers
A. Breard: Problems of Pursuit: Recreational Mathematics or Astronomy?
K. Chemla / A. Keller: The Sanskrit karanis and the Chinese mian
S. R. Sarma: Rule of Three and its Variations in India
L. Dun: A Homecoming Stranger: Transmission of the Method of Double False Position and the Story of Hiero's Crown
K. Plofker: Use and Transmission of Iterative Approximations in India and the Islamic World
J. P. Hogendijk: Anthyphairetic Ratio Theory in Medieval Islamic Mathematics
U. Rebstock: An Early Link of the Arabic Tradition of Practical Arithmetic: The Kitab al -Thadhkira bi-usul al-hisab wa 'l-fara'id wa-'awliha wa-tashihiha
A. Djebbar: La circulation des mathematiques entre l'Orient et l'Occident musulmans: Interrogations anciennes et elements nouveaux
C. Burnett: Indian Numerals in the Mediterranean Basin in the Twelfth Century, with Special Reference to the oEastern Formso
R. Franci: Jealous Husbands Crossing the River: A Problem from Alcuin to Tartaglia
T. Levy: De l'arabe a l'hebreu: la constitution de la litterature mathematique hebraique (XIIe-XVIe siecle)
B. van Dalen: Islamic and Chinese Astronomy under the Mongols: a Little-Known Case of Transmission
M. Bagheri: A New Treatise by al-Kashi on the Depression of the Visible Horizon
A. Volkov: On the Origins of the Toan phap dai thanh (Great Compendium of Mathematical Methods)
M. Folkerts: Regiomontanus' Role in the Transmission of Mathematical Problems
D. Pingree: Philippe de la Hire's Planetary Theories in Sanskrit. (Franz Steiner 2002)

The Mathematical Experience, Study Edition

Philip J. Davis, Reuben Hersh

 Birkhäuser; 1st Reprint of the 1995 Edition ed. 2012. Updated with Epilogues by the Authors edition |  2011 | 527 páginas | rar - pdf | 14,1 Mb

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Winner of the 1983 National Book Award!

"…a perfectly marvelous book about the Queen of Sciences, from which one will get a real feeling for what mathematicians do and who they are. The exposition is clear and full of wit and humor..." - The New Yorker (1983 National Book Award edition)

Mathematics has been a human activity for thousands of years. Yet only a few people from the vast population of users are professional mathematicians, who create, teach, foster, and apply it in a variety of situations. The authors of this book believe that it should be possible for these professional mathematicians to explain to non-professionals what they do, what they say they are doing, and why the world should support them at it. They also believe that mathematics should be taught to non-mathematics majors in such a way as to instill an appreciation of the power and beauty of mathematics. Many people from around the world have told the authors that they have done precisely that with the first edition and they have encouraged publication of this revised edition complete with exercises for helping students to demonstrate their understanding. This edition of the book should find a new generation of general readers and students who would like to know what mathematics is all about. It will prove invaluable as a course text for a general mathematics appreciation course, one in which the student can combine an appreciation for the esthetics with some satisfying and revealing applications.

The text is ideal for 1) a GE course for Liberal Arts students 2) a Capstone course for perspective teachers 3) a writing course for mathematics teachers. A wealth of customizable online course materials for the book can be obtained from Elena Anne Marchisotto (elena.marchisotto@csun.edu) upon request.

Problems in Solid Geometry

(Science for Everyone)
I. F. Sharygin

MIR | 1986 | pdf

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From the Preface:

This book contains 340 problems in solid geometry and is a natural continuation of Problems in Plane Geometry, Nauka, Moscow, 1982. It is therefore possible to confine myself here to those points where this book differs from the first. The problems in this collection are grouped into (1) computational problems and (2) problems on proof.

The simplest problems in Section 1 only have answers, others, have brief hints, and the most difficult, have detailed hints and worked solutions. There are two reservations. Firstly, in most cases only the general outline of the solution is given, a number of details being suggested for the reader to consider. Secondly, although the suggested solutions are valid, they are not patterns (models) to be used in examinations. Sections 2-4 contain various geometric facts and theorems, problems on maximum and minimum (some of the problems in this part could have been put in Section 1), and problems on loci. Some questions pertaining to the geometry of tetrahedron, spherical geometry, and so forth are also considered here.

As to the techniques for solving all these problems, I have to state that I prefer analytical computational methods to those associated with plane geometry. Some of the difficult problems in solid geometry will require a high level of concentration from the reader, and an ability to carry out some rather complicated work.

Índice:
Preface . 6
Section 1. Computational Problems. 7
Section 2. Problems on Proof . 37
Section 3. Problems on Extrema. Geometric Inequalities. 47
Section 4. 
Loci of Points. 54
An Arbitrary Tetrahedron 59. 
An Equi-faced Tetrahedron 61. 
An Orthocentric Tetrahedron 64. ´
An Arbitrary Polyhedron. The Sphere 65. 
An Outlet into Space 68.
Answers, Hints, Solutions . 6

Duelling Idiots and Other Probability Puzzlers

Paul J. Nahin

Princeton University Press | 2000| 256 páginas | PDF | 9 Mb

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Referência em: MathEduc

Written for undergraduates and mathematics enthusiasts, this book teaches the fundamentals of elementary probability theory using problems that are familiar to everyone. Light-hearted exercises include determining the odds of winning the World Series and how to obtain answers to an embarassing question using probability. MATLAB M-files are given to solve the problems presented.


Outros livros da série Paradoxes, Perplexities & Mathematical Conundrums
for the Serious Head Scratcher, publicados pela Princeton University Press, disponíveis no blog:





- Chases and Escapes: The Mathematics of Pursuit and Evasion (2007), de Paul J. Nahin
- Slicing Pizzas, Racing Turtles, and Further Adventures in Applied Mathematics
 (2012), de Robert B. Banks 
- Across the Board: The Mathematics of Chessboard Problems (2004),
de John J. Watkins