A Brief Guide to the Great Equations: The Hunt for Cosmic Beauty in Numbers

Robert Crease

Robinson Publishing | 2009 | 2727 páginas | epub | Mb

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mobi - 1,9 Mb - link

Here are the stories of the ten most popular equations of all time as voted for by readers of "Physics World", including - accessibly described here for the first time - the favourite equation of all, Euler's equation. Each is an equation that captures with beautiful simplicity what can only be described clumsily in words. Euler's equation [eip + 1 = 0] was described by respondents as 'the most profound mathematic statement ever written', 'uncanny and sublime', 'filled with cosmic beauty' and 'mind-blowing'. Collectively these equations also amount to the world's most concise and reliable body of knowledge. Many scientists and those with a mathematical bent have a soft spot for equations. This book explains both why these ten equations are so beautiful and significant, and the human stories behind them.

CONTENTS

Illustration Credits
Introduction
1   ‘The Basis of Civilization’: The Pythagorean Theorem
Interlude: Rules, Proofs, and the Magic of Mathematics
2   ‘The Soul of Classical Mechanics’: Newton’s Second Law of Motion
Interlude: The Book of Nature
3   ‘The High Point of the Scientific Revolution’: Newton’s Law of Universal Gravitation
Interlude: That Apple
4   ‘The Gold Standard for Mathematical Beauty’: Euler’s Equation
Interlude: Equations as Icons
5   The Scientific Equivalent of Shakespeare: The Second Law of Thermodynamics
Interlude: The Science of Impossibility
6   ‘The Most Significant Event of the Nineteenth Century’: Maxwell’s Equations
Interlude: Overcoming Anosognosia; or Restoring the Vitality of the Humanities
7   Celebrity Equation: E = mc2
Interlude: Crazy Ideas
8   The Golden Egg: Einstein’s Equation for General Relativity
Interlude: Science Critics
9   ‘The Basic Equation of Quantum Theory’: Schrödinger’s Equation
Interlude: The Double Consciousness of Scientists
10 Living with Uncertainty: The Heisenberg Uncertainty Principle
Interlude: The Yogi and the Quantum
Conclusion: Bringing the Strange Home
Notes
Acknowledgements
Index

Fundamentals of Modern Mathematics: A Practical Review

(Dover Books on Mathematics)

David B. MacNeil

Dover Publications | 2013 | páginas | rar - epub | 17,67 Mb

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Students and others wishing to know a little more about the practical side of mathematics will find this volume a highly informative resource. An excellent supplement to college and high school courses as well as a guide to independent study, the book covers examples of pure mathematics as well as concepts of applied mathematics useful for solving problems that arise in business, industry, science, and technology.
Contents include examinations of the theory of sets, numbers and groups; matrices and determinants; probability, statistics, and quality control; and game theory. Additional subjects include inequalities, linear programming, and the transportation problem; combinatorial mathematics; transformations and transforms; and numerical analysis. Accessible explanations of important concepts feature a total of more than 150 diagrams and graphs, in addition to worked-out examples with step-by-step explanations of methods. Answers to exercises and problems appear at the end.


CONTENTS
CHAPTER 1 THEORY OF SETS, NUMBERS AND GROUPS
1.SET MEMBERSHIP
2.EQUALITY
3.SETS, SUBSETS AND INCLUSION
4.SET OF SETS
5.NEGATIVES
6.UNIONS AND INTERSECTIONS
7.RELATIONS INVOLVING UNIONS AND INTERSECTIONS
8.THE COMPLEMENT
9.THE ABSOLUTE COMPLEMENT
10.POWERS
11.ORDERED PARTS AND CARTESIAN PRODUCTS
12.RELATIONS: FUNCTION, DOMAIN AND RANGE
13.FUNCTIONS
14.NUMBERED SETS
15.OPERATIONS WITH NATURAL NUMBERS
16.INTEGRAL NUMBERS OR INTEGERS
17.RATIONAL NUMBERS
18.REAL NUMBERS
19.COMPLEX NUMBERS
20.TRIGONOMETRIC AND LOGARITHMIC NUMBERS
21.TRANSCENDENTAL NUMBERS
22.TRANSFINITE NUMBERS
23.GROUPS, DEFINITION OF
24.PERMUTATION GROUPS
CHAPTER 2 MATRICES AND DETERMINANTS
25.ADDITION OF MATRICES
26.SCALAR MULTIPLICATION OF MATRICES
27.MULTIPLICATION OF MATRICES BY MATRICES
28.APPLICATION OF MATRICES
29.DETERMINANTS
30.FINDING THE DETERMINANTS OF 2 × 2 AND 3 × 3 MATRICES
31.PROPERTIES OF MATRICES AND DETERMINANTS
32.MINORS AND THE EVALUATION OF 4TH ORDER DETERMINANTS
33.THE SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS BY DETERMINANTS
34.RANK OF A MATRIX AND CONSISTENCY OF EQUATIONS
35.CHARACTERISTIC EQUATION OF A MATRIX
36.VECTORS
37.THE APPLICATION OF MATRICES IN DESCRIBING GEOMETRICAL DISTORTIONS AND TRANSFORMATIONS
38.MATRICES. OTHER OPERATIONS AND DEFINITIONS
CHAPTER 3 PROBABILITY, STATISTICS, AND QUALITY CONTROL
39.INTRODUCTION
40.FUNDAMENTAL CONCEPTS
41.PROBABILITY
42.GAMES OF CHANCE
43.RANDOM WALK PROCESSES
44.MARKOV PROCESSES
45.RANDOM VARIABLES
46.STATISTICAL DEFINITIONS AND THEIR NOTATION
47.IMPORTANT DISTRIBUTIONS. THE BINOMIAL DISTRIBUTION
48.ELEMENTS OF STATISTICS
49.OTHER FUNDAMENTAL CONCEPTS
50.STATISTICAL QUALITY CONTROL
CHAPTER 4THE THEORY OF GAMES
51.INTRODUCTION
52.TWO-PERSON ZERO-SUM GAMES
53.SADDLE POINTS
54.MIXED STRATEGIES
55.2 × N GAMES
56.3 × 3 GAMES
57.CONCLUSION
CHAPTER 5 INEQUALITIES, LINEAR PROGRAMMING, AND THE TRANSPORTATION PROBLEM
58.INTRODUCTION
59.FUNDAMENTAL SYMBOLS AND AXIOMS
60.FUNDAMENTAL OPERATIONS
61.INEQUALITIES OF AVERAGES
62.PROPER-NAME INEQUALITIES
63.SYSTEMS OF INEQUALITIES
64.LINEAR PROGRAMMING
65.THE TRANSPORTATION PROBLEM
66.THE TRANSPORTATION PROBLEM REVISED
67.DEGENERACY AND FORMAL CHARACTERISTICS
68.THE SIMPLEX METHOD
69.THE DUAL SIMPLEX METHOD
CHAPTER 6 COMBINATORIAL MATHEMATICS
70.INTEGER PROGRAMMING
71.LINEAR PROGRAMMING AND GAME THEORY
72.NETWORK FLOW PROBLEMS
73.TREES AND LOOPS
CHAPTER 7 TRANSFORMATIONS AND TRANSFORMS
74.COORDINATE SYSTEMS
75.CARTESIAN COORDINATES
76.SPHERICAL POLAR COORDINATES
77.CYLINDRICAL COORDINATES
78.THE POLAR COORDINATE SYSTEM
79.HYPERBOLIC FUNCTIONS
80.BIPOLAR COORDINATES
81.TRANSLATION OF COORDINATE AXES
82.ROTATION OF COORDINATE AXES
83.LAPLACE TRANSFORMATIONS. GENERAL CONSIDERATIONS
84.EVALUATING LAPLACE TRANSFORMS
85.PROPERTIES OF THE LAPLACE TRANSFORM
86.THE INVERSE LAPLACE TRANSFORM
87.APPLICATIONS OF THE LAPLACE TRANSFORM
88.HEAVISIDE OPERATIONAL CALCULUS
89.OTHER TRANSFORMS
CHAPTER 8 NUMERICAL ANALYSIS
90.NATURE OF NUMERICAL ANALYSIS
91.DIFFERENCE TABLES
92.DIFFERENCE TABLES USED FOR INTERPOLATION
93.NUMERICAL SOLUTION OF ALGEBRAIC EQUATIONS
94.NUMERICAL INTEGRATIONS
95.NUMERICAL DIFFERENTIATION
96.THE METHOD OF LEAST SQUARES
ANSWERS TO EXERCISES AND PROBLEMS
INDEX

Construction Mathematics

Surinder Virdi, Roy Baker e Narinder Kaur Virdi

Routledge |  2014 - 2ª edição |336 páginas | rar - pdf | 3 Mb

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Construction Mathematics is an introductory level mathematics text, written specifically for students of construction and related disciplines.

• Learn by tackling exercises based on real-life construction maths. Examples include: costing calculations, labour costs, cost of materials and setting out of building components.

• Suitable for beginners and easy to follow throughout.

• Learn the essential basic theory along with the practical necessities.

The second edition of this popular textbook is fully updated to match new curricula, and expanded to include even more learning exercises. End of chapter exercises cover a range of theoretical as well as practical problems commonly found in construction practice, and three detailed assignments based on practical tasks give students the opportunity to apply all the knowledge they have gained.

Construction Mathematics addresses all the mathematical requirements of Level 2 construction NVQs from City & Guilds/CITB and Edexcel courses, including the BTEC First Diploma in Construction. Additional coverage of the core unit Mathematics in Construction and the Built Environment from BTEC National Construction, Civil Engineering and Building Services courses makes this an essential revision aid for students who do not have Level 2 mathematics experience before commencing their BTEC National studies. This is also the ideal primer for any reader who wishes to refresh their mathematics knowledge before going into a construction HNC or BSc.

Contents

1. Using a Scientific Calculator 
2. Numbers
3.Basic Algebra 
4. Indices and Logarithms 
5. Standard Form, Significant Figures and Estimation 
6. Transposition and Evaluation of Formulae 
7. Fractions and Percentages 
8. Graphs 
9. Units and their Conversion 
10. Geometry 
11. Areas (1) 
12. Volumes (1) 
13. Trigonometry (1) 
14. Setting Out 
15. Costing - Materials and Labour 
16. Statistics 
17. Areas and Volumes (2) 
18. Areas and Volumes (3) 
19. Trigonometry (2) 
20. Computer Techniques 
21. Assignments 
Appendix 1 Concrete Mix 
Appendix 2 Solutions for Excercises 
Appendix 3 Assignment Solutions

Goedel's Way: Exploits into an undecidable world

Gregory Chaitin, Francisco A Doria e Newton C.A. da Costa

CRC Press | 2011 | 162 páginas | pdf | 1,1 Mb

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Kurt Gödel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein’s general relativity, as he proved that Einstein’s theory admits time machines. 
The Gödel incompleteness theorem - one cannot prove nor disprove all true mathematical sentences in the usual formal mathematical systems- is frequently presented in textbooks as something that happens in the rarefied realm of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin’s groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the Gödel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life.
This accessible book gives a new, detailed and elementary explanation of the Gödel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book’s writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer science.
See also: http://www.youtube.com/watch?v=REy9noY5Sg8

Contents
1. Gödel, Turing 
2. Complexity, randomness 
3. A list of problems 
4. The halting function and its avatars 
5. Entropy, P vs. NP
6. Forays into uncharted landscapes.

Harmony of the World - 75 Years of Mathematics Magazine

Gerald L. Alexanderson e Peter Ross 

 Mathematical Association of America | 2007 | 302 páginas | rar - pdf |3,8 Mb

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Who would expect to find in the pages of Mathematics Magazine the first full treatment of one of the more important and oft-cited twentieth century theorems in analysis, the Stone-Weierstrass Theorem in an article by Marshall Stone himself? Where else would one look for proofs of trigonometric identities using commutative ring theory? Or one of the earliest and best expository articles on the then new Jones knot polynomials, an article that won the prestigious Chauvenet Prize? Or an amusing article purporting to show that the value of has been time dependent over the years? These and much more are in this collection of the best from Mathematics Magazine. Readers are inundated with new material in the many mathematical journals. Gems from past issues of Mathematics Magazine or the Monthly or the College Mathematics Journal are read with pleasure when they appear but get pushed into the background when the next issues arrive. So from time to time it is rewarding to go back and see just what marvelous material has been published over many years, articles now to some extent forgotten. There is history of mathematics (algebraic numbers, inequalities, probability and the Lebesgue integral, quaternions, Pólya s enumeration theorem, and group theory) and stories of mathematicians (Hypatia, Gauss, E. T. Bell, Hamilton, and Euler). The list of authors is star-studded: E. T. Bell, Otto Neugebauer, D. H. Lehmer, Morris Kline, Einar Hille, Richard Bellman, Judith Grabiner, Paul Erdos, B. L. van der Waerden, Paul R. Halmos, Doris Schattschneider, J. J. Burckhardt, Branko Grunbaum, and many more. Eight of the articles included have received the Carl B. Allendoerfer or Lester R. Ford Awards.

Contents

The name of each article is followed by a notation indicating the field of mathematics from which it comes: (Al) algebra, (AM) applied mathematics, (An) analysis, (CG) combinatorics and graph theory, (G) geometry, (H) history, (L) logic, (M) miscellaneous, (NT) number theory, (PS) probability/statistics, and (T) topology.

Introduction .  .vii

A Brief History of Mathematics Magazine .  . xi

Part I: The First Fifteen Years .. .1

Perfect Numbers, Zena Garrett (NT) .. .3

Rejected Papers of Three Famous Mathematicians, Arnold Emch (H) .  5

Review of Men of Mathematics, G. Waldo Dunnington (H) .. 9

Oslo under the Integral Sign, G. Waldo Dunnington (H) . 11

Vigeland’s Monument to Abel in Oslo, G. Waldo Dunnington (H) . .19

The History of Mathematics, Otto Neugebauer (H) . .. .23

Numerical Notations and Their Influence on Mathematics, D. H. Lehmer (NT) .  .29

Part II: The 1940s  .33

The Generalized Weierstrass Approximation Theorem, Marshall H. Stone (An) . . .35

Hypatia of Alexandria, A. W. Richeson (H) .. . 45

Gauss and the Early Development of Algebraic Numbers, E. T. Bell (Al)  . . 51

Part III: The 1950s . . 69

The Harmony of the World, Morris Kline (M) .. 71

What Mathematics Has Meant to Me, E. T. Bell (M) .. .79

Mathematics and Mathematicians from Abel to Zermelo, Einar Hille (H) .  81

Inequalities, Richard Bellman (An) . . 95

A Number System with an Irrational Base, George Bergman (NT) . 99

Part IV: The 1960s  .107

Generalizations of Theorems about Triangles, Carl B. Allendoerfer (G) . .109

A Radical Suggestion, Roy J. Dowling (NT) . .115

Topology and Analysis, R. C. Buck (An, T). 117

The Sequence fsin ng, C. Stanley Ogilvy (An) . .. . 121

Probability Theory and the Lebesgue Integral, Truman Botts (PS) . . . 123

On Round Pegs in Square Holes and Square Pegs in Round Holes, David Singmaster (G) . . 129

t : 1832–1879, Underwood Dudley (M) . . . . 133

Part V: The 1970s .  . 135

Trigonometric Identities, Andy R. Magid (Al) . .  .137

A Property of 70, Paul Erdos (NT) . . . .139

Hamilton’s Discovery of Quaternions, B. L. van der Waerden (Al, H) .  . 143

Geometric Extremum Problems, G. D. Chakerian and L. H. Lange (G . .151

Polya’s Enumeration Theorem by Example, Alan Tucker (CG) . 161

Logic from A to G, Paul R. Halmos (L) . . . . 169

Tiling the Plane with Congruent Pentagons, Doris Schattschneider (G) .. . 175

Unstable Polyhedral Structures, Michael Goldberg (G) . . 191

Part VI: The 1980s .  .197

Leonhard Euler, 1707–1783, J. J. Burckhardt (H) .  . .199

Love Affairs and Differential Equations, Steven H. Strogatz (An)  . 211

The Evolution of Group Theory, Israel Kleiner (Al) . . . 213

Design of an Oscillating Sprinkler, Bart Braden (AM) . . . 229

The Centrality of Mathematics in the History of Western Thought, Judith V. Grabiner (M) . ..237

Geometry Strikes Again, Branko Gr¨unbaum (G) .. 247

Why Your Classes Are Larger than “Average”, David Hemenway (PS) . 255

The New Polynomial Invariants of Knots and Links, W. B. R. Lickorish and Kenneth C. Millett (CG, T)  . 257

Briefly Noted .. 273

The Problem Section . . . 279

Index . . . .281

About the Editors . . . 287

Explaining Beauty in Mathematics: An Aesthetic Theory of Mathematics

(Synthese Library) 

Ulianov Montano 

Springer | 2014 | 224 páginas | rar - pdf | 1,1 Mb

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This book develops a naturalistic aesthetic theory that accounts for aesthetic phenomena in mathematics in the same terms as it accounts for more traditional aesthetic phenomena. Building upon a view advanced by James McAllister, the assertion is that beauty in science does not confine itself to anecdotes or personal idiosyncrasies, but rather that it had played a role in shaping the development of science. Mathematicians often evaluate certain pieces of mathematics using words like beautiful, elegant, or even ugly. Such evaluations are prevalent, however, rigorous investigation of them, of mathematical beauty, is much less common. The volume integrates the basic elements of aesthetics, as it has been developed over the last 200 years, with recent findings in neuropsychology as well as a good knowledge of mathematics.

The volume begins with a discussion of the reasons to interpret mathematical beauty in a literal or non-literal fashion, which also serves to survey historical and contemporary approaches to mathematical beauty. The author concludes that literal approaches are much more coherent and fruitful, however, much is yet to be done. In this respect two chapters are devoted to the revision and improvement of McAllister’s theory of the role of beauty in science. These antecedents are used as a foundation to formulate a naturalistic aesthetic theory. The central idea of the theory is that aesthetic phenomena should be seen as constituting a complex dynamical system which the author calls the aesthetic as processtheory.

The theory comprises explications of three central topics: aesthetic experience (in mathematics), aesthetic value and aesthetic judgment. The theory is applied in the final part of the volume and is used to account for the three most salient and often used aesthetic terms often used in mathematics: beautiful, elegant and ugly. This application of the theory serves to illustrate the theory in action, but also to further discuss and develop some details and to showcase the theory’s explanatory capabilities.

Contents
Introduction.
Part 1. Antecedents.
Chapter 1. On Non-literal Approaches.
Chapter 2. Beautiful, Literally.
Chapter 3. Ugly, Literally.
Chapter 4. Problems of the Aesthetic Induction.
Chapter 5. Naturalizing the Aesthetic Induction.
Part 2. An Aesthetics of Mathematics.
Chapter 6. Introduction to a Naturalistic Aesthetic Theory.
Chapter 7. Aesthetic Experience.
Chapter 8. Aesthetic Value.
Chapter 9. Aesthetic Judgement I: Concept.
Chapter 10. Aesthetic Judgement II: Functions.
Chapter 11. Mathematical Aesthetic Judgements.
Part 3. Applications.
Chapter 12. Case Analysis I: Beauty.
Chapter 13. Case Analysis II: Elegance.
Chapter 14. Case Analysis III: Ugliness, Revisited.
Chapter 15. Issues of Mathematical Beauty, Revisited.

The Abel Prize: 2003-2007 The First Five Years

Helge Holden e Ragni Piene

Springer | 2010 | 245 páginas | pdf | 2,9 Mb 

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link1

The book presents the winners of the first five Abel Prizes in mathematics: 2003 Jean-Pierre Serre; 2004 Sir Michael Atiyah and Isadore Singer; 2005 Peter D. Lax; 2006 Lennart Carleson; and 2007 S.R. Srinivasa Varadhan.

Each laureate provides an autobiography or an interview, a curriculum vitae, and a complete bibliography. This is complemented by a scholarly description of their work written by leading experts in the field and by a brief history of the Abel Prize.

Livro relacionado

Abel prize 2008-2012 Idioma: Inglês   Editora: [S.l.] : Springer-Verlag Berlin An, 2013

More Fallacies, Flaws & Flimflam

(Spectrum) 

 Edward Barbeau

The Mathematical Association of America | 2013 | páginas | rar - pdf |966 kb

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Mistakes in mathematical reasoning can range from outlandish blunders to deep and subtle oversights that evade even the most watchful eye. This book represents the second collection of such errors to be compiled by Edward Barbeau. Like Barbeau's previous book, Mathematical Fallacies, Flaws and Flimflam, material is drawn from a variety of sources including the work of students, textbooks, the media, and even professional mathematicians. The errors presented here serve both to entertain, and to emphasize the need to subject even the most "obvious" assertions to rigorous scrutiny, as intuition and facile reasoning can often be misleading. Each item is carefully analysed and the source of the error is exposed. All students and teachers of mathematics, from school to university level, will find this book both enlightening and entertaining.

Contents
Arithmetic
School algebra
Geometry
Limits, sequences and series
Differential calculus
Integral calculus
Combinatorics
Probability and statistics
Complex analysis
Linear and modern algebra
Miscellaneous

Outros livros do mesmo autor:

Challenging mathematics in and beyond the classroom : the 16th ICMI study por Edward Barbeau; P J Taylor; International Commission on Mathematical Instruction.; Idioma: Inglês   Editora: New York ; London : Springer, ©2009.

Mathematical fallacies, flaws, and flimflam por Edward Barbeau Idioma: Inglês   Editora: Washington, DC : Mathematical Association of America, ©2000.

Five hundred mathematical challenges por Edward Barbeau; Murray S Klamkin; W O J Moser Idioma: Inglês   Editora: [Washington, DC] : Mathematical Association of America, ©1995.

The Mathematical Heritage of C.F. Gauss: A Collection of Papers in Memory of C.F. Gauss

George M. Rassias

World Scientific Pub Co Inc | 1991 | 916 páginas | rar - pdf |27,75 Mb

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A collection of of original and expository papers in the fields of mathematics in which Gauss has made many fundamental discoveries.

Contents
Preface ix
A summary of C. F. Gauss's life and mathematical work 1
G. M. Rassias
On Gauss' differential equation and its twenty-four Rummer's solutions 12
M. A. Al-Bassam
On the Diophantine equation (X + Y)A = ZB 32
L. J. Alex
Partitions and the Gaussian sum 35
G. E. Andrews
The periodicity of an algorithm over the complex number field (ACF) and the solution of the Hermite problem 43
M. Baica
Lorentzian distance and curvature 53
J. K. Beem
The decomposition theory and its applications 66
N. Bokan
Spaces of morphisms between algebraic schemes 100
P. Cherenack, L. Guerra
Uniqueness of solutions of electromagnetic interaction problems associated with scattering by bianisotropic bodies covered with impedance sheets 119
D. K. Cohoon
On the topological structure of curves 133
P. J. Collins
Gauss, Bayes, Kalman: State-space models 137
P. Daffer
Waves, quanta, E = mc2, and perihelion shifts: A new sciencehistorical perspective and maathematical unification 157
K. Demys
Uniformly continuous multi-valued mappings 172
D. Doitchinov
Computers in algebraic topology 179
E. Dominguez and J. Rubio
Factorization in quaternion orders over number fields 195
D. R. Estes
Thue inequalities with a small number of solutions 204
J.-H. Evertse and K. Gyory
A load balanced algorithm for the calculation of the polynomial knot and link invariants 225
B. Ewing and K. C. Millett
Convex polyhedral models for the finite three-dimensional isometry groups 267
L. L. Foster
The Lorentzian modular group and nonlinear lattices 282
G. J. Fox and P. E. Parker
Integral operators for harmonic functions 304
A. Fry ant
Quadrature and harmonic L1 -approximation 321
M. Goldstein
The Theorema Egregium of Gauss from a viewpoint of partial differential equations 326
C. K. Han
A new cosine functional equation 334
H. Haruki
On paralindelof and metalindelof spaces 342
H. Z. Hdeib
The Maxwell condition in Friedmann cosmology 349
C. D. Hill
Space-time compactification and Riemannian submersions 358
S. Ianus and M. Visinescu
Independence and scrambled sets for chaotic mappings 372
A. Iwanik
A recent modification of iterative methods for solving nonlinear problems 379
A. J. Jerri
Expansions of special cases of Gauss' hypergeometric functions using generalized calculus 405
R. N. Kalia
Gauge-natural operators transforming connections to the tangent bundle 416
I. Koldf
Returns under bounded number of iterations 427
Z. S. Kowalski
On a structural scheme of physical theories proposed by E. Tonti 432
E. A. Lacomb and F. Ongay
Archimedes versus Gauss: The construction of a regular heptagon 454
/. F. Lamb, Jr.
Some properties of covariant operators in Gauge theories 458
K. B. Marathe and G. Giachetta
A signal discriminator , 479
F. McNolty, W. Sherwood, and J. Mirra
Powers of 2, continued fractions, and the class number one problem for real quadratic fields Q(Vd), with d = 1 (mod 8) 505
R. A. Mollin and H. C. Williams
The validity of Gaussian electrodynamics 517
P. Moon, D. E. Spencer, S. Y. Uma, and P, J. Mann
Dimensions, fractals, and sphere packing 526
C. Muses
Second cohomology spaces and flexible Lie-admissible algebras 544
H. C. Myung and A. A. Sagle
New Fibonacci and Lucas identities 562
S. A. Obaid
Hyper-Kahler metrics and monopoles 573
H. Pedersen
On certain mathematical problems connected with the use of the complex variable boundary element method to the problems of plane hydrodynamics, Gauss' variant of the procedure 585
T. Peirila
A survey on the Poincare conjecture of the topology of 3-manifolds 605
G. M. Rassias
Adjoint connections on group manifolds and gauge transformations 621
H. Rund
An abstract fixed-point theorem of Vanderbauwhede-VanGils type 645
K. P. Rybakowski
Formulas for higher-order finite expansions of composite maps 652
K. P. Rybakowski
Infinite order differential operators in generalized Fock spaces 670
J. Schmeelk
Gauss and the electrodynamic force 685
D. E. Spencer and S. Y. Uma
Some operational techniques in the theory of generalized Gaussian and Clausenian functions 712
H. M. Srivastava
Gauss' gamma multiplication theorem: Analogues and extensions 733
K. B. Stolarsky
Some properties of hereditarily locally connected continua related to the Hann-Mazurkiewicz theorem 758
L. B. Treybig
Convex nonholonomic hyper surfaces 769
C. Udri§te, 0. Dogaru
The measure of covering the Euclidean space by group-translates of a set 785
B. Uhrin
A non-Archimedean number field and its applications in modern physics 810
S. T. Wang
The differential geometry of two types of almost contact metric submersions 827
B. Watson
Hypersurface with constant mean curvature in # n + 1 862
B. Q. Wu
The Poincare density 872
S. Yamashita
Sophie Germain primes 882
5. Yates
On sampling theorems and the Gauss-Jacobi mechanical quadrature 887
A. I. Zayed
Author index 901

Math For Real Life For Dummies

Barry Schoenborn

For Dummies | 2013 | 291 páginas | rar - pdf | 5,2 Mb

link (password: matav)

Learn to:

• Get the skills you need to tackle everyday math problems
• Know which math to use when shopping, driving, and investing
• Brush up on basic math skills and concepts

Brush up on the math skills you need in your everyday life

Need to sharpen your math skills to handle everyday encounters, like calculating restaurant tips, understanding interest rates, and figuring out percentages and odds? Packed with real-world examples, Math For Real Life For Dummies gives you plain-English explanations of the simple math formulas and operations you're likely to encounter in the workplace, the kitchen, and even when playing games.

• Brush up on the basics — get basic math from counting and simple arithmetic to broader concepts like statistics
• Math to the rescue — discover how to do the calculations that spring up while shopping, cooking, dining out, trying to lose weight, and more
• Manage money with math — get a handle on the general principles, specialized terms, and strategies to create a budget, better manage your bank account and check register, avoid credit card debt, and invest more wisely
• Room for improvement —see calculations you can do in your head and games you can play to build your math skills and sharpen your critical thinking

Open the book and find:

• Math tricks that help you perform quick calculations in your head
• Ways to apply math formulas and principles to craft, home improvement, and yard projects
• How to make conversions, understand statistics, calculate odds, use percentages, and more
• Math solutions for day-to-day activities such as cooking, dining out, shopping, and banking
• Ten games that build math skills

Contents at a Glance

Introduction........... 1

Part I: Boning Up on Math Basics.... 7

Chapter 1: Awesome Operations: Math Fundamentals.... 9

Chapter 2: High School Reunion: Revisiting Key Principles of Algebra and Geometry... 27

Chapter 3: Becoming a Believer: Conversion, Statistics, Probability and More ... 47

Chapter 4: The Miracle of Mental Math....... 59

Part II: Math for Everyday Activities....... 71

Chapter 5: Let’s Make a Deal! Math You Use When Shopping...... 73

Chapter 6: Mmm, Mmm, Good: Kitchen Calculations............. 97

Chapter 7: It Does a Body Good: Math for Health and Well-Being.... 109

Chapter 8: Putting Geometry to Work at Home... 129

Chapter 9: Math and Statistics around Town and on the Road..... 141

Part III: Math to Manage Your Personal Finances... 161

Chapter 10: Budgets, Bank Accounts, Credit Cards, and More... 163

Chapter 11: Key Principles of Investment Math..... 183

Chapter 12: Covering Your Assets: Insurance Math.... 203

Chapter 13: Taking Math to Work.... 215

Chapter 14: How Taxing! (Almost) Understanding the Government.... 229

Part IV: The Part of Tens... 241

Chapter 15: Ten Quick Calculations You Can Do in Your Head..... 243

Chapter 16: Ten Activities That Build Math Skills... 249

Index........ 255

Mathematics Tomorrow

Lynn A. Steen


Springer | 1981 | 244 páginas | pdf |6,9 Mb

link

Contents
Introduction ... 1
What Is Mathematics?
Applied Mathematics Is Bad Mathematics
Paul R. Halmos ... 9
Solving Equations Is Not Solving Problems
Jerome Spanier... 21
The Unexpected Art of Mathematics
Jerry P. King .. 29
Redefining the Mathematics Major
Alan Tucker ... 39
Purity in Applications
Tim Poston .... 49
Growth and New Intuitions: Can We Meet the Challenge?
William F. Lucas ... 55
Teaching and Learning Mathematics
A voiding Math Avoidance
Peter J. Hilton. . 73
Learning Mathematics
Anneli Lax and Giuliana Groat 83
Teaching Mathematics
Abe Shenitzer .... 95
Read the Masters!
Harold M. Edwards .... 105
Mathematics as Propaganda
Neal Koblitz .. 111
Mathematicians Love Books
Walter Kaufmann-Buhler, Alice Peters, and Klaus Peters .. 121
A Faculty in Limbo
Donald J. Albers
Junior's All Grown Up Now
George M. Miller..... 135
NSF Support for Mathematics Education
E. P. Miles. Jr... 139
Issues of Equality
The Real Energy Crisis
Eileen L. Poiani ... 155
Women and Mathematics
Alice T. Schafer .... 165
Spatial Separation in Family Life: A Mathematician's Choice
Marian Boykan Pour-EI .... 187
Mathematics for Tomorrow
Applications of Undergraduate Mathematics
Ross L. Finney ... 197
The Decline of Calculus-The Rise of Discrete Mathematics
Anthony Ralston .. 213
Mathematical Software: How to Sell Mathematics
Paul T. Boggs.. 221
Physics and Mathematics
Hartley Rogers. Jr.
Readin', 'Ritin', and Statistics
Tim Robertson and Robert V. Hogg
Mathematization in the Sciences
Maynard Thompson ... 243

The Beauty of Fractals Six Different Views

 Denny Gulick e Jon Scott 

The Mathematical Association of America | 2011 | páginas | rar - pdf | 16,5 Mb

link (password : matav)

With the coming of the computer age, fractals have emerged to play a significant role in art images, scientific application and mathematical analysis. The Beauty of Fractals is in part an exploration of the nature of fractals, including examples which appear in art, and in part a close look at famous classical fractals and their close relatives. The final essay examines the relationship between fractals and differential equations. The essays that appear in The Beauty of Fractals contain perspectives different enough to give the reader an appreciation of the breadth of the subject. The essays are self-contained and expository, and are intended to be accessible to a broad audience that includes advanced undergraduate students and teachers at both university and secondary-school level. The book is also a useful complement to the material on fractals which can be found in textbooks.

Contents
Mathscapes--fractal scenery / Anne M. Burns
Chaos, fractals, and Tom Stoppard's Arcadia / Robert L. Devaney
Excursions through a forest of golden fractal trees / T.D. Taylor
Exploring fractal dimension, area, and volume / Mary Ann Connors
Points in sierpiński-like fractals / Sandra Fillebrown, ... [et al.]
Fractals in the 3-body problem via symplectic integration / Daniel Hemberger, James A. Walsh

The Genius of Euler: Reflections on his Life and Work

(Spectrum)

William Dunham (Editor)

The Mathematical Association of America | 2007 | 309 páginas | DjVu (11.8 mb)

link

This book celebrates the 300th birthday of Leonhard Euler (1707 1783), one of the brightest stars in the mathematical firmament. The book stands as a testimonial to a mathematician of unsurpassed insight, industry, and ingenuity one who has been rightly called the master of us all. The collected articles, aimed at a mathematically literate audience, address aspects of Euler s life and work, from the biographical to the historical to the mathematical. The oldest of these was written in 1872, and the most recent dates to 2006. Some of the papers focus on Euler and his world, others describe a specific Eulerian achievement, and still others survey a branch of mathematics to which Euler contributed significantly. Along the way, the reader will encounter the Konigsberg bridges, the 36-officers, Euler s constant, and the zeta function. There are papers on Euler s number theory, his calculus of variations, and his polyhedral formula. Of special note are the number and quality of authors represented here. Among the 34 contributors are some of the most illustrious mathematicians and mathematics historians of the past century e.g., Florian Cajori, Carl Boyer, George Polya, Andre Weil, and Paul Erdos. And there are a few poems and a mnemonic just for fun.

Contents
Acknowledgments ix
Preface xi
About the Authors xiii
Part I: Biography and Background
Introduction to Part I 3
Leonhard Euler, B. F. Finkel (1897) 5
Leonard Euler, Supreme Geometer (abridged), C. Truesdell (1972) 13
Euler (abridged), Andre Weil (1984) 43
Frederick the Great on Mathematics and Mathematicians (abridged),
Florian Cajori (1927) 51
The Euler-Diderot Anecdote, B. H. Brown (1942) 57
Ars Expositionis: Euler as Writer and Teacher, G. L. Alexanderson (1983) 61
The Foremost Textbook of Modern Times, C. B. Boyer (1951) 69
Leonhard Euler, 1707-1783, J. J. Burckhardt (1983) 75
Euler's Output, A Historical Note, W W. R. Ball (1924) 89
Discoveries (a poem), Marta Sved and Dave Logothetti (1989) 91
Bell's Conjecture (a poem), J. D. Memory (1997) 93
A Response to "Bell's Conjecture" (a poem),
Charlie Marion and William Dunham (1997) 95
Part II: Mathematics
Introduction to Part 2 99
Euler and Infinite Series, Morris Kline (1983) 101
The Genius of Euler: Reflections on his Life and Work
Euler and the Zeta Function, Raymond Ayoub (1974) 113
Addendum to: "Euler and the Zeta Function, " A. G. Howson (1975) 133
Euler Subdues a Very Obstreperous Series (abridged), E. J. Barbeau (1979) 135
On the History ofEuler's Constant, J. W. L. Glaisher (1872) 147
A Mnemonic for Euler's Constant, Morgan Ward (1931) 153
Euler and Differentials, Anthony P. Ferzola (1994) 155
Leonhard Euler's Integral: A Historical Profile of the
Gamma Function, Philip J. Davis (1959) 167
Change of Variables in Multiple Integrals: Euler to Cartan, Victor J. Katz (1982) 185
Euler's Vision of a General Partial Differential Calculus for a
Generalized Kind of Function, Jesper LUtzen (1983) 197
On the Calculus of Variations and Its Major Influences on the
Mathematics of the First Half of Our Century, Erwin Kreyszig (1994) 209
Some Remarks and Problems in Number Theory Related to the
Work of Euler, Paul Erdos and Underwood Dudley (1983) 215
Euler's Pentagonal Number Theorem, George E. Andrews (1983) 225
Euler and Quadratic Reciprocity, Harold M. Edwards (1983) 233
Euler and the Fundamental Theorem of Algebra, William Dunham (1991) 243
Guessing and Proving, George P6lya (1978) 257
The Truth about Kdnigsberg, Brian Hopkins and Robin J. Wilson (2004) 263
Graeco-Latin Squares and a Mistaken Conjecture of Euler,
Dominic Klyve and Lee Stemkoski (2006) 273
Glossary 289
List of Photos 303
Index 305
About the Editor 309

The Simpsons and Their Mathematical Secrets

Bloomsbury USA | 2013 | 279 páginas | epub/mobi

link (epub)
link (mobi)

You may have watched hundreds of episodes of The Simpsons (and its sister show Futurama) without ever realizing that cleverly embedded in many plots are subtle references to mathematics, ranging from well-known equations to cutting-edge theorems and conjectures. That they exist, Simon Singh reveals, underscores the brilliance of the shows’ writers, many of whom have advanced degrees in mathematics in addition to their unparalleled sense of humor.
While recounting memorable episodes such as “Bart the Genius” and “Homer3,” Singh weaves in mathematical stories that explore everything from p to Mersenne primes, Euler’s equation to the unsolved riddle of P v. NP; from perfect numbers to narcissistic numbers, infinity to even bigger infinities, and much more. Along the way, Singh meets members of The Simpsons’ brilliant writing team—among them David X. Cohen, Al Jean, Jeff Westbrook, and Mike Reiss—whose love of arcane mathematics becomes clear as they reveal the stories behind the episodes.
With wit and clarity, displaying a true fan’s zeal, and replete with images from the shows, photographs of the writers, and diagrams and proofs, The Simpsons and Their Mathematical Secrets offers an entirely new insight into the most successful show in television history.

** 

Contents
CHAPTER 0 The Truth About The Simpsons
CHAPTER 1 Bart the Genius
CHAPTER 2 Are you π-Curious?
CHAPTER 3 Homer’s Last Theorem
CHAPTER 4 The Puzzle of Mathematical Humor
EXAMINATION I
CHAPTER 5 Six Degrees of Separation
CHAPTER 6 Lisa Simpson, Queen of Stats and Bats
CHAPTER 7 Galgebra and Galgorithms
EXAMINATION II
CHAPTER 8 A Prime-Time Show
CHAPTER 9 To Infinity and Beyond
CHAPTER 10 The Scarecrow Theorem
EXAMINATION III
CHAPTER 11 Freeze-Frame Mathematics
CHAPTER 12 Another Slice of π
CHAPTER 13 Homer3
EXAMINATION IV
CHAPTER 14 The Birth of Futurama
CHAPTER 15 1,729 and a Romantic Incident
CHAPTER 16 A One-Sided Story
CHAPTER 17 The Futurama Theorem
EXAMINATION V
EπLOGUE
APPENDIX 1 The Sabermetrics Approach in Soccer
APPENDIX 2 Making Sense of Euler’s Equation
APPENDIX 3 Dr. Keeler’s Recipe for the Sum of Squares
APPENDIX 4 Fractals and Fractional Dimensions
APPENDIX 5 Keeler’s Theorem
ACKNOWLEDGMENTS
ONLINE RESOURCES
PICTURE CREDITS
BY THE SAME AUTHOR

Mathematical Fallacies, Flaws and Flimflam

Edward J. Barbeau

The Mathematical Association of America | 2000 | 167 páginas | rar - pdf | 1,3 Mb

link (novo ficheiro)
(password: matav)

Djvu | 3,1 Mb 
link
depositfiles.com
rapidgator.net


Through hard experience mathematicians have learned to subject even the most 'evident' assertions to rigorous scrutiny, as intuition and facile reasoning can often be misleading. However, errors can slip past the most watchful eye, they are often subtle and difficult to detect; but when found they can teach us a lot and can present a real challenge to straighten out. This book collects together a mass of such errors, drawn from the work of students, textbooks, and the media, as well as from professional mathematicians themselves. Each of these items is carefully analysed and the source of the error is exposed. All serious students of mathematics will find this book both enlightening and entertaining.

Outros livros do mesmo autor, disponíveis no blog:

Five Hundred Mathematical Challenges (1997). The Mathematical Association of America

Challenging Mathematics In and Beyond the Classroom: The 16th ICMI Study (2008). Springer