(Mathematical Olympiad Series)
Bin Xiong e Peng Yee Lee
World Scientific Publishing Company | 2013 | 205 páginas | rar - pdf | 15 Mb
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The International Mathematical Olympiad (IMO) is a competition for high school students. China has taken part in the IMO 21 times since 1985 and has won the top ranking for countries 14 times, with a multitude of gold's for individual students. The six students China has sent every year were selected from 20 to 30 students among approximately 130 students who took part in the annual China Mathematical Competition during the winter months. This volume of comprises a collection of original problems with solutions that China used to train their Olympiad team in the years from 2009 to 2010. Mathematical Olympiad problems with solutions for the years 2002 - 2008 appear in an earlier volume, "Mathematical Olympiad in China".
Jean-Pierre Alem
Seuil | 1990| French | DJVU | 328 pages | 4,2 Mb
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Ce recueil propose 128 problèmes où les mathématiques se mêlent parfois étroitement à la logique particulière des jeux ou de la cryptographie et même à la fantaisie. L'auteur a inséré de nombreuses notes relatives à des curiosités mathématiques.
Girolamo Cardano
tradução de Jean Stoner
New York: ep Dutton & Co. | 1930 | 362 páginas | pdf | 6,8 Mb
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A bright star of the Italian Renaissance, Girolamo Cardano was an internationally-sought-after astrologer, physician, and natural philosopher, a creator of modern algebra, and the inventor of the universal joint. Condemned by the Inquisition to house arrest in his old age, Cardano wrote The Book of My Life, an unvarnished and often outrageous account of his character and conduct. Whether discussing his sex life or his diet, the plots of academic rivals or meetings with supernatural beings, or his deep sorrow when his beloved son was executed for murder, Cardano displays the same unbounded curiosity that made him a scientific pioneer. At once picaresque adventure and campus comedy, curriculum vitae, and last will, The Book of My Life is an extraordinary Renaissance self-portrait.
Livro relacionado:
(Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts)
Michael O'Leary
Wiley | 2010 | 607 páginas | pdf | 7 Mb
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Guides readers through the development of geometry and basic proof writing using a historical approach to the topic
In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfully equipped with the necessary logic to develop a full understanding of geometric theorems.
Following a presentation of the geometry of ancient Egypt, Babylon, and China, the author addresses mathematical philosophy and logic within the context of works by Thales, Plato, and Aristotle. Next, the mathematics of the classical Greeks is discussed, incorporating the teachings of Pythagoras and his followers along with an overview of lower-level geometry using Euclid's Elements. Subsequent chapters explore the work of Archimedes, Viete's revolutionary contributions to algebra, Descartes' merging of algebra and geometry to solve the Pappus problem, and Desargues' development of projective geometry. The author also supplies an excursion into non-Euclidean geometry, including the three hypotheses of Saccheri and Lambert and the near simultaneous discoveries of Lobachevski and Bolyai. Finally, modern geometry is addressed within the study of manifolds and elliptic geometry inspired by Riemann's work, Poncelet's return to projective geometry, and Klein's use of group theory to characterize different geometries
Table of Contents
Preface.
Acknowledgments.
PART I FOUNDATIONS.
1 The First Geometers.
1.1 Egypt.
1.2 Babylon.
1.3 China.
2 Thales.
2.1 The Axiomatic System.
2.2 Deductive Logic.
2.3 Proof Writing.
3 Plato and Aristotle.
3.1 Form.
3.2 Categorical Propositions..
3.3 Categorical Syllogisms.
3.4 Figures.
PART II THE GOLDEN AGE.
4 Pythagoras.
4.1 Number Theory.
4.2 The Pythagorean Theorem.
4.3 Archytas.
4.4 The Golden Ratio.
5 Euclid.
5.1 The Elements.
5.2 Constructions.
5.3 Triangles.
5.4 Parallel Lines.
5.5 Circles.
5.6 The Pythagorean Theorem Revisited.
6 Archimedes.
6.1 The Archimedean Library.
6.2 The Method of Exhaustion.
6.3 The Method.
6.4 Preliminaries to the Proof.
6.5 The Volume of a Sphere.
PART III ENLIGHTENMENT.
7 François Viète.
7.1 The Analytic Art.
7.2 Three Problems.
7.3 Conic Sections.
7.4 The Analytic Art in Two Variables.
8 René Descartes.
8.1 Compasses.
8.2 Method.
8.3 Analytic Geometry.
9 Gérard Desargues.
9.1 Projections.
9.2 Points at Infinity.
9.3 Theorems of Desargues and Menelaus.
9.4 Involutions.
PART IV A STRANGE NEW WORLD.
10 Giovanni Saccheri.
10.1 The Question of Parallels.
10.2 The Three Hypotheses.
10.3 Conclusions for Two Hypotheses.
10.4 Properties of Parallel Lines.
10.5 Parallelism Redefined.
11 Johann Lambert.
11.1 The Three Hypotheses Revisited.
11.2 Polygons.
11.3 Omega Triangles.
11.4 Pure Reason.
12 Nicolai Lobachevski and János Bolyai.
12.1 Parallel Fundamentals.
12.2 Horocycles.
12.3 The Surface of a Sphere.
12.4 Horospheres.
12.5 Evaluating the Pi Function.
PART V NEW DIRECTIONS.
13 Bernhard Riemann.
13.1 Metric Spaces.
13.2 Topological Spaces.
13.3 Stereographic Projection.
13.4 Consistency of Non-Euclidean Geometry.
14 Jean-Victor Poncelet.
14.1 The Projective Plane.
14.2 Duality.
14.3 Perspectivity.
14.4 Homogeneous Coordinates.
15 Felix Klein.
15.1 Group Theory.
15.2 Transformation Groups.
15.3 The Principal Group.
15.4 Isometries of the Plane.
15.5 Consistency of Euclidean Geometry.
References.
Index.
Franc Klaassen e Jan R. Magnus
Oxford University Press | 2014 | 269 páginas | rar - pdf | 1,5 Mb
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The game of tennis raises many questions that are of interest to a statistician. Is it true that beginning to serve in a set gives an advantage? Are new balls an advantage? Is the seventh game in a set particularly important? Are top players more stable than other players? Do real champions win the big points? These and many other questions are formulated as "hypotheses" and tested statistically.
Analyzing Wimbledon also discusses how the outcome of a match can be predicted (even while the match is in progress), which points are important and which are not, how to choose an optimal service strategy, and whether "winning mood" actually exists in tennis. Aimed at readers with some knowledge of mathematics and statistics, the book uses tennis (Wimbledon in particular) as a vehicle to illustrate the power and beauty of statistical reasoning.
Herb Reich
Skyhorse Publishing | 2011 | 512 páginas | epub | 720 kb
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mobi - 820 kb
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What does the number 67 mean to you? Do you associate it with a year? After all, 1967 was the year The Beatles released bothSgt. Pepper’s Lonely Hearts Club Band and Magical Mystery Tour. It was also the year the first Super Bowl was held and in which Ernesto “Che” Guevara was executed. But maybe the year 1967 isn’t the first thing that comes to your mind. Maybe when you think about the number 67, you think of the . . .
- Age of George Washington at the time of his death, on December 14, 1799.
- Atomic number of the chemical element holmium, symbol Ho.
- Number of counties in each of the states of Alabama, Florida, and Pennsylvania.
- Most doubles hit in a season in Major League Baseball history (Earl Webb, Boston Red Sox, 1931).
- Number worn by partners Jane Fonda and Michael Sarrazin in the dance marathon scene in the 1969 film They Shoot Horses, Don’t They?
- Estimate number of miles, in millions, from Venus to the sun
In Numberpedia, author Herb Reich examines all of the random, seemingly unrelated trivia related to numbers 1 to 100 in painstaking detail, revealing lore, myths, and every bizarre factoid you’d ever want to know about those numbers—except, of course, those concerning math.
Carole Skinner, Judith Stevens
Featherstone Education | 2013 | 137 páginas | rar - pdf | 12 Mb
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Foundations of Mathematics outlines seven strands of practice which underpin successful mathematical development inchildren aged 3-7. Early years mathematics specialists, Carole and Judith, draw on their experience of working with early years practitioners, including consultants and advisers, across the UK and internationally. The book is completely up-to-date and embeds the Revised Early Years Foundation Stage throughout the book. The book brims with multi-sensory ideas that will trigger children's curiosity, measuring using sand mousse, hunting for buried treasure and building secret dens outdoors.
There are:
- activities that involve playing and exploring,
- games to make learning active, and
- experiences to develop creative and critical thinking.
Alongside these practical experiences and activities are clear explanations of the reasoning behind the ideas with clear guidance on the role of the practitioner and 'Home Challenges' to promote the engagement of families. The authors provide straightforward advice to support the development of a mathematically-enriched learning environment and ideas to help children transfer learning into their own child-initiated play, to build a genuine and solid foundation for mathematics.
Contents
Chapter 1: All about number....7.
Numbers in order; Counting; Recognising numerals; Mathematical mark-making;
The role of the adult; Maths home challenges
Chapter 2: Doing calculations....25.
Adding; Subtracting; Multiplying and dividing ; The role of the adult; Maths home challenges
Chapter 3: Working with shapes...41.
3D shapes; 2D shapes.; Position, direction and movement.; Pattern and symmetry; The role of the adult; Maths home challenges
Chapter 4: Learning to measure....59.
Length; Weight; Capacity; Time; The role of the adult; Maths home challenges
Chapter 5: Solving problems...77
Problem solving on a maths trail; Problem solving using number; Problems involving doubling, halving and sharing; The role of the adult; Maths home challenges
Chapter 6: Collecting and sorting ...89.
Collecting; Sorting; Collections; The role of the adult; Maths home challenges
Chapter 7: Stories and rhymes...103.
Traditional stories; Core rhymes; Contemporary stories; The role of the adult; Maths home challenges ;Books and rhyme lists
Chapter 8: Maths outdoors...121
Extending indoor learning experiences outdoors.; Extending indoor role play to include
outdoor role play; Outdoor learning zones and resources.; Games to play outdoors; Tallying and scoring; The role of the adult
Aide memoire....133.
References and further reading...135
