(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
Alan Lipp
Anthem Press | 2011 | 147 páginas | rar - pdf | 238 kb
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The book presents 18 games and develops the concepts of game analysis and winning strategies. Students are encouraged to play these mathematical games together, collect data developed through their play, and analyze the data to develop a winning strategy. Through the exploration of mathematical games, ‘The Play’s the Thing’ introduces teachers and students to the fun of play and to the mathematics behind the fun.
ContentsAcknowledgments xi
Prologue To the Teacher xiii
Act 0 To the Student xv
Act 1 Blockers 1
Act 1 Exercises 2
Act 2 Nimble 5
Act 2 Exercises 6
Act 3 More Variations 9
Act 3 Exercises 10
Act 4 Take Away 1, 2, 3 13
Looking for a Strategy 13
Act 4 Exercises 14
Act 5 Two Piles: A Hidden Game 17
Act 6 Two Piles 1, 2, 3 21
Act 7 Nim 29
Act 8 Flit 37
Act 8 Exercises 38
Act 9 Mr Flit 41
Act 10 Landis 47
Act 10 Exercises 48
Act 11 Add’em Up 51
Act 11 Exercises 52
Act 12 Connect-the-Dots 55
Act 12 Exercises 55
Act 13 Boxes 59
Act 13 Exercises 60
Act 14 Hold That Line 65
Act 14 Exercises 66
Act 15 The Fifteen Game 69
Act 15 Exercises 70
Act 16 Sliders 73
Act 16 Exercises 75
Act 17 Lynch 76
Act 17 Exercises 78
Act 18 Progression: Down and Up 81
Act 19 Harder Stuff 87
Answers 97
John H. Mason
Woodhead Publishing | 2002 | 231 páginas | rar - pdf | 11,6 Mb
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Mathematics; Clarifying the distinction between mathematical research and mathematics education, this book offers hundreds of suggestions for making small and medium sized changes for lectures, tutorials, task design, or problem solving. Here is guidance and inspiration for effective mathematics teaching in a modern technological environment, directed to teachers who are unhappy with results or experience, or those now in teacher training or new to the profession. Commencing with a range of student behaviours and attitudes that have struck and amazed tutors and lecturers, Proffessor Mason offers a wealth of partial diagnoses, followed by specific advice and suggestions for remedial actions.
Contents:
Student difficulties with mathematics;
Lecturing;
Tutoring;
Constructing tasks;
Marking and commenting;
Making use of history;
Issues and concerns in teaching mathematics;
Appendix A Exploratory tasks;
Appendix B Convergence case study;
Bibliography
Theoni Pappas
Wide World Publishing, Tetra | 2013 | 158 páginas | rar - pdf | 8,4 Mb
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The famous mathematical cat Penrose takes us on a trip though puzzleland, while sharing fascinating and challenging puzzles in this uniquely designed mini book. Each page's puzzle is introduced by our star Penrose or one of his quirky friends. Readers are treated to page after page of Penrose antics and problems, while the over 100 mind teasers stimulate and engage its readers gray cells, This book's mini format and fun graphics makes it hard to resist picking up, and its characters and puzzles are sure to entertain both kids or adults.
