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sábado, 28 de julho de 2012

The Mathematical Collage

Ronald Staszkow, Robert Bradshaw 

Custom Publishing | 2006 | 

Versão draft

online: (capítulos)

PDF (link direto)

The Mathematical Collage has been written to meet an Associate Degree general education requirement of a mathematics course with a Beginning Algebra prerequisite. The text shows that mathematics is alive in today's world and helps students see the beauty and power of mathematics. Its contents consists of chapters on the lore of numbers, finance matters, measurement geometry and trigonometry, probability and statistics, and math in sports, It also includes Mathematical Excursions, short trips into various areas where mathematics is used, such as math and the tourist, math and the internet, math and voting, math and nursing, math and the automobile, math and cooking, math and the angler, math and the World Series of Poker.

quinta-feira, 26 de julho de 2012

Complex Numbers from A to ...Z

Titu Andreescu , Dorin Andrica

Birkhäuser Boston | 2006 | 321 páginas


PDF - 3 Mb (link direto)

It is impossible to imagine modern mathematics without complex numbers. Complex Numbers from A to . . . Z introduces the reader to this fascinating subject that, from the time of L. Euler, has become one of the most utilized ideas in mathematics.

Mathematical Omnibus: Thirty Lectures on Classic Mathematics

Dmitry Fuchs, Serge Tabachnikov

American Mathematical Society | 465 páginas | PDF | 7 Mb
Versão draft

links diretos:

The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an award-winning artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher.

terça-feira, 17 de julho de 2012

Minilessons for Math Practice, Grades 3-5

Rusty Bresser, Caren Holtzman

Math Solutions | 2006 | 176 páginas | PDF | 920 Kb

These two books present an innovative approach to reinforcing students' math skills. The 27 engaging lessons in each book are easy to implement, require little or no preparation, and take only 5 to 15 minutes to teach. Designed for use during transition times, the minilessons help students practice math concepts, skills, and processes by applyingthem in a variety of problem-solving contexts throughout the school day. Content areas explored include: number and operations; algebra; geometry; data analysis and probability; and measurement. Each activity includes a materials list, teaching directions, a list of key questions, and ideas for extending the activity throughout the year.

segunda-feira, 16 de julho de 2012

Reform in School Mathematics and Authentic Assessment

(SUNY Series, Reform in Mathematics Education)

Thomas A. Romberg

State University of New York Press | 1995 | 299 páginas | PDF | 2,29 Mb (password: matav)

ERIC (13,2 MB)

This volume is concerned with the alignment between the way the mathematical performance of students is assessed and the reform agenda in school mathematics. The chapters in this book have been prepared to raise a set of issues that scholars are addressing during this period of transition from traditional schooling practices toward the reform vision of school mathematics. Chapters are: (1) "Issues Related to the Development of an Authentic Assessment System for School Mathematics" (T. A. Romberg and L. D. Wilson), (2) "A Framework for Authentic Assessment in Mathematics" (S. P. Lajoie), (3) "Sources of Assessment Information for Instructional Guidance in Mathematics" (E. A. Silver and P. A. Kenney), (4) "Assessment: No Change without Problems" (J. De Lange), (5) "The Invalidity of Standardized Testing for Measuring Mathematics Achievement" (R. E. Stake), (6) "Assessment Nets: An Alternative Approach to Assessment in Mathematics Achievement" (M. Wilson), and (7) "Connecting Visions of Authentic Assessment to the Realities of Educational Practice

Preface vii
1 Issues Related to the Development of an Authentic Assessment System for School Mathematics

2 A Framework for Authentic Assessment in Mathematics

3 Sources of Assessment Information for Instructional Guidance in Mathematics

4 Assessment: No Change without Problems

5 The Invalidity of Standardized Testing for Measuring Mathematics Achievement

6 Assessment Nets: An Alternative Approach to Assessment in Mathematics Achievement

7 Connecting Visions of Authentic Assessment to the Realities of Educational Practice

Contributors 277

segunda-feira, 9 de julho de 2012

Curves and Their Properties

(NCTM Classics in Mathematics Education A Series, Volume 4)

Robert C. Yates

National Council of Teachers of Mathematics | 1974 (reimpressão de 1952) | djvu | 2,6 Mb

PDF (link direto)

This volume, a reprinting of a classic first published in 1952, presents detailed discussions of 26 curves or families of curves, and 17 analytic systems of curves. For each curve the author provides a historical note, a sketch or sketches, a description of the curve, a discussion of pertinent facts, and a bibliography. Depending upon the curve, the discussion may cover defining equations, relationships with other curves (identities, derivatives, integrals), series representations, metrical properties, properties of tangents and normals, applications of the curve in physical or statistical sciences, and other relevant information. The curves described range from the familiar conic sections and trigonometric functions through the less well known Deltoid, Kieroid and Witch of Agnesi. Curve related systems described include envelopes, evolutes and pedal curves. A section on curve sketching in the coordinate plane is included.

A Handbook on Curves and their Properties (1947)


sábado, 7 de julho de 2012

Mathematics Counts: Report of the Committee of Inquiry into the Teaching of Mathematics in Schools

Dept.of Education & Science 

1982 |  328 páginas

domingo, 1 de julho de 2012

Math in Society

David Lippman

DL, LuLu | 2011 | 215 páginas | PDF | 5 Mb

online :

A survey of math for liberal arts majors. This book is a survey of contemporary mathematical topics: voting theory, weighted voting, fair division, graph theory, scheduling, growth models, finance math, statistics, and historical counting systems. Core material for each topic is covered in the main text, with additional depth available through exploration exercises appropriate for in-class, group, or individual investigation.

The text is designed so that most chapters are independent, allowing the instructor to choose a selection of topics to be covered. 
Emphasis is placed on the applicability of the mathematics. 

Voting Theory
Weighted Voting
Fair Division
Graph Theory
Growth Models
Describing Data by David Lippman, Jeff Eldridge
Historical Counting Systems by Lawrence Morales
Solutions to Selected Exercises

quinta-feira, 28 de junho de 2012

Geometric Exercises in Paper Folding

Sundara T. Row 

Chicago, The Open Court pub. co | 1917


online: (html)

PDF (link direto)

The idea of this book was suggested to me by Kindergarten Gift No. VIII. - Paper-folding. The gift consists of two hundred variously colored squares of paper, a folder, and diagrams and instructions for folding. The paper is colored and glazed on one side. The paper may, however, be of self-color, alike on both sides. In fact, any paper of moderate thickness will answer the purpose, but colored paper shows the creases better, and is more attractive. The kindergarten gift is sold by any dealers in school supplies ; but colored paper of both sorts can be had from stationery dealers. Any sheet of paper can be cut into a square as explained in the opening articles of this book, but it is neat and convenient to have the squares ready cut.

domingo, 24 de junho de 2012

Sorting: Groups and Graphs. Used Numbers. Grades 2-3

Rebecca B. Corwin e Susan Jo Russell

Dale Seymour Publications | 1990 | 132 páginas | PDF | 3,2 Mb (link direto)

A unit of study that introduces sorting and classification as a way of organizing data is presented. Suitable for students in grades 2 and 3, it provides a foundation for further work in statistics and data analysis. The investigations may extend from one to five class sessions and are grouped into three parts: "Introduction to Sorting"; "Sorting and Classifying Data"; and "Projects in Data Analysis." An overview of the investigation, session activities, dialogue boxes, and teacher notes are included in each investigation. The major goals developed in each part of this guide are: (1) examining differences and similarities of objects or data; (2) decision making; (3) using negative information to clarify the definition of a category; (4) making sketches of data; (5) thinking flexibly about the characteristics of data; (6) articulating logical reasoning; (7) constructing categories to describe data; (8) inventing representations of data; (9) building theories about data; (10) collecting and recording survey data; (11) comparing two data sets; and (12) experiencing the phases of a data analysis investigation. Appended are reproducible student materials, including two sets of cards for developing sorting skills.

Measuring: From Paces to Feet. Used Numbers: Real Data in the Classroom. Grades 3-4

Rebecca B. Corwin;  Susan Jo Russell

Addison-Wesley | 1990 | PDF | 2,6 Mb (link direto)

A unit of study that introduces measuring as a way of collecting data is presented. Suitable for students in grades 3 and 4, it provides a foundation for further work in statistics and data analysis. The investigations may extend from one to four class sessions and are grouped into three parts: "Introduction to Measurement"; "Using Standard Measures"; and "A Project in Data Analysis." An overview of the investigation, session activities, dialogue boxes, and teacher notes are included in each investigation. The major goals developed in each part of this guide are: (1) moving through space and counting the movements; (2) comparing units of measure; (3) estimating distances; (4) defining a measurement method; (5) writing directions involving distances; (6) recording and displaying the results of measurement; (7) experiencing a need to standardize; (8) understanding that standard measures were invented to solve real data collection problems; (9) estimating lengths; (10) measuring accurately, using feet and inches; (11) describing the shape of the data; (12) analyzing data through landmarks and features of the data; (13) using standard measures to compare data sets; and (14) experiencing all the phases of a data analysis investigation in which measuring is used to collect data. Seven student sheets are attached.

Statistics: The Shape of the Data. Used Numbers: Real Data in the Classroom. Grades 4-6.

Susan Jo Russell e Rebecca B. Corwin

Pearson Learning | 1989| 88 páginas | PDF | 2,4 Mb (link direto)

A unit of study that introduces collecting, representing, describing, and interpreting data is presented. Suitable for students in grades 4 through 6, it provides a foundation for further work in statistics and data analysis. The investigations may extend from one to four class sessions and are grouped into three parts: "Introduction to Data Analysis"; "Learning About Landmarks in the Data"; and "A Project in Data Analysis." An overview of the investigation, session activities, dialogue boxes, and teacher notes are included in each investigation. The major goals developed in each part of this guide are: (1) describing the shape of the data; (2) defining the way data will be collected; (3) summarizing what is typical of the data; (4) making quick sketches of the data; (5) inventing ways to compare two sets of data; (6) representing data first through sketches, then through a presentation graph or chart; (7) using the median as a landmark in the data; (8) understanding that the median is only one landmark in the data; and (9) experiencing all the stages of a data analysis investigation. Attached are 10 student sheets

segunda-feira, 18 de junho de 2012

Knowing and Learning Mathematics for Teaching: Proceedings of a Workshop

Mathematics Teacher Preparation Content Workshop Program Steering Committee, 
Center for Education , National Research Council 

National Academies Press | 2001| 236 páginas 


There are many questions about the mathematical preparation teachers need. Recent recommendations from a variety of sources state that reforming teacher preparation in postsecondary institutions is central in providing quality mathematics education to all students. The Mathematics Teacher Preparation Content Workshop examined this problem by considering two central questions: what is the mathematical knowledge teachers need to know in order to teach well?, and how teachers can develop the mathematical knowledge they need to teach well? The Workshop activities focused on using actual acts of teaching such as examining student work, designing tasks, or posing questions, as a medium for teacher learning. The Workshop proceedings, "Knowing and Learning Mathematics for Teaching", is a collection of the papers presented, the activities, and plenary sessions that took place.

domingo, 10 de junho de 2012

Fair Voting - Weighted Votes for Unequal Constituencies

William F. Lucas

 COMAP, Inc. |  1992  |  81 páginas | PDF


Students are challenged to use the mathematics of weighted voting to wrestle with important social issues such as how power can be measured quantitatively, and how power is divided in our government. HiMAP Module 19. 

Table of Contents:










The Mathematical Theory of Elections

Joseph Malkevitch

COMAP, Inc. | 1999 |  68 páginas | PDF


This module illustrates how mathematics can design and analyze election and ranking methods. Preference schedules, fairness criteria, and weighted voting all demonstrate that how votes are counted can affect the outcome of an election. HiMAP Module 1.

Table of Contents:









Math Trails

Joel Schneider, Henry Pollak and Mary Margaret Shoaf

Comap | 2004 | 136 páginas | PDF



A mathematics trail is a walk to discover mathematics. A math trail can be almost anywhere—a neighborhood, a business district or shopping mall, a park, a zoo, a library, even a government building. The math trail map or guide points to places where walkers formulate, discuss, and solve interesting mathematical problems. Anyone can walk a math trail alone, with the family, or with another group. Walkers cooperate along the trail as they talk about the problems. There’s no competition or grading. At the end of the math trail they have the pleasure of having walked the trail and of having done some interesting mathematics. Everyone, no matter what age, gets an “I Walked the Math Trail” button to wear. 

This book is a guide to blazing a math trail. We’ll review the history of math trails and discuss their attributes. We’ll also discuss practical issues of organization and logistics in setting up and maintaining a math trail. We’ll discuss mathematical issues in choosing and describing problems and tasks along a trail. And we’ll also describe a variety of specific examples of trails and of problems. 

Joel Schneider began his personal math trail in junior high school with a geometry problem found in a science fiction novel. His other stops included some modest research in commutative algebra; helping to develop an elementary school math curriculum and its teacher education program; leading the math team for Square One, a television series about math that PBS broadcast in the 90s; and developing a math game show for children’s television in several countries. Having worked at Sesame Workshop for more than 20 years, Joel passed away in 2004. 

After a rather pure education in mathematics, Henry Pollak spent the major part of his career at Bell Laboratories, including 22 years as Director of Mathematics and Statistics Research. At the same time, a growing interest in mathematics education led to his involvement in the Mathematical Association of America, and in a large variety of projects, from the School Mathematics Study Group to Mathematics: Modeling Our World. A recurring theme in much of his work is the need to wear the two hats of mathematics in the real world and mathematics education on the same head. Dr. Pollak has been a Visiting Professor at Teachers College of Columbia University since 1987. 

Mary Margaret Shoaf received her Ph.D. in Mathematics Education from Columbia University under the direction of Dr. Henry O. Pollak. Dr. Shoaf lives in Waco, Texas where she is an Associate Professor of Mathematics in the Department of Mathematics at Baylor University. Dr. Shoaf wishes to thank her Department Chairperson at Baylor University, Dr. Edwin Oxford, for all of his support and encouragement during the writing of this book. Her areas of research and interest are hand-held mathematics technology, the use of computers in the mathematics classroom, and designing and implementing mathematics curriculum for Grades 3–12 preservice and inservice mathematics teachers

Part 1: Purposes and Organization of a Math Trail
Introduction 6
Background and History 6
Characteristics of Math Trails 8
Blazing a Trail 10
Organizing a Math Trail Project 14

Part 2: Examples of Math Trails
Recreational Mathematics in the Park 16
Recreational Mathematics Around Town 34
Recreational Mathematics at the Zoo 47
Recreational Mathematics in a Mall 57

Part 3: Mathematics of Several Kinds of Trail Situations
Parking 70
Supermarkets 78
Buildings 82
A Hike in the Country 85
Tilings 88
American Flags 99
Moving Vans 106
Estimation 108

References 112

Appendix: “A Mathematics Trail Around the City of Melbourne”

sábado, 9 de junho de 2012

A treatise on plane trigonometry

Ernest William Hobson

1918 | Cambridge University Press


sexta-feira, 8 de junho de 2012

The Algebra Initiative Colloquium

Papers presented at a conference on reform in algebra, December 9-12, 1993

Carole Lacampagne | 1995 | PDF

Vol. 1

This volume contains the plenary or reactor papers presented at a conference on reform in algebra held in Leesburg, Virginia, December 9-12, 1993. Papers included are: (1) "Introduction" (C. B. Lacampagne); (2) "Summary" (C. B. Lacampagne); (3) "Recommendations" (C. B. Lacampagne); (4) "The Development of Algebra and Algebra Education" (V. J. Katz); (5) "Long-Term Algebra Reform: Democratizing Access to Big Ideas" (J. J. Kaput); (6) "Algebra in the K-12 Curriculum" (G. Burrill); (7) "What Is the Appropriate K-12 Algebra Experience for Various Students?" (J. Fey); (8) "Algebra at the College Level" (M. Artin); (9) "Algebra Initiative" (V. Pless); (10) "Algebra and the Technical Workforce" (H. Pollak); (11) "Reshaping Algebra to Serve the Evolving Needs of the Technical Workforce" (S. Garfunkel); (12) "A Cognitive Perspective in the Mathematical Preparation of Teachers: The Case of Algebra" (A. G. Thompson & P. W. Thompson); (13) "Preparing Teachers to Teach Algebra for All: Preliminary Musings and Questions" (M. Enneking); and (14) "Algebra for All: Dumbing Down or Summing Up?" (L. A. Steen). Appendices include the conference agenda; Conceptual Framework for the Algebra Initiative of the National Institute on Student Achievement, Curriculum, and Assessment; and a participant list.

Vol. 2

This volume presents recommendations from four working groups at a conference on reform in algebra held in Leesburg, Virginia, December 9-12, 1993. Working Group 1: Creating an Appropriate Algebra Experience for All Grades K-12 Students produced the following papers: (1) "Report" (A. H. Schoenfeld); (2) "Five Questions About Algebra Reform (and a thought experiment)" (D. Chazan); (3) "Algebra and the Democratic Imperative" (R. B. Davis); (4) "Realism(s) for Learning Algebra" (R. Hall); (5) "Algebra, The New Civil Right" (B. Moses); (6) "Issues Surrounding Algebra" (E. Phillips); (7) "Is Thinking About 'Algebra' a Misdirection?" (A. H. Schoenfeld); and (8) "Thoughts Preceding the Algebra Colloquium" (Z. Usiskin). Working Group 2: Educating Teachers, Including K-8 Teachers, to Provide These Algebra Experiences produced: (1) "Report" (A. Buccino); (2) "Educating Teachers to Provide Appropriate Algebra Experiences: Practicing Elementary and Secondary Teachers--Part of the Problem or Part of the Solution?" (C. Gifford-Banwart); (3) "Educating Teachers for Algebra" (A. Buccino); (4) "Experience, Abstraction, and 'Algebra for All': Some Thoughts on Situations, Algebra, and Feminist Research" (S. K. Damarin); (5) "Educating Teachers, Including K-8 Teachers, to Provide Appropriate Algebra Experiences" (N. D. Fisher); (6) "On the Learning and Teaching of Linear Algebra" (G. Harel); and (7) "Algebra: The Next Public Stand for the Vision of Mathematics for All Students" (H. S. Kepner, Jr.). Working Group 3: Reshaping Algebra to Serve the Evolving Needs of the Technical Workforce produced: (1) "Report" (S. Forman); (2) "Algebra, Jobs, and Motivation" (P. Davis); (3) "To Strengthen Technical Education Systematically" (J. G. Greeno); (4) "Thoughts About Reshaping Algebra to Serve the Evolving Needs of a Technical Workforce" (R. Lesh); (5) "Algebra for the Technical Workforce of the 21st Century" (P. D. McCray); (6) "Some Thoughts on Algebra for the Evolving Work Force" (T. A. Romberg & M. Spence); and (7) "Algebra: A Vision for the Future" (S. S. Wood). Working Group 4: Renewing Algebra at the College Level to Serve the Future Mathematician, Scientist, and Engineer produced: (1) "Report" (J. Gallian); (2) "Some Thoughts on Teaching Undergraduate Algebra" (W. D. Blair); (3) "Toward One Meaning for Algebra" (A. Cuoco); (4) "Some Thoughts on Abstract Algebra" (S. Montgomery); and (5) "Suggestions for the Teaching of Algebra" (W. Y. Velez). Appendices include the conference agenda; Conceptual Framework for the Algebra Initiative of the National Institute on Student Achievement, Curriculum, and Assessment; and a participant list.

terça-feira, 5 de junho de 2012

Mathematicians Delight

W.W. Sawyer

1943 | Harmondsworth, Middlesex, Eng., New York, Penguin Books


Penguin Books | 1969 | 238 páginas | PDF | 12,8 Mb

An introduction to mathematics which starts with simple arithmetic and algebra and proceeds through to graphs, logarithms, trigonometry to calculus and imaginary numbers. The author, who is internationally renowned for his innovative teaching methods, offers insights into the pleasures of mathematics that will appeal to readers of all backgrounds.

domingo, 3 de junho de 2012

Statistics: A Guide To The Unknown

Judith M. Tanur

1972 | djvu


This collection of intriguing essays describes important applications of statistics and probability in many fields. Instead of teaching methods, the essays illustrate past accomplishments and current uses of statistics and probability. Surveys, questionnaires, experiments, and observational studies are also presented to help the student better understand the importance of the influence of statistics on each topic covered within the separate essays.

sexta-feira, 1 de junho de 2012

Geometry, Relativity and the Fourth Dimension

Rudolf v.B. Rucker

Dover Publications | 1977

online: (link direto)

Exposition of 4th dimension, concepts of relativity as Flatland characters continue adventures. Popular, easily followed yet accurate, profound. Topics include curved space time as a higher dimension, special relativity, and shape of space-time. Accessible to lay readers but also of interest to specialists. Includes 141 illustrations

quinta-feira, 31 de maio de 2012

An Introduction to Mathematics

Alfred North Whitehead

1911 | London : Williams & Northgate: [New York, H. Holt 


This distinguished little book is a brisk introduction to a series of mathematical concepts, a history of their development, and a concise summary of how today's reader may use them.

Plane Geometry

Edward Rutledge Robbins

New York ; Cincinnati : American Book Company | 1915


Geometry have been :(a) To present a book that has been written for the pupil. The object sought in the study of Geometry is not solely to train the mind to accept only those statements as truth for which convincing reasons can be provided, but to cultivate a foresight that will appreciate both the purpose in making a statement and the process of reasoning by which the ultimate truth is established. Thus, the study of this formal science should develop in the pupil the ability to pursue argument coherently, and to establish one truth by the aid of other known truths, in logical order. The more mature members of a class do not require that the reason for every declaration be given in full in the text; still, to omit it altogether, wrongs those pupils who do not know and cannot perceive the correct reason. But to ask for the reason and to print the paragraph reference meets the requirements of the various degrees of intellectual capacity and maturity in every class. The pupil who knows and knows that he knows need not consult the paragraph cited ;the pupil who does not know may learn for himself the correct reason by the reference. It is obvious that the greater progress an individual makes in assimilating the subject and in entering into its spirit, the less need there will be for the printed reference.

segunda-feira, 28 de maio de 2012

Recreations in Mathematics and Natural Philosophy

Jacques Ozanam



842 páginas | DJVU | 35,7 Mb

This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.

sábado, 5 de maio de 2012

What are the Odds?: Understanding the Risks : Education Kit for Stage 4 & 5 Students

Sue Thomson

Sydney : Powerhouse Museum | 2004 | 42 páginas | PDF



Using What are the odds? Understanding the risks education kit in your teaching .... 4
Syllabus links ...... 6
Mathematics and games of chance: a snapshot ... 8
Calculating probabilities ... 10
Poker machines ......... 12
Scratch lottery tickets: Jackson’s story .........17
Scratch lotteries ....... 19
Internet gambling: Michael’s story .....22
Lotto probability ...............24
Calculating the odds doesn’t always stop gambling: Ada Lovelace ..... 27
Horseracing .......... 29
Gambling and social issues: try this quick quiz .....32
Budgets and gambling ........... 34
The costs of problem gambling ............... 36
G-line NSW ................. 37
Answers ...... 38

segunda-feira, 30 de abril de 2012

Circle in a Box

Sam Vandervelde

AMS | 2009 | 185 Páginas | PDF

versão draft (link direto - incompleto - falta apêndice D)

PDF | 6 Mb

Math circles provide a setting in which mathematicians work with secondary school students who are interested in mathematics. This form of outreach, which has existed for decades in Russia, Bulgaria, and other countries, is now rapidly spreading across the United States as well. The first part of this book offers helpful advice on all aspects ofmath circle operations, culled from conversations with over a dozen directors of successful math circles. Topics include creative means for getting the word out to students, sound principles for selecting effective speakers, guidelines for securing financial support, and tips for designing an exciting math circle session. The purpose of this discussion is to enable math circle coordinators to establish a thriving group in which students can experience the delight of mathematical investigation. The second part of the book outlines ten independent math circle sessions, covering a variety of topics and difficulty levels. Each chapter contains detailed presentation notes along with a useful collection of problems and solutions. This book will be an indispensable resource for any individual involved with a math circle or anyone who would like to see one begin in his or her community. Sam Vandervelde teaches at St. Lawrence University. He launched the Stanford Math Circle and also writes and coordinates the Mandelbrot Competition, a math contest for high schools.

Link para a página do projeto:

domingo, 29 de abril de 2012

The Survival of a Mathematician: From Tenure to Emeritus

Steven G. Krantz

American Mathematical Society | 2008 | 310 páginas | PDF

versão draft - online:

A successful mathematical career involves doing good mathematics, to be sure, but also requires a wide range of skills that are not normally taught in graduate school. The purpose of this book is to provide guidance to the professional mathematician in how to develop and survive in the profession. There is information on how to begin a research program, how to apply for a grant, how to get tenure, how to teach, and how to get along with one's colleagues. After tenure, there is information on how to direct a Ph.D. student, how to serve on committees, and how to serve in various posts in the math department. There is extensive information on how to serve as Chairman. There is also material on trouble areas: sexual harassment, legal matters, disputes with colleagues, dealing with the dean, and so forth. One of the themes of the book is how to have a fulfilling professional life. In order to achieve this goal, Krantz discusses keeping a vigorous scholarly program going and finding new challenges, as well as dealing with the everyday tasks of research, teaching, and administration. In short, this is a survival manual for the professional mathematician--both in academics and in industry and government agencies. It is a sequel to the author's A Mathematician's Survival Guide.

The Proof Is in the Pudding: The Changing Nature of Mathematical Proof

Steven G. Krantz

Springer-Verlag | 2010 | 240 Páginas | PDF | 3,9 Mb

Versão draft - online:

Krantz takes the reader on a journey around the globe and through centuries of history, exploring the many transformations that mathematical proof has undergone from its inception at the time of Euclid and Pythagoras to its versatile, present-day use. The author elaborates on the beauty, challenges and metamorphisms of thought that have accompanied the search for truth through proof. The first two chapters examine the early beginnings of concept of proof and the creation of its elegant structure and language, touching on some of the logic and philosophy behind these developments. The history then unfolds as the author explains the changing face of proofs. The more well-known proofs , the mathematicians behind them, and the world that surrounded them are all highlighted. Each story has its own unique past; there was often a philosophical, sociological, technological or competitive edge that restricted or promoted progress. But the author's commentary and insights create a seamless thread throughout the many vignettes Though there are many truths to be discovered in this book, by the end it is clear that there is no formalized approach or standard method of discovery to date. This is shown in noting some of the more prominent discussions currently underway, such as Gorenstein's effort to classify finance groups, Thomas Hale's resolution of the Kepler sphere-packing problem, and other modern tales. Most of the proofs are discussed in detail with figures and some equations accompanying them, allowing both the professional mathematician and those less familiar with mathematics to derive the same joy from reading this book.

quarta-feira, 11 de abril de 2012

Chance And Choice By Card Pack And ChessBoard Vol I

 Hogben Lancelot M.A

Max Parrish And Co | 1950 


segunda-feira, 2 de abril de 2012

Coordinate Geometry

Luther Pfahler Eisenhart 

Dover Publishing Inc. | 1939 |


A thorough, complete, and unified introduction, this volume affords exceptional insights into coordinate geometry. Invariants of conic sections and quadric surfaces receive full treatments. Algebraic equations on the first degree in two and three unknowns are carefully reviewed. Throughout the book, results are formulated precisely, with clearly stated theorems. More than 500 helpful exercises.

College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle

Nathan Altshiller-Court

New York : Barnes & Noble | 1952

Preface -- To the instructor -- To the student -- Geometric constructions -- Similitude and homothecy -- Properties of the triangle -- The quadrilateral -- The Simson line -- Transversals -- Harmonic division -- Circles -- Recent geometry of the triangle

Dover Publications | 2009 | 336 páginas | PDF | 31 Mb

Translated into many languages, this book has been the standard university-level text for decades. Revised and enlarged by the author in 1952, it offers today's students exercises in construction problems, similitude, and homothecy, properties of the triangle and the quadrilateral, harmonic division, and circle and triangle geometry. 

sexta-feira, 30 de março de 2012

The Elements Of Non Euclidean Geometry

Julian Lowell Coolidge



Chapters Include: Foundation For Metrical Geometry In A Limited Region; Congruent Transformations; The Three Hypotheses; The Introduction Of Trigonometric Formulae; Analytic Formulae; Consistency And Significance Of The Axioms; The Geometric And Analytic Extension Of Space; The Groups Of Congruent Transformations; Point, Line, And Plane Treated Analytically; The Higher Line Geometry; The Circle And The Sphere; Conic Sections; Quadric Surfaces; Areas And Volumes; Introduction To Differential Geometry; etc.

Introduction To Non Euclidean Geometry

Harold E. Wolfe

The Dryden Press | 1945


PDF - 8,11 Mb

Introduction to NON-EUCLIDEAN GEOMETRY by HAROLD E. WOLFE . PREFACE This book has been written in an attempt to provide a satisfactory textbook to be used as a basis for elementary courses in Non-Euclid ean Geometry. The need for such a volume, definitely intended for classroom use and containing substantial lists of exercises, has been evident for some time. It is hoped that this one will meet the re quirements of those instructors who have been teaching the subject tegularly, and also that its appearance will encourage others to institute such courses. x The benefits and amenities of a formal study of Non-Euclidean Geometry are generally recognized. Not only is the subject matter itself valuable and intensely fascinating, well worth the time of any student of mathematics, but there is probably no elementary course which exhibits so clearly the nature and significance of geometry and, indeed, of mathematics in general. However, a mere cursory acquaintance with the subject will not do. One must follow its development at least a little way to see how things come out, and try his hand at demonstrating propositions under circumstances such that intuition no longer serves as a guide. For teachers and prospective teachers of geometry in the secondary schools the study of Non-Euclidean Geometry is invaluable. With out it there is strong likelihood that they will not understand the real nature of the subject they are teaching and the import of its applications to the interpretation of physical space. Among the first books on Non-Euclidean Geometry to appear in English was one, scarcely more than a pamphlet, written in 1880 by G. Chrystal. Even at that early date the value of this study for those preparing to teach was recognized. In the preface to this little brochure, Chrystal expressed his desire to bring pangeometrical speculations under the notice of those engaged in the teaching of geometry He wrote It will not be supposed that I advocate the introduction of pan geometry as a school subject it is for the teacher that I advocate vi PREFACE such a study. It is a great mistake to suppose that it is sufficient for the teacher of an elementary subject to be just ahead of his pupils. No one can be a good elementary teacher who cannot handle his subject with the grasp of a master. Geometrical insight and wealth of geometrical ideas, either natural or acquired, are essential to a good teacher of geometry and I know of no better way of cultivat ing them than by studying pan geometry. Within recent years the number of American colleges and uni versities which offer courses in advanced Euclidean Geometry has increased rapidly. There is evidence that the quality of the teaching of geometry in our secondary schools has, accordingly, greatly improved. But advanced study in Euclidean Geometry is not the only requisite for the good teaching of Euclid. The study of Non-Euclidean Geometry takes its place beside it as an indispensable part of the training of a well-prepared teacher of high school geometry. This book has been prepared primarily for students who have completed a course in calculus. However, although some mathe matical maturity will be found helpful, much of it can be read profitably and with understanding by one who has completed a secondary school course in Euclidean Geometry. He need only omit Chapters V and VI, which make use of trigonometry and calcu lus, and the latter part of Chapter VII. In Chapters II and III, the historical background of the subject has been treated quite fully. It has been said that no subject, when separated from its history, loses more than mathematics. This is particularly true of Non-Euclidean Geometry...

Non-Euclidean Geometry: A Critical And Historical Study Of Its Development

Roberto Bonola

Chicago Open Court Pub. Co | 1912


PDF - 11,2 Mb

Examines various attempts to prove Euclid's parallel postulate — by the Greeks, Arabs and Renaissance mathematicians. Ranging through the 17th, 18th, and 19th centuries, it considers forerunners and founders such as Saccheri, Lambert, Legendre, W. Bolyai, Gauss, Schweikart, Taurinus, J. Bolyai and Lobachewsky. Includes 181 diagrams.

Table of Contents

Chapter I. The Attempts to prove Euclid's Parallel Postulate.
1-5. The Greek Geometers and the Parallel Postulate
6. The Arabs and the Parallel Postulate
7-10. The Parallel Postulate during the Renaissance and the 17th Century
Chapter II. The Forerunners on Non-Euclidean Geometry.
11-17. GEROLAMO SACCHERI (1667-1733)
18-22. JOHANN HEINRICH LAMBERT (1728-1777)
23-26. The French Geometers towards the End of the 18th Century
27-28. ADRIEN MARIE LEGENDRE (1752-1833)
29. WOLFGANG BOLYAI (1775-1856)
30. (bis) BERNHARD FRIEDRICH THIBAUT (1776-1832)
Chapter III. The Founders of Non-Euclidean Geometry.
31-34. KARL FRIEDRICH GAUSS (1777-1855)
36-38. FRANZ ADOLF TAURINUS (1794-1874)
Chapter IV. The Founders of Non-Euclidean Geometry (Cont.).
46-55. JOHANN BOLYAI (1802-1860)
56-58. The Absolute Trigonometry
59. Hypotheses equivalent to Euclid's Postulate
60-65. The Spread of Non-Euclidean Geometry
Chapter V. The Later Development of Non-Euclidean Geometry.
66. Introduction
Differential Geometry and Non-Euclidean Geometry
67-69. Geometry upon a Surface
70-76. Principles of Plane Geometry on the Ideas of RIEMANN
77. Principles of RIEMANN'S Solid Geometry
78. The Work of HELMHOLTZ and the Investigations of LIE
Projective Geometry and Non-Euclidean Geometry
79-83. Subordination of Metrical Geometry to Projective Geometry
84-91. Representation of the Geometry of LOBATSCHEWSKY-BOLYAI on the Euclidean Plane
92. Representation of RIEMANN'S Elliptic Geometry in Euclidean Space
93. Foundation of Geometry upon Descriptive Properties
94. The Impossibility of proving Euclid's Postulate
Appendix I. The Fundamental Principles of Statistics and Euclid's Postulate.
1-3. On the Principle of the Lever
4-8. On the Composition of Forces acting at a Point
9-10. Non-Euclidean Statics
11-12. Deduction of Plane Trigonometry from Statics
Appendix II. CLIFFORD'S Parallels and Surface. Sketch of CLIFFFORD-KLEIN'S Problems.
1-4. CLIFFORD'S Parallels
5-8. CLIFFORD'S Surface
9-11. Sketch of CLIFFORD-KLEIN'S Problem
Appendix III. The Non-Euclidean Parallel Construction and other Allied Constructions.
1-3. The Non-Euclidean Parallel Construction
4. Construction of the Common Perpendicular to two non-intersecting Straight Lines
5. Construction of the Common Parallel to the Straight Lines which bound an Angle
6. Construction of the Straight Line which is perpendicular to one of the lines bounding an acute Angle and Parallel to the other
7. The Absolute and the Parallel Construction
Appendix IV. The Independence of Projective Geometry from Euclid's Postu
1. Statement of the Problem
2. Improper Points and the Complete Projective Plane
3. The Complete Projective Line
4. Combination of Elements
5. Improper Lines
6. Complete Projective Space
7. Indirect Proof of the Independence of Projective Geometry from the Fifth Postulate
8. BELTRAMI'S Direct Proof of this Independence
Appendix V. The Impossibility of proving Euclid's Postulate. An Elementary Demonstration of this Impossibility founded upon the Properties of the System of Circles orthogonal to a Fixed Circle.
1. Introduction
2-7. The System of Circles passing through a Fixed Point
8-12. The System of Circles orthogonal to a Fixed Circle
Index of Authors
The Science of Absolute Space and the Theory of Parallels

sábado, 24 de março de 2012

A source book in mathematics

David Eugene Smith

New York : McGraw-Hill Book Co. | 1929


Vol. 1

Dover Publications Inc. | 1993 | 324 páginas | djvu | 10,87 Mb

PDF - 35,4 Mb

The writings of Newton, Liebniz, Pascal, Riemann, Bernoulli, and others in a comprehensive selection of 125 treatises, articles from the Renaissance to end of the 19th century—most unavailable elsewhere. Grouped in five sections: Number; Algebra; Geometry; Probability; and Calculus, Functions, and Quaternions. Index. 83 illustrations.

Vol. 2

Dover Publications Inc. | 1993 | 418 páginas | djvu | 12,53Mb

PDF - 41 Mb 

sexta-feira, 16 de março de 2012

A Long Way from Euclid

Constance Reid

 Thomas Y. Crowell Company | 1834


Dover Publications | 2004 | 304 páginas

This lively guide by a prominent historian focuses on the role of Euclid's Elements in mathematical developments of the last 2,000 years. No mathematical background beyond elementary algebra and plane geometry is necessary to appreciate the clear and simple explanations, which are augmented by more than 80 drawings. 1963 edition. 

terça-feira, 13 de março de 2012

The Canterbury Puzzles with Solutions

Henry Ernest Dudeney

W. Heinemann | 1907 |195 páginas  |


PDF | 14 MB (link direto)

This book includes 110 puzzles, not as individual problems but as incidents in connected stories. The first 31 are amusingly posed by pilgrims in Chaucer's Canterbury Tales. Additional puzzles are presented using different characters. Many require only the ability to exercise logical or visual skills; others offer a stimulating challenge to the mathematically advanced.

sábado, 3 de março de 2012

The foundations of mathematics; a contribution to the philosophy of geometry

Paul Carus

Chicago, The Open Court Publishing Co. | 1908


terça-feira, 28 de fevereiro de 2012

Magic squares and cubes

William Symes Andrews

online: (link direto)

In the introduction to Magic Squares and Cubes, W.S. Andrews wrote writes, "The study of magic squares probably dates back to prehistoric times. Examples have been found in Chinese literature written about A. D. 1125 which were evidently copied from still older documents. It is recorded that as early as the ninth century magic squares were used by Arabian astrologers in their calculations of horoscopes, etc. Hence, the probable origin of the term magic, which has survived to the present day." He added that "a magic square consists of a series of numbers so arranged in a square that the sum of each row and column and of both the corner diagonals shall be the same amount which may be termed the summation.

quarta-feira, 22 de fevereiro de 2012

Mathematics and the Imagination

Edward Kasner & James Newman

G. Bell & Sons Ltd.| 1949 | 393 páginas |  pdf | 52,1 Mb


Anyone who gambles, plays cards, loves puzzles, or simply seeks an intellectual challenge will love this amusing and thought-provoking book. With wit and clarity, the authors deftly progress from simple arithmetic to calculus and non-Euclidean geometry. "Charming and exciting." — Saturday Review of Literature. Includes 169 figures.