sábado, 22 de março de 2014

Pythagoras the Mathemagician


Karim El Koussa


Sunbury Press, Inc. | 2010 | 412 páginas | rar - epub | 417 kb

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Discover who the real Pythagoras was within the pages of this philosophical work of historical fiction. This controversial novel looks at the first philosopher from an unfamiliar perspective to most Western readers and scholars. El Koussa stands in the vanguard of a new generation of writers and thinkers who are bringing the rich and diverse history of the Phoenician culture to a new audience. 

Social Statistics: Managing Data, Conducting Analyses, Presenting Results

Thomas J. Linneman

Routledge | 2014 - 2ª edição | 657 páginas | rar - pdf | 9,3 Mb

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Many fundamentally important decisions about our social life are a function of how well we understand and analyze DATA. This sounds so obvious but it is so misunderstood. Social statisticians struggle with this problem in their teaching constantly. This book and its approach is the ally and support of all instructors who want to accomplish this hugely important teaching goal.
This innovative text for undergraduate social statistics courses is, (as one satisfied instructor put it), a "breath of fresh air." It departs from convention by not covering some techniques and topics that have been in social stat textbooks for 30 years, but that are no longer used by social scientists today. It also includes techniques that conventional wisdom has previously thought to be the province of graduate level courses.
Linneman’s text is for those instructors looking for a thoroughly "modern" way to teach quantitative thinking, problem-solving, and statistical analysis to their students…an undergraduate social statistics course that recognizes the increasing ubiquity of analytical tools in our data-driven age and therefore the practical benefit of learning how to "do statistics," to "present results" effectively (to employers as well as instructors), and to "interpret" intelligently the quantitative arguments made by others.

BRIEF CONTENTS
Preface xxix
Acknowledgments xxxvii
Chapter 1: Life in a Data-Laden Age: Finding and Managing Datasets 1
Chapter 2: The Art of Visual Storytelling: Creating Accurate Tables and Graphs 46
Chapter 3: Summarizing Center and Diversity: Basic Descriptive Statistics 92
Chapter 4: Using Sample Crosstabs to Talk about Populations: The Chi-Square Test 141
Chapter 5: Using a Sample Mean or Proportion to Talk about a Population: Confidence Intervals 189
Chapter 6: Using Multiple Sample Means to Talk about Populations: t-Tests and ANOVA 231
Chapter 7: Give Me One Good Reason Why: Bivariate Correlation and Regression 264
Chapter 8: Using Sample Slopes to Talk about Populations: Inference and Regression 303
Chapter 9: It’s All Relative: Dichotomies as Independent Variables in Regression 326
Chapter 10: Above and Beyond: The Logic of Controlling and the Power of Nested Regression Models 348
Chapter 11: Some Slopes Are Bigger than Others: Calculating and Interpreting Beta Coefficients 384
Chapter 12: Different Slopes for Different Folks: Interaction Effects 402
Chapter 13: Explaining Dichotomous Outcomes: Logistic Regression 435
Chapter 14: Visualizing Causal Stories: Path Analysis 467
Chapter 15: Questioning the Greatness of Straightness: Nonlinear Relationships 493
Chapter 16: Problems and Prospects: Regression Diagnostics, Advanced Techniques, and Where to Go Now 532
Appendix A: Variables and Indexes from the Datasets Used in the End-of-Chapter Exercises A-1
Appendix B: 86 Articles That Use Statistics in Less Than Scary Ways B-1
Appendix C: Statistical Tables C-1
Appendix D: Answers to Selected End-of-Chapter Exercises D-1
Bibliography R-1
Glossary/Index I-1

Undiluted Hocus-Pocus: The Autobiography of Martin Gardner


Martin Gardner, James Randi e Persi Diaconis

Princeton University Press | 2013 | 289 páginas | rar - pdf |  2,7 Mb


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Martin Gardner wrote the Mathematical Games column forScientific American for twenty-five years and published more than seventy books on topics as diverse as magic, philosophy, religion, pseudoscience, and Alice in Wonderland. His informal, recreational approach to mathematics delighted countless readers and inspired many to pursue careers in mathematics and the sciences. Gardner's illuminating autobiography is a disarmingly candid self-portrait of the man evolutionary theorist Stephen Jay Gould called our "single brightest beacon" for the defense of rationality and good science against mysticism and anti-intellectualism.Gardner takes readers from his childhood in Oklahoma to his college days at the University of Chicago, his service in the navy, and his varied and wide-ranging professional pursuits. Before becoming a columnist for Scientific American, he was a caseworker in Chicago during the Great Depression, a reporter for the Tulsa Tribune, an editor for Humpty Dumpty, and a short-story writer for Esquire, among other jobs. Gardner shares colorful anecdotes about the many fascinating people he met and mentored, and voices strong opinions on the subjects that matter to him most, from his love of mathematics to his uncompromising stance against pseudoscience. For Gardner, our mathematically structured universe is undiluted hocus-pocus--a marvelous enigma, in other words.

Contents
Foreword: Magic, Mathematics, and Mysterians, by Persi Diaconis xi
Preface xxiii
Prologue: I Am a Mysterian xxv
1 Earliest Memories 1
2 Lee School 10
3 Tulsa Central High, I 21
4 Central High, II 28
5 Hutchins and Adler 40
6 Richard McKeon 47
7 I Lose My Faith 53
8 Chicago, I 62
9 Chicago, II 76
10 I Become a Journalist 88
11 Mother and Dad 98
12 The Navy, I 111
13 The Navy, II 119
PHOTO ESSAY follows page 124
14 Esquire and Humpty 125
15 Scientific American 134
16 Pseudoscience 150
17 Math and Magic Friends 160
18 Charlotte 173
19 Bob and Betty 185
20 God 191
21 My Philosophy 195
Afterword: My Most Elegant Friend . . . , by James Randi 209
Index 215

Three Views of Logic: Mathematics, Philosophy, and Computer Science


Donald W. Loveland, Richard E. Hodel e S. G. Sterrett


Princeton University Press | 2014 | 339 páginas | rar - pdf |1,85 Mb

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Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity.
The proof theory portion presents classical propositional logic and first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time.
Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings.
  • Gives an exceptionally broad view of logic
  • Treats traditional logic in a modern format
  • Presents relevance logic with applications
  • Provides an ideal text for a variety of one-semester upper-level undergraduate courses

Contents
Preface ix
Acknowledgments xiii
PART 1. Proof Theory 1
DONALD W. LOVELAND
1 Propositional Logic 3
1.1 Propositional Logic Semantics 5
1.2 Syntax: Deductive Logics 13
1.3 The Resolution Formal Logic 14
1.4 Handling Arbitrary PropositionalWffs 26
2 Predicate Logic 31
2.1 First-Order Semantics 32
2.2 Resolution for the Predicate Calculus 40
2.2.1 Substitution 41
2.2.2 The Formal System for Predicate Logic 45
2.2.3 Handling Arbitrary PredicateWffs 54
3 An Application: Linear Resolution and Prolog 61
3.1 OSL-Resolution 62
3.2 Horn Logic 69
3.3 Input Resolution and Prolog 77
Appendix A: The Induction Principle 81
Appendix B: First-Order Valuation 82
Appendix C: A Commentary on Prolog 84
References 91
PART 2. Computability Theory 93
RICHARD E. HODEL
4 Overview of Computability 95
4.1 Decision Problems and Algorithms 95
4.2 Three Informal Concepts 107
5 A Machine Model of Computability 123
5.1 RegisterMachines and RM-Computable Functions 123
5.2 Operations with RM-Computable Functions; Church-Turing Thesis; LRM-Computable Functions 136
5.3 RM-Decidable and RM-Semi-Decidable Relations; the Halting Problem 144
5.4 Unsolvability of Hilbert’s Decision Problem and Thue’sWord Problem 154
6 A Mathematical Model of Computability 165
6.1 Recursive Functions and the Church-Turing Thesis 165
6.2 Recursive Relations and RE Relations 175
6.3 Primitive Recursive Functions and Relations; Coding 187
6.4 Kleene Computation Relation Tn(e, a1, . . . , an, c) 197
6.5 Partial Recursive Functions; Enumeration Theorems 203
6.6 Computability and the Incompleteness Theorem 216
List of Symbols 219
References 220
PART 3. Philosophical Logic 221
S. G. STERRETT
7 Non-Classical Logics 223
7.1 Alternatives to Classical Logic vs. Extensions of
Classical Logic 223
7.2 From Classical Logic to Relevance Logic 228
7.2.1 The (So-Called) “Paradoxes of Implication” 228
7.2.2 Material Implication and Truth Functional Connectives 234
7.2.3 Implication and Relevance 238
7.2.4 Revisiting Classical Propositional Calculus: What to Save,What to Change, What to Add? 240
8 Natural Deduction: Classical and Non-Classical 243
8.1 Fitch’s Natural Deduction System for Classical
Propositional Logic 243
8.2 Revisiting Fitch’s Rules of Natural Deduction to Better Formalize the Notion of Entailment—Necessity 251
8.3 Revisiting Fitch’s Rules of Natural Deduction to Better Formalize the Notion of Entailment—Relevance 253
8.4 The Rules of System FE (Fitch-Style Formulation of the Logic of Entailment) 261
8.5 The Connective “Or,” Material Implication, and the Disjunctive Syllogism 281
9 Semantics for Relevance Logic: A Useful Four-Valued Logic 288
9.1 Interpretations, Valuations, and Many Valued Logics 288
9.2 Contexts in Which This Four-Valued Logic Is Useful 290
9.3 The Artificial Reasoner’s (Computer’s) “State of Knowledge” 291
9.4 Negation in This Four-Valued Logic 295
9.5 Lattices: A Brief Tutorial 297
9.6 Finite Approximation Lattices and Scott’s Thesis 302
9.7 Applying Scott’s Thesis to Negation, Conjunction, and Disjunction 304
9.8 The Logical Lattice L4 307
9.9 Intuitive Descriptions of the Four-Valued Logic Semantics 309
9.10 Inferences and Valid Entailments 312
10 Some Concluding Remarks on the Logic of
Entailment 315
References 316
Index 319

Windows on Mathematical Meanings: Learning Cultures and Computers



Richard Noss; Celia Hoyles

Mathematics education library, 17.

Springer | 1996 | 287  páginas | pdf | 5,2 Mb

link1

This book challenges some of the conventional wisdoms on the learning of mathematics. The authors use the computer as a window onto mathematical meaning-making. The pivot of their theory is the idea of webbing, which explains how someone struggling with a new mathematical idea can draw on supportive knowledge, and reconciles the individual's role in mathematical learning with the part played by epistemological, social and cultural forces.

CONTENTS
Visions of the Mathematical
Laying the Foundations
Tools and Technologies
Ratioworld
Webs and Situated Abstractions
Beyond the Individual Learner
Cultures and Change
A Window on Teachers
A Window on Schools
Re-Visioning Mathematical Meanings

Proceedings of the Sixth International Congress on Mathematical Education



ICME-6    1988      Budapest (Hungary) 

Ann & Keith Hirst

Janos Bolyai Mathematical Society | 398 páginas 

pdf (no OCR) | 38 Mb
online: mathematik.uni-bielefeld.de

djvu (OCR) | 21,6 Mb
online: mathematik.uni-bielefeld.de

The contributions to the Fifth Day Special were published in C. Keitel, A. Bishop, P. Damerow & P. Gerdes (Eds.) Mathematics, Education, and Society. Paris, UNESCO, Science and Technology Education, Document Series, 1989. 

Contents
Foreword (p. 5) 
Plenary Presentations B. Nebres: School Mathematics in the 1990's: the Challenge of Change especially for Developing Countries (p. 11) G. Vergnaud: Theoretical Frameworks and Empirical Facts in the Psychology of Mathematics Educationn (p. 29) A. Ershov: Computerization of Schools and Mathematical Education (p. 49) L. Lovász: Algorithmic Mathematics: An Old Aspect with a New Emphasis (p. 67) J. - P. Kahane: La Grande Figure de Georges Polya (p. 79) 
Action Groups A1. L. P. Steffe: Early Childhood Years (Ages 4 - 8) (p. 101) A2. A. C. J. Colomb: Elementary School (Ages 7-12) (p. 117) A3. I. Hirabayashi: Junior Secondary School (Ages 11-16) (p. 133) A4. J. Da Lange: Senior Secondary School (Ages 15-19) (p. 143) A5. J. Mack: Tertiary (Post-Secondary) academic institutions (ages 18+) (p. 159) A6. W. Dörfler: Pre-Service Teacher Education (p. 177) A7. R. Strässer: Adult, Technical and Vocational Education (p. 191) 
Theme Groups T1. P. A. House: The Profession of Teaching (p. 205) T2. R. Fraser: Computers and the Teaching of Mathematics (p. 215) T3. M. Niss: Problem Solving, Modelling and Applications (p. 237) T4. D. F. Robitaille: Evaluation and Assessment (p. 253) T5. N. Balacheff: The Practice of Teaching and Research in Didactics (p. 263) T6. W. Blum: Mathematics and Other Subjects (p. 277) T7. H. Burkhardt, J. A. Malone: Curriculum Towards the Year 2000 (p. 293) 
Fifth Day Special: MES A. Bishop, P. Damerow, P. Gerdes, Ch. Keitel: Mathematics, Education, Society (p. 311) 


Topic Areas and International Study Groups 
To1. M. Emmer: Video, Film (p. 329) 
To2. I. Lénárt: Visualization (p. 332) 
To3. G. Berzsenyi: Competitions (p. 334) 
To4. E. Csocsán: Problems of Handicapped Students (p. 339) 
To5. D. A. Quadling: Comparative Education (p. 342) 
To6. K. J. Travers: Probability Theory and Statistics (p. 346) 
To7. D. Pimm: Proofs, Justification and Conviction (p. 350) 
To8. C. Laborde: Language and Mathematics (p. 354) 
To9. [NOT LISTED] 
To10. P. S. Kenderov: Students of High Ability (p. 358) 
To11. D. Singmaster: Mathematical Games and Recreation (p. 361) 
To12. [NOT LISTED] 
To13. L. Burton: Women and Mathematics (p. 365) 
To14. [NOT LISTED] 
To15. H.-G. Steiner: Theory of Mathematics Education (p. 371) 
To16. W. R. Bloom: Spaces and Geometry (p. 375) 
To17. G. König: Information and Documentation (p. 379) 
To18. B. Christiansen, P. F. L. Verstappen: Systematic Cooperation between Theory and Practice in Mathematics Education (p. 382) 
HPM. U. D'Ambrosio: History and Pedagogy of Mathematics (p. 389) 
Projects (p. 393) 
ICMI 
A. G. Howson: The International Commission on Mathematical Instruction (p. 395) 
Projects (p. 393) 
ICMI 
A. G. Howson: The International Commission on Mathematical Instruction (p. 395) 


Learning Mathematics in Elementary and Middle Schools A Learner-Centered Approach


George S. Cathcart, Yvonne M. Pothier, James H. Vance e Nadine S. Bezuk

Pearson | 2010 - 5.ª edição | páginas | rar - pdf | 12,4 Mb


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This popular text and it's new integrated online resource, MyEducationLab, promotes a learner-centered approach to teaching elementary and middle school mathematics. These resources provide valuable research-based instructional strategies, resources, and activities to help you learn to evaluate how children think mathematically and how to link that knowledge to developmentally appropriate teaching practices. A strong focus on NCTM Standards and developing critical tools to meet the individual needs of students ensures all students and teachers can be successful with math.

Brief Contents
1 Teaching Mathematics: Influences and Directions 1
2 Learning and Teaching Mathematics 15
3 Developing Mathematical Thinking and Problem-Solving Ability 39
4 Assessing Mathematics Understanding 60
5 Developing Number Concepts 76
6 Developing Understanding of Numeration 99
7 Developing Whole-Number Operations: Meaning of Operations 126
8 Developing Whole-Number Operations: Mastering the Basic Facts 149
9 Estimation and Computational Procedures for Whole Numbers 170
10 Developing Fraction Concepts 207
11 Developing Fraction Computation 234
12 Developing Decimal Concepts and Computation 259
13 Understanding Ratio, Proportion, and Percent 282
14 Developing Geometric Thinking and Spatial Sense 297
15 Developing Measurement Concepts and Skills 331
16 Collecting, Organizing, and Interpreting Data 363
17 Developing Algebraic Thinking 396
References 435
Index 443