On the Shape of Mathematical Arguments

On the Shape of Mathematical Arguments

This book deals with the presentation and systematic design of mathematical proofs, including correctness proofs of algorithms.

Author: Antonetta J.M. van Gasteren

Publisher: Springer Science & Business Media

ISBN: 3540528490

Category: Computers

Page: 180

View: 452

This book deals with the presentation and systematic design of mathematical proofs, including correctness proofs of algorithms. A technical rather than psychological view of heuristics and a stress on exploiting for- malism effectively are two key features.
Categories: Computers

Active galaxies educational unit

Active galaxies educational unit

Geometry : Analyze characteristics and properties of two- and three - dimensional
geometric shapes and develop mathematical arguments about geometric
relationships Students observe the finished models and create illustrations to
show ...

Author:

Publisher:

ISBN: UIUC:30112064011866

Category: Active galaxies

Page: 36

View: 299

Categories: Active galaxies

The Math of Life and Death

The Math of Life and Death

7 Mathematical Principles That Shape Our Lives Kit Yates ... Such was the
opacity of Bertillon's mathematical argument that neither Dreyfus's defense team
nor the government commissioner present at the court understood any of the
argument ...

Author: Kit Yates

Publisher: Scribner

ISBN: 9781982111878

Category: Mathematics

Page: 288

View: 178

A brilliant and entertaining mathematician illuminates seven mathematical principles that shape our lives. “Kit Yates shows how our private and social lives are suffused by mathematics. Ignorance may bring tragedy or farce. This is an exquisitely interesting book. It’s a deeply serious one too and, for those like me who have little math, it’s delightfully readable.” —Ian McEwan, author of Atonement “Kit Yates is a natural storyteller. Through fascinating stories and examples, he shows how maths is the beating heart of so much of modern life. An exciting new voice in the world of science communication.” —Marcus du Sautoy, author of The Music of the Primes From birthdays to birth rates to how we perceive the passing of time, mathematical patterns shape our lives. But for those of us who left math behind in high school, the numbers and figures hurled at us as we go about our days can sometimes leave us scratching our heads and feeling as if we’re fumbling through a mathematical minefield. In this eye-opening and extraordinarily accessible book, mathemati­cian Kit Yates illuminates hidden principles that can help us understand and navigate the chaotic and often opaque surfaces of our world. In The Math of Life and Death, Yates takes us on a fascinating tour of everyday situations and grand-scale applications of mathematical concepts, including exponential growth and decay, optimization, statistics and probability, and number systems. Along the way he reveals the mathematical undersides of controversies over DNA testing, medical screening results, and historical events such as the Chernobyl disaster and the Amanda Knox trial. Readers will finish this book with an enlightened perspective on the news, the law, medicine, and history, and will be better equipped to make personal decisions and solve problems with math in mind, whether it’s choosing the shortest checkout line at the grocery store or halting the spread of a deadly disease.
Categories: Mathematics

MathScape Seeing and Thinking Mathematically Course 2 Making Mathematical Arguments Student Guide

MathScape  Seeing and Thinking Mathematically  Course 2  Making Mathematical Arguments  Student Guide

In this phase , you will write mathematical arguments about patterns involving
divisibility , prime numbers , and factors . ... squares , or cubes MathScape Online
mathscape2.com/self_check_quiz Three - Stack Shape Sums In the last phase ,.

Author: McGraw Hill

Publisher: McGraw-Hill Education

ISBN: 0078668107

Category: Mathematics

Page:

View: 760

Making Mathematical Arguments, Student Guide
Categories: Mathematics

Ptolemy s Philosophy

Ptolemy s Philosophy

He supports this hypothesis with several arguments, mathematical and physical,
which he presents in Almagest 1.3 and I paraphrase here: 1. The size and mutual
distances of the stars do not appear to change.23 2. The spherical shape of the ...

Author: Jacqueline Feke

Publisher: Princeton University Press

ISBN: 9780691179582

Category: Science

Page: 256

View: 123

The Greco-Roman mathematician Claudius Ptolemy is one of the most significant figures in the history of science. He is remembered today for his astronomy, but his philosophy is almost entirely lost to history. This groundbreaking book is the first to reconstruct Ptolemy’s general philosophical system—including his metaphysics, epistemology, and ethics—and to explore its relationship to astronomy, harmonics, element theory, astrology, cosmology, psychology, and theology. In this stimulating intellectual history, Jacqueline Feke uncovers references to a complex and sophisticated philosophical agenda scattered among Ptolemy’s technical studies in the physical and mathematical sciences. She shows how he developed a philosophy that was radical and even subversive, appropriating ideas and turning them against the very philosophers from whom he drew influence. Feke reveals how Ptolemy’s unique system is at once a critique of prevailing philosophical trends and a conception of the world in which mathematics reigns supreme. A compelling work of scholarship, Ptolemy’s Philosophy demonstrates how Ptolemy situated mathematics at the very foundation of all philosophy—theoretical and practical—and advanced the mathematical way of life as the true path to human perfection.
Categories: Science

Reliability Abstracts and Technical Reviews

Reliability Abstracts and Technical Reviews

... primary problem in most applications would be the amount of testing required
to convince one of the adequacy of or a preference for the GGD or one of its
specialized forms with shape parameter less than unity . The mathematical
arguments ...

Author:

Publisher:

ISBN: UOM:39015002937921

Category: Reliability (Engineering)

Page:

View: 923

Categories: Reliability (Engineering)

Dr Dobb s Journal

Dr  Dobb s Journal

It's called On the Shape of Mathematical Arguments, but I think it should be called
The Programmer Over Your Shoulder. The digression which follows will explain
why. I've long thought that there should be a software developer's version of ...

Author:

Publisher:

ISBN: UOM:39015081529169

Category: Microcomputers

Page:

View: 837

Categories: Microcomputers

Connected mathematics two

Connected mathematics two

... for trusses) (6) • Build and visualize three-dimensional figures from various two
-dimensional representations and vice versa (7) • Recognize and use shapes
and their properties to make mathematical arguments and to solve problems (6, 7
, ...

Author: Glenda Lappan

Publisher:

ISBN: 0131339478

Category: Mathematics

Page:

View: 247

Categories: Mathematics

Teaching Children Mathematics

Teaching Children Mathematics

They will also use the properties of a geometrical shape to determine whether
they have actually created that shape. ... the characteristics and properties of two-
dimensional geometrical shapes and develop mathematical arguments about ...

Author:

Publisher:

ISBN: UOM:39015058197552

Category: Mathematics

Page:

View: 497

Categories: Mathematics

Teaching and Learning Mathematics

Teaching and Learning Mathematics

The skills of geometry involve readily identifying and analyzing shapes and
relationships , developing mathematical arguments about geometric
relationships , copying and constructing shapes , visualizing and spatial
reasoning , and using ...

Author: Linda Jensen Sheffield

Publisher: John Wiley & Sons Incorporated

ISBN: UVA:X004773710

Category: Business & Economics

Page: 544

View: 838

Reflecting the state-of-the-art in mathematics education, this book prepares teachers from pre-school through grade 8, with the skills they need to allow their students to grasp the concepts and develop the skills they will need for the future.
Categories: Business & Economics

Dr Dobb s Journal of Software Tools for the Professional Programmer

Dr  Dobb s Journal of Software Tools for the Professional Programmer

In On the Shape lack of a better term , softness . Most of prefer not to believe that
there are that of Mathematical Arguments , van Gasus , I think , would describe
the B items many rigorous rules of good writing . It's teren , a colleague of Edsger
 ...

Author:

Publisher:

ISBN: CHI:51518784

Category: Microcomputers

Page:

View: 818

Categories: Microcomputers

Navigating Through Problem Solving and Reasoning in Grade 3

Navigating Through Problem Solving and Reasoning in Grade 3

Goals • Improve students ' reasoning about decomposing and recomposing
shapes . ... and threedimensional geometric shapes and develop mathematical
arguments about geometric relationships • Identify , compare , and analyze
attributes ...

Author: Karol L. Yeatts

Publisher: National Council of Teachers of English

ISBN: STANFORD:36105122965291

Category: Matemáticas

Page: 65

View: 283

Through the investigations in this book, children reason about place value by making and using pedometers, understand related changes in two quantities by exploring parade formations of thirty-six marchers and analyse data by devising rules for earning reading certificates. Students apply mathematical ideas from the five main content areas-number, algebra, geometry, measurement and data analysis. As they work, they infer, generalise, reason by analogy, recognise relationships and make representations, and they also guess, check and revise and verify their results. The supplemental CD-ROM features interactive electronic activities, master copies of activity pages for students and additional readings for teachers.
Categories: Matemáticas

Philosophica

Philosophica

Annals of Mathematics , Second Series , vol . 141 , 3 , 553 - 572 . Tymoczko ,
Thomas ( ed . ) ( 1986 ) . New Directions in the Philosophy of Mathematics .
Stuttgart : Birkhäuser . ... On the Shape of Mathematical Arguments . Heidelberg ...

Author:

Publisher:

ISBN: UOM:39015061292630

Category: Philosophy

Page:

View: 235

Categories: Philosophy

Navigating Through Problem Solving and Reasoning in Grade 4

Navigating Through Problem Solving and Reasoning in Grade 4

Goals Sta end • Improve reasoning about decomposing and recomposing
shapes • Develop skill in decomposing ... of two - and three - dimensional
geometric shapes and develop mathematical arguments about geometric
relationships o ...

Author: Karol L. Yeatts

Publisher: National Council of Teachers of English

ISBN: STANFORD:36105122965366

Category: Fourth grade (Education)

Page: 83

View: 853

This book features investigations in each of the five content areas of Principles and Standards for School Mathematics. In addition to using Eratosthenes' sieve to identify prime numbers, fourth graders evaluate algebraic relationships in contracts between theatre owners and movie distributors. They consider geometric possibilities for rectangular puzzles, convert surprising real-world measures into equivalent but more comprehensible measures and examine tables and graphs to extrapolate missing data. As they work, they infer, generalise, reason by analogy, recognise relationships and make representations and they also guess, check and revise and verify their results. The supplemental CD-ROM features interactive electronic activities, master copies of activity pages for students and additional readings for teachers.
Categories: Fourth grade (Education)

Philosophy of Mathematics

Philosophy of Mathematics

We also require that the shape of the distribution is such that it delivers a low
probability to the carbon - based - life - permitting ... These mathematical
reflections on the problem don't provide a knock - down argument against all fine
tuning ...

Author: Vincent F. Hendricks

Publisher: Automatic Press / VIP

ISBN: PSU:000065254035

Category: Mathematics

Page: 342

View: 284

Interviews of more than two dozen scholars about the philosophy of mathematics, their interests in the field, and their ideas about future developments.
Categories: Mathematics

Mathematics for Elementary School Teachers

Mathematics for Elementary School Teachers

Instructional programs from prekindergarten through grade 12 should enable all
students to: • Analyze characteristics and properties of two- and three-
dimensional geometric shapes and develop mathematical arguments about
geometric ...

Author: Tom Bassarear

Publisher: Houghton Mifflin College Division

ISBN: 0618348867

Category: Education

Page: 704

View: 360

Mathematics for Elementary School Teachers, 3/e, offers pre-service teachers a comprehensive mathematics course designed to foster concept development through examples, investigations, and explorations. Visual icons throughout the main text allow instructors to easily connect the text to the hands-on activities in the corresponding Explorations Manual. Classroom Connections in both the exposition and the exercises guide students to connect the mathematics being taught with effective teaching strategies. Students must analyze educational mathematics research, evaluate common student errors, and see alternative solution methods, enabling them to better prepare for their future teaching careers. Investigations encourage students to think about a topic before discussing the math or viewing examples. These can be used as classroom discussion questions, for independent reading, or as review. Multiple Strategies presented throughout the examples and exposition of the text allow students to analyze numerous approaches to solving problems.
Categories: Education

Mathematics for Every Student

Mathematics for Every Student

The instructional goals for the unit included teaching students how to “ analyze
characteristics and properties of twoand three - dimensional geometric shapes
and develop mathematical arguments about geometric relationships ” ( NCTM
2000 ...

Author: Dorothy Y. White

Publisher: National Council of Teachers of

ISBN: UCSD:31822037172525

Category: Education

Page: 177

View: 954

Demonstrates how connecting real-life activities with mathematical concepts, and building on students' knowledge and experiences, can help them excel in the classroom. Strategies that can immediately be implemented to help students form better connections with the content they are studying are also described. --from publisher description.
Categories: Education

Programming Concepts Methods and Calculi

Programming Concepts  Methods and Calculi

A support system for formal mathematical reasoning . In Denvir ( 11 ) . 2 . ...
Implementing Mathematics with the NuPRL Proof Development System . Prentice
Hall ... On the Shape of Mathematical Arguments , volume 445 of LNCS .
Springer ...

Author: E.-R. Olderog

Publisher: North-Holland

ISBN: STANFORD:36105016305612

Category: Computers

Page: 592

View: 492

Categories: Computers

Theorem Proving in Higher Order Logics

Theorem Proving in Higher Order Logics

103 of Studies in Logic and the Foundations of Mathematics , revised edn , North
Holland . Carrington , D . , Hayes , I . , Nickson , R . , Watson ... Gasteren , A . J . M
. v . ( 1987 ) , On the Shape of Mathematical Arguments , LNCS 445 , Springer .

Author:

Publisher:

ISBN: UOM:39015039942605

Category: Automatic theorem proving

Page:

View: 758

Categories: Automatic theorem proving