Author: Antonetta J.M. van GasterenPublish On: 1990-07-24
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.
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 ...
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.
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 ,.
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.
... 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 ...
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 ...
... 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
, ...
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: Linda Jensen SheffieldPublish On: 2004-03-29
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.
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
...
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.
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 ...
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.
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.
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.
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.
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 ...
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 .
