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Author: Laurie Endicott Thomas
Publisher:
ISBN: 9781938634994
Category : College students
Languages : en
Pages : 372
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Book Description
Why phonics and grammar are not trivial. Why have our political discussions in the United States become so ugly and pointless? Why are we suffering from such a breakdown in civility? In Not Trivial: How Studying the Traditional Liberal Arts Can Set You Free, Laurie Endicott Thomas explains that the problem boils down to education. The word civility originally meant training in the liberal arts. The classical liberal arts were a set of seven disciplines that were developed largely in ancient Athens to promote productive political discussions within Athenian democracy. They included three verbal arts (the trivium): grammar, logic, and rhetoric. They also included four arts of number, space, and time (the quadrivium): mathematics, geometry, music, and astronomy. These arts helped students learn to think rationally and to express themselves persuasively. The ancient Romans called these studies the liberal arts because they were considered appropriate for freeborn men, as opposed to slaves. Slaves were taught only the servile and mechanical arts, to make them more productive as workers. During the Renaissance, the classical liberal arts curriculum was supplemented by the humanities, including history, philosophy, literature, and art. Like the liberal arts, the humanities were intended to promote productive and even pleasant discussions among political decision-makers. Today, the sciences would have to be added to that curriculum. Thomas explains that the problems in our political system start in first grade. Our teachers are being trained and often forced to use a method of reading instruction that does not work. As a result, many children suffer from lifelong problems with reading. Our teachers are also being pressured to neglect the teaching of grammar. As a result, many children end up with poor reading comprehension and lifelong problems with logical thinking. Thus, they will have difficulty in making or appreciating reasonable arguments. Thomas argues that we cannot hope to enjoy freedom and equality until all children get the kind of education that is appropriate for free people. She concludes with a clear explanation of what that curriculum would be like.
Author: Laurie Endicott Thomas
Publisher:
ISBN: 9781938634994
Category : College students
Languages : en
Pages : 372
Get Book Here
Book Description
Why phonics and grammar are not trivial. Why have our political discussions in the United States become so ugly and pointless? Why are we suffering from such a breakdown in civility? In Not Trivial: How Studying the Traditional Liberal Arts Can Set You Free, Laurie Endicott Thomas explains that the problem boils down to education. The word civility originally meant training in the liberal arts. The classical liberal arts were a set of seven disciplines that were developed largely in ancient Athens to promote productive political discussions within Athenian democracy. They included three verbal arts (the trivium): grammar, logic, and rhetoric. They also included four arts of number, space, and time (the quadrivium): mathematics, geometry, music, and astronomy. These arts helped students learn to think rationally and to express themselves persuasively. The ancient Romans called these studies the liberal arts because they were considered appropriate for freeborn men, as opposed to slaves. Slaves were taught only the servile and mechanical arts, to make them more productive as workers. During the Renaissance, the classical liberal arts curriculum was supplemented by the humanities, including history, philosophy, literature, and art. Like the liberal arts, the humanities were intended to promote productive and even pleasant discussions among political decision-makers. Today, the sciences would have to be added to that curriculum. Thomas explains that the problems in our political system start in first grade. Our teachers are being trained and often forced to use a method of reading instruction that does not work. As a result, many children suffer from lifelong problems with reading. Our teachers are also being pressured to neglect the teaching of grammar. As a result, many children end up with poor reading comprehension and lifelong problems with logical thinking. Thus, they will have difficulty in making or appreciating reasonable arguments. Thomas argues that we cannot hope to enjoy freedom and equality until all children get the kind of education that is appropriate for free people. She concludes with a clear explanation of what that curriculum would be like.
Author: J. E. Wolff
Publisher: Oxford University Press
ISBN: 0192573934
Category : Philosophy
Languages : en
Pages : 226
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Book Description
What are physical quantities, and in particular, what makes them quantitative? This book articulates and defends an original answer to this important, insufficiently understood question through the novel position of substantival structuralism. This position argues that quantitativeness is an irreducible feature of attributes, and quantitative attributes are best understood as substantival structured spaces. The book first explores what it means for an attribute to be quantitative, and what metaphysical implications a commitment to quantitative attributes has. It then sets the stage to address the metaphysical and ontological consequences of the existence of quantitative attributes.
Author: Bin Fu
Publisher: Springer Science & Business Media
ISBN: 3642226841
Category : Computers
Languages : en
Pages : 662
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Book Description
This book constitutes the refereed proceedings of the 16th Annual International Conference on Computing and Combinatorics, held in Dallas, TX, USA, in August 2011. The 54 revised full papers presented were carefully reviewed and selected from 136 submissions. Topics covered are algorithms and data structures; algorithmic game theory and online algorithms; automata, languages, logic, and computability; combinatorics related to algorithms and complexity; complexity theory; computational learning theory and knowledge discovery; cryptography, reliability and security, and database theory; computational biology and bioinformatics; computational algebra, geometry, and number theory; graph drawing and information visualization; graph theory, communication networks, and optimization; parallel and distributed computing.
Author: Anatoly Fomenko
Publisher: Springer
ISBN: 3319234889
Category : Mathematics
Languages : en
Pages : 635
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Book Description
This textbook on algebraic topology updates a popular textbook from the golden era of the Moscow school of I. M. Gelfand. The first English translation, done many decades ago, remains very much in demand, although it has been long out-of-print and is difficult to obtain. Therefore, this updated English edition will be much welcomed by the mathematical community. Distinctive features of this book include: a concise but fully rigorous presentation, supplemented by a plethora of illustrations of a high technical and artistic caliber; a huge number of nontrivial examples and computations done in detail; a deeper and broader treatment of topics in comparison to most beginning books on algebraic topology; an extensive, and very concrete, treatment of the machinery of spectral sequences. The second edition contains an entirely new chapter on K-theory and the Riemann-Roch theorem (after Hirzebruch and Grothendieck).
Author: Alan Jeffrey
Publisher: CRC Press
ISBN: 9780412621505
Category : Mathematics
Languages : en
Pages : 934
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Book Description
This edition of the book has been revised with the needs of present-day first-year engineering students in mind. Apart from many significant extensions to the text, attention has been paid to the inclusion of additional explanatory material wherever it seems likely to be helpful and to a lowering of the rigour of proofs given in previous editions - without losing sight of the necessity to justify results. New problem sets are included for use with commonly available software products. The mathematical requirements common to first year engineering students of every discipline are covered in detail with numerous illustrative worked examples given throughout the text. Extensive problem sets are given at the end of each chapter with answers to odd-numbered questions provided at the end of the book.
Author: Álvaro Lozano-Robledo
Publisher: American Mathematical Soc.
ISBN: 147045016X
Category : Mathematics
Languages : en
Pages : 506
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Book Description
Geometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two subjects and recorded them in such classical texts as Euclid's Elements and Diophantus's Arithmetica. Nowadays, the field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book is an introduction to number theory and arithmetic geometry, and the goal of the text is to use geometry as the motivation to prove the main theorems in the book. For example, the fundamental theorem of arithmetic is a consequence of the tools we develop in order to find all the integral points on a line in the plane. Similarly, Gauss's law of quadratic reciprocity and the theory of continued fractions naturally arise when we attempt to determine the integral points on a curve in the plane given by a quadratic polynomial equation. After an introduction to the theory of diophantine equations, the rest of the book is structured in three acts that correspond to the study of the integral and rational solutions of linear, quadratic, and cubic curves, respectively. This book describes many applications including modern applications in cryptography; it also presents some recent results in arithmetic geometry. With many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level.
Author: Benjamin Fine
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110673401
Category : Mathematics
Languages : en
Pages : 339
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Book Description
This book gives an advanced overview of several topics in infinite group theory. It can also be considered as a rigorous introduction to combinatorial and geometric group theory. The philosophy of the book is to describe the interaction between these two important parts of infinite group theory. In this line of thought, several theorems are proved multiple times with different methods either purely combinatorial or purely geometric while others are shown by a combination of arguments from both perspectives. The first part of the book deals with Nielsen methods and introduces the reader to results and examples that are helpful to understand the following parts. The second part focuses on covering spaces and fundamental groups, including covering space proofs of group theoretic results. The third part deals with the theory of hyperbolic groups. The subjects are illustrated and described by prominent examples and an outlook on solved and unsolved problems.
Author: Peter Eades
Publisher: World Scientific
ISBN: 9814498378
Category : Computers
Languages : en
Pages : 284
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Book Description
The term “software visualisation” refers to the graphical display of characteristics and behaviour of all aspects of software: design and analysis methods, systems, programs and algorithms. The purpose of this book is to collect and compare different experiences of software visualisation both from fundamental and applied viewpoints.The book is divided into four parts, covering important aspects of software visualisation. Part 1 covers a survey on existing software visualisation tools and environments, the strategies for making a software visualisation system language independent, and program animation for C language. Part 2 presents topics and techniques on graph drawing, which supports efficient and aesthetically pleasing visualisation. Some recently developed graph drawing systems and techniques used are described. Part 3 discusses visual programming concepts and techniques for supporting parallel and heterogeneous distributed programming. Part 4 includes several case studies of software visualisation, concentrating on the broader field of software engineering ranging from software metrics to reverse engineering.
Author: Arnold Beckmann
Publisher: Springer
ISBN: 3319401890
Category : Computers
Languages : en
Pages : 388
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Book Description
This book constitutes the refereed proceedings of the 12th Conference on Computability in Europe, CiE 2016, held in Paris, France, in June/July 2016. The 18 revised full papers and 19 invited papers and invited extended abstracts were carefully reviewed and selected from 40 submissions. The conference CiE 2016 has six special sessions – two sessions, cryptography and information theory and symbolic dynamics, are organized for the first time in the conference series. In addition to this new developments in areas frequently covered in the CiE conference series were addressed in the following sessions: computable and constructive analysis; computation in biological systems; history and philosophy of computing; weak arithmetic.
Author: Jorge M. Andr
Publisher: World Scientific
ISBN: 9812707387
Category : Mathematics
Languages : en
Pages : 288
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Book Description
This festschrift volume in honour of Donald B McAlister on the occasion of his 65th birthday presents papers from leading researchers in semigroups and formal languages. The contributors cover a number of areas of current interest: from pseudovarieties and regular languages to ordered groupoids and one-relator groups, and from semigroup algebras to presentations of monoids and transformation semigroups. The papers are accessible to graduate students as well as researchers seeking new directions for future work.
