Not Trivial

Download or read book Not Trivial written by Laurie Endicott Thomas and published by . This book was released on 2013-08 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Metaphysics of Quantities written by J. E. Wolff and published by Oxford University Press. This book was released on 2020-05-27 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Computing and Combinatorics written by Bin Fu and published by Springer Science & Business Media. This book was released on 2011-07-18 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Homotopical Topology written by Anatoly Fomenko and published by Springer. This book was released on 2016-06-24 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Download or read book Mathematics for Engineers and Scientists, 5th Edition written by Alan Jeffrey and published by CRC Press. This book was released on 1996-06-13 with total page 934 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Number Theory and Geometry: An Introduction to Arithmetic Geometry written by Álvaro Lozano-Robledo and published by American Mathematical Soc.. This book was released on 2019-03-21 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Topics in Infinite Group Theory written by Benjamin Fine and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-08-23 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.