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Author: David Lindsay Roberts
Publisher: Johns Hopkins University Press
ISBN: 1421433087
Category : Mathematics
Languages : en
Pages : 255
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Book Description
This fascinating narrative history of math in America introduces readers to the diverse and vibrant people behind pivotal moments in the nation's mathematical maturation. Once upon a time in America, few knew or cared about math. In Republic of Numbers, David Lindsay Roberts tells the story of how all that changed, as America transformed into a powerhouse of mathematical thinkers. Covering more than 200 years of American history, Roberts recounts the life stories of twenty-three Americans integral to the evolution of mathematics in this country. Beginning with self-taught Salem mathematician Nathaniel Bowditch's unexpected breakthroughs in ocean navigation and closing with the astounding work Nobel laureate John Nash did on game theory, this book is meant to be read cover to cover. Revealing the marvelous ways in which America became mathematically sophisticated, the book introduces readers to Kelly Miller, the first black man to attend Johns Hopkins, who brilliantly melded mathematics and civil rights activism; Izaak Wirszup, a Polish immigrant who survived the Holocaust and proceeded to change the face of American mathematical education; Grace Hopper, the "Machine Whisperer," who pioneered computer programming; and many other relatively unknown but vital figures. As he brings American history and culture to life, Roberts also explains key mathematical concepts, from the method of least squares, propositional logic, quaternions, and the mean-value theorem to differential equations, non-Euclidean geometry, group theory, statistical mechanics, and Fourier analysis. Republic of Numbers will appeal to anyone who is interested in learning how mathematics has intertwined with American history.
Author: David Lindsay Roberts
Publisher: Johns Hopkins University Press
ISBN: 1421433087
Category : Mathematics
Languages : en
Pages : 255
Get Book Here
Book Description
This fascinating narrative history of math in America introduces readers to the diverse and vibrant people behind pivotal moments in the nation's mathematical maturation. Once upon a time in America, few knew or cared about math. In Republic of Numbers, David Lindsay Roberts tells the story of how all that changed, as America transformed into a powerhouse of mathematical thinkers. Covering more than 200 years of American history, Roberts recounts the life stories of twenty-three Americans integral to the evolution of mathematics in this country. Beginning with self-taught Salem mathematician Nathaniel Bowditch's unexpected breakthroughs in ocean navigation and closing with the astounding work Nobel laureate John Nash did on game theory, this book is meant to be read cover to cover. Revealing the marvelous ways in which America became mathematically sophisticated, the book introduces readers to Kelly Miller, the first black man to attend Johns Hopkins, who brilliantly melded mathematics and civil rights activism; Izaak Wirszup, a Polish immigrant who survived the Holocaust and proceeded to change the face of American mathematical education; Grace Hopper, the "Machine Whisperer," who pioneered computer programming; and many other relatively unknown but vital figures. As he brings American history and culture to life, Roberts also explains key mathematical concepts, from the method of least squares, propositional logic, quaternions, and the mean-value theorem to differential equations, non-Euclidean geometry, group theory, statistical mechanics, and Fourier analysis. Republic of Numbers will appeal to anyone who is interested in learning how mathematics has intertwined with American history.
Author: Plato
Publisher: E-Kitap Projesi & Cheapest Books
ISBN: 6155564574
Category : Biography & Autobiography
Languages : en
Pages : 664
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Book Description
The Republic (Greek: Politeia) is a Socratic dialogue, written by Plato around 380 BC, concerning the definition of (justice), the order and character of the just city-state and the just man, reason by which ancient readers used the name On Justice as an alternative title (not to be confused with the spurious dialogue also titled On Justice). The dramatic date of the dialogue has been much debated and though it must take place some time during the Peloponnesian War, "there would be jarring anachronisms if any of the candidate specific dates between 432 and 404 were assigned". It is Plato's best-known work and has proven to be one of the most intellectually and historically influential works of philosophy and political theory. In it, Socrates along with various Athenians and foreigners discuss the meaning of justice and examine whether or not the just man is happier than the unjust man by considering a series of different cities coming into existence "in speech", culminating in a city (Kallipolis) ruled by philosopher-kings; and by examining the nature of existing regimes. The participants also discuss the theory of forms, the immortality of the soul, and the roles of the philosopher and of poetry in society. Short Summary (Epilogue): X.1—X.8. 595a—608b. Rejection of Mimetic Art X.9—X.11. 608c—612a. Immortality of the Soul X.12. 612a—613e. Rewards of Justice in Life X.13—X.16. 613e—621d. Judgment of the Dead The paradigm of the city — the idea of the Good, the Agathon — has manifold historical embodiments, undertaken by those who have seen the Agathon, and are ordered via the vision. The centre piece of the Republic, Part II, nos. 2–3, discusses the rule of the philosopher, and the vision of the Agathon with the allegory of the cave, which is clarified in the theory of forms. The centre piece is preceded and followed by the discussion of the means that will secure a well-ordered polis (City). Part II, no. 1, concerns marriage, the community of people and goods for the Guardians, and the restraints on warfare among the Hellenes. It describes a partially communistic polis. Part II, no. 4, deals with the philosophical education of the rulers who will preserve the order and character of the city-state. In Part II, the Embodiment of the Idea, is preceded by the establishment of the economic and social orders of a polis (Part I), followed by an analysis (Part III) of the decline the order must traverse. The three parts compose the main body of the dialogues, with their discussions of the "paradigm", its embodiment, its genesis, and its decline. The Introduction and the Conclusion are the frame for the body of the Republic. The discussion of right order is occasioned by the questions: "Is Justice better than Injustice?" and "Will an Unjust man fare better than a Just man?" The introductory question is balanced by the concluding answer: "Justice is preferable to Injustice". In turn, the foregoing are framed with the Prologue (Book I) and the Epilogue (Book X). The prologue is a short dialogue about the common public doxai (opinions) about "Justice". Based upon faith, and not reason, the Epilogue describes the new arts and the immortality of the soul.
Author: Plato Plato
Publisher: Xist Publishing
ISBN: 1532405006
Category : Philosophy
Languages : en
Pages : 625
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Book Description
ePub Copyright © 2017 Classic Book Series
Author: Plato
Publisher: Binker North
ISBN:
Category : History
Languages : en
Pages : 632
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Book Description
The Republic is a Socratic dialogue, written by Plato around 380 BC, concerning justice, the order and character of the just city-state, and the just man. It is Plato's best-known work, and has proven to be one of the world's most influential works of philosophy and political theory, both intellectually and historically. In the dialogue, Socrates talks with various Athenians and foreigners about the meaning of justice and whether the just man is happier than the unjust man. They consider the natures of existing regimes and then propose a series of different, hypothetical cities in comparison, culminating in Kallipolis, a city-state ruled by a philosopher king. They also discuss the theory of forms, the immortality of the soul, and the role of the philosopher and of poetry in society. The dialogue's setting seems to be during the Peloponnesian War. In the first book, two definitions of justice are proposed but deemed inadequate.[14] Returning debts owed, and helping friends while harming enemies, are commonsense definitions of justice that, Socrates shows, are inadequate in exceptional situations, and thus lack the rigidity demanded of a definition. Yet he does not completely reject them, for each expresses a commonsense notion of justice that Socrates will incorporate into his discussion of the just regime in books II through V. At the end of Book I, Socrates agrees with Polemarchus that justice includes helping friends, but says the just man would never do harm to anybody. Thrasymachus believes that Socrates has done the men present an injustice by saying this and attacks his character and reputation in front of the group, partly because he suspects that Socrates himself does not even believe harming enemies is unjust. Thrasymachus gives his understanding of justice and injustice as "justice is what is advantageous to the stronger, while injustice is to one's own profit and advantage".[15] Socrates finds this definition unclear and begins to question Thrasymachus. Socrates then asks whether the ruler who makes a mistake by making a law that lessens their well-being, is still a ruler according to that definition. Thrasymachus agrees that no true ruler would make such an error. This agreement allows Socrates to undermine Thrasymachus' strict definition of justice by comparing rulers to people of various professions. Thrasymachus consents to Socrates' assertion that an artist is someone who does his job well, and is a knower of some art, which allows him to complete the job well. In so doing Socrates gets Thrasymachus to admit that rulers who enact a law that does not benefit them firstly, are in the precise sense not rulers. Thrasymachus gives up, and is silent from then on. Socrates has trapped Thrasymachus into admitting the strong man who makes a mistake is not the strong man in the precise sense, and that some type of knowledge is required to rule perfectly. However, it is far from a satisfactory definition of justice.
Author: George Szpiro
Publisher: Princeton University Press
ISBN: 0691209081
Category : History
Languages : en
Pages : 240
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The author takes the general reader on a tour of the mathematical puzzles and paradoxes inherent in voting systems, such as the Alabama Paradox, in which an increase in the number of seats in the Congress could actually lead to a reduced number of representatives for a state, and the Condorcet Paradox, which demonstrates that the winner of elections featuring more than two candidates does not necessarily reflect majority preferences. Szpiro takes a roughly chronological approach to the topic, traveling from ancient Greece to the present and, in addition to offering explanations of the various mathematical conundrums of elections and voting, also offers biographical details on the mathematicians and other thinkers who thought about them, including Plato, Pliny the Younger, Pierre Simon Laplace, Thomas Jefferson, John von Neumann, and Kenneth Arrow.
Author: League of Nations
Publisher:
ISBN:
Category : Czechoslovakia
Languages : en
Pages : 82
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Author: Plato
Publisher: DigiCat
ISBN:
Category : Political Science
Languages : en
Pages : 690
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Book Description
"The Republic" is a Socratic dialogue, authored by the famed Greek Philosopher Plato around 375 BC, concerning justice, the order and character of the just city-state, and the just man. It is Plato's best-known work, and one of the world's most influential works of philosophy and political theory, both intellectually and historically. In the dialogue, Socrates discusses the meaning of justice and whether the just man is happier than the unjust man with various Athenians and foreigners. They consider the natures of existing regimes and then propose a series of different, hypothetical cities in comparison, culminating in Kallipolis, a utopian city-state ruled by a philosopher-king. They also discuss the theory of forms, the immortality of the soul, and the role of the philosopher and of poetry in society. The dialogue's setting seems to be during the Peloponnesian War.
Author:
Publisher:
ISBN:
Category : United States
Languages : en
Pages : 1674
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Author: Plato
Publisher: Lulu.com
ISBN: 1773563483
Category :
Languages : en
Pages : 368
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Book Description
Author: Plato
Publisher:
ISBN:
Category :
Languages : en
Pages : 814
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