{"title":"Godel: A Life of Logic","authors":"J. Rauff","doi":"10.5860/choice.38-4504","DOIUrl":"https://doi.org/10.5860/choice.38-4504","url":null,"abstract":"","PeriodicalId":365977,"journal":{"name":"Mathematics and Computer Education","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122955024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Triumph of the Nerds","authors":"C. Ashbacher","doi":"10.5860/choice.37-3938","DOIUrl":"https://doi.org/10.5860/choice.37-3938","url":null,"abstract":"","PeriodicalId":365977,"journal":{"name":"Mathematics and Computer Education","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124026613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity","authors":"J. Rauff","doi":"10.5860/choice.38-4502","DOIUrl":"https://doi.org/10.5860/choice.38-4502","url":null,"abstract":"","PeriodicalId":365977,"journal":{"name":"Mathematics and Computer Education","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122155645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Life and Legacy of G. I. Taylor","authors":"C. M. Kirk","doi":"10.5860/choice.34-3274","DOIUrl":"https://doi.org/10.5860/choice.34-3274","url":null,"abstract":"THE LIFE AND LEGACY OF G. I. TAYLOR by George Batchelor, Cambridge University Press, 1996 When students encounter the work of Geoffrey Ingram (G. I.) Taylor in their fluid mechanics courses (Taylor-Couette flows and Rayleigh-Taylor instabilities), they are generally unaware of the extraordinary scope and depth of Taylor's contributions to modern classical physics. Indeed, G. I. Taylor is one of the great applied scientists of the 20th century. He ranks with von Karman, Prandtl, and Burgers as one of the foremost leaders in mechanics. Taylor's numerous contributions include fundamental research in fluid dynamics, turbulence theory, and plasticity. He made discoveries related to shock formations in gases and to the mechanics of explosions, as well as developing basic principles in oceanography, meteorology, and aerodynamics. Contrary to the popular notion that mathematicians and scientists do their most consequential work during their early years, Taylor was in his 70's when he produced results that helped launch the field of electro-hydrodynamics. Many of his results continue to influence the course of research in modern classical physics today. Taylor was active during that extraordinary period in physics when the fields of quantum mechanics and relativity were emerging. Taylor was the first to demonstrate one of the basic results of quantum mechanics: namely, that the diffraction patterns from light shining on a needle do not change with the intensity of the light. However, it became his habit to eschew fashionable research topics such as quantum mechanics and to devote himself to the exploration of more classical mechanics and less popular subjects. Taylor was often instrumental in establishing an area of research, but would drop it and begin something different when the subject became popular. Taylor's approach to research was simple yet elegant, and usually involved a complimentary blend of theory and experiment. He brought originality and insight to problems, as well as a fabulous intuition, which enabled him to construct models that elucidated the important features of a problem. This biography focuses primarily on Taylor's scientific contributions and less so on his personal life. The technical descriptions of Taylor's work are sometimes at the advanced undergraduate or beginning graduate level. The author does an excellent job of communicating Taylor's work in descriptive, qualitative terms. Mathematical formulas appear rarely and derivations not at all; therefore, most of the text is readable by a general reader. …","PeriodicalId":365977,"journal":{"name":"Mathematics and Computer Education","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131086247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Introduction to Ordinary Differential Equations","authors":"T. H. Fay","doi":"10.1016/c2013-0-08204-7","DOIUrl":"https://doi.org/10.1016/c2013-0-08204-7","url":null,"abstract":"","PeriodicalId":365977,"journal":{"name":"Mathematics and Computer Education","volume":"334 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115877007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Proof without words","authors":"J. O. Chilaka","doi":"10.1080/0025570X.1996.11996388","DOIUrl":"https://doi.org/10.1080/0025570X.1996.11996388","url":null,"abstract":"","PeriodicalId":365977,"journal":{"name":"Mathematics and Computer Education","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131981098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Roads to Infinity: The Mathematics of Truth and Proof","authors":"J. Rauff","doi":"10.5860/choice.48-3928","DOIUrl":"https://doi.org/10.5860/choice.48-3928","url":null,"abstract":"ROADS TO INFINITY: THE MATHEMATICS OF TRUTH AND PROOF by John Stillwell A. K. Peters, 2010, 203 pp. ISBN: 978-1-56881-466-7 Roads to Infinity: The Mathematics of Truth and Proof 'is an account of the discovery of the uncountably infinite; the interaction between set theory and logic in the realm of the irifinite; and the mathematical consequences of accepting the infinite levels of infinity. The book follows essentially two roads to infinity: Cantor's diagonal argument and Cantor's construction of the ordinals. Stillwell shows how these two themes intertwine and influence a wide range of mathematical questions including consistency, provability, computability, and existence. Roads to Infinity comprises seven chapters, each based upon a mathematical question. The historical responses to the question are explored and the concepts and theorems resulting from these responses are explained in essentially non-technical language. However, the abiiity to read mathematical symbolism and understand mathematical argumentation is required. Still well begins with Cantor's diagonal argument. His focus is the uncountability of the real continuum and he includes in the discussion the ever-amazing uncountability of transcendental numbers, an application of the diagonal argument to the rate of growth of functions, the paradoxes of set theory, and the axioms of Zermelo-Fraenkel set theory. Next, the book examines the transfinite ordinals, the continuum hypothesis, the axiom of choice and well-ordering, measurability of sets, and Cohen's technique of forcing. Also included here is a discussion of how Cantor's set theory arose from his investigation Fourier series. In the third chapter, Stillwell turns his attention to questions of computability and provability. Here we encounter Godei' s first and second incompleteness theorems, Turing machines, the Halting Problem (which Stillwell finds lurking in Cervantes' Don Quixote^!), and Hubert's Entscheidungsproblem for predicate logic. The chapter leads nicely into Chapter 4 on the consistency and completeness of propositional and predicate logic. A major theme in this chapter on logic is \"cut-elimination\", a way of inference in logic that replaces modus ponens by falsification trees. Chapter 5 focuses on arithmetic. Here we find a detailed discussion of Peano Aritiimetic, and an infinite extension of Peano Arithmetic and how the extension may be used to prove the consistency of Peano Arithmetic (which cannot prove its own consistency). The diagonal argument theme is reinforced in this chapter as Stillwell shows how the unprovability of consistency of Peano Arithmetic within Peano Arithmetic is related to the argument that 2N\" is uncountable. …","PeriodicalId":365977,"journal":{"name":"Mathematics and Computer Education","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115583115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Unknown Quantity: A Real and Imaginary History of Algebra","authors":"J. Rauff","doi":"10.5860/choice.44-3328","DOIUrl":"https://doi.org/10.5860/choice.44-3328","url":null,"abstract":"If you are searched for a book by John Derbyshire Unknown Quantity: A Real and Imaginary History of Algebra in pdf form, in that case you come on to the faithful site. We furnish full edition of this ebook in ePub, txt, doc, DjVu, PDF formats. You can read Unknown Quantity: A Real and Imaginary History of Algebra online either download. In addition to this ebook, on our site you may reading the guides and different artistic eBooks online, or download their. We will draw on attention that our site not store the book itself, but we grant url to the website wherever you can load either read online. So if want to load Unknown Quantity: A Real and Imaginary History of Algebra by John Derbyshire pdf, then you have come on to loyal website. We own Unknown Quantity: A Real and Imaginary History of Algebra txt, DjVu, PDF, ePub, doc formats. We will be happy if you return over.","PeriodicalId":365977,"journal":{"name":"Mathematics and Computer Education","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126890697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Algebraic and Discrete Mathematical Methods for Modern Biology","authors":"Chris Arney","doi":"10.1016/c2013-0-18496-6","DOIUrl":"https://doi.org/10.1016/c2013-0-18496-6","url":null,"abstract":"","PeriodicalId":365977,"journal":{"name":"Mathematics and Computer Education","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134524070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}