{"title":"Craig Smorynski","description":null,"products":[{"product_id":"chapters-in-mathematics-from-pi-to-pell-book-craig-smorynski-9781848900530","title":"Chapters in Mathematics. From Pi to Pell","description":"Growing out of a course in the history of mathematics given to school teachers, the present book covers a number of topics of elementary mathematics from both the mathematical and historical perspectives. Included are topics from geometry (π, Napoleon's Theorem, trigonometry), recreational mathematics (the Pell equation, Fibonacci numbers), and computational mathematics (finding square roots, mathematical tables). Although written with the needs of the mathematics teacher in mind, the book can be read profitably by any high school graduate with a liking for mathematics.","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":51057169858833,"sku":"NIN9781848900530","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ GARDNERS","offer_id":51630433272081,"sku":"NGR9781848900530","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52483004956945,"sku":"NLS9781848900530","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1848900538.jpg?v=1750866659"},{"product_id":"adventures-in-formalism-book-craig-smorynski-9781848900608","title":"Adventures in Formalism","description":"Mathematics originates with intuition. But intuition alone can only go so far and formalism develops to handle the more difficult problems. Formalism, however, has its inherent dangers. There are three types of formalism. Type I formalism, exemplified in the work of Euler, is basically heuristic reasoning, the use of familiar reasoning in areas where the reasoning might not or ought not apply. The results include startling successes, and also theorems admitting exceptions. Type I formalism, associated with names like Bolzano, Cauchy, and Weierstrass, attempts to clarify the situation by means of precise definitions of the terms used. Type I formalism, the axiomatic method, leaves the fundamental concepts undefined, but offers precise rules for their use. Such precision deserts intuition and one pays the price. Most dramatically, the formal definitions of Type I formalism allow for the construction of monsters - bizarre counterexamples that exhibit behaviour inconsistent with existing intuition. The initially repellant nature of these monsters leads to dissatisfaction that is only dispelled by their growing familiarity and applicability. The present book covers the history of formalism in mathematics from Euclid through the 20th century. It should be of interest to advanced mathematics students, anyone who teaches mathematics, and anyone generally interested in the foundation of mathematics.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51057193484561,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51057195942161,"sku":"NIN9781848900608","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52135791624465,"sku":"NLS9781848900608","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1848900600.jpg?v=1750725196"},{"product_id":"treatise-on-the-binomial-theorem-book-craig-smorynski-9781848900851","title":"A Treatise on the Binomial Theorem","description":"The binomial theorem is usually quite rightly considered as one of the most important theorems in the whole of analysis. Thus wrote Bernard Bolzano in 1816 in introducing the first correct proof of Newton's generalisation of a century and a half earlier of a result familiar to us all from elementary algebra. Bolzano's appraisal may surprise the modern reader familiar only with the finite algebraic version of the Binomial Theorem involving positive integral exponents, and may also appear incongruous to one familiar with Newton's series for rational exponents. Yet his statement was a sound judgment back in the day. Here the story of the Binomial Theorem is presented in all its glory, from the early days in India, the Moslem world, and China as an essential tool for root extraction, through Newton's generalisation and its central role in infinite series expansions in the 17th and 18th centuries, and to its rigorous foundation in the 19th. The exposition is well-organised and fairly complete with all the necessary details, yet still readable and understandable for those with a limited mathematical background, say at the Calculus level or just below that. The present book, with its many citations from the literature, will be of interest to anyone concerned with the history or foundations of mathematics.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51057251975441,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51057254039825,"sku":"NIN9781848900851","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":51514129744145,"sku":"GOR014310996","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52657878368529,"sku":"NLS9781848900851","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1848900856.jpg?v=1751313897"},{"product_id":"mvt-a-most-valuable-theorem-book-craig-smorynski-9783319529554","title":"MVT: A Most Valuable Theorem","description":"This book is about the rise and supposed fall of the mean value theorem. It discusses the evolution of the theorem and the concepts behind it, how the theorem relates to other fundamental results in calculus, and modern re-evaluations of its role in the standard calculus course.    The mean value theorem is one of the central results of calculus. It was called “the fundamental theorem of the differential calculus” because of its power to provide simple and rigorous proofs of basic results encountered in a first-year course in calculus. In mathematical terms, the book is a thorough treatment of this theorem and some related results in the field; in historical terms, it is not a history of calculus or mathematics, but a case study in both.    MVT: A Most Valuable Theorem is aimed at those who teach calculus, especially those setting out to do so for the first time. It is also accessible to anyone who has finished the first semester of the standard course in the subject and will be of interest to undergraduate mathematics majors as well as graduate students. Unlike other books, the present monograph treats the mathematical and historical aspects in equal measure, providing detailed and rigorous proofs of the mathematical results and even including original source material presenting the flavour of the history.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51060851573009,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51060854227217,"sku":"NIN9783319529554","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52146183569681,"sku":"NLS9783319529554","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3319529552.jpg?v=1751349540"},{"product_id":"history-of-mathematics-book-craig-smorynski-9780387754802","title":"History of Mathematics","description":"1 An Initial Assignment I haven't taught the history of mathematics that often, but I do rather like the course. The chief drawbacks to teaching it are that i. it is a lot more work than teaching a regular mathematics course, and ii. in American colleges at least, the students taking the course are not mathematics majors but e- cation majors- and and in the past I had found education majors to be somewhat weak and unmotivated. The last time I taught the course, however, themajorityofthestudentsweregraduateeducationstudentsworkingtoward their master's degrees. I decided to challenge them right from the start: 1 Assignment. In An Outline of Set Theory, James Henle wrote about mat- matics: Every now and then it must pause to organize and re?ect on what it is and where it comes from. This happened in the sixth century B. C. when Euclid thought he had derived most of the mathematical results known at the time from ?ve postulates. Do a little research to ?nd as many errors as possible in the second sentence and write a short essay on them. Theresponsesfarexceededmyexpectations. Tobesure,someoftheund- graduates found the assignment unclear: I did not say how many errors they 2 were supposed to ?nd. But many of the students put their hearts and souls 1 MyapologiestoProf. Henle,atwhoseexpenseIpreviouslyhadalittlefunonthis matter. I used it again not because of any animosity I hold for him, but because I was familiar with it and, dealing with Euclid, it seemed appropriate for the start of my course.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51828489650449,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ GOOD \/ SBYB","offer_id":51828489879825,"sku":"CIN0387754806G","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52538610123025,"sku":"NLS9780387754802","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780387754802.jpg?v=1752755100"},{"product_id":"history-of-mathematics-book-craig-smorynski-9781441925930","title":"History of Mathematics","description":"1 An Initial Assignment I haven't taught the history of mathematics that often, but I do rather like the course. The chief drawbacks to teaching it are that i. it is a lot more work than teaching a regular mathematics course, and ii. in American colleges at least, the students taking the course are not mathematics majors but e- cation majors- and and in the past I had found education majors to be somewhat weak and unmotivated. The last time I taught the course, however, themajorityofthestudentsweregraduateeducationstudentsworkingtoward their master's degrees. I decided to challenge them right from the start: 1 Assignment. In An Outline of Set Theory, James Henle wrote about mat- matics: Every now and then it must pause to organize and re?ect on what it is and where it comes from. This happened in the sixth century B. C. when Euclid thought he had derived most of the mathematical results known at the time from ?ve postulates. Do a little research to ?nd as many errors as possible in the second sentence and write a short essay on them. Theresponsesfarexceededmyexpectations. Tobesure,someoftheund- graduates found the assignment unclear: I did not say how many errors they 2 were supposed to ?nd. But many of the students put their hearts and souls 1 MyapologiestoProf. Henle,atwhoseexpenseIpreviouslyhadalittlefunonthis matter. I used it again not because of any animosity I hold for him, but because I was familiar with it and, dealing with Euclid, it seemed appropriate for the start of my course.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52355642327313,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52355645767953,"sku":"NLS9781441925930","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781441925930.jpg?v=1758185215"},{"product_id":"logical-number-theory-i-book-craig-smorynski-9783540522362","title":"Logical Number Theory I","description":"Number theory as studied by the logician is the subject matter of the book. This first volume can stand on its own as a somewhat unorthodox introduction to mathematical logic for undergraduates, dealing with the usual introductory material: recursion theory, first-order logic, completeness, incompleteness, and undecidability. In addition, its second chapter contains the most complete logical discussion of Diophantine Decision Problems available anywhere, taking the reader right up to the frontiers of research (yet remaining accessible to the undergraduate). The first and third chapters also offer greater depth and breadth in logico-arithmetical matters than can be found in existing logic texts. Each chapter contains numerous exercises, historical and other comments aimed at developing the student's perspective on the subject, and a partially annotated bibliography.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52404395704593,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52404396130577,"sku":"NLS9783540522362","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540522362.jpg?v=1758764128"},{"product_id":"chapters-in-probability-book-craig-smorynski-9781848900677","title":"Chapters in Probability","description":"This book introduces elementary probability through its history, eschewing the usual drill in favour of a discussion of the problems that shaped the field's development. Numerous excerpts from the literature, both from the pioneers in the field and its commentators, some given new English translations, pepper the exposition. First, for the reader without a background in the Calculus, it offers a brief intuitive explanation of some of the concepts behind the notation occasionally used in the text, and, for those with a stronger background, it gives more detailed presentations of some of the more technical results discussed in the text. Special features include two appendices on the graphing calculator and on mathematical topics. The former begins with a short course on the use of the calculator to raise the reader up from the beginner to a more advanced level, and then finishes with some simulations of probabilistic experiments on the the calculator. The mathematical appendix likewise serves a dual purpose. The book should be accessible to anyone taking or about to take a course in the Calculus, and certainly is accessible to anyone who has already had such a course. It should be of special interest to teachers, statisticians, or anyone who uses probability or is interested in the history of mathematics or science in general.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52614342410513,"sku":"NLS9781848900677","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53084094857489,"sku":"NIN9781848900677","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781848900677.jpg?v=1761520955"},{"product_id":"self-reference-and-modal-logic-book-craig-smorynski-9780387962092","title":"Self-Reference and Modal Logic","description":"It is Sunday, the 7th of September 1930. The place is Konigsberg and the occasion is a small conference on the foundations of mathematics. Arend Heyting, the foremost disciple of L. E. J. Brouwer, has spoken on intuitionism; Rudolf Carnap of the Vienna Circle has expounded on logicism; Johann (formerly Janos and in a few years to be Johnny) von Neumann has explained Hilbert's proof theory-- the so-called formalism; and Hans Hahn has just propounded his own empiricist views of mathematics. The floor is open for general discussion, in the midst of which Heyting announces his satisfaction with the meeting. For him, the relationship between formalism and intuitionism has been clarified: There need be no war between the intuitionist and the formalist. Once the formalist has successfully completed Hilbert's programme and shown finitely that the idealised mathematics objected to by Brouwer proves no new meaningful statements, even the intuitionist will fondly embrace the infinite. To this euphoric revelation, a shy young man cautions According to the formalist conception one adjoins to the meaningful statements of mathematics transfinite (pseudo-')statements which in themselves have no meaning but only serve to make the system a well-rounded one just as in geometry one achieves a well- rounded system by the introduction of points at infinity.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52617429385489,"sku":"NLS9780387962092","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780387962092.jpg?v=1761530263"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-craig-smorynski.oembed","provider":"World of Books ","version":"1.0","type":"link"}