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# Topic: Mathematical practice

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 Mathematical proof - Wikipedia, the free encyclopedia In mathematics, a proof is a demonstration that, given certain axioms, some statement of interest is necessarily true. The distinction has led to much examination of current and historical mathematical practice, quasi-empiricism in mathematics, and so-called folk mathematics (in both senses of that term). The philosophy of mathematics is concerned with the role of language and logic in proofs, and mathematics as a language. en.wikipedia.org /wiki/Mathematical_proof   (549 words)

 Mathematical practice - Wikipedia, the free encyclopedia This distinction is considered especially important by adherents of quasi-empiricism in mathematics, which denies the possibility of foundations of mathematics and attempts to refocus attention on the ways in which mathematicians arrive at mathematical statements. The evolution of mathematical practice was slow, and some contributors to modern mathematics did not follow even the practice of their time, e.g. One motivation to study mathematical practice is that, despite much work in the 20th century, some still feel that the foundations of mathematics remain unclear and ambiguous. en.wikipedia.org /wiki/Mathematical_practice   (327 words)

 Mathematical practice: Definition and Links by Encyclopedian.com - All about Mathematical practice   (Site not responding. Last check: 2007-11-07) The term mathematical practice arose in the philosophy of mathematics to distinguish actual practices of working mathematicians (choices of theorems to prove, informal notations to persuade themselves and others that various steps in the final proof are formalizable, peer review and publication) from the final result: proven and published theorems. This distinction is considered especially important by adherents of quasi-empiricism in mathematics, a school in the philosophy of mathematics that denies the possibility of foundations of mathematics and attempts to refocus attention on the ways mathematical statements are arrived at. One motivation to study mathematical practice is that despite much work in the 20th century, the foundations of mathematics remain unclear and ambiguous. www.encyclopedian.com /ma/Mathematical-practice.html   (331 words)

 Encyclopedia: Mathematical practice   (Site not responding. Last check: 2007-11-07) Quasi-empiricism in mathematics is the movement in the philosophy of mathematics to reject as pointless the foundations problem in mathematics, and re-focus philosophers on mathematical practice itself, in particular relations with physics and social sciences. As the term is understood by mathematicians, folk mathematics or mathematical folklore means theorems, definitions, proofs, or mathematical facts or techniques that circulate among mathematicians by word-of-mouth but have not appeared in print, either in books or in scholarly journals. Categories: Philosophy of mathematics As the term is understood by mathematicians, folk mathematics or mathematical folklore means theorems, definitions, proofs, or mathematical facts or techniques that circulate among mathematicians by word-of-mouth but have not appeared in print, either in books or in scholarly journals. www.nationmaster.com /encyclopedia/mathematical-practice   (860 words)

 Wikinfo | Mathematics   (Site not responding. Last check: 2007-11-07) Mathematics (often abbreviated to math or, in British English, maths) is commonly defined as the study of patterns of structure, change, and space. In general the philosophy of mathematics one adopts has little effect on mathematical practice: mathematicians all over the world can rely on mathematics as a language even if there are arguments about the meaning or reliability of certain constructs or "words" or "phrases" used in any given "sentence". It is the practices, not the proofs, that define mathematics as a discipline, though the proofs remain persistent over time to a remarkable degree: Euclid's are still in use and are 2000 years old. www.wikinfo.org /wiki.php?title=Mathematics   (2233 words)

 Mathematical practice -- Facts, Info, and Encyclopedia article   (Site not responding. Last check: 2007-11-07) The modern mathematical practices are what distinguish modern professional mathematicians from older ideas of (Click link for more info and facts about folk mathematics) folk mathematics. Likewise there is contrast between the practices of (Greek philosopher and mathematician who proved the Pythagorean theorem; considered to be the first true mathematician (circa 580-500 BC)) Pythagoras and (Greek geometer (3rd century BC)) Euclid. One motivation to study mathematical practice is that, despite much work in the 20th century, some still feel that the (Click link for more info and facts about foundations of mathematics) foundations of mathematics remain unclear and ambiguous. www.absoluteastronomy.com /encyclopedia/m/ma/mathematical_practice.htm   (344 words)

 Steen: Twenty Questions about Mathematical Reasoning Mathematics teachers often claim that all types of critical thinking and problem solving are really examples of mathematical reasoning. Although mathematical performance generally involves a blend of skills, knowledge, procedures, understanding, reasoning, and application, the public mantra for improving mathematics education focuses on skills, knowledge, and performance–what students "know and are able to do." To this public agenda mathematics educators consistently add reasoning and understanding–why and how mathematics works as it does. Despite the dominance of proof as the methodology of advanced mathematics courses, contemporary advances in applied, computer-aided, and so-called "experimental" mathematics have restored to mathematical practice much of the free-wheeling spirit of earlier eras. www.stolaf.edu /people/steen/Papers/reason.html   (5493 words)

 Nat' Academies Press, Knowing and Learning Mathematics for Teaching: Proceedings of a Workshop (2001) Teachers who believe that mathematics is no more than a set of rules, a collection of techniques, or a list of vocabulary terms are less likely to see mathematical inquiry as relevant to the teaching process and, therefore, less likely to take advantage of teachable moments that fall outside of these definitions. Mathematics teacher educators are encouraged to study and articulate the connections that are most helpful for teachers. Mathematics teacher educators are encouraged to design experiences for prospective teachers and teachers to study and analyze “teachable moments” in the classroom (some where teachers capitalize on such moments and others where teachers miss teachable moments). www.nap.edu /books/0309072522/html/155.html   (3460 words)

 Mathematics in Kant's critical philosophy: Reflections on mathematical practice. Mathematics in Kant's critical philosophy: Reflections on mathematical practice. I aim to give a new reading of some of Kant's most important claims about mathematical cognition by examining them within the context of the eighteenth century mathematical practice with which he was engaged. In particular, I analyze the method of "constructing equations" and conclude that algebra was not conceived as an independent discipline with its own object of investigation, but rather was a method of reasoning about the constructible objects of arithmetic and geometry. repository.upenn.edu /dissertations/AAI9829986   (229 words)

 Geometrical Landscapes: The Voyages of Discovery and the Transformation of Mathematical Practice - Amir R. Alexander Mathematics, formerly praised for its logic, clarity, and inescapable truths, was for them a hazardous voyage in inhospitable geometrical lands. This was no coincidence: the heroic tales of exploration and discovery helped shape a new form of mathematical practice, complete with new questions, new acceptable answers, and new standards of evidence. It was this new vision of mathematics as a grand adventure that allowed for the development of the new techniques that led to the Newtonian calculus. www.sup.org /cgi-bin/search/getmoreinfo.cgi?bookid=3260+&q=quote   (409 words)

 Study of Teachers’ Pedagogical Content Knowledge in Mathematics The primary knowledge of instructional practice that was suggested from teachers was to engage in problem solving in cooperative small groups. The categories of teachers’ knowledge of instructional practice included: (a) instructing directly by Oral Explanation and demonstration; (b) enabling children to communicate and engage in problem solving in Cooperative Small Groups; (c) demonstrating the solution steps in a procedure, then having their students to Repeatedly Practice the steps. Teachers who had a limited view of how mathematical knowledge is acquired could alienate themselves from the reasonability of the subject matter structure in their teaching (Lampert, 1986). www.nku.edu /~sheffield/edithpbyd3.html   (1916 words)

 Making Mathematical Practice | Abstract   (Site not responding. Last check: 2007-11-07) This dissertation studies the culture of mathematical practice in Elizabethan England. As well as the disciplinary territory of mathematical practice, I also attend to its topography, to the places where the practitioners worked to master both nature and the manual labours of subordinates and workmen. Using these resources, the mathematical practitioners successfully created a public culture in which mathematics was promoted as worldly, morally safe and useful to both the civil and military order. www.mhs.ox.ac.uk /staff/saj/thesis/abstract.htm   (432 words)

 Mary E. Brenner   (Site not responding. Last check: 2007-11-07) A central theme of this volume is that mathematics classrooms need to become communities of practice, a theme that is common in current research on mathematics education. Although mathematics reform stipulates that mathematics classrooms should become contexts of authentic mathematical practice as done by mathematicians or other practitioners of mathematics such as engineers, classrooms do not typically incorporate such practitioners. Given the fact that mathematical achievement differs by gender and cultural group, it is surprising that differences in discourse patterns have been neglected by mathematics educators. www.aaanet.org /cae/aeq/br/lampert.htm   (940 words)

 STATSnetBASE: Statistical Sciences Online Traditional texts in mathematical statistics can seem - to some readers-heavily weighted with optimality theory of the various flavors developed in the 1940s and50s, and not particularly relevant to statistical practice. While mathematically rigorous, its focus is on providing a set of useful tools that allow students to understand the theoretical underpinnings of statistical methodology. The result reaches beyond "nice" mathematics to provide a balanced, practical text that brings life and relevance to a subject so often perceived as irrelevant and dry. www.statsnetbase.com /ejournals/books/book_summary/summary.asp?id=713   (199 words)

 Active Skim View of: Investigating Teaching Practice: What Mathematical Knowledge, Skills, and Sensibilities Does It ... One must be informed about human development, knowledgeable of mathematics content, curious about how mathematical knowledge is constructed, patient with the knowledge that understanding is developed over time, and possess a disposition towards learning and teaching that capitalizes on the dynamics of the learning environment—the people, their ideas and experiences, and the physical materials. Mathematics entailed in the task Participants identified several mathematics content areas embedded in the “Mixing Juice” task. A growing awareness of these issues has led to the development of curricular materials to support teacher learning of mathematics that attempt to connect that learning to the contexts of classrooms by embedding the mathematics into classroom contexts, students' work on mathematics, and teacher interactions about their own classroom mathematizations. www.nap.edu /nap-cgi/skimit.cgi?isbn=0309072522&chap=39-64   (1208 words)

 Amazon.com: Books: The Concepts and Practice of Mathematical Finance (Mathematics, Finance and Risk)   (Site not responding. Last check: 2007-11-07) An Introduction to the Mathematics of Financial Derivatives by Salih N. Neftci Joshi's "Concepts and Practice" serves a two fold purpose for a qaunt: it provides an additional voice and explanation of inescapably fundamental material, while bridging the gap of technical deployment for front line practitioners. In summary, Dr. Mark Joshi advances his excellent reputation as an intelligent, practical, and generous quant in offering "The Concepts and Practice of Mathematical Finance" and I recommend this book's wide adoption in graduate programs and its addition to reference libraries. www.amazon.com /exec/obidos/tg/detail/-/0521823552?v=glance   (2354 words)

 Geometrical Landscapes -- The Voyages of Discovery and the Transformation of Mathematical Practice -- Amir Alexander The Voyages of Discovery and the Transformation of Mathematical Practice This book argues that a new way of speaking of mathematics and describing it emerged at the end of the sixteenth century. Moving into an uncharted field, namely mathematics and the turn toward infinitesimals, Alexander develops a controversial argument--and that is a tribute to its originality. www.frontlist.com /detail/0804732604   (351 words)

 Linear logic in mathematical practice   (Site not responding. Last check: 2007-11-07) I am looking for papers addressing the role of linear logic in mathematical practice. Of particular interest would be extracts from the mathematical literature illustrating either the actual use of linear logic or the improvement possible with linear logic. Assessments of the benefits of linear logic for working mathematicians would also be of interest. www.seas.upenn.edu /~sweirich/types/archive/1996/msg00118.html   (54 words)

 Alexander, Amir R. Geometrical Landscapes: The Voyages of Discovery and the Transformation of Mathematical Practice   (Site not responding. Last check: 2007-11-07) Although the book is written by a philosophical mathematician and primarily aimed at academic mathematicians, there is much within its scope of interest to the student of early exploration and the cartography resulting from this exploration. Its value to the historian lies in the fact that the converse of this theme is also covered, to show how the advances in mathematics in the sixteenth century had a significant effect on exploration and the development of accurate cartography resulting from these explorations. The book treats this relationship between the advances in mathematics and the ocean navigation of early explorers chronologically from Columbus’s voyage in 1492 to the voyages of the late seventeenth century. www.sochistdisc.org /2003_book_reviews/alexander.htm   (850 words)

 The Concepts and Practice of Mathematical Finance (Mathematics, Finance and Risk)   (Site not responding. Last check: 2007-11-07) What was once a cross-over subfield of finance with a veneer of mathematics is now a field unto itself, and hence, in the past decade there have been an explosion of books which often replicate or restate what has been said before with little new to add. Also, there remains an unforgiving gap between introductory texts that are too superficial and specialists' mathematics books that are rigorous and difficult works beyond the commitment for mastery of the busy, intelligent, practical front-line quant. That is why they call it "work." Therefore the practical quant should look to this text as a reference guidebook in a tool box. 494042.onlinesportdiscount.com /3439343034322d312d30353231383233353532.html   (1668 words)

 Amazon.ca: Books: The Concepts and Practice of Mathematical Finance   (Site not responding. Last check: 2007-11-07) Finding the right level of mathematical sophistication is a difficult balancing act in which it is impossible to please all readers. Here, the author has had a clear vision that the principal audience is the practising or potential quantitative analyst (or quant) and writes accordingly; it is impossible to do better than taking an approach of this sort. Integrated into this mathematical work is a good deal of information about how markets, banks and other corporations operate in practice, not found in more academically-oriented books. www.amazon.ca /exec/obidos/ASIN/0521823552   (1129 words)

 ACM Transactions on Mathematical Software The Transactions on Mathematical Software (TOMS) is part of the family of journals produced by the Association for Computing (ACM). We maintain a list of Web resources for research in mathematical software for the convenience of TOMS readers. These web pages are provided courtesy of the Guide to Available Mathematical Software project of the National Institute of Standards and Technology; NIST Privacy Policy. math.nist.gov /toms/Overview.html   (280 words)

 Intuitionistic Logic Philosophically, intuitionism differs from logicism by treating logic as a part of mathematics rather than as the foundation of mathematics; from finitism by allowing (constructive) reasoning about infinite collections; and from platonism by viewing mathematical objects as mental constructs with no independent ideal existence. Hilbert's formalist program, to justify classical mathematics by reducing it to a formal system whose consistency should be established by finitistic (hence constructive) means, was the most powerful contemporary rival to Brouwer's developing intuitionism. Brouwer, L. J., 1923, 1954, "On the significance of the principle of excluded middle in mathematics, especially in function theory," "Addenda and corrigenda," and "Further addenda and corrigenda," English translation in van Heijenoort, ed., 1967: 334-345. plato.stanford.edu /entries/logic-intuitionistic   (6042 words)

 Amazon.co.uk: Books: The Concepts and Practice of Mathematical Finance (Mathematic, Finance & Risk S.)   (Site not responding. Last check: 2007-11-07) The author brings to this book a blend of practical experience and rigorous mathematical background, and supplies here the working knowledge needed to become a good quantitative analyst. Joshi's "Concepts and Practice" serves a two fold purpose: it provides an additional voice and explanation of inescapably fundamental material, while bridging the gap of technical deployment for front line practitioners. It manages to engage the mathematical interest of the reader, without ever loosing its pace and focus; learning from it is a genuine pleasure. www.amazon.co.uk /exec/obidos/ASIN/0521823552   (2062 words)

 Mathematical Modeling Today The applications of mathematical methods in management and economics today are so manifold that it is difficult to find a single person who is aware of their full scope. One is that students often believe that mathematics can be learned simply by studying a book. A book can get one started, but learning to work problems is like learning to play basketball or play the piano--it requires practice, practice, practice. mat.gsia.cmu.edu /QUANT/NOTES/chap0/node7.html   (323 words)

 The Concepts and Practice of Mathematical Finance Both Baxter and Rennie and Neftci focus more on exploring advanced mathematical concepts or the theory underlying financial engineering. About half the book is dedicated to practical discussions of the pricing of exotics, interest rate derivatives, stochastic volatility and smile dynamics. A positive aspect of the book is that it does illustrate plenty of practical financial engineering in a manner that will appeal to readers with a firm understanding of calculus and probability and passing familiarity with more advanced math and basic financial engineering. www.riskbook.com /titles/joshi_m_2003.htm   (396 words)

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