Search results for 'Mathematical analysis' (try it on Scholar)

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  1. Kajsa Bråting (2012). Ambiguities of Fundamental Concepts in Mathematical Analysis During the Mid-Nineteenth Century. Foundations of Science 17 (4):301-320.score: 90.0
    In this paper we consider the major development of mathematical analysis during the mid-nineteenth century. On the basis of Jahnke’s (Hist Math 20(3):265–284, 1993 ) distinction between considering mathematics as an empirical science based on time and space and considering mathematics as a purely conceptual science we discuss the Swedish nineteenth century mathematician E.G. Björling’s general view of real- and complexvalued functions. We argue that Björling had a tendency to sometimes consider mathematical objects in a naturalistic way. (...)
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  2. David S. G. Stirling (2009). Mathematical Analysis and Proof. Horwood Pub..score: 87.0
    This fundamental and straightforward text addresses a weakness observed among present-day students, namely a lack of familiarity with formal proof. Beginning with the idea of mathematical proof and the need for it, associated technical and logical skills are developed with care and then brought to bear on the core material of analysis in such a lucid presentation that the development reads naturally and in a straightforward progression. Retaining the core text, the second edition has additional worked examples which (...)
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  3. Nicolas Fillion & Robert M. Corless (2014). On the Epistemological Analysis of Modeling and Computational Error in the Mathematical Sciences. Synthese 191 (7):1451-1467.score: 63.0
    Interest in the computational aspects of modeling has been steadily growing in philosophy of science. This paper aims to advance the discussion by articulating the way in which modeling and computational errors are related and by explaining the significance of error management strategies for the rational reconstruction of scientific practice. To this end, we first characterize the role and nature of modeling error in relation to a recipe for model construction known as Euler’s recipe. We then describe a general model (...)
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  4. G. C. Smith (1983). Boole's Annotations on 'the Mathematical Analysis of Logic'. History and Philosophy of Logic 4 (1-2):27-39.score: 60.0
    George Boole collected ideas for the improvement of his Mathematical analysis of logic(1847) on interleaved copies of that work. Some of the notes on the interleaves are merely minor changes in explanation. Others amount to considerable extension of method in his mathematical approach to logic. In particular, he developed his technique in solving simultaneous elective equations and handling hypotheticals and elective functions. These notes and extensions provided a source for his later book Laws of thought(1854).
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  5. Thomas Mormann, Mathematical Aspects of Similarity and Quasi-Analysis - Order, Topology, and Sheaves.score: 57.0
    The concept of similarity has had a rather mixed reputation in philosophy and the sciences. On the one hand, philosophers such as Goodman and Quine emphasized the „logically repugnant“ and „insidious“ character of the concept of similarity that allegedly renders it inaccessible for a proper logical analysis. On the other hand, a philosopher such as Carnap assigned a central role to similarity in his constitutional theory. Moreover, the importance and perhaps even indispensibility of the concept of similarity for many (...)
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  6. Geoffrey Hellman (2006). Mathematical Pluralism: The Case of Smooth Infinitesimal Analysis. [REVIEW] Journal of Philosophical Logic 35 (6):621 - 651.score: 54.0
    A remarkable development in twentieth-century mathematics is smooth infinitesimal analysis ('SIA'), introducing nilsquare and nilpotent infinitesimals, recovering the bulk of scientifically applicable classical analysis ('CA') without resort to the method of limits. Formally, however, unlike Robinsonian 'nonstandard analysis', SIA conflicts with CA, deriving, e.g., 'not every quantity is either = 0 or not = 0.' Internally, consistency is maintained by using intuitionistic logic (without the law of excluded middle). This paper examines problems of interpretation resulting from this (...)
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  7. D. L. Herr (1938). A Mathematical Analysis of the Experiments in Extra-Sensory Perception. Journal of Experimental Psychology 22 (5):491.score: 51.0
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  8. C. P. Bhunu, W. Garira & G. Magombedze (2009). Mathematical Analysis of a Two Strain Hiv/Aids Model with Antiretroviral Treatment. Acta Biotheoretica 57 (3).score: 48.0
    A two strain HIV/AIDS model with treatment which allows AIDS patients with sensitive HIV-strain to undergo amelioration is presented as a system of non-linear ordinary differential equations. The disease-free equilibrium is shown to be globally asymptotically stable when the associated epidemic threshold known as the basic reproduction number for the model is less than unity. The centre manifold theory is used to show that the sensitive HIV-strain only and resistant HIV-strain only endemic equilibria are locally asymptotically stable when the associated (...)
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  9. Reinhard Kahle (2002). Mathematical Proof Theory in the Light of Ordinal Analysis. Synthese 133 (1/2):237 - 255.score: 48.0
    We give an overview of recent results in ordinal analysis. Therefore, we discuss the different frameworks used in mathematical proof-theory, namely "subsystem of analysis" including "reverse mathematics", "Kripke-Platek set theory", "explicit mathematics", "theories of inductive definitions", "constructive set theory", and "Martin-Löf's type theory".
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  10. Ting-Chao Chou (2008). A New Look at the Ancient Asian Philosophy Through Modern Mathematical and Topological Scientific Analysis. Proceedings of the Xxii World Congress of Philosophy 2:21-39.score: 48.0
    The unified theory of dose and effect, as indicated by the median-effect equation for single and multiple entities and for the first and higher order kinetic/dynamic, has been established by T.C. Chou and it is based on the physical/chemical principle of the massaction law (J. Theor. Biol. 59: 253-276, 1976 (質量作用中效定理) and Pharmacological Rev. 58: 621-681, 2006) (普世中效指數定理). The theory was developed by the principle of mathematical induction and deduction (數學演繹歸納法). Rearrangements of the median-effect equation lead to Michaelis-Menten, Hill, (...)
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  11. Marvin R. G. Schiller (2013). Granularity Analysis for Mathematical Proofs. Topics in Cognitive Science 5 (2):251-269.score: 48.0
    Mathematical proofs generally allow for various levels of detail and conciseness, such that they can be adapted for a particular audience or purpose. Using automated reasoning approaches for teaching proof construction in mathematics presupposes that the step size of proofs in such a system is appropriate within the teaching context. This work proposes a framework that supports the granularity analysis of mathematical proofs, to be used in the automated assessment of students' proof attempts and for the presentation (...)
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  12. V. V. Cifarelli & V. Sevim (2014). Examining the Role of Re-Presentation in Mathematical Problem Solving: An Application of Ernst von Glasersfeld's Conceptual Analysis. Constructivist Foundations 9 (3):360-369.score: 48.0
    Context: The paper utilizes a conceptual analysis to examine the development of abstract conceptual structures in mathematical problem solving. In so doing, we address two questions: 1. How have the ideas of RC influenced our own educational theory? and 2. How has our application of the ideas of RC helped to improve our understanding of the connection between teaching practice and students’ learning processes? Problem: The paper documents how Ernst von Glasersfeld’s view of mental representation can be illustrated (...)
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  13. G. F. Roach, I. G. Stratis & A. N. Yannacopoulos (2012). Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics. Princeton University Press.score: 48.0
    But a body of rigorous mathematical theory has also gradually developed, and this is the first book to present that theory.
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  14. P. F. Strawson (1950). The Mathematical Analysis of Logic. By George Boole. Pp. 82. (Oxford: Basil Black Well. 1948. Price 7s. 6d.). Philosophy 25 (95):350-.score: 45.0
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  15. Wiebke Petersen (2004). A Mathematical Analysis of Pānini's Śivasūtras. Journal of Logic, Language and Information 13 (4):471-489.score: 45.0
    In Pninis grammar of Sanskrit one finds the ivastras, a table which defines the natural classes of phonological segments in Sanskrit by intervals. We present a formal argument which shows that, using his representation method, Pninis way of ordering the phonological segments to represent the natural classes is optimal. The argument is based on a strictly set-theoretical point of view depending only on the set of natural classes and does not explicitly take into account the phonological features of the segments, (...)
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  16. C. West Churchman (1949). Book Review:The Mathematical Analysis of Logic George Boole. [REVIEW] Philosophy of Science 16 (1):88-.score: 45.0
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  17. Alonzo Church (1948). Review: George Boole, The Mathematical Analysis of Logic, Being an Essay Towards a Calculus of Deductive Reasoning. [REVIEW] Journal of Symbolic Logic 13 (4):216-216.score: 45.0
  18. William M. O'Fallon, Richard I. Walker & H. Robert Van Der Vaart (1971). The Study of Granulocyte Kinetics by Mathematical Analysis of DNA Labelling. Acta Biotheoretica 20 (3-4).score: 45.0
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  19. Risto Vilkko (2004). George Boole. The Mathematical Analysis of Logic. Being an Essay Towards a Calculus of Deductive Reasoning by George Boole—Die Mathematische Analyse der Logik. Der Versuch Eines Kalküls des Deduktiven Schließens von George Boole, Schriftenreihe Zur Geistes-Und Kulturgeschichte: Texte Und Dokumente. Hallescher Verlag, Halle, Saale, 2001, 195 Pp. [REVIEW] Bulletin of Symbolic Logic 10 (1):108-109.score: 45.0
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  20. Eliahu Shamir (1968). Review: Joachim Lambek, The Mathematics of Sentence Structure; Joachim Lambek, Contributions to a Mathematical Analysis of the English Verb-Phrase; Joachim Lambek, Structure of Languages and its Mathematical Aspects. [REVIEW] Journal of Symbolic Logic 33 (4):627-628.score: 45.0
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  21. George Boole (1948). The Mathematical Analysis of Logic. Philosophical Library.score: 45.0
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  22. J. Houska (1981). The Principles of Mathematical-Analysis in Bolzanos Work in Reference to the Scientific Development of His Time. Filosoficky Casopis 29 (6):933-941.score: 45.0
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  23. C. A. Jimenez (forthcoming). Mathematical Analysis and Analytical Science. Boston Studies in the Philosophy of Science.score: 45.0
     
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  24. A. Moretto (1991). The'theorie Des Fonctions Analytiques'of Lagrange and the Problem of Being Rigorous in Demonstrations of Mathematical-Analysis. Verifiche: Rivista Trimestrale di Scienze Umane 20 (1-2):83-122.score: 45.0
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  25. N. A. Shanin (2001). On a Finitary Version of Mathematical Analysis. Annals of Pure and Applied Logic 113 (1-3):261-295.score: 45.0
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  26. Thomas L. Saaty (1959). Mathematical Methods of Operations Research. New York, Mcgraw-Hill.score: 40.0
    This text is an ideal introduction for students to the basic mathematics of operations research as well as a valuable source of references to early literature ...
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  27. Jaakko Hintikka (2011). Method of Analysis: A Paradigm of Mathematical Reasoning? History and Philosophy of Logic 33 (1):49 - 67.score: 39.0
    The ancient Greek method of analysis has a rational reconstruction in the form of the tableau method of logical proof. This reconstruction shows that the format of analysis was largely determined by the requirement that proofs could be formulated by reference to geometrical figures. In problematic analysis, it has to be assumed not only that the theorem to be proved is true, but also that it is known. This means using epistemic logic, where instantiations of variables are (...)
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  28. Andrés Rivadulla (1991). Mathematical Statistics and Metastatistical Analysis. Erkenntnis 34 (2):211 - 236.score: 39.0
    This paper deals with meta-statistical questions concerning frequentist statistics. In Sections 2 to 4 I analyse the dispute between Fisher and Neyman on the so called logic of statistical inference, a polemic that has been concomitant of the development of mathematical statistics. My conclusion is that, whenever mathematical statistics makes it possible to draw inferences, it only uses deductive reasoning. Therefore I reject Fisher's inductive approach to the statistical estimation theory and adhere to Neyman's deductive one. On the (...)
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  29. Michel J. Blais (1989). A Pragmatic Analysis of Mathematical Realism and Intuitionism. Philosophia Mathematica (1):61-85.score: 36.0
  30. Joseph W. Dauben (2003). Mathematics, Ideology, and the Politics of Infinitesimals: Mathematical Logic and Nonstandard Analysis in Modern China. History and Philosophy of Logic 24 (4):327-363.score: 36.0
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  31. Paul Humphreys (2013). Data Analysis: Models or Techniques? [REVIEW] Foundations of Science 18 (3):579-581.score: 36.0
    In this commentary to Napoletani et al. (Found Sci 16:1–20, 2011), we argue that the approach the authors adopt suggests that neural nets are mathematical techniques rather than models of cognitive processing, that the general approach dates as far back as Ptolemy, and that applied mathematics is more than simply applying results from pure mathematics.
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  32. Hans-Jürgen Engfer (1983). Philosophy as Analysis. Studies of the Development of Philosophical Conceptions of Analysis as Influenced by Mathematical Methodology in the 17th and Early 18th Centuries. [REVIEW] Philosophy and History 16 (2):107-108.score: 36.0
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  33. Yvon Gauthier (1985). The Logical Analysis of Mathematical Physics. Journal for General Philosophy of Science 16 (2):251-260.score: 36.0
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  34. Saunders MacLane (1935). A Logical Analysis of Mathematical Structure. The Monist 45 (1):118-130.score: 36.0
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  35. M. Machover (1996). Review: Joseph Warren Dauben. Abraham Robinson: The Creation of Nonstandard Analysis: A Personal and Mathematical Odyssey. [REVIEW] British Journal for the Philosophy of Science 47 (1):137-140.score: 36.0
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  36. Thomas M. Norton-Smith (1991). A Note on Philip Kitcher's Analysis of Mathematical Truth. Notre Dame Journal of Formal Logic 33 (1):136-139.score: 36.0
  37. D. N. Hoover (1990). Albeverio Sergio, Fenstad Jens Erik, HØEgh-Krohn Raphael, and Lindstrom Tom. Nonstandard Methods in Stochastic Analysis and Mathematical Physics. Pure and Applied Mathematics, Vol. 122. Academic Press, Orlando Etc. 1986, Xi+ 514 Pp. [REVIEW] Journal of Symbolic Logic 55 (1):362-363.score: 36.0
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  38. Saunders Mac Lane (1935). A Logical Analysis of Mathematical Structure. The Monist 45 (1):118 - 130.score: 36.0
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  39. William Brown (1910). Note on a Quantitative Analysis of Mathematical Intelligence. Journal of Philosophy, Psychology and Scientific Methods 7 (19):526-528.score: 36.0
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  40. Peter Hylton (2008). Propositions, Functions, and Analysis: Selected Essays on Russell's Philosophy. OUP Oxford.score: 36.0
    The work of Bertrand Russell had a decisive influence on the emergence of analytic philosophy, and on its subsequent development. The essays collected in this volume, by one of the leading authorities on Russell's philosophy, all aim at recapturing and articulating aspects of Russell's philosophical vision during his most influential and important period, the two decades following his break with Idealism in 1899. One theme of the collection concerns Russell's views about propositions and their analysis, and the relation of (...)
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  41. Georg Kreisel (1966). Review: N. A. Sanin, On the Constructive Interpretation of Mathematical Judgments; S. C. Kleene, A Formal System of Intuitionistic Analysis. [REVIEW] Journal of Symbolic Logic 31 (2):258-261.score: 36.0
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  42. Claude Laflamme (2001). Bartoszynski Tomek. On the Structure of Measurable Filters on a Countable Set. Real Analysis Exchange, Vol. 17 No. 2 (1992), Pp. 681–701. Bartoszynski Tomek and Shelah Saharon. Intersection of Archive for Mathematical Logic, Vol. 31 (1992), Pp. 221–226. Bartoszynski Tomek and Judah Haim. Measure and Category—Filters on Ω. Set Theory of the Continuum, Edited by Judah H., Just W., and Woodin H., Mathematical Sciences Research Institute Publications, Vol. 26, Springer-Verlag, New York, Berlin, Heidelberg ... [REVIEW] Bulletin of Symbolic Logic 7 (3):388-389.score: 36.0
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  43. José Pierrez & Xavier Ronot (1992). Flow Cytometric Analysis of the Cell Cycle: Mathematical Modeling and Biological Interpretation. Acta Biotheoretica 40 (2-3).score: 36.0
    Estimation of the repartition of asynchronous cells in the cell cycle can be explained by two hypotheses:– - the cells are supposed to be distributed into three groups: cells with a 2c DNA content (G0/1 phase), cells with a 4c DNA content (G2+M phase) and cells with a DNA content ranging from 2c to 4c (S phase); – - there is a linear relationship between the amount of fluorescence emitted by the fluorescent probe which reveals the DNA and the DNA (...)
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  44. Oliver Aberth (1991). Pour-El Marian B. And Richards J. Ian. Computability in Analysis and Physics. Perspectives in Mathematical Logic. Springer-Verlag, Berlin, Heidelberg, New York, Etc., 1989, Xi+ 206 Pp. [REVIEW] Journal of Symbolic Logic 56 (2):749-750.score: 36.0
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  45. Andrzej Blikle (1964). Review: A. A. Markov, Mathematical Logic and Numerical Analysis. [REVIEW] Journal of Symbolic Logic 29 (4):209-209.score: 36.0
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  46. Niccolò Guicciardini (2002). Analysis and Synthesis in Newton's Mathematical Work. In I. Bernard Cohen & George E. Smith (eds.), The Cambridge Companion to Newton. Cambridge University Press.score: 36.0
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  47. Joseph Warren Dauben & Moshe Machover (1996). Abraham Robinson: The Creation of Nonstandard Analysis: A Personal and Mathematical Odyssey. British Journal for the Philosophy of Science 47 (1):137-140.score: 36.0
     
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  48. Antony Eagle (2008). Mathematics and Conceptual Analysis. Synthese 161 (1):67–88.score: 33.0
    Gödel argued that intuition has an important role to play in mathematical epistemology, and despite the infamy of his own position, this opinion still has much to recommend it. Intuitions and folk platitudes play a central role in philosophical enquiry too, and have recently been elevated to a central position in one project for understanding philosophical methodology: the so-called ‘Canberra Plan’. This philosophical role for intuitions suggests an analogous epistemology for some fundamental parts of mathematics, which casts a number (...)
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  49. Vasco Brattka & Guido Gherardi (2011). Effective Choice and Boundedness Principles in Computable Analysis. Bulletin of Symbolic Logic 17 (1):73-117.score: 33.0
    In this paper we study a new approach to classify mathematical theorems according to their computational content. Basically, we are asking the question which theorems can be continuously or computably transferred into each other? For this purpose theorems are considered via their realizers which are operations with certain input and output data. The technical tool to express continuous or computable relations between such operations is Weihrauch reducibility and the partially ordered degree structure induced by it. We have identified certain (...)
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  50. Peter Hylton (2005/2008). Propositions, Functions, and Analysis: Selected Essays on Russell's Philosophy. Oxford University Press.score: 33.0
    The work of Bertrand Russell had a decisive influence on the emergence of analytic philosophy, and on its subsequent development. The prize-winning Russell scholar Peter Hylton presents here some of his most celebrated essays from the last two decades, all of which strive to recapture and articulate Russell's monumental vision. Relating his work to that of other philosophers, particularly Frege and Wittgenstein, and featuring a previously unpublished essay and a helpful new introduction, the volume will be essential for anyone engaged (...)
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