Robert Goldstone, David Landy, and Ji Y Son
- Published in print:
- 2008
- Published Online:
- March 2012
- ISBN:
- 9780199217274
- eISBN:
- 9780191696060
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199217274.003.0016
- Subject:
- Psychology, Cognitive Psychology
This chapter describes two separate lines of research on college students' performance on scientific and mathematical reasoning tasks. The first research line studies how students transfer scientific ...
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This chapter describes two separate lines of research on college students' performance on scientific and mathematical reasoning tasks. The first research line studies how students transfer scientific principles governing complex systems across superficially dissimilar domains. The second line studies how people solve algebra problems. Consistent with an embodied perspective on cognition, both lines show strong influences of perception on cognitive acts that are often associated with amodal, symbolic thought, namely cross-domain transfer and mathematical manipulation.Less
This chapter describes two separate lines of research on college students' performance on scientific and mathematical reasoning tasks. The first research line studies how students transfer scientific principles governing complex systems across superficially dissimilar domains. The second line studies how people solve algebra problems. Consistent with an embodied perspective on cognition, both lines show strong influences of perception on cognitive acts that are often associated with amodal, symbolic thought, namely cross-domain transfer and mathematical manipulation.
Odo Diekmann, Hans Heesterbeek, and Tom Britton
- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691155395
- eISBN:
- 9781400845620
- Item type:
- book
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691155395.001.0001
- Subject:
- Biology, Disease Ecology / Epidemiology
Mathematical modeling is critical to our understanding of how infectious diseases spread at the individual and population levels. This book gives readers the necessary skills to correctly formulate ...
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Mathematical modeling is critical to our understanding of how infectious diseases spread at the individual and population levels. This book gives readers the necessary skills to correctly formulate and analyze mathematical models in infectious disease epidemiology, and is the first treatment of the subject to integrate deterministic and stochastic models and methods. The book fully explains how to translate biological assumptions into mathematics to construct useful and consistent models, and how to use the biological interpretation and mathematical reasoning to analyze these models. It shows how to relate models to data through statistical inference, and how to gain important insights into infectious disease dynamics by translating mathematical results back to biology. This comprehensive and accessible book also features numerous detailed exercises throughout; full elaborations to all exercises are provided. The book covers the latest research in mathematical modeling of infectious disease epidemiology; it integrates deterministic and stochastic approaches; and teaches skills in model construction, analysis, inference, and interpretation.Less
Mathematical modeling is critical to our understanding of how infectious diseases spread at the individual and population levels. This book gives readers the necessary skills to correctly formulate and analyze mathematical models in infectious disease epidemiology, and is the first treatment of the subject to integrate deterministic and stochastic models and methods. The book fully explains how to translate biological assumptions into mathematics to construct useful and consistent models, and how to use the biological interpretation and mathematical reasoning to analyze these models. It shows how to relate models to data through statistical inference, and how to gain important insights into infectious disease dynamics by translating mathematical results back to biology. This comprehensive and accessible book also features numerous detailed exercises throughout; full elaborations to all exercises are provided. The book covers the latest research in mathematical modeling of infectious disease epidemiology; it integrates deterministic and stochastic approaches; and teaches skills in model construction, analysis, inference, and interpretation.
Nicholas Griffin
- Published in print:
- 1991
- Published Online:
- March 2012
- ISBN:
- 9780198244530
- eISBN:
- 9780191680786
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198244530.003.0007
- Subject:
- Philosophy, History of Philosophy
This chapter discusses Russell's attempts to fashion a Kantian philosophy of pure mathematics where the concept of quantity played a central role. The chapter also introduces another of Russell's ...
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This chapter discusses Russell's attempts to fashion a Kantian philosophy of pure mathematics where the concept of quantity played a central role. The chapter also introduces another of Russell's work, ‘An Analysis of Mathematical Reasoning’.Less
This chapter discusses Russell's attempts to fashion a Kantian philosophy of pure mathematics where the concept of quantity played a central role. The chapter also introduces another of Russell's work, ‘An Analysis of Mathematical Reasoning’.
Ofer Gal and Raz Chen-Morris
- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780226923987
- eISBN:
- 9780226923994
- Item type:
- chapter
- Publisher:
- University of Chicago Press
- DOI:
- 10.7208/chicago/9780226923994.003.0008
- Subject:
- History, History of Science, Technology, and Medicine
This chapter focuses on the persona of the new savant during the baroque period. It relates the story of how Princess Elisabeth of Bohemia sought the advice of Rene Descartes whom she considered the ...
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This chapter focuses on the persona of the new savant during the baroque period. It relates the story of how Princess Elisabeth of Bohemia sought the advice of Rene Descartes whom she considered the best doctor for her soul. It discusses Descartes’ recommendation of mathematics to Princess Elisabeth as a means to exercise the imagination and achieve the anxiously sought balance between body and soul, desire, and reason. This chapter also considers Descartes’ realization that imagination was as essential to morals as it was to mathematical reasoning.Less
This chapter focuses on the persona of the new savant during the baroque period. It relates the story of how Princess Elisabeth of Bohemia sought the advice of Rene Descartes whom she considered the best doctor for her soul. It discusses Descartes’ recommendation of mathematics to Princess Elisabeth as a means to exercise the imagination and achieve the anxiously sought balance between body and soul, desire, and reason. This chapter also considers Descartes’ realization that imagination was as essential to morals as it was to mathematical reasoning.
Michael Siegal
- Published in print:
- 2010
- Published Online:
- March 2012
- ISBN:
- 9780199582884
- eISBN:
- 9780191702358
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199582884.003.0006
- Subject:
- Psychology, Developmental Psychology
To characterize and act upon the world of objects, children in every culture count. Counting is as natural as walking and talking – an adaptive specialization for numerical problem solving. But are ...
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To characterize and act upon the world of objects, children in every culture count. Counting is as natural as walking and talking – an adaptive specialization for numerical problem solving. But are children's number abilities tied to understanding the meaning of the words that we use for counting? This chapter examines related issues: whether children's early theory of number is limited to the discrete whole numbers that are used for counting or whether they are prompted to accommodate their theory to take into account numerical relations which fill the gap between integers. It also examines children in aboriginal cultures, such as those found in Brazil and Australia, who acquire a language with few words for counting, taking into account their mathematical reasoning.Less
To characterize and act upon the world of objects, children in every culture count. Counting is as natural as walking and talking – an adaptive specialization for numerical problem solving. But are children's number abilities tied to understanding the meaning of the words that we use for counting? This chapter examines related issues: whether children's early theory of number is limited to the discrete whole numbers that are used for counting or whether they are prompted to accommodate their theory to take into account numerical relations which fill the gap between integers. It also examines children in aboriginal cultures, such as those found in Brazil and Australia, who acquire a language with few words for counting, taking into account their mathematical reasoning.
Niccolo Guicciardini
- Published in print:
- 2009
- Published Online:
- August 2013
- ISBN:
- 9780262013178
- eISBN:
- 9780262258869
- Item type:
- book
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262013178.001.0001
- Subject:
- History, History of Science, Technology, and Medicine
Historians of mathematics have devoted considerable attention to Isaac Newton’s work on algebra, series, fluxions, quadratures, and geometry. This book examines a critical aspect of Newton’s work ...
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Historians of mathematics have devoted considerable attention to Isaac Newton’s work on algebra, series, fluxions, quadratures, and geometry. This book examines a critical aspect of Newton’s work that has not been tightly connected to his actual practice: His philosophy of mathematics. Newton aimed to inject certainty into natural philosophy by deploying mathematical reasoning (titling his main work The Mathematical Principles of Natural Philosophy most probably to highlight a stark contrast to Descartes’ Principles of Philosophy). To that end he paid concerted attention to method, particularly in relation to the issue of certainty, participating in contemporary debates on the subject and elaborating his own answers. The author shows how Newton carefully positioned himself against two giants in the “common” and “new” analysis, Descartes and Leibniz. Although his work was in many ways disconnected from the traditions of Greek geometry, Newton portrayed himself as antiquity’s legitimate heir, thereby distancing himself from the moderns. The author reconstructs Newton’s own method by extracting it from his concrete practice and not solely by examining his broader statements about such matters. He examines the full range of Newton’s works, from his early treatises on series and fluxions to the late writings, which were produced in direct opposition to Leibniz. The complex interactions between Newton’s understanding of method and his mathematical work then reveal themselves through the author’s analysis of selected examples. The book uncovers what mathematics was for Newton, and what being a mathematician meant to him.Less
Historians of mathematics have devoted considerable attention to Isaac Newton’s work on algebra, series, fluxions, quadratures, and geometry. This book examines a critical aspect of Newton’s work that has not been tightly connected to his actual practice: His philosophy of mathematics. Newton aimed to inject certainty into natural philosophy by deploying mathematical reasoning (titling his main work The Mathematical Principles of Natural Philosophy most probably to highlight a stark contrast to Descartes’ Principles of Philosophy). To that end he paid concerted attention to method, particularly in relation to the issue of certainty, participating in contemporary debates on the subject and elaborating his own answers. The author shows how Newton carefully positioned himself against two giants in the “common” and “new” analysis, Descartes and Leibniz. Although his work was in many ways disconnected from the traditions of Greek geometry, Newton portrayed himself as antiquity’s legitimate heir, thereby distancing himself from the moderns. The author reconstructs Newton’s own method by extracting it from his concrete practice and not solely by examining his broader statements about such matters. He examines the full range of Newton’s works, from his early treatises on series and fluxions to the late writings, which were produced in direct opposition to Leibniz. The complex interactions between Newton’s understanding of method and his mathematical work then reveal themselves through the author’s analysis of selected examples. The book uncovers what mathematics was for Newton, and what being a mathematician meant to him.
