Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics
Dover Publications (1951)
| Abstract | "With exceptional clarity, but with no evasion of essential ideas, the author outlines the fundamental structure of mathematics."--Carl B. Boyer, Brooklyn College. This enlightening survey of mathematical concept formation holds a natural appeal to philosophically minded readers, and no formal training in mathematics is necessary to appreciate its clear exposition. Contents include examinations of arithmetic and geometry; the rigorous construction of the theory of integers; the rational numbers and their foundation in arithmetic; and the rigorous construction of elementary arithmetic. Advanced topics encompass the principle of complete induction; the limit and point of accumulation; operating with sequences and differential quotient; remarkable curves; real numbers and ultrareal numbers; and complex and hypercomplex numbers. 1959 ed. 27 Figures. Index. | |||||||||
| Keywords | Mathematics Philosophy Number concept | |||||||||
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| Buy the book | $14.02 direct from Amazon (7% off) Amazon page | |||||||||
| Call number | QA9.W33213 2003 | |||||||||
| ISBN(s) | 0486428044 9780486428048 | |||||||||
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Robert Rogers (1964). Mathematical and Philosophical Analyses. Philosophy of Science 31 (3):255-264.
M. Giaquinto (2007). Visual Thinking in Mathematics: An Epistemological Study. Oxford University Press.
Kristina Engelhard & Peter Mittelstaedt (2008). Kant's Theory of Arithmetic: A Constructive Approach? Journal for General Philosophy of Science 39 (2):245 - 271.
Charles Sayward (2002). A Conversation About Numbers and Knowledge. American Philosophical Quarterly 39 (3):275-287.
Andrew Arana (2007). Review of D. Corfield, Toward a Philosophy of Real Mathematics. [REVIEW] Mathematical Intelligencer 29 (2).
John Bigelow (1988). The Reality of Numbers: A Physicalist's Philosophy of Mathematics. Oxford University Press.
Christopher Pincock (2009). Towards a Philosophy of Applied Mathematics. In Otávio Bueno & Øystein Linnebo (eds.), New Waves in Philosophy of Mathematics. Palgrave Macmillan.
Alfred Tarski (1994). Introduction to Logic and to the Methodology of the Deductive Sciences. Oxford University Press.
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