{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T21:52:25Z","timestamp":1725486745822},"publisher-location":"Berlin, Heidelberg","reference-count":20,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540719854"},{"type":"electronic","value":"9783540719861"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2007]]},"DOI":"10.1007\/978-3-540-71986-1_11","type":"book-chapter","created":{"date-parts":[[2007,6,28]],"date-time":"2007-06-28T22:39:16Z","timestamp":1183070356000},"page":"193-213","source":"Crossref","is-referenced-by-count":11,"title":["Mathematics through Diagrams: Microscopes in Non-Standard and Smooth Analysis"],"prefix":"10.1007","author":[{"given":"Riccardo","family":"Dossena","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lorenzo","family":"Magnani","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"11_CR1_Ref","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-8562-0","volume-title":"Abduction, Reason, and Science. Processes of Discovery and Expla-nation","author":"L Magnani","year":"2001","unstructured":"Magnani, L.: Abduction, Reason, and Science. Processes of Discovery and Expla-nation. Kluwer Academic\/Plenum Publishers, New York (2001)"},{"key":"11_CR2_Ref","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1007\/978-1-4615-0605-8_18","volume-title":"Model-Based Reasoning: Science, Technol-ogy, Values","author":"L Magnani","year":"2002","unstructured":"Magnani, L.: Epistemic mediators and model-based discovery in science. In Magnani, L., Nersessian, N., eds.: Model-Based Reasoning: Science, Technol-ogy, Values, New York, Kluwer Academic\/Plenum Publishers (2002) 305-329"},{"key":"11_CR3_Ref","doi-asserted-by":"crossref","unstructured":"Sullivan, K.A.: The teaching of elementary calculus using the non-standard approach. American Mathematical Monthly (1976) 370-375","DOI":"10.1080\/00029890.1976.11994130"},{"key":"11_CR4_Ref","volume-title":"Non-Standard Analysis","author":"A Robinson","year":"1966","unstructured":"Robinson, A.: Non-Standard Analysis. North Holland, Amsterdam (1966)"},{"key":"11_CR5_Ref","volume-title":"Synthetic Differential Geometry. LMS Lecture Notes Series 51","author":"A Kock","year":"1981","unstructured":"Kock, A.: Synthetic Differential Geometry. LMS Lecture Notes Series 51. Cambridge University Press, Cambridge (1981)"},{"key":"11_CR6_Ref","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/S0049-237X(08)71552-0","volume-title":"Contributions to Non-Standard Analysis","author":"KD Stroyan","year":"1972","unstructured":"Stroyan, K.D.: Uniform continuity and rates of growth of meromorphic func-tions. In Luxemburg, W.J., Robinson, A., eds.: Contributions to Non-Standard Analysis, Amsterdam, North-Holland (1972) 47-64"},{"key":"11_CR7_Ref","first-page":"43","volume":"18","author":"D Tall","year":"1982","unstructured":"Tall, D.: Elementary axioms and pictures for infinitesimal calculus. Bulletin of the IMA 18 (1982) 43-48","journal-title":"Bulletin of the IMA"},{"key":"11_CR8_Ref","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1023\/A:1016000710038","volume":"48","author":"D Tall","year":"2001","unstructured":"Tall, D.: Natural and formal infinities. Educational Studies in Mathematics 48 (2001) 199-238","journal-title":"Educational Studies in Mathematics"},{"key":"11_CR9_Ref","volume-title":"Elementary Calculus","author":"HJ Keisler","year":"1976","unstructured":"Keisler, H.J.: Elementary Calculus. Prindle, Weber, and Schmidt, Boston (1976)"},{"key":"11_CR10_Ref","volume-title":"Foundations of Infinitesimal Calculus","author":"HJ Keisler","year":"1976","unstructured":"Keisler, H.J.: Foundations of Infinitesimal Calculus. Prindle, Weber, and Schmidt, Boston (1976)"},{"key":"11_CR11_Ref","volume-title":"An Introduction to Nonstandard Real Analysis","author":"AE Hurd","year":"1985","unstructured":"Hurd, A.E., Loeb, P.A.: An Introduction to Nonstandard Real Analysis. Acad-emic Press, Orlando (1985)"},{"key":"11_CR12_Ref","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0615-6","volume-title":"Lectures on the Hyperreals","author":"R Goldblatt","year":"1998","unstructured":"Goldblatt, R.: Lectures on the Hyperreals: An Introduction to Nonstandard Analysis. Springer-Verlag, New York (1998)"},{"key":"11_CR13_Ref","volume-title":"Introduction to the Theory of Infinitesimals","author":"KD Stroyan","year":"1976","unstructured":"Stroyan, K.D., Luxemburg, W.A.J.: Introduction to the Theory of Infinitesimals. Academic Press, New York (1976)"},{"key":"11_CR14_Ref","volume-title":"A Primer of Infinitesimal Analysis","author":"JL Bell","year":"1998","unstructured":"Bell, J.L.: A Primer of Infinitesimal Analysis. Cambridge University Press, Cambridge (1998)"},{"key":"11_CR15_Ref","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-4143-8","volume-title":"Models for Smooth Infinitesimal Analysis","author":"I Moerdijk","year":"1991","unstructured":"Moerdijk, I., Reyes, G.E.: Models for Smooth Infinitesimal Analysis. Springer-Verlag, New York (1991)"},{"key":"11_CR16_Ref","first-page":"66","volume-title":"Philosophy of Mathematics. Selected Readings","author":"LEJ Browuer","year":"1964","unstructured":"Browuer, L.E.J.: Intuitionism and formalism. In Benacerraf, P., Putnam, H., eds.: Philosophy of Mathematics. Selected Readings. Prentice-Hall, Inc., Englewood Cliffs, New Jersey (1964) 66-77"},{"volume-title":"Browuer\u2019s Cambridge Lectures on Intuitionism","year":"1981","key":"11_CR17_Ref","unstructured":"Dalen, D.V., ed.: Browuer\u2019s Cambridge Lectures on Intuitionism. Cambridge University Press, Cambridge (1981)"},{"key":"11_CR18_Ref","first-page":"55","volume-title":"Philosophy of Mathematics. Selected Readings","author":"A Heyting","year":"1964","unstructured":"Heyting, A.: Disputation. In Benacerraf, P., Putnam, H., eds.: Philosophy of Mathematics. Selected Readings. Prentice-Hall, Inc., Englewood Cliffs, New Jersey (1964) 55-65"},{"key":"11_CR19_Ref","first-page":"42","volume-title":"Philosophy of Mathematics. Selected Readings","author":"A Heyting","year":"1964","unstructured":"Heyting, A.: The intuitionist foundations of mathematics. In Benacerraf, P., Putnam, H., eds.: Philosophy of Mathematics. Selected Readings. Prentice-Hall, Inc., Englewood Cliffs, New Jersey (1964) 42-54"},{"key":"11_CR20_Ref","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-4588-7","volume-title":"Basic Concepts of Synthetic Differential Geometry","author":"R Lavendhomme","year":"1996","unstructured":"Lavendhomme, R.: Basic Concepts of Synthetic Differential Geometry. Kluwer Academic Publisher, Dordrecht (1996)"}],"container-title":["Studies in Computational Intelligence","Model-Based Reasoning in Science, Technology, and Medicine"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-71986-1_11.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,27]],"date-time":"2021-04-27T10:02:55Z","timestamp":1619517775000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-71986-1_11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007]]},"ISBN":["9783540719854","9783540719861"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-71986-1_11","relation":{},"ISSN":["1860-949X","1860-9503"],"issn-type":[{"type":"print","value":"1860-949X"},{"type":"electronic","value":"1860-9503"}],"subject":[],"published":{"date-parts":[[2007]]}}}