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The History of Mathematics: A Source-Based Approach, Volume 1 is a substantial, well-written text... more The History of Mathematics: A Source-Based Approach, Volume 1 is a substantial, well-written textbook that derives from correspondence materials developed for the Open University's year-long undergraduate history of mathematics course, which was regularly offered to distance learners from 1987 to 2007. This volume focuses on the first half of that course: The mathematics of Egypt and Mesopotamia (Chapter 2), Classical Greek and Hellenistic mathematics (Chapters 3-6), The mathematics of India and China (Chapter 7), Islamic mathematics (Chapter 8), Medieval European mathematics (Chapter 9), Renaissance mathematics in Europe and Great Britain (Chapters 10-11), The astronomical revolution of the mid-16th to early-17th century (Chapter 12), and early 17th-century European mathematics (Chapter 13). Volume 2 will resume with the rise of the calculus and take the story at least through 19th-century European developments in a variety of fields if the 1987 Open University sourcebook The History of Mathematics: A Reader by John Fauvel and Jeremy Gray remains a trusty guide for the project.
Bloomsbury Academic eBooks, 2023
This is an expanded version of the first chapter Richard Whately's Revitalization of Syllogistic ... more This is an expanded version of the first chapter Richard Whately's Revitalization of Syllogistic Logic in Aristotle's Syllogism and the Creation of Modern Logic Aristotle's Syllogism and the Creation of Modern Logic edited by Lukas M. Verburgt and Matteo Cosci (Bloomsbury, 2023). Drawing upon the author's 1982 Ph. D. dissertation (https://digitalcollections.dordt.edu/faculty_work/230/) and more current scholarship, this essay traces the critical historical background to Whately's work in more detail than could be done in the published version.
Reviewed Title: Boole\u27s Algebra Isn\u27t Boolean Algebra by Theodore Hailperin. Mathematics Ma... more Reviewed Title: Boole\u27s Algebra Isn\u27t Boolean Algebra by Theodore Hailperin. Mathematics Magazine, v. 54:4, pp. 172-184. ISSN: 0025-570
The American Mathematical Monthly, 2017
Mathematics is a living plant which has flourished and languished with the rise and fall of civil... more Mathematics is a living plant which has flourished and languished with the rise and fall of civilizations. Created in some prehistoric period it struggled for existence through centuries of prehistory and further centuries of recorded history. It finally secured a firm grip on life in the highly congenial soil of Greece and waxed strong for a brief period. In this period it produced one perfect flower, Euclidean geometry. The buds of other flowers opened slightly . . . but these flowers withered with the decline of Greek civilization, and the plant remained dormant for one thousand years. Such was the state of mathematics when the plant was transported to Europe proper and once more imbedded in fertile soil. By A.D. 1600 it had regained the vigor it had possessed at the very height of the Greek period and was prepared to break forth with unprecedented brilliance.
British Journal for the History of Mathematics, 2020
Sourcebook in the Mathematics of Medieval Europe and North Africa, 2017
The College Mathematics Journal, 1991
Reviewed Title: Galileo\u27s Muse: Renaissance Mathematics and the Arts by Mark A. Peterson. Camb... more Reviewed Title: Galileo\u27s Muse: Renaissance Mathematics and the Arts by Mark A. Peterson. Cambridge, MA: Harvard University Press, 2011, 336 pages. ISBN 9780674059726
The History of Mathematics: A Source-Based Approach, Volume 1 is a substantial, well-written text... more The History of Mathematics: A Source-Based Approach, Volume 1 is a substantial, well-written textbook that derives from correspondence materials developed for the Open University's year-long undergraduate history of mathematics course, which was regularly offered to distance learners from 1987 to 2007. This volume focuses on the first half of that course: The mathematics of Egypt and Mesopotamia (Chapter 2), Classical Greek and Hellenistic mathematics (Chapters 3-6), The mathematics of India and China (Chapter 7), Islamic mathematics (Chapter 8), Medieval European mathematics (Chapter 9), Renaissance mathematics in Europe and Great Britain (Chapters 10-11), The astronomical revolution of the mid-16th to early-17th century (Chapter 12), and early 17th-century European mathematics (Chapter 13). Volume 2 will resume with the rise of the calculus and take the story at least through 19th-century European developments in a variety of fields if the 1987 Open University sourcebook The History of Mathematics: A Reader by John Fauvel and Jeremy Gray remains a trusty guide for the project.
Bloomsbury Academic eBooks, 2023
This is an expanded version of the first chapter Richard Whately's Revitalization of Syllogistic ... more This is an expanded version of the first chapter Richard Whately's Revitalization of Syllogistic Logic in Aristotle's Syllogism and the Creation of Modern Logic Aristotle's Syllogism and the Creation of Modern Logic edited by Lukas M. Verburgt and Matteo Cosci (Bloomsbury, 2023). Drawing upon the author's 1982 Ph. D. dissertation (https://digitalcollections.dordt.edu/faculty_work/230/) and more current scholarship, this essay traces the critical historical background to Whately's work in more detail than could be done in the published version.
Reviewed Title: Boole\u27s Algebra Isn\u27t Boolean Algebra by Theodore Hailperin. Mathematics Ma... more Reviewed Title: Boole\u27s Algebra Isn\u27t Boolean Algebra by Theodore Hailperin. Mathematics Magazine, v. 54:4, pp. 172-184. ISSN: 0025-570
The American Mathematical Monthly, 2017
Mathematics is a living plant which has flourished and languished with the rise and fall of civil... more Mathematics is a living plant which has flourished and languished with the rise and fall of civilizations. Created in some prehistoric period it struggled for existence through centuries of prehistory and further centuries of recorded history. It finally secured a firm grip on life in the highly congenial soil of Greece and waxed strong for a brief period. In this period it produced one perfect flower, Euclidean geometry. The buds of other flowers opened slightly . . . but these flowers withered with the decline of Greek civilization, and the plant remained dormant for one thousand years. Such was the state of mathematics when the plant was transported to Europe proper and once more imbedded in fertile soil. By A.D. 1600 it had regained the vigor it had possessed at the very height of the Greek period and was prepared to break forth with unprecedented brilliance.
British Journal for the History of Mathematics, 2020
Sourcebook in the Mathematics of Medieval Europe and North Africa, 2017
The College Mathematics Journal, 1991
Reviewed Title: Galileo\u27s Muse: Renaissance Mathematics and the Arts by Mark A. Peterson. Camb... more Reviewed Title: Galileo\u27s Muse: Renaissance Mathematics and the Arts by Mark A. Peterson. Cambridge, MA: Harvard University Press, 2011, 336 pages. ISBN 9780674059726
Corcoran and Jongsma review a Boolean-algebra article This article uses contemporary mathematics... more Corcoran and Jongsma review a Boolean-algebra article
This article uses contemporary mathematics to elucidate a classic text in the history of mathematics. It exemplifies what Corcoran calls “mathematical archeology”.
Today we consider algebra to involve in an essential way study of algebraic structures, and we consider logic to involve in an essential way study of logical deductions (including mathematical proofs). The author emphasizes the fact that Boole thought of himself as using mathematical ideas to deal with logic. But it is also true, as can be inferred from this article, that Boole had no thought of algebra as a study of structures. There is some irony, therefore, in the fact that this article treats Boole's work entirely from the perspective of algebraic structures omitting altogether mention of any contributions to the study of deductions that Boole may have made.
The author's overall approach to Boole's work is not narrowly historical, but at the same time it is not in conflict with a strict historical approach. Moreover, because of the author's command of relevant historical material and his efforts to represent the technical aspects of Boole's work faithfully, historians of algebra and logic can read this article with profit.
1983 MATHEMATICAL REVIEWS: Review of Hailperin, T., "Boole's Algebra Isn't Boolean Algebra" (198... more 1983 MATHEMATICAL REVIEWS: Review of Hailperin, T., "Boole's Algebra Isn't Boolean Algebra" (1981) in Mathematical Reviews 83e:01038 by J. Corcoran and C. Jongsma.
This article is an example of “mathematical archeology”: the use of contemporary mathematics to elucidate a classic text in the history of mathematics. Its goals are: (1) to unravel "the nascent abstract algebra ideas" underlying Boole's approach to logic, and (2) to provide a contemporary algebraic justification of some ideas and procedures that have seemed mysterious or unfounded to Boole's successors. One of its useful, albeit now familiar, points is that BOOLEAN ALGEBRA—a calculus or formalism—is not one of the BOOLEAN ALGEBRAS—set-theoretic structures or models—and that none of the above are what Boole created in 1847 or 1954, which is now properly called BOOLE’S ALGEBRA. The terminology is still confused and still confusing to students.
Richard Whately's Revitalization of Syllogistic Logic, 2023
This is an expanded version of the first chapter "Richard Whately’s Revitalization of Syllogistic... more This is an expanded version of the first chapter "Richard Whately’s Revitalization of Syllogistic Logic" in *Aristotle’s Syllogism and the Creation of Modern Logic* edited by Lukas M. Verburgt and Matteo Cosci (Bloomsbury, 2023). Drawing upon the author’s 1982 Ph. D. dissertation (https://digitalcollections.dordt.edu/faculty_work/230/ ) and more current scholarship, this essay traces the critical historical background to Whately’s work in more detail than could be done in the published version.