The Mathematical Trinity
Imagination, Inference and Insight
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Beschreibung
The book discusses nine popular propositions in Mathematics: “The Consistency Theorem” from Logic; “Isosceles Triangle Theorem” and “Pythagorean Theorem” from Geometry; “Ordered Pair Proposition” and “Mathematical Induction Principle” from Zermelo–Fraenkel set theory; “Remainder Theorem” from Number theory; “The Quadratic Equation Proposition” and “The Subgroup Theorem” from Algebra; and “Dedekind Continuum Theorem” from Analysis, and thereby covers a sufficiently wide cross-section of modern mathematical sub-domains. Using these propositions, the book primarily has three objectives: to offer a deeper appreciation of these propositions and related concepts; to provide a better understanding of their relationship with other topics of Mathematics; and, above all, to throw light on the profound nature of the discipline that has developed and advanced over the millennia through a synergistic combination of imagination, inference, and insight.
The book meticulously dissects each of these chosen propositions in separate chapters while simultaneously probing their intricate interrelationships. This approach yields a heightened appreciation of their mathematical significance, bridging the divide between educational levels. These propositions often appear poised between school-level mathematics and university-level rigour, and the book adeptly navigates this middle ground. Furthermore, it goes beyond mere logical inference, embracing the realms of imagination and insight. It offers a holistic, historical, and intellectual perspective, unravelling not just the necessity of each proposition but also its unique contributions to the fabric and evolution of Mathematics. In doing so, it sheds light on a constellation of interconnected mathematical concepts, enriching the reader's comprehension of this remarkable discipline.
The book discusses nine popular propositions in Mathematics: “The Consistency Theorem” from Logic; “Isosceles Triangle Theorem” and “Pythagorean Theorem” from Geometry; “Ordered Pair Proposition” and “Mathematical Induction Principle” from Zermelo–Fraenkel set theory; “Remainder Theorem” from Number theory; “The Quadratic Equation Proposition” and “The Subgroup Theorem” from Algebra; and “Dedekind Continuum Theorem” from Analysis, and thereby covers a sufficiently wide cross-section of modern mathematical sub-domains. Using these propositions, the book primarily has three objectives: to offer a deeper appreciation of these propositions and related concepts; to provide a better understanding of their relationship with other topics of Mathematics; and, above all, to throw light on the profound nature of the discipline that has developed and advanced over the millennia through a synergistic combination of imagination, inference, and insight.
The book meticulously dissects each of these chosen propositions in separate chapters while simultaneously probing their intricate interrelationships. This approach yields a heightened appreciation of their mathematical significance, bridging the divide between educational levels. These propositions often appear poised between school-level mathematics and university-level rigour, and the book adeptly navigates this middle ground. Furthermore, it goes beyond mere logical inference, embracing the realms of imagination and insight. It offers a holistic, historical, and intellectual perspective, unravelling not just the necessity of each proposition but also its unique contributions to the fabric and evolution of Mathematics. In doing so, it sheds light on a constellation of interconnected mathematical concepts, enriching the reader's comprehension of this remarkable discipline.
Demonstrates the nine familiar mathematical propositions and studies their inter-related roles of imagination, inference and insight Presents simple proofs of some important theorems in set theory, number theory and analysis Examines the growth of the discipline and the inference of the popular propositions with their historic and philosophical perspectives
Autor*in
Balkrishna Shetty
Themen in »The Mathematical Trinity«
the consistency theorem isosceles triangle theorem the ordered pair theorem mathematical induction principle remainder theorem the quadratic equation proposition the subgroup proposition the pythagorean theorem Bolzano–Weierstrass theorem