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Product details:
- Publisher Springer Nature Singapore
- Date of Publication 12 December 2025
- Number of Volumes 1 pieces, Book
- ISBN 9789819618026
- Binding Hardback
- No. of pages386 pages
- Size 235x155 mm
- Language English
- Illustrations XVI, 386 p. 92 illus., 41 illus. in color. Illustrations, black & white 700
Categories
Long description:
"
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.
" MoreTable of Contents:
Chapter 1 The Consistency Theorem.- Chapter 2 Isosceles Triangle Theorem.- Chapter 3 The Ordered Pair Proposition.- Chapter 4 Mathematical Induction Theorem.- Chapter 5 The Remainder Theorem.- Chapter 6 The Pythagorean Theorem.- Chapter 7 The Quadratic Equation Proposition.- Chapter 8 Dedekind Continuum Theorem.- Chapter 9 The Subgroup Proposition.
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