Why Prove it Again? Alternative Proofs in Mathematical Practice /

• Κύριος συγγραφέας: Dawson, Jr., John W. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Birkhäuser, 2015.
• Θέματα: Mathematics.; Algebra.; Mathematical analysis.; Analysis (Mathematics).; Geometry.; History.; Topology.; History of Mathematical Sciences.; Analysis.

This monograph considers several well-known mathematical theorems and asks the question, “Why prove it again?” while examining alternative proofs.   It  explores the different rationales mathematicians may have for pursuing and presenting new proofs of previously established results, as well as how...

Πίνακας περιεχομένων:

• Proofs in Mathematical Practice
• Motives for Finding Alternative Proofs
• Sums of Integers
• Quadratic Surds
• The Pythagorean Theorem
• The Fundamental Theorem of Arithmetic
• The Infinitude of the Primes
• The Fundamental Theorem of Algebra
• Desargues's Theorem
• The Prime Number Theorem
• The Irreducibility of the Cyclotomic Polynomials
• The Compactness of First-Order Languages
• Other Case Studies.