home libri books Fumetti ebook dvd top ten sconti 0 Carrello

Torna Indietro

toth gabor - elements of mathematics

Elements of Mathematics A Problem-Centered Approach to History and Foundations

Disponibilità: Normalmente disponibile in 15 giorni

54,98 €
52,23 €

Questo prodotto usufruisce delle SPEDIZIONI GRATIS
selezionando l'opzione Corriere Veloce in fase di ordine.

Pagabile anche con 18App Bonus Cultura e Carta del Docente

Facebook Twitter Aggiungi commento

Spese Gratis


Lingua: Inglese


Pubblicazione: 09/2022
Edizione: 1st ed. 2021


This textbook offers a rigorous presentation of mathematics before the advent of calculus. Fundamental concepts in algebra, geometry, and number theory are developed from the foundations of set theory along an elementary, inquiry-driven path. Thought-provoking examples and challenging problems inspired by mathematical contests motivate the theory, while frequent historical asides reveal the story of how the ideas were originally developed.

Beginning with a thorough treatment of the natural numbers via Peano’s axioms, the opening chapters focus on establishing the natural, integral, rational, and real number systems. Plane geometry is introduced via Birkhoff’s axioms of metric geometry, and chapters on polynomials traverse arithmetical operations, roots, and factoring multivariate expressions. An elementary classification of conics is given, followed by an in-depth study of rational expressions. Exponential, logarithmic, and trigonometric functions complete the picture, driven by inequalities that compare them with polynomial and rational functions. Axioms and limits underpin the treatment throughout, offering not only powerful tools, but insights into non-trivial connections between topics.

Elements of Mathematics is ideal for students seeking a deep and engaging mathematical challenge based on elementary tools. Whether enhancing the early undergraduate curriculum for high achievers, or constructing a reflective senior capstone, instructors will find ample material for enquiring mathematics majors. No formal prerequisites are assumed beyond high school algebra, making the book ideal for mathematics circles and competition preparation. Readers who are more advanced in their mathematical studies will appreciate the interleaving of ideas and illuminating historical details.


0. Preliminaries: Sets, Relations, Maps.- 1. Natural, Integral and Rational Numbers.- 2. Real Numbers.- 3. Rational and Real Exponentiation.- 4. Limits of Real Functions.- 5. Real Analytic Plane Geometry.- 6. Polynomial Expressions.- 7. Polynomial Functions.- 8. Conics.- 9. Rational and Algebraic Expressions and Functions.- 10. Exponential and Logarithmic Functions.- 11. Trigonometry.- Further Reading.- Index.


Gabor Toth is Distinguished Professor of Mathematics at Rutgers University, Camden. His research interests include convex geometry and differential geometry, in particular, harmonic maps and minimal immersions. Beyond mathematics, he teaches Ancient Egyptian Grammar and the history of precolonial Africa. He regularly trains gifted high school students for mathematical contests in Princeton. His previous books include Measures of Symmetry for Convex Sets and Stability, Glimpses of Algebra and Geometry, and Finite Möbius Groups, Spherical Minimal Immersions, and Moduli.

Altre Informazioni



Condizione: Nuovo
Collana: Undergraduate Texts in Mathematics
Dimensioni: 235 x 155 mm Ø 968 gr
Formato: Brossura
Illustration Notes:XV, 527 p. 33 illus., 3 illus. in color.
Pagine Arabe: 527
Pagine Romane: xv

Dicono di noi