What Is Mathematics ?

From the reviews: "These books (Introduction to Calculus and Analysis Vol. I/II) are very well written. The mathematics are rigorous by the many examples that are given and the applications that are treated make the books extremely readable and the arguments easy to understand. These books are ideally suited for an undergraduate calculus course. Each chapter is followed by a number of interesting exercises. More difficult parts are marked with an asterisk. There are many illuminating figures... Of interest to students, mathematicians, scientists and engineers. Even more than that."
Newsletter on Computational and Applied Mathematics, 1991.
"Although the first volume of this book was originally published in 1969 and the second one in 1974 it remained one of the best textbooks introducing several generations of mathematicians to higher mathematics. ...This excellent book is highly recommended both to instructors and students."
Acta Scientiarum Mathematicarum, 1991.

Introduction to Calculus and Analysis - Tome 2, 2 ; Chapters 5-8

Introduction to Calculus and Analysis: Volume I

Methods of Mathematical Physics - Volume 2 : Partial Differential Equations

Springer-Verlag began publishing books in higher mathematics in 1920, when the series Grundlehren der mathematischen Wissenschaften, initially conceived as a series of advanced textbooks, was founded by Richard Courant. A few years later, a new series Ergebnisse der Mathematik und ihrer Grenzgebiete, survey reports of recent mathematical research, was added. Of over 400 books published in these series, many have become recognized classics and remain standard references for their subject. Springer is reissuing a selected few of these highly successful books in a new, inexpensive softcover edition, to make them easily accessible to younger generations of students and researchers. Introduction to Calculus and Analysis I : From the reviews : "Volume 1 covers a basic course in real analysis of one variable and Fourier series. It is well-illustrated, well-motivated and very well-provided with a multitude of unusually useful and accessible exercises. (...) There are three aspects of Courant and John in which it outshines (several) contemporaries : (i) the extensive historical references, (ii) the chapter on numerical methods, and (iii) the two chapters on physics and geometry. The exercises in Courant and John are put together purposefully, and either look numerically interesting, or are intuitively significant, or lead to applications. It is the best text known to the reviewer for anyone trying to make an analysis course less abstract. (...)" (The Mathematical Gazette [75.1991.471])

Introduction to Calculus and Analysis - Tome 1

"Pendant plus de 2000 ans, une certaine familiarité avec les mathématiques a été considérée comme un élément indispensable du bagage intellectuel de toute personne cultivée. Aujourd'hui, cette place traditionnelle des mathématiques dans l'éducation court un grave danger, dont malheureusement les professionnels portent une part de responsabilité. L'enseignement des mathématiques s'est parfois appauvri, et limité à quelques apprentissages techniques, en laissant de côté ce qui conduit à une compréhension réelle et à une plus grande autonomie intellectuelle". Ces lignes de Richard Courant et Herbert Robbins appartiennent à une autre génération et à un autre continent. Et pourtant, elles sonnent étrangement actuelles. Pour contribuer à résoudre le problème, Courant et Robbins ont écrit Qu'est-ce que les mathématiques ?, qu'ils destinaient "au débutant et au savant, à l'étudiant et au professeur, au philosophe et à l'ingénieur". Avec la publication de cette première traduction en français de leur grand classique, nous poursuivons le même objectif : redonner du sens à l'enseignement des mathématiques.

What Is Mathematics ?

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