Real Numbers Functions And Graphs

Engineering Mathematics: Vol. 1

College Algebra

Based on years of experience teaching and writing supplemental materials for more traditional precalculus books, Reva Narasimhan takes a functions-focused approach to teaching and learning algebra and trigonometry concepts. This new series builds up relevant concepts using functions as a unifying theme, repeating and expanding on connections to basic functions. Visualization and analysis motivate the functions-based approach, enabling users to better retain the material for use in later calculus courses.

Mathematical Analysis

For more than two thousand years some familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today the traditional place of mathematics in education is in grave danger. Unfortunately, professional representatives of mathematics share in the reponsibiIity. The teaching of mathematics has sometimes degen erated into empty drill in problem solving, which may develop formal ability but does not lead to real understanding or to greater intellectual indepen dence. Mathematical research has shown a tendency toward overspecialization and over-emphasis on abstraction. Applications and connections with other fields have been neglected . . . But . . . understanding of mathematics cannot be transmitted by painless entertainment any more than education in music can be brought by the most brilliant journalism to those who never have lis tened intensively. Actual contact with the content of living mathematics is necessary. Nevertheless technicalities and detours should be avoided, and the presentation of mathematics should be just as free from emphasis on routine as from forbidding dogmatism which refuses to disclose motive or goal and which is an unfair obstacle to honest effort. (From the preface to the first edition of What is Mathematics? by Richard Courant and Herbert Robbins, 1941.