Making Mathematics Come to Life: A Guide for Teachers and StudentsShare this page
O. A. Ivanov
“It is difficult to define the genre of the book. It is not a problem book, nor a textbook, nor a ‘book for reading about mathematics’. It is most of all reminiscent of a good lecture course, from which a thoughtful student comes away with more than was actually spoken about in the lectures.”
—from the Preface by A. S. Merkurjev
If you are acquainted with mathematics at least to the extent of a standard high school curriculum and like it enough to want to learn more, and if, in addition, you are prepared to do some serious work, then you should start studying this book.
An understanding of the material of the book requires neither a developed ability to reason abstractly nor skill in using the refined techniques of mathematical analysis. In each chapter elementary problems are considered, accompanied by theoretical material directly related to them. There are over 300 problems in the book, most of which are intended to be solved by the reader. In those places in the book where it is natural to introduce concepts outside the high school syllabus, the corresponding definitions are given with examples. And in order to bring out the meaning of such concepts clearly, appropriate (but not too many) theorems are proved concerning them.
Unfortunately, what is sometimes studied at school under the name “mathematics” resembles real mathematics not any closer than a plucked flower gathering dust in a herbarium or pressed between the pages of a book resembles that same flower in the meadow besprinkled with dewdrops sparkling in the light of the rising sun.
Table of Contents
Table of Contents
Making Mathematics Come to Life: A Guide for Teachers and Students
- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Foreword ix10 free
- Introduction 112 free
- Induction 718 free
- Combinatorics 2738
- The whole numbers 5970
- Geometric transformations 89100
- Inequalities 117128
- Graphs 151162
- The pigeonhole principle 185196
- Complex numbers and polynomials 205216
- Rational approximations 233244
- Mathematics and the computer 265276
- Instead of a conclusion: teaching how to look for solutions of problems, or fantasy in the manner of Pólya 287298
- Solutions of the supplementary problems 295306
- Bibliography 329340
- Index 331342 free
- Back Cover Back Cover1349
High school teachers, undergraduate and graduate students interested in learning and teaching mathematics.