“ON READING BOOKS

This part of the book can really be read at any time. We put it in the middle because that’s as good as any place to start reading a book. Very few books are meant to be read from beginning to end, and there are many ways of reading a book. One of them is to start in the middle, and go simultaneously backwards and forward, looking back for the definitions of any terms you don’t understand, while going ahead to see applications and motivation which are very hard to put coherently in a systematic development. For instance, although we must do algebra first, it is quite appealing to look simultaneously at the geometry, in wihich we use algebraic tools to systematize our geometric intuition.

In writing the book, the whole subject has to be organized in a totally ordered way, along lines and pages, which is not the way our brain works naturally. But it is unavoidable that some topics have to be placed before others, even though our brain would like to perceive them simultaneously. This simultaneity cannot be achieved in writing, which thus gives a distortion of the subject. It is clear, however, that I cannot substitute for you in perceiving various sections of this book together. You must do that yourself. The book can only help you, and must be organized so that any theorem or definition which you need can be easily found.

Another way of reading this book is to start at the beginning, and then skip what you find obvious or skip what you find boring, while going ahead to further sections which appeal to you more. If you meet some term you don’t understand, or if you need some previous theorem to push through the logical development of that section, you can look back to the proper reference, which now becomes more appealing to you because you need it for something which you already find appealing.

Finally, you may want to skim through the book rapidly from beginning to end, looking just at the statements of theorems, or at the discussions between theorems, to get an overall impressionof the whole subject. Then you can go back to cover the material more systematically.

Any of these ways is quite valid, and which one you follow depends on your taste. When you take a course, the material will useually be covered in the same order as the book, because that is the safest way to keep going logically. Don’t let that prevent you from experimenting with other ways.”

Yukarıdaki yazı matematikçi Serge Lang‘ın Basic Mathematics kitabının 93. ve 94. sayfalarından alınma (koyu renkli vurgular bana ait). Serge Lang’dan Ali Nesin ve İlhan İkeda’nın 2005 yılındaki Matematik Dünyası yazıları sayesinde haberdar olmuştum:

Benim Serge Lang’ım [PDF]
Serge Lang [PDF]

3 sene sonra bir kez daha Lang’dan bir şeyler öğrenme imkanı bulduğum için çok sevindim. Yukarıdaki kısacık yazı belki de gelecek 50 yılda eğitim dediğimiz şeyi nasıl şekillendirmemiz gerektiğine dair çok şey anlatıyor…

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