Appearances to the contrary, no writer deliberately sets out to produce an un readable book; we all do what we can and hope for the best. Naturally, I hope that my language will be clear and helpful to students, and in the end only they are qualified to judge. However, it would be a great advantage to all of us teachers and students alike-if student users of mathematics textbooks could somehow be given a few hints on the art of reading mathematics, which is a very different thing from reading novels or magazines or newspapers.
没有哪位作家会故意写没有可读性的书;我们也尽我们能做并抱以最好的希望。当然，我希望我的语言对于学生来说是清晰的，而最终也只有他们有资格来评判。但是，对所有教师和学生一样，如果学生的数学教科书在某种程度上给出一些读数学的方法，那将是非常有益的事。当然这与阅读小说或杂志或报纸并不是一回事。
In high school mathematics courses, most students are accustomed to tackling their homework problems first, out of impatience to have the whole burdensome task over and done with as soon as possible. These students read the explana tions in the text only as a last resort, if at all. This is a grotesque reversal of rea sonable procedure, and makes about as much sense as trying to put on one’s shoes before one’s socks. I suggest that students should read the text first, and when this has been thoroughly assimilated, then and only then turn to the home work problems. After all, the purpose of these problems is to nail down the ideas and methods described and illustrated in the text.
在高中数学课程中，大多数学生都习惯于首先处理家庭作业，对整体的课程任务没有耐心也希望尽快结束。这些学生只有在万不得已的时候才会阅读书上的解释。这真是完全颠倒的方法，相当于教一个人穿袜子之前先穿鞋。我建议学生首先阅读书本，当只是被彻底理解了，再转到作业上的问题。毕竟，这些问题的目的是为了确定书中描述与说明的想法与方法。
How should a student read the text in a book like this? Slowly and carefully, and in full awareness that a great many details have been deliberately omitted. If this book contained every detail of every discussion, it would be five times as long, which God forbid! There is a saying of Voltaire: “The secret of being a bore is to tell everything.” Every writer of a book of this kind tries to walk a nar row path between saying too much and saying too little.
学生想这样读书将会如何呢？慢慢地，会意识到许多细节被故意省略了。如果这本书写下讨论的所有细节，那么它会有现在的五倍之多。伏尔泰曾说:”无聊的秘诀在于告诉他一切”。每个作家试图在说得太多和太少选择折中的做法。
The words “clearly,” “it is easy to see,” and similar expressions are not in tended to be taken literally, and should never be interpreted by any student as a putdown on his or her abilities. These are code-phrases that have been used in mathematical writing for hundreds ofyears. Their purpose is to give a signal to the careful reader that in this particular place, the exposition is somewhat con densed, and perhaps a few details of calculations have been omitted. Any phrase like this amounts to a friendly hint to the student that it might be a good idea to read even more carefully and thoughtfully in order to fill in omissions in the ex position, or perhaps get out a piece of scratch paper to verify omitted details of calculations. Or better yet, make full use of the margins of this book to empha size points, raise questions, perform little computations, and correct misprints.
单词”很明显”“很容易看出”以及类似的表达式不应作就字面意思来理解，学生也不该理解为不需要去思考证明。这些是代码短语，曾出在数百年来的数学写作中。他们的目的是在那个特别的地方向细心的读者发出一个信号，（the exposition is somewhat condensed）计算的一些细节也许被省略。任何此类短语是对更细心学生的友好提示，或许需要拿出一张草稿纸验证省略的细节部分，或者可以充分利用这本书的空白地方，提出问题，简单计算一下或写出没有打印的部分。
George F. Simmons