Help me publish a calculus textbook. May 19, 6: I am confident that I can write a good book, appropriate for the target audience.
If I were to express my major objection in the most charitable possible way, it is that most textbooks are written like reference books. They are usually very good at recording the basic facts of a subject and proving them with admirable rigor.
If you just need to look up some elementary theorem or formal definition, then by all means consult a textbook.
The trouble, though, is that textbooks are seldom written from the perspective of a student encountering the material for the first time. If I were to express things more melodramatically, I would say that the problem is that textbooks seldom tell a story. They have no plot, no characters.
Good mathematical writing is marked by a progression from the initial statement of a problem, through the rising action of our initial, fumbling attempts to solve it, reaching its climax with the solution itself, and then proceeding to its denouement in the form of a proper, rigorous proof.
The best part is that the story never really ends, since the solution to one problem leads inevitably to new problems. Over time, however, I have come to the sad realization that many of my colleagues do not share my view.
A piece of mathematical writing with two consecutive sentences of exposition will be derided by many as too wordy. Books that are nothing but a sequence of dense, unmotivated definitions followed by equally unmotivated theorems are praised for being concise.
It has happened many times that I have heard people gush about textbooks I would be embarrassed to use to level off a table. Occasionally, though, I grow uncertain. That is, after all, how most mathematicians write.
Who am I to argue? Every once in a while, though, I come across a book that really does it right! I have just finished reading one such book. It is called Measurement, by Paul Lockhart.
It is quite simply the best math book I have read in quite some time. Anyone thinking about writing a math textbook should be required to read it.
It is possible that I am a little biased. Lockhart was a post-doc at Brown when I was an undergraduate there in the early nineties.
I had two courses with him, one in linear algebra, the other in complex analysis. He had a big influence on me, especially during my periodical crises of confidence about my future in mathematics.
Sometimes I would feel beaten down by the drudgery of my courses and start wondering if maybe I should pursue something else. Professor Lockhart played a big role in getting me over that. I mostly remember him as the funniest, but also the most lucid, math teacher I have ever had. I am happy to report that he writes the way he teaches.
The book has two main sections. The first deals with certain topics from Euclidean geometry, while the second discusses calculus. I found myself learning many new things, and looking at some old things in a new way. More than that, though, what impressed me was the naturalness of the discussion.
Take the section on calculus, for example. Instead he describes a certain problem: How should we think about the motion of a particle through space? Then, with some clear thinking and a sequence of natural questions, he develops all of the standard ideas presented in the calculus sequence.
In around pages, he starts from scratch and gets to some fairly sophisticated ideas in multi-variable calculus. It all seems so natural and inevitable and interesting, and not at all like the tedious, symbol-laden, thousand-pagers we inflict on freshman math majors.
Lockhart is contrasting the approach toward calculating areas taken by the ancient Greeks with the more modern approach we employ in calculus.With a math textbook, each lesson builds on the last.
For example, you might explain what fractions are in one lesson, compare them in the next lesson, add and subtract them in the third, and so on. Make sure you include everything on the list of standards for your state.
For any technical writing, I recommend LaTeX for typesetting because the equation formatting is unrivaled, and using a simple vector drawing program like xfig, which is great for 2D diagrams. I confess LaTeX has a learning curve, but you will appreciate the results. There are many resources on the.
Aug 25, · Hello, I am wanting to write a math/physics book or possibly a PDF online book and I'm wondering if anyone knows of any programs that exists for making pictures and drawing diagrams.
Writing a math book requires careful and meticulous planning. Every chapter must introduce new concepts, and the problem sets, ideas and explanations must be carefully designed to .
Many students resist writing the problem. But this can lead to doing the wrong problem, misreading it or even frustration while looking back and forth from the book to the paper. And for teachers and tutors, it’s especially annoying. Built with iridis-photo-restoration.comon.