Old Mathematics Textbooks Versus New Mathematics Textbooks
Perhaps one of the key factors to success in a mathematics-based course is the textbook. Why the textbook? I say the textbook because it contains the methods and the practice problems necessary to develop skills in mathematical reasoning. The hard truth to getting “good” at mathematics is that simply reading a maths book does not help you improve much. Solving many problems is the reality of getting good at mathematics. The best way to compare the old versus new textbooks is to look at the pros and cons of each. Ideally having both is superior to having one or the other, but this is not always possible as one shall see from some of the cons.
The first thing they should be of note is that when I use the word “old” I am referring to maths textbooks from before at least 1970, and thus “new” will refer to any material after 1970. One of the first sorts of pros of the old maths books is that they tend to contain what I call “hidden gems” in them. I found from reading maths books from before the age of calculators that for certain areas like trigonometry, mathematicians had to use a bit more algebraic manipulation to get the same answers as opposed to after the 70s one would just use an algebraic calculator or calculator to solve. This can be beneficial because this gives a few more alternative methods of solving problems that would not ordinarily be available. For example, in trigonometry, vers(θ) was historically considered the most important trigonometric function, and yet the probability of a maths student knowing what that is quite low and is pretty much zero if you are trying to find a student that can tell you what is hav(θ). Another pro about old maths textbooks that I have also noticed is that they tend to have much harder exercises in them than the new textbooks. Having harder exercises in the context of maths is a benefit to the student because by solving difficult problems one’s problem-solving skills become much stronger in less time and fosters outside the box thinking. If one is used to difficult problems by the time the test comes around the test will feel like a review. Another one of the pros of old math books is that the cost of the books is often not as expensive as some of the new textbooks.
Now it is time to look at the cons of old maths books. The first con is that if one is not used to reading old maths books the wording can be quite tricky and takes some practice to get decent at reading. This con will, however, disappear as one gets comfortable reading them. So, this con is that old maths books are a slow start. The next con and probably the most notable con of old maths books is that old maths books may not contain the most up to date theory in that branch, but I think in the case of first timers knowing the latest breakthrough in that branch of mathematics is not going to help with learning the branch and it is unlikely a first timer will understand the modern advancements anyways. Unless of course one of the modern advancements is a new and more efficient way to solve a problem by not using computer assistance. Another con of the old maths books is accessibility. They can be quite hard to get access considering most of them are not getting reprinted anymore.
Overall, I would say ideally get an old maths textbook; the older the better, and a new one and use them to complement each other, but if I had to pick, I would choose the old textbook. Of course, if a certain textbook is required for a course one should invest in that textbook. But if the option is available, getting an old textbook will be of great benefit.
N. Monk, Futurist d Philosopher
