University, College, High School, & Hobby

Mathematics Wizard ™


This is good advice about math textbooks,
especially for students or anyone serious about actually studying.

Good Advice








Why Math?


Confusion about Algebra textbooks:

Algebra in textbooks has been split up into 3 major blocks:
a) Elementary or Introductory or Algebra I (or high school algebra, an even less helpful name),
b) Intermediate or Algebra II (or College Algebra, an even less helpful name)
c) Algebra and Trigonometry with analytic geometry, Algebra III with Trig, or Pre Calculus.

The simple rule: The above sets of expressions for a) above, are equivalent expressions, no pun intended. And much the same for b) & c) above as well.

The collective ambiguities of names for different textbooks don’t help anyone. Considerations such as depending on how large teachers want the textbooks to be, or the maximum weight students can carry, how much material should be covered in a single textbook for a particular class, the expected number of years a textbook is likely to be used by the same student, and of course the expected life span of the book itself also go into designing a textbook.

However the situation is made more complicated. For example in Elementary or Introductory Algebra books usually don’t cover a topic like factoring as thoroughly as an intermediate textbook, leaving some concepts un-addressed, expecting those areas to be covered again more thoroughly when the student takes intermediate or Algebra III.

An example of the confusion is the course entitled, "intro to linear algebra." This is not an introductory level course, not a first year course in algebra, not what one would think of when we speak of high school algebra or college algebra, but rather a highly specialized subject. Such a course’s pre-requisites would likely include elementary and intermediate algebra, Algebra III and trigonometry, and the first three semesters of introductory calculus. "Intro to linear algebra" is an "intermediate level course." However in this context, intermediate refers to a course which may be taken anywhere between 2nd and 4th year. This particular course would likely be considered a required course for any physical science major, and certainly for any math major. Side Note: My opinion is that we need to make this course a requirement for all science majors, even psychology, since it’s a pre-requisite for multivariate statistical analysis. Other examples include, "intro vector analysis" or "intro to complex analysis" which are actually intermediate level courses, with substantial pre-requisites in calculus.

Selecting an Algebra Textbook:

First, when we talk about textbooks related to algebra, in the first 3 semesters of studying algebra, the words "Elementary Algebra" means the exact same thing as "Introductory Algebra", "Starting Algebra", or "Algebra I". And the words "Elementary and Intermediate Algebra" means the text book was designed to cover introductory algebra and intermediate algebra or Algebra I and II. Whereas "Intermediate Algebra", may or may not actually cover all the material in an Elementary Algebra textbook.

First my advice is to follow the level of the textbook you are already using, especially when in school. On the one hand, going directly to a textbook covering both introductory and intermediate level Algebra may save money. On the other hand, going with two separate textbooks would increase the total number of math problems to be solved. And of course, the more problems you work, the more likely the knowledge will last a life time.

I wouldn’t worry too much about the content, if the textbook was written by a math professor from any public university, and even better is actually used at a major or public university. In such circumstances, it’s safe to assume they cover everything the book should for intro, intermediate, or in combined intro and intermediate textbooks. Simply follow the level of the textbook. Few things change on a subject so well worked out, taught, learned, re-written about, and polished from generation to generation of math students to math professors. After all, Math is the study of quantifiable logic. And math is the one subject where everything you need to know is in the book. That’s not true for any other subject.

Should I skip?

I advise, so long as it does not compromise your current academic trajectory, start with the area of math you’re working on, then watch all the rest.
It can’t do any harm,
may actually help,
and it’s always better than watching television. Let it massage your brain.