Concepts or technique for Precalc self-study?

[MJC684]

I'm going to be taking a precalculus course in the fall. I'd like to be as prepared as possible for it so that I will be able to get as much out of the class as possible. I have access to a variety of textbooks, some are rather rigourous Precalc texts from the 60s and some are the "modern" precalculus texts from 1990-present. I plan on starting my self study now this semester in my free time and all through the summer. Here is how I see it: the 1960s texts are obviously better because of their rigourous treatment of the topics, however-- their problem sets are small and their list of topics are narrow. The modern precalculus texts have huge problem sets and are probably better for learning technique. Also I've never even had trig yet. I'm not sure which I should go with for my self study.

Do I use the modern precalc text and learn the fundamentals of technique? Or do I use the 1960s text and understand the concepts more thoroughly? I cannot make up my mind! Someone help me!

 

[phreak]

Use the modern text. The main fault with an old text is that standard elementary topics change over time rather rapidly, and you won't get all that you need out of an old book, not to mention that you'll learn a whole lot in excess that you'll never need because of narrow scope.

I'm not quite sure how you would make precalculus any more rigorous than it is in modern classrooms, except by making it more theoretical and less based on problem-solving. The thing is, with many modern treatments, a theoretical derivation is often included, although not used by the teacher. I remember looking back at my calculus textbook a while ago and seeing proofs of all of the theorems, and thinking to myself, "Where did all these proofs come from? We never did these in class!"

 

[khemix]

What 60s book are you referring to?

 

[MJC684]

Just to name a few:

University Algebra and Trigonometry - Howard Taylor and Thomas Wade
Principles of Mathematics - Carl Allendoefer
Modern Algebra & Trigonometry - Elbridge Vance
Fields and Functions - Crayton Bedford
An Elementary Approach to Functions - Korn Liberi

A couple may actually be from the early 70s. Anyways how important is it that I be able to right proofs at the precalculus level? Should I be spending my self-study time learning how to right proofs and learn the precalc later in class this fall? Ort should I do just the opposite? I'm just not sure what the right move is. I am torn between the two options. Help!

 

[khemix]

Go with the rigorous ones. You can easily learn precalc in class. Most students don't even use textbooks when learning precalc, it is that shallow. You will get hit hard in college if you don't know how to write proofs, and as it is a difficult skill to develop, you would do wonders starting out now. University will ASSUME you can write basic proofs at the level of geometry or basic number theory (see Niven).

I am not familiar with any of your books except Alendeofer. Your free time should be spent on developing proof skills if you intend to pursue a math major. School will prepare you in terms of calculation and technique. Other titles I recommend at your level are as follows:

How to Prove It - Velleman
Numbers: Rational and Irrational - Niven
Trigonometry - Gelfand
Geometry Revisited - Coexeter

Use the modern text. The main fault with an old text is that standard elementary topics change over time rather rapidly, and you won't get all that you need out of an old book, not to mention that you'll learn a whole lot in excess that you'll never need because of narrow scope.

I'm not quite sure how you would make precalculus any more rigorous than it is in modern classrooms, except by making it more theoretical and less based on problem-solving. The thing is, with many modern treatments, a theoretical derivation is often included, although not used by the teacher. I remember looking back at my calculus textbook a while ago and seeing proofs of all of the theorems, and thinking to myself, "Where did all these proofs come from? We never did these in class!"

Yes, but he can save that for class. Modern texts tend to be a shallow coverage of a lot of topics, more suited towards engineers than mathies. I think I'd rather see him understand what a logarithm is for instance than to have extra practice in performing calculations in it. And you can make precalc quite theoretical, studying various properties of functions such as odd/even and periodicity. The nature of the questions in books like Gelfand for example is more akin to what you'd see in a book like Spivak. Modern precalc books assume you will be learning calculus out of stewart or something.

 

[MJC684]

I have the Velleman book. I'll have to see if I can get those two other texts you mentioned. Any other advice?

 

[Raizy]

Does anyone have opinions about Sullivan's Precalculus 8th edition? I found the book to be nicely organized. It had it's own syllabus, and before each section it would tell you the prerequisites before starting the new section (and the prerequisites are contained in the book).

But this is coming from a newbie high school drop out, so I can't recommend it with confidence.

 

[khemix]

Sullivan is a modern precalculus book. Focuses on computation and problem solving, with a tiny bit a theory sprinked in it.

 

[physicsnoob93]

Sullivan is good. I used it. Another one is "Algebra and Trigonometry" By Young.