Khan Academy vs. Textbooks: Which is Better for Pre-University Math Review?

[The PAQI Monsta]

Should I use khan academy or just by a textbook to learn and review some pre-uni & 1st year undergrad level mathematics for a physics degree? Which would be more fluid and clearer? Is there questions for khan academy? Is a maths books on mechanics relevant, or will any good physics book teach me all the mechanics I need?

Background: I've been out of maths for a year but I'm going uni to study physics in a few months, so I want to brush up on my maths skills during that time. Some topics I covered at school were complex numbers, polar coordinates, calculus(taylor&maclaurin, 1st&2nd order diff, integrals), introductory vector algebra.

I was thinking about getting Mathematical Methods in The Physical Sciences by Mary L. Boas.

 

[micromass]

Textbook, without a doubt. Khan Academy is pretty nice, but you can't rely only on that alone. You need to get a textbook and work through the problems.

Boas is a very nice book if you're comfortable with calculus. Definitely recommended!

 

[Intrastellar]

Boas is a very nice book if you're comfortable with calculus. Definitely recommended!

Out of curiosity, are you saying this as a mathematician ? What do mathematicians think of this book ?

 

[micromass]

Out of curiosity, are you saying this as a mathematician ? What do mathematicians think of this book ?

If your goal is to learn mathematics for physics, then Boas is a good choice. If your goal is to learn mathematics for mathematics, then it's not a good choice.

 

[Intrastellar]

If your goal is to learn mathematics for physics, then Boas is a good choice. If your goal is to learn mathematics for mathematics, then it's not a good choice.

That is definitely the case. What I meant was more like, do you have to unlearn things from this book if you want to do mathematics for mathematics later ? Is this book better than other methods books in that aspect ?

 

[RJLiberator]

Based on what you want to brush up on I would also agree that a textbook is a great idea.

Khan Academy would be idea if you need help with anything elementary, basic algebra, some trig, geometry, and calculus, but beyond those subjects there isn't too much help there.

I would suggest looking at a local library for some good textbooks or finding some free ones online. And then using Khan Academy's calculus sections to work on Calc 1 and Calc II material. If you go to Khan Academy and check the subjects --> Calc I or Calc II you can shift through the available questionaire's and videos and work on some problems.
Unfortunately, they don't have any problems for Calc III material.

 

[atyy]

A nice free text is http://www.physics.miami.edu/~nearing/mathmethods/.

Some useful notes are:
http://www.math.umn.edu/~olver/ln_/vc2.pdf
http://www.math.umn.edu/~olver/ln_/vc3.pdf
http://www.math.umn.edu/~olver/ln_/odq.pdf

 

[gillouche]

I would suggest something else.

Paul Online notes are awesome : http://tutorial.math.lamar.edu/ You can find Algebra, Calculus I, II, III and differential equations. For the trigonometry, Paul Dawkins doesn't have great ressource on this topic, there is just a small chapter but that's not engouh in my opinion so I would subject a textbook or KA.

I mastered all the master challenge on Khan Academy and thought I knew those subjects. It turned out that I had a good grasp of things but it was not perfect. I started using Paul Online Notes and A first course in Calculus by Serge Lang and I can say that Khan Academy is great but not enough. KA gives you a false feeling of knowledge. At least, that was the case for me. I agree with micromass that KA is really great but only if it is coupled with a textbook.

Good luck.

 

[Sync]

Cosign. KA is not enough tbh.

 

[micromass]

That is definitely the case. What I meant was more like, do you have to unlearn things from this book if you want to do mathematics for mathematics later ? Is this book better than other methods books in that aspect ?

No, you don't have to unlearn anything. Boas offers great intuition and applications. It's just not rigorous (which is obvious immediately), and offers not really many proofs. It's not like a math book where everything is proven and stated rigorously.

 

[The PAQI Monsta]

No, you don't have to unlearn anything. Boas offers great intuition and applications. It's just not rigorous (which is obvious immediately), and offers not really many proofs. It's not like a math book where everything is proven and stated rigorously.

I think I'm going to go for Engineering Mathematics by Stroud; Boas seems to expect a level of calculus which I'd say is too high for where I'm at right now.

 

[micromass]

Why not just do a good calculus book?

 

[The PAQI Monsta]

Why not just do a good calculus book?

Is a calculus book not too narrow, or does it go in depth with other topics?

 

[micromass]

Too narrow for what? You need to know calculus anyway. What is your goal at this point?

 

[The PAQI Monsta]

Too narrow for what? You need to know calculus anyway. What is your goal at this point?

What I mean't was, since a calculus is an actual branch of maths will it not be specialised on that topic leaving other topics uncovered?

 

[micromass]

What I mean't was, since a calculus is an actual branch of maths will it not be specialised on that topic leaving other topics uncovered?

But what other topics? I'm not sure I know what you're trying to do. You can learn other topics after you've done calculus.

 

[The PAQI Monsta]

But what other topics? I'm not sure I know what you're trying to do. You can learn other topics after you've done calculus.

Well when I did maths, I remember not just covering diff & int but also topics such as vectors, complex numbers, vectors, series, matrics, polar coordinates etc, not just calculus on its own.

 

[micromass]

Well when I did maths, I remember not just covering diff & int but also topics such as vectors, complex numbers, vectors, series, matrics, polar coordinates etc, not just calculus on its own.

In high school, that is true. But if you go to university, you will meet far less courses that cover many general topics like his. They are split up in several courses. Calculus, for example, will cover differentials, integrals, vectors (in multivariable calculus), series, matrices (in multivariable calculus) and polar coordinates. Another useful course is linear algebra which covers complex numbers, vectors and matrices. Those are two important courses. If you're interested in physics, then you can complete your math knowledge with a methods course which uses Boas.

 

[Arnaldy Jr.]

Sometimes I go for to khan academy just for refreshing purposes, but to solidify my skills I prefer a textbook. A good calculus mathematics textbook that I can recommend to you is Calculus: Early Transcendentals by James Stewart. This book is good on applications of engineering and other sciences, I don't remind if this book has some physics exercises. Also this book covers various topics of calculus like multivariable calculus and series, etc.

 

[Intrastellar]

I think I'm going to go for Engineering Mathematics by Stroud; Boas seems to expect a level of calculus which I'd say is too high for where I'm at right now.

Along with Boas, the beginning mathematical methods textbook in the UK is:
http://www.amazon.com/dp/0521679710/?tag=pfamazon01-20

See if it has what you want.

 

[vanhees71]

It depends on what you want. As already discussed pure math has another aim than applied math. Pure math aims at rigorous proofs of theorems from a given set of axioms (or even investigates the implications of this idea itself in terms of formal logics). This is, of course, important also for the applications, because the proven theorems and the discovery of other theorems in proving provides the idea, how to apply mathematics to the description of the real world. The goal of the theoretical sciences is to find the right mathematical structures to describe some particular aspect of nature, e.g., the motion of bodies and continua (fluids and solid) in Newtonian or relativistic classical mechanics. For this you need to know the mathematical structures, found by the pure mathematicians, to find such a description. E.g., for Einstein when he looked for the right description of gravity within relativistic physics, he could build on the notion of Riemannian geometry, which was developed by pure mathematicians like Gauß, Lobatchevsky, Riemann, Minkowski, Levi-Civita et al. in the goal to investigate the status of the parallel axiom in Euclidean geometry, which is a completely pure-math academic question.

It's of course true that also the pure mathematicians need heuristic ideas before they build their abstract edifices. One famous example is Functional Analysis, which was developed to give unrigorous mathematical manipulations by physicists and engineers like the Dirac $\delta$ distribution (which was in fact invented much earlier by Sommerfeld) a solid foundation. From this Functional Analysis as a whole branch of mathematics developed.

That said, you must be clear about what's the goal you aim at before reading a math textbook: If you want to apply mathematics to real-world problems you need more something like applied calculus, where you learn the calculational techniques used in the theoretical sciences to describe and solve real-world problems. If you want to learn how to make the applied math rigorous and watertight, you should use an analysis textbook. The former kind of books won't teach you the rigorous math and the latter won't teach you how to calculate things in practice. I think, however, a good mathematician should also know a bit about how to calculate mundane things like an integral or solve a given differential equation as well as a good scientist should know a bit about the rigorous foundations of the math he/she applies in their daily work.

 

[MidgetDwarf]

Problems with watching course videos online is that they do the thinking for you. It takes away from the critical thinking process. Videos can be great if you happen to have been working on a particular section and after going to office hours or tutoring you still don't get it. These videos are not intended as a replacement for an actual book. It is important to build the school of learning from a book and thinking for oneself. After a time period, most students come to realization that their is no course material on line for a particular class. After maybe Analysis the material becomes scarce or nonexistent.

Learn Calculus. If you need books. I liked Thomas Calculus with Analytical Geometry 3rd ed, Simmons Calculus, and any edition of Stewart for the exercises not the material in the book.

What seems to me from reading your responses is that you want to take shortcuts. There are no shortcuts in STEM.