Learning maths concepts …not just how to do an equation

[urbano]

I tried posting in the education section but was unable to start a topic…

Anyways…I'm trying to reteach myself maths from back in the school days in hope of doing a calculus paper at university.

I have realized that a lot of books and materials seem to teach you how so l've equations and what formulas to use etc, but nothing I have come across actually explains WHY.

WHY does the formual work , WHY doesn't a formal used before work etc.

Are there any recommendations for books or materials that actually explain why and how maths works as opposed to just 'do this','do that ' etc


TIA

 

[symbolipoint]

The logical way to reach understanding is to use the same books of introductory and intermediate algebra, geometry, trigonometry, college algebra and calculus with analytic geometry that the colleges and universities would use for teaching. The books used for these places are usually designed for actual understanding, and not simply to learn to use formulas. The good books (which are many) will give proofs and derivations.

 

[homeomorphic]

You might try Khan academy. I've been looking at some of his stuff for the past couple years as one source of teaching/tutoring ideas because students seem to like him, and he's good at putting himself in the place of someone who doesn't already know the subject, which is a huge challenge for someone who already knows the stuff. Students might not appreciate how hard teaching is for that reason. He's not perfect, by any means, but he attempts to address the why questions a fair amount of the time. You have to make sure to find the exercises, though, and not just watch the videos.

Other than that, since I don't remember any particularly good books that are below calculus level, aside from Lines and Curves, A Practical Geometry Handbook, for geometry, the only thing I can say is that if the book doesn't say why, you have to try to come up with your own explanation, if you can. A lot of the "why" stuff for low-level math, I just sort of had to invent for myself.

Another book that you might be able to read parts of is Hilbert's Geometry and the Imagination, but it doesn't really follow the high school curriculum or anything.

You're definitely right that the why is missing from a lot of expositions, but on the other hand, sometimes, it might be just because the author finds the why to be obvious, so you have to take that into account, too. Trust me, it can be hard to explain math to beginners and to even know that there's even a why question involved for the student sometimes once you've really mastered the subject and everything's pretty much just obvious to you.

 

[symbolipoint]

The important question is, what variety of books are available for you? Are you near a university or a community college? Does the school hold annual used book sales? Do your local libraries give used book sales through out the year? Whatever anyone on the forums suggests, you may be able to find available through half.com or amazon.com.

 

[CellCoree]

I completely understand the frustration of not understanding the "why" behind mathematical concepts. In order to truly understand and apply mathematics, it is important to not only know how to solve equations, but also understand the underlying principles and reasoning behind them. This is especially crucial when studying more advanced topics such as calculus.

I would recommend seeking out resources that focus on conceptual understanding rather than just rote memorization and equations. Some good places to start are textbooks that have a strong emphasis on conceptual understanding, online resources such as Khan Academy or Coursera, and seeking out a tutor or mentor who can explain the reasoning behind mathematical concepts. Additionally, practicing mathematical problem-solving and critical thinking skills can also help in developing a deeper understanding of the subject.

Remember that mathematics is not just about getting the right answer, but also about understanding the process and reasoning behind it. With dedication and persistence, I am confident that you will be able to develop a strong understanding of mathematics and achieve your goal of studying calculus at university. Best of luck on your mathematical journey!