Books for self-learning Mathematics

In summary, "Calculus Made Easy" by Silvanus Thompson is a helpful book for those looking to self-learn calculus, as it explains concepts in a simple and understandable manner. However, the user is also open to other books and branches of mathematics. Suggestions include "Practical analysis in one variable" by Estep, and Stewart's books on calculus and precalculus. The edition of the book does not matter, and it is recommended to avoid editions with excessive visuals. Ultimately, the most important factor is finding a book that explains concepts clearly and has helpful exercises to test understanding.
  • #1
shihabdider
9
0
First of all, let me just say hello to the community here, as I am new and this is my first post (hopefully of many).

Now on to business. Recently I have been reading a book by Silvanus Thompson called Calculus Made Easy. Now, I took Calculus in my junior year of H.S (I am a senior now) but it was the teacher's first time teaching the subject, and the assigned text was too convoluted to read. (In fact the only times I opened it were to do H.W assignments.) In either case, I did not care enough about the class to self-study by some other means and was somehow able to pass.

A year later I have come to realize my ignorance in even the most basic concepts in calculus and decided to try and self-learn it. Calculus Made Easy was pretty much a godsend, as it explained all of the conceptual ideas in an easy and readable format. Some of the ideas in the book, such as the explanation of the derivative in terms of "little bits of x and y" (i.e dx and dy) and the derivation of the exponential series blew my mind. Now, you might laugh at me but it was really the first time that calculus was more than "plug and chug" to me.

But I digress. The point of this story and this post is this question: Are there any other books out there like Calculus Made Easy? Books that clarify the arcane mysteries of the mathematical world in a simple, easy to understand, mathematical jargon free speech. Now while I would like to pursue Calculus a bit further, I am equally open to other branches of mathematics. What I would especially like is some sort of progression. (e.g Trigonometry comes before Calculus and Algebra before Trigonometry).

In the end though it doesn't matter, I am willing to read any book on any topic so long as it is as simple and enlightening as Calculus Made Easy has been.
 
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  • #2
Hi!

In my opinion, if you want to continue studying mathematics (in college for example) then you shouldn't use books of the type " x made easy" or "x for dummies".

Try the real stuff. It WILL NOT be easy at first, but it will make you stronger in mathematics. Any learning process is painful, and if it ain't, then it's not a proper learning process.

I think anyone is capable of self-learning Calculus from Stewart's[\b] book. If you find its too difficult, then try "Precalculus" also by Stewart. Don't buy it, any science library has it.

Good luck!
 
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  • #3
How about some Spivak?

Also, get some linear algebra done!
Linear Algebra is an incredibly pretty subject, makes calculus look like a contraption sellotaped together imo :3
 
  • #4
genericusrnme said:
How about some Spivak?

Also, get some linear algebra done!
Linear Algebra is an incredibly pretty subject, makes calculus look like a contraption sellotaped together imo :3

If he is asking for a "student-friendly" book I don't think Spivak is a good choice, it's a difficult book for a self-learner.

For Linear Algebra he could use Larson's. I very much agree in that it is a pretty subject. The best of Linear Algebra is that you don't need any basis at all for learning it besides the very basic arithmetics
 
  • #5
Alpha Floor said:
If he is asking for a "student-friendly" book I don't think Spivak is a good choice, it's a difficult book for a self-learner.

I don't think there ARE any good books for self-learning rigorous calculus/analysisy type stuff sadly..
I managed to self learn from it well enough though
 
  • #6
Try the book "Practical analysis in one variable" by Estep. It's meant to be easy and rigorous. It's easier than Spivak, but it does cover some theory.
 
  • #7
Thanks for the quick and numerous reply's. I will look into Esteps book and I have actually taken a look at Spivak. I found the explanations to be mostly intuitive and understandable, but the questions seem to be where the real learning takes place and I am afraid I am not quite up to the challenge (yet).

I also agree with Alpha Floor in that difficulty usually equates to better understanding but I just want a text that doesn't have to much techinical jargon (though perhaps that may be asking to much). I will however look into Stewart's book.

Thanks again guys
 
  • #8
I'd like to second Stewart's books on calculus and precalculus. His books also contain tons of interesting exercises to test if you've actually understood all of it - definitely recommended.
 
  • #9
I was looking at some of Stewart's Calculus books and now am confused on which one to get. There is: Early Transcendental, Concepts and Contexts, and then just Calculus, also does the edition matter? I'm looking to get 5th edition (its the only one my library has).
 
  • #10
Don't bother about the edition, in fact, the earlier the better (in my opinion). Newer editions have too much "eye-candy", colours, pictures... it looks rather like a comic book for 4-years old instead of a mathematics text

As for the book itself, between "early trascendentals" and "calculus" the only difference is that the second one includes a chapter on inverse functions (inverse exponential, inverse trigonometric functions etc)

Concepts and contexts must be how they call the new "precalculus"...

EDIT: I've checked, and seems to be a sort of theory backup

Just get the classical "Calculus", the shorter the name, the better :)
 
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  • #11
I recommend Early Transcendentals. There's not much difference between that one and the 'normal' Calculus book, but I've got this one (6E) and can vouch for its usefulness. I don't know Concepts and Contexts. Personally, I haven't seen much of a difference between 6E and 7E, although I suspect many errors have been fixed (with so many examples, I suspect it's impossible not to make quite a few of them). I recommend getting the newest edition if you can, but there's no harm in getting a 6E, either - the concepts stay the same, and if something seems out of place you can always google it.
 

Related to Books for self-learning Mathematics

1. What are the benefits of using books for self-learning mathematics?

Using books for self-learning mathematics allows for a personalized and flexible learning experience. It also helps develop critical thinking and problem-solving skills, as well as a deeper understanding of mathematical concepts.

2. How do I choose the right book for my level and learning style?

When choosing a book for self-learning mathematics, consider your current level of understanding and identify your preferred learning style (visual, auditory, kinesthetic). Look for books with clear explanations, practice problems, and examples that align with your learning style.

3. Are there any specific books that are recommended for self-learning mathematics?

There are many great books for self-learning mathematics, and the best one for you will depend on your specific needs. Some popular options include "A Mind for Numbers" by Barbara Oakley, "The Art of Problem Solving" by Richard Rusczyk, and "How to Solve It" by George Polya.

4. Can I use books for self-learning if I have no prior knowledge of mathematics?

Yes, books for self-learning mathematics can be used by individuals with no prior knowledge. Look for books that start with the basics and progress gradually to more advanced concepts. It is also helpful to supplement your learning with online resources or a tutor.

5. How can I make the most out of using books for self-learning mathematics?

To make the most out of using books for self-learning mathematics, set aside dedicated study time, and establish a consistent study routine. Take notes, practice problems, and review your progress regularly. Don't be afraid to seek help or clarification when needed.

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