What Are the Best Books for Complete Beginners to Learn Mathematics?

[drguildo]

Hi,

As it stands, I am borderline clueless when it comes to mathematics. I had bad teachers in school and so was pretty much doomed from the offset.

Anyway, I have recently developed an interest in learning more and improving my abilities but am having a thoroughly frustrating problem that I hope somebody can appreciate and help me with. I have been trying to find some good books to learn from and every single one that I've looked at seems to fall into one of two camps:

• "Text books" that are explicitly aimed at teaching mathematics. They are laid out well and progress in a nice fashion; building on what's come before but that don't attempt to impart any kind of understanding but rather teach you a bunch of plug-and-chug algorithms with no kind of attempt at explaining how or why things work. A good example is Foundation Maths (0131979213).
• More conventional books that receive a lot of praise as introductions to mathematics, that are supposedly aimed at (or at least understandable by) non-mathematicians, but within the first chapter they are already assuming that you are perfectly comfortable with topics such as algebra and geometry. Examples are Mathematics for the Million (039331071X) and What is Mathematics? (0195025172)

Can anybody recommend any introductory mathematics books that don't suffer from the aforementioned problems? I have already spent a good amount of money on books only to be disappointed and disheartened.

Many thanks.

 

[ice109]

look at the curriculum of a university. in fact i would suggest taking those classes at said university.

 

[Vid]

https://www.amazon.com/dp/0387967877/?tag=pfamazon01-20

 

[drguildo]

look at the curriculum of a university. in fact i would suggest taking those classes at said university.

I don't understand. How is looking at the "curriculum of a university" going to help? I think I made it fairly clear in my original post that I am pretty awful at mathematics so I don't understand why you think I would be capable of studying it at university level.

Very strange.

 

[ice109]

I don't understand. How is looking at the "curriculum of a university" going to help? I think I made it fairly clear in my original post that I am pretty awful at mathematics so I don't understand why you think I would be capable of studying it at university level.

Very strange.

because most universities start their students off with college algebra which is equivalent to algebra 1 and 2 from a high school. if you can't start there then you should look at community college which has college prep classes which start at a more elementary level.

 

[mathwonk]

maybe you do not appreciate how hard you have to work to understand mathematics. e.g. "what is mathematics" is indeed aimed at beginners, but is still very challenging to read. try it again, more slowly, and count a single page as a success.

or if you really do not know even high school math, try one of the textbooks "geometry" or "algebra" by harold jacobs. get an old edition used and cheap, the older the better, as the geometry books were dumbed down in later editions.

 

[Quantumduck]

To expound on what MathWonk said. We have a perception in our country of math being a 'genius' thing or a 'gene' thing.

Either we have the math gene or we don't, meaning either we have the capacity to understand math or we don't.

However, we need to look at Cezanne vs. Picasso. Cezanne spent hours and hours and weeks painting and repainting each element of his paintings. He agonized over each brush stroke, and did his best paintings later in life, after he spent thousands of hours working and agonizing over each little element of his work. He is a genius with his paintings, but it is not an easy genius.

Contrast this with Picasso. He was a genius with a brush, painting quickly and without much correction. He painted his best works young, with his later paintings less valued.

We, and I am American, so I mean the American We, tend to think of genius only in terms of Picasso. Easy, quick, and fast. Genius also takes the Cezanne approach, agonizingly slow, hard work.

Math sometimes is a Cezanne, where we need to work and work and work to get good, despite what the media tells us to do.

[not my original idea. The author of Blink and The Tipping Point said this in a presentation to the NCTM national conference.]

 

[Werg22]

Perhaps you might want to take a look at this book:

https://www.amazon.com/dp/0817636773/?tag=pfamazon01-20

From the preview and some of the reviews, it looks like the type of book you are looking for.

 

[drguildo]

Perhaps I did a poor job of explaining. When I say I am "awful" at mathematics, I don't mean that I have put in massive amounts of effort and that is the end result. I mean that during my formative years I was unlucky enough to have some pretty poor teachers who, like most others I suppose, prescribe to the "ours is not to reason why, just invert and multiply" school of teaching. Needless to say, I did not pay much attention. I have forgotten most of what I learned (mostly because I never really learned it to begin with), and what I do remember feels disjointed and incomplete. I definitely do not feel that I understand it.

Since developing an interest I've tried to find a good (also meaning appropriate) book but have encountered the problem I outlined in my original post.

Thanks for all the advice and suggestions thus far.

 

[symbolipoint]

drguildo, you approached the wrong kinds of textbooks. The kind that you would want are the kind designed to teach you the foundation, fundamental concepts and skills at the elementary level. You want a good book first on Arithmetic, and maybe once you are finished with this, you want a good rigorous book on Elementary or Introductory Algebra. You can find these things at used books stores or sales. They do NOT need to be recent publications; in fact, books of Algebra or Arithmetic which are 20 or more years old might be far better and easier to use than anything published within the last 10 years.

If you are so underdeveloped in mathematics, then a university is not the right level for you to start studying. Check with a community college about the remedial courses available. Build up your knowledge and skills in Arithmetic and Algebra 1. Then, you will be more aware how to study Mathematics.

 

[symbolipoint]

drguildo, I just read the post #9. If you have a very minimal understanding of "basic arithmetic", you might be able, if you study very regularly and intensively, find that Algebra 1 will help you to understand many things that were not well explained to you when you studied Arithmetic/Basic Math. If you want to know more, send me a private message.

 

[drguildo]

Do you have any recommendations of such books? I think it would be best to post here rather than in private message because then other people will have access to the information, if you don't mind.

I think my arithmetic is fine; however, a good example of the kind of thing that annoys me is that when most people are taught long multiplication and long division, the algorithm is just presented as-is, with no attempt made to provide an explanation or to convey understanding resulting in insight into decimal and place-value notation. I am looking to completely avoid material that does this. I don't mind starting right back at the beginning if need be.

 

[symbolipoint]

Do you have any recommendations of such books? I think it would be best to post here rather than in private message because then other people will have access to the information, if you don't mind.

One good type of source is any library used book sale. I say this to anyone who asks about where to find used, very inexpensive books. If you are concerned with WHAT to look for, a few good Algebra authors to target are Lial & Miller, Larson & Hostetler, Aufmann & Barker, Drooyan, Dulciani, and some others that I do not remember. Those would be for authors of Algebra books like Introductory or Elementary.

The words you want to see in the titles are "Algebra 1", "Introductory Algebra", "Elementary Algebra", "Beginning Algebra".

I think my arithmetic is fine; however, a good example of the kind of thing that annoys me is that when most people are taught long multiplication and long division, the algorithm is just presented as-is, with no attempt made to provide an explanation or to convey understanding resulting in insight into decimal and place-value notation. I am looking to completely avoid material that does this. I don't mind starting right back at the beginning if need be.

Right. Some of those are not always well explained. You learn them better when you explore on your own, critically examing the process; and Algebra can also give you a better understanding of the division algorithm. You will also find that Algebra helps you understand longhand multiplication and relate it to the distributive property, and this can also be demonstrated graphically. You will probably find many other benefits of studying Introductory Algebra.

 

[Gary_123]

A book that you can use in your own without a teacher is
Engineering Mathematics Through Applications by Kuldeep Singh.
It got complete solutions to all the exercises online.