I personally think that there is a perfectly valid question hiding behind the words. So this post is split into two parts. The first part consists of what I think might be an appropriate formulation of the question. The second part, mainly directed at Iyengar, consists of a breakdown of what I assume are the major problems people here have with his formulation.
Part 1: Title: "Popular Math books with Depth" [community wiki]
I'm interested in books such as "Fearless Symmetry" by Avner Ash and Robert Gross that.
require little background knowledge beyond highschool math,
provide lots of intuition, and
still develop their topic with some depth.
Any mathematical area is fine with me.
Part 2: The problem starts with the title "Existence of Good mathematical books". There are a lot of mathematical books out there, and restricting oneself to the ones that are not universally agreed not to be good isn't of much help. People can have different views on what makes a book good and you are ultimately imposing your opinion on the matter on other people. The two sentences
I am going to ask a question about some mathematical references.
Actually its a search of mathematical books that are good.
are completely unnecessary. People will see exactly what you are going to do, even if you do not announce it in advance.
But if you carefully observe the things, any mathematical book just
speaks about theory , " raw theory ", they just speak about the
equations and directly go into their applications ( Problems and
theorems ), with-out giving a proper intuition, without telling what
is going on behind every concept and every equation .
This is you giving your opinion on the majority of mathematical literature. Even if your asessment would be correct, it is clear from the context that you consider this to be bad writing, which can offend those who write such books and those who enjoy such books. There are different intuitions behind a topic. Also, people with some mathematical experience can often supply the intuition themselves and get distracted by verbosity. Some books are written as references for material mostly familiar already.
The most wonderful book I have ever read in my life was Fearless
Symmetry by Avner Ash and Robert Gross, which is a greatest book that
gives an intuition behind the need to consider fields, need for Galois
One "greatest" is enough. This of course is again a value judgement others might disagree with. Also, it is not in any way part of a question.
I wanted to know whether any such rare books exists in other areas
Whether such books are rare or not is something you can only judge when you have seen most of them- in which case you probably wouldn't need to ask the question in the first place.
Which possess the following characteristics :
- A very good introduction to the concept, giving the reasons behind
introducing theory X or some jargon Y in the particular field.
fantastic intuition by providing a view of concept from a different
perspective, rather than the general picturization of concepts given
in the normal books.
Ask for "intuition" and "perspective", whether one thinks it is "very good" or even "fantastic" is ultimately too subjective to be useful. Also, leave out your judgement on "normal books".