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I am a 17-year old student in India, in the standard 12th grade. Recently, I found the fascination in mathematics, and I am eager to dig in further.

Currently, the only textbooks I have are the ones at school: M.L Agrawal's of 11th and 12th. I don't find them very supportive. They are educational, but quite exam centered. Almost everything around me is exam centered, as students study math primarily so that they can qualify for board exams and engineering entrances.

Not to sell myself short, but hey, not everyone can be Ramanujan and derive wonders from schoolbooks. Could anyone suggest someplace to start? I am really interested in coordinate geometry and calculus.

I have considered buying an S.L Loney, but every suggestion would be valuable. Thank you.

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  • $\begingroup$ Well you do have the internet, but I'm assuming you want something a little more specific than that. $\endgroup$ – recursive recursion Jun 8 '14 at 12:50
  • $\begingroup$ I, being from the same country, know what you feel right now. When you say calculus, you mean just the integration and differentiation we are taught in 12th, or do you mean the more abstract form that is taught in college level courses? $\endgroup$ – Swapnil Tripathi Jun 8 '14 at 13:01
  • $\begingroup$ The site libgen.info has a massive number of scanned math books. Just search for what you are interested in. $\endgroup$ – Rene Schipperus Jun 8 '14 at 13:02
  • $\begingroup$ The website How to Become a Pure Mathematician (or Statistician) is great for that purpose. It contains lots of references from basic to not-so-basic disciplines. Of course, you shouldn't study ALL the books listed there. Try to compare and choose one from each topic you like (and come here ask for opinions or help whenever needed). It's very important to do exercises, specially the hard ones. $\endgroup$ – Luiz Cordeiro Jun 8 '14 at 13:24
  • $\begingroup$ @swapnil I dont know what they teach in colleges. I am looking to it as a study $\endgroup$ – Rohit Jun 8 '14 at 16:06
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Some books that I found helpful when I first started in math were the following:

Elementary Number Theory by James Strayer. It's a straightforward textbook on number theory, and you can get your feet wet learning how to prove some basic things.

Elementary Geometry from an Advanced Standpoint by Edwin Moise. This is a nice textbook on Geometry. Here you develop everything from the ground up. I really enjoyed my time going through it on my own.

Introduction to Analysis by Maxwell Rosenlicht. This was the textbook that was required for my senior Advanced Calculus course in undergrad. It's a dover book and pretty cheap. Also it has good explanations for the concepts in Advance Calculus, including metric space topology, convergence of functions, etc.

I also enjoyed Number Theory by George Andrews. It's a more combinatorial approach to Number Theory. The book is cheap and speaking of Ramanujan, George Andrews is a world class expert on his works.

Just some ideas.

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  • $\begingroup$ That is really very helpful, and some resonating. Thank you very much! :) $\endgroup$ – Rohit Jun 8 '14 at 16:01
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Please note I am not in a position to guide how you can take forward your interest in Geometry, but I feel that following are math foundation books.

  1. Coordinate Geomerty - S L Loney (http://archive.org/)
  2. Plane Trigonometry - S L Loney (http://archive.org/)
  3. Higher Algebra - Hall & Knight (http://archive.org/)
  4. Challenging Problems in Algebra - ALFRED S. POSAMENTIER & CHARLES T. SALKIND
  5. Problems in Elementary Mathematics - V. LIDSKY,L. OVSYANNIKOV,A. TULAIKOV,M. SHABUNIN (Mir Publication)
  6. INEQUALITIES - P. P. Korovkin (Mir Publication)
  7. Methos of Mathematical Induction - I. S. SOMINSKII (Mir Publication)
  8. The Differential and Integral Calculus - N P Piskunov (Mir Publication)
  9. Trigonometric Function (Problem Solving Approach) - A. Panchishkin, E. Shavgulidze (Mir Publication)
  10. Class 11 & 12 math books from site http://ncert.nic.in/NCERTS/textbook/textbook.htm
  11. Calculus - Thomas & Finney

All the archive.org and Mir Publication books are available free on internet.

I feel book 8 and 11 should be kept last.

My reply includes Geometry, Algebra and Calculus.

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  • $\begingroup$ Great list of books ! Can you give a link to where the Mir books can be found ? I am not familar with them. $\endgroup$ – Rene Schipperus Jun 8 '14 at 13:43
  • $\begingroup$ @ReneSchipperus, mirtitles.org $\endgroup$ – Vikram Jun 8 '14 at 13:58
  • $\begingroup$ I'll check them out. Thank you $\endgroup$ – Rohit Jun 8 '14 at 16:00
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You might check the lists of free online math courses offered by the very best universities: https://www.coursera.org and https://www.edx.org/ -- probably start with some basic linear algebra and/or calculus courses.

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