Beginning of Romance

Question

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.

Answer 1

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.

Answer 2

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.

Answer 3

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.