Hello Everyone I am a high school student currently doing Extension 1 Mathematics at my school. I am currently looking for a high quality mathematics book. Although I am not looking for a book, like many others that I have already read, which teaches you the content in a topic such as circle geometry or integration, but rather a book that teaches you, and shows you tips that will help improve you general mathematical ability, skills and frame of mind.
It has occurred to me that maths is not just about manipulating numbers, or solving a problem through changing for example the place of the x variable until you come to an answer, but also includes a certain frame of mind that allows you to break a certain problem into something that can be solved through numbers(like thinking about a tree as a length instead), and as efficiently as possible. This is the book I am more trying to find. A book that could give me tips on ways to think about a problem analytically and tips to allow problem solving to be easier in this area.
Specifics traits I am looking for:
methods or tricks in mathematics to help simplify or solve hard questions involving algebraic manipulation, basic problems involving sketching parabolas, hyperbolas and circles.
The history of how mathematics was formed( I am interested in this area of mathematics) This is not as important as other dot points
processes or procedures I can apply to mathematical problems that will help improve my ability to break down a problem and solve it effectively ~ I have an issue where I will look at a problem and not know what to do
Improve my understanding on the actual idea of mathematics, not necessarily the content associated with it
I also understand that practice questions will help improve my ability, but a maths book that will give me an understanding and specific skills in breaking down questions and converting them as to say into an analytic form will definitely help me.
Thank you guys for your input.