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I am 73 yo who has not been to a math class for 50 years. I know there is a completely new mind set needed to approach math problems and I need a starting point. What is the best Algebra book available to start my journey back?

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First I'm impressed with your strong desire to learn linear algebra and refresh your mind, good luck Sir!

For the book recommendation, I highly recommend this book, which I used during my learning trip through this important topic: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares this is the link where you can buy it.

I wish that you'll find all your questions answered there, and again good luck!

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You used the "linear algebra" tag for your question, but in your question you asked about algebra. They are different subjects; linear algebra is more advanced. I am going to assume that you are interested in basic algebra.

I have no idea if it's the best book, but I've found Basic Mathematics by Lang to be a reasonable introduction.

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good luck in your mathematical endeavour, many wonders await :) In answer to your question, I believe the ultimate guides to Mathematics on a high school level are the CGP study guides, which are commonly used in UK high schools such as the one I attend. If you're unfamiliar with the UK education system then GCSE is the first level of high school examinations and you may want to start from the CGP GCSE Mathematics guides. They will serve you well. Good luck!