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As it stands, I am borderline clueless when it comes to mathematics. I had bad teachers in school and so was pretty much doomed from the offset.

Anyway, I have recently developed an interest in learning more and improving my abilities but am having a thoroughly frustrating problem that I hope somebody can appreciate and help me with. I have been trying to find some good books to learn from and every single one that I've looked at seems to fall into one of two camps:

- "Text books" that are explicitly aimed at teaching mathematics. They are laid out well and progress in a nice fashion; building on what's come before
that don't attempt to impart any kind of understanding but rather teach you a bunch of plug-and-chug algorithms with no kind of attempt at explaining how or why things work. A good example is Foundation Maths (0131979213).*but* - More conventional books that receive a lot of praise as introductions to mathematics, that are supposedly aimed at (or at least understandable by) non-mathematicians, but within the first chapter they are already assuming that you are perfectly comfortable with topics such as algebra and geometry. Examples are Mathematics for the Million (039331071X) and What is Mathematics? (0195025172)

Can anybody recommend any introductory mathematics books that don't suffer from the aforementioned problems? I have already spent a good amount of money on books only to be disappointed and disheartened.

Many thanks.