What does mathematics mean? Is it numbers or arithmetic, proofs or equations? Jan Gullberg starts his massive historical overview with some insight into why human beings find it necessary to "reckon," or count, and what math means to us. From there to the last chapter, on differential equations, is a very long, but surprisingly engrossing journey. Mathematics covers how symbolic logic fits into cultures around the world, and gives fascinating biographical tidbits on mathematicians from Archimedes to Wiles. It's a big book, copiously illustrated with goofy little line drawings and cartoon reprints. But the real appeal (at least for math buffs) lies in the scads of problems--with solutions--illustrating the concepts. It really invites readers to sit down with a cup of tea, pencil and paper, and (ahem) a calculator and start solving. Remember the first time you "got it" in math class? With Mathematics you can recapture that bliss, and maybe learn something new, too. Everyone from schoolkids to professors (and maybe even die-hard mathphobes) can find something useful, informative, or entertaining here. --Therese Littleton
You might try checking out the book, "Mathematics: From the Birth of Numbers"
Well, if you want something light and accessible and suitable for the layperson, I'm quite fond of Jan Gullberg's Mathematics from the Birth of Numbers. It goes over basically everything you would typically learn in primary and secondary school, and it presents everything with historical background. But it doesn't go into tremendous detail on each topic, and it doesn't provide the most rigorous development. It's more of a high-level overview.
But if you really want to learn some mathematics, on a deep and serious level, be prepared to read and study a lot. It's a rewarding journey, and we can give you book recommendations for specific topics, but it does take a lot of discipline and a lot of time. If you want to go that route, I would recommend starting with an intro to proofs book. I like Peter J. Eccles's An Introduction to Mathematical Reasoning, but there are many other popular books along the same line. And you can supplement it with a book on the history of mathematics (or just read Gullberg alongside the more serious texts).
A couple of recommendations (not specific to just Calculus):
- What is Mathematics? (Courant http://www.amazon.com/Mathematics-Elementary-Approach-Ideas-...)
- Calculus (Apostle http://www.amazon.com/Calculus-Vol-One-Variable-Introduction...).
- Mathematics from the Birth of Numbers (http://www.amazon.com/Mathematics-Birth-Numbers-Jan-Gullberg...) This book was written by a Swedish surgeon without any background in Mathematics. He started working on this when his son started attending university. A recommended read.
- The Calculus Lifesaver (Adrian Banner). This book is supposed to be a guide for students to crack their exams. But I found the book surprisingly informative. http://press.princeton.edu/titles/8351.html
- Godel Escher Bach. I've read only the first couple of chapters. My interest in mathematics was rekindled to a great degree by Godel and the Incompleteness Theorem. (http://en.wikipedia.org/wiki/Kurt_G%C3%B6del#The_Incompleten...)
- http://us.metamath.org/. The concept alone makes me happy! Metamath is a collection of machine verifiable proofs. It uses ZFG to use prove complicated proofs by breaking it down to the most basic axioms. The fundamental idea is substitution - take a complicated proof, substitute it with valid expressions from a lower level and keep at it. It introduced me to ZFG and after wondering why 'Sets' were being taught repeatedly over the course of years when the only useful thing I found was Venn diagrams and calculating intersection and union counts, I finally understood that Set theory underpins Mathematical logic and vaguely how.
- The Philosophy of Mathematics. From the wiki: studies the philosophical assumptions, foundations, and implications of mathematics. It helped me understand how Mathematics is a science of abstractions. It finally validated the science as something that could be interesting and creative. http://plato.stanford.edu/entries/philosophy-mathematics/
I think the Philosophy of Mathematics should be taught during undergraduate courses that has Maths. It helps the students understand the nature of mathematics (at least the debates about it), which is usually pretty fuzzy for everyone.
http://www.amazon.com/Mathematics-Birth-Numbers-Jan-Gullberg...It's filled with a lot of history on why things are as they are and it builds up a substantial base of math knowledge from there. I can't comment on whether the additional background information would help someone who is math shy to "get it" but, from the parts I read, it certainly rounded out (and expanded) my knowledge.
It's filled with a lot of history on why things are as they are and it builds up a substantial base of math knowledge from there. I can't comment on whether the additional background information would help someone who is math shy to "get it" but, from the parts I read, it certainly rounded out (and expanded) my knowledge.
If asked, I tend to direct people towards the following books:
Note: you need both the student manual (which most people don't know exists) and The Art Of Electronics.
To cover the maths background required, I recommend:
They are not cheap but worth it.
Oh and a calculator. Any old cheap scientific (Casio/TI/HP) will do as long as it doesn't make errors.
The big problem for me was the maths initially. It doesn't take long before you hit a brick wall at the age of 12. My 10 year old daughter is learning algebra and programming (in python!) though at school so things are looking up.