I need some recommendations for a good linear algebra textbook, something that's actually used in schools. I've finished linear 1 and 2 and I'm doing some preparation during the summer.
This might not be what you're looking for but here's one that I'm enjoying at the moment: http://www.math.miami.edu/~ec/book/ I'm really not very advanced in it (pp.31 of 146) but I've browsed a lot and from what I understand, the author used the first half of the book (75 pages) to enunciate the main concepts and results about groups, rings and matrices that he's gonna need for his complete study of linear algebra in other half of the book.
these are similar to ones used in school,s except these are free: free books: http://joshua.smcvt.edu/linearalgebra/ http://www.math.miami.edu/~ec/book/ http://mathforum.org/library/topics/linear/ http://dmoz.org/Science/Math/Publications/Online_Texts/ http://www.math.miami.edu/~ec/book/ http://www.math.uga.edu/~roy/
Dang that's a lot of ebooks! Got anymore links mathwonk? What about ebooks on set theory and (introductory) Fourier theory?
Yes, about set theory... in what class were we supposed to be formally introduced to it? What I've learned about it so far is from a collection of subtle exposures in other courses. The main idea and fundamentals I had to read on my own.
I learned set theory in high school from a book by allendoerfer and oakley (principles of mathematics), and books by erich kamke and paul halmos (naive set theory). Since then I have enjoyed the book of Felix Hausdorff, and the original work by Georg Cantor (contributions to the theory of transfinite numbers.). a nice work on fourier series is the little benjamin (not an e) book by robert t seeley. i only know the linear algebra ebooks from having to teach the course and needing a reference for my students. a suitable one is hard to find. i.e. most decent books assume students know how to read and do proofs, but most students today do not. the ones i listed run the gamut from mickey mouse (matthews) to excellent (sharipov), and i let the reader choose his own poison.
How many sessions have you completed Ice? And what program are you studying in? Mathwonk: It is true that we don't know how to read and do proofs. There are many proofs in my analysis textbook that completely eludes me, and most proofs that are not straightfoward, I cannot do on my own. And I know it is the same for most of my classmates. What do you think is different now that makes it so students don't know how to read and do proofs?
high schools no longer teach euclid. that is the main thing i guess. also there is a general response that if it is difficult to teach, then just stop trying to teach it, "they'll get it in college". the official response in the US to the poor high school preparation we provide, is to assume colleges can magically make up the deficit. this is leading to a watering down of what used to be the best higher education system in the world, to one that accomodates the weakest graduates of US high schools. US college education is now what used to be US high school education. High school is now essentially nothing at all except at a few excellent schools. Students used to learn to read and write and reason logically in high school, now many college bound students do not learn any of these. High school courses designed to prepare a person to take a certain test, are a joke compared to courses that were intended to teach people to read critically, understand, and write intelligently.
Math, but I switched over from another program. Long story. I suppose there's a reason for the 10 character minimum.
That's sad mathwonk. Ice: I have two friends there who just completed their first year. William and Tayeb. Do you know them?
it is certainly a challenge. how can we combat the tendency to market education, via appealing only to the greed of people, such as by "hope scholarships" based on falsely inflated grades in high school, as opposed to "merit scholarships" as in the 60's, based on competitive tests? In the 1960's president kennedy actually inspired people to want to achieve more. remember his speech: " ask not what your country can do for you, but what you can do for your country." where is the leader today who inspires people to achieve and to give, rather than to covet? not to mention m.l.k., who inspired people to risk life and limb for freedom and equality. it is so disturbing that thes people were murdered that i hesitate to draw the obvious conclusions as to who had the most to gain from their disappearance from the political scene. It is not just sad, it is crucial to the future of our world, for the younger generation to take control of their future, and not let it be stolen from them. In particualr, anyone who wants an A for a course he has not understood is marching to the same tune as a crooked politician trying to divert taxes to his own gain. I am very encouraged by most of the posts on this forum, for they give evidence of a genuine desire to learn and improve oneself by todays young students, and some not so young. to do ones best, and help others to do theirs, is to fight the good fight. more power to you.
mathwonk: Thanks for posting those links to the free books. I took a look at the first few pages of Sharipov's book, and saw a footnote that said the axioms for the the operations of vector addition and scalar multiplication are not independent! I was surprised to see that. Is this common knowledge? I thought maybe Sharipov had come up with his own set of axioms to make things as general as possible, but it turns out Gelfand uses the same ones in his little book from the 60's.