As I have said in the first post on my blog, welcome to the house that Yahoo made. What is already here and up with 21 entries is an answers blog, something that has started out as a philosophy and general advice blog that grew out of my Yahoo answers page. Where it will be going, in part with your help as I help you, is not where it has been. While the philosophy and advice will still be there, and you'll see more of it, the primary emphasis will be on post-Calculus mathematics, and unlike many of those you will see blathering away about such matters online, I am professionally qualified to post on this topic. I do have a graduate degree in the subject. I've run discussion sections at the collegiate level in it, and having been the grader for a number of classes, am doing rather more that guessing when I tell you what graders are looking for.
Most of the problems you see worked on my blog and on this site will be of my own choosing, examples that I think that you'll find helpful, but I do welcome submissions of problems that you're having difficulty with. I won't promise that I'll be able to solve every one, especially as the problems go up in complexity, in some cases because I've gotten rusty - yes, I'm working on that - and in others, because there is some degree of specialization in Mathematics. I hope that the problems on which I choose to work will give you some idea of where my areas of expertise and interest are, but I should be able to handle undergraduate material without much difficulty.
Be forewarned that I don't log in every day, so there might be long, very long delays before I answer. If you're here looking for help with tonight's homework, you probably won't get a response in time to help, and that's probably for the best. There are going to be those who want others, online, to do their homework for them, submitting other people's work as their own. That's cheating, plagiarism to be exact, and rather unwise in addition to being morally wrong, because I already have enough traffic that there is a not completely remote chance that one's instructor will see this blog, sooner or later. Submitting somebody else's work as one's own is a breach of the ethics policy and grounds for expulsion at almost any university. I'll never knowingly help anybody break trust with his teachers and fellow students and harm himself in this manner.
What I hoping that you will do is study on your own, bringing me problems that you encounter in the course of your not for credit work. This really is the secret to success in college, anyway - not merely keeping up with the material, but being so well ahread of it, that one could, in principle, skip studying for a few weeks, and still be ahead, and yes, that is possible. Panic is what kills students more than anything else in my experience and yes, sometimes quite literally. We're going to be more in the realm of pure math on this blog, so lab accidents aren't likely to become an issue, but I have known of students who've committed suicide after their lives, to them, have seemed to fall apart. Always a terrible shame to see that happen, especially since those around them never seem to know that they're up on that ledge until it's too late to talk them off of it. I won't claim to be able to offer you more than a sympathetic ear, and the assurance that things are never as irredeamably bad as they seem in such moments, but I might be able to at least offer you some helpful advice about how to avoid the need for that specific type of despair in the first place.
While maybe a third of my students thought, incorrectly, that I was very mean, a bit over half of them would have vocally disagreed, I did have a history of conducting sections whose average grades were better than most. I won't tell you that you can be a nobel laureate. G-d and nature make that decision, not me. I won't even tell you that you can pass the class. There is a matter of innate ability, and that varies from person to person. I will tell you, with little likelihood of being wrong, that you do have innate abilities that you never suspected that were there. I'll also tell you that intelligence is not a thing that can really be described with a single number. There are many ways to be talented or brilliant, which is one of many reasons why I hope nobody who passes by here will ever succumb and commit the "sin of despair". Even if you don't have the innate ability to do what you set out to do in college, the odds are very, very good that you're remarkable in some other, unexplored way, something on which you can build. It's a thought to focus on which can carry you through your studies, and help drive away the panic that can keep you from living up to your potential. The only thing that might happen this year that really might be tragic, is you giving something less than your best, because that can keep you from being where you were supposed to be. Wherever that is. So don't worry about it.
What I did for my students, and hope that you will do for yourself, was really push them, but never let them think that I wanted to see them stumble, as I admit that some instructors do, and no, I don't understand such attitudes, either. I don't believe that I want to. The best way for you to push youself is to find books that cover the material that will be covered in a class that you intend to take, and work your way through them, before you take the class, so you hit the ground running. Look up the reading lists for the course in years past, and see if you can find those books in your school library. I'll be suggesting a few titles. Math books are not cheap, usually running a minimum of 50 dollars per volume unless we're talking about Dover's reprints of books that have been public domained by expiring copyrights - often well worth buying - and often aren't available in the local bookstores at any price. Walking into Borders, a few years ago, looking for Statistics books, I found that there was no such section, and that the DaVinci code, by itself, took up almost four times as much shelf space as all of Mathematics put together. So really, you want to track down those college libraries, some of which might surprise you with the breadth of their selections, even when the schools have no graduate programs. Their professors usually do have PhDs, and seem to have some influence on the book selection process.
This might be enough to get you what you need. If not, there are e-texts, and if those don't help, we'll see what we can do. Again, I can't make you any promises, but don't be shy about asking me to see if I can find sources. Mathematics isn't just an interest for me, it's a profession of choice, and the help I give you today, is help I can give again to a co-worker or a student tomorrow. I'll be happy to look.
Again, as I explained in that first post, Yahoo's practices shoved me into doing the answers thing as a blogger far more than as a participant in their answers service, everything you see there eventually being seen there, with the possible exception of a little drama, when I run into somebody who's a little crazy. But this is a definite step upwards, because Mathematics becomes very difficult to follow in an all text, strictly alphanumeric environment. On a blog, one gets to have pictures, and pictures allow one to show equations clearly, when all else fails. They allow one to illustrate geometric proofs, enter those special characters that Mathematicians must use so lavishly, and they make life easier. The move is one I'm glad to have made.
I run my pages according to the "better than full webring navigability" standard, which means that you won't just see a path back to the ring from this site and my main blog, but from all related pages as well - my Flickr profile, my Youtube channel, and a few side blogs, on which I'll discuss discussions on the various blog hosting services in which I've found myself, linking from my main blog to them, for those who want to know more about some of the articles I've read. I'm also starting a real time Microblog to share some of what I see as I commute to wherever I'm going, if you are curious about that, and a side blog for counterexamples in Mathematics, named ... take a guess ... and most pointedly, no page of music. I will stand firm on the position that headphones have no place in study, and that anybody who says otherwise is either fooling himself, or trying to fool his parents. All of this being tied together into a unified whole through the running of feeds and interlinking - don't see this as a collection of blogs, but one blog with a lot of footnoting.
This directory is where you'll find material written more in a lecture format, when it gets written. With the exception of Yahoo Answers, these all can be followed through Feedburner or Mybloglog, the former being recommended.