Part I -- General > Why not quit my job and go back to school? Well, that’s not really for me. Reading books at my own pace lets me try a subject out without

Part I -- General > Why not quit my job and go back to school? Well, that’s not really for me. Reading books at my own pace lets me try a subject out without fully committing to it and making it a necessity that I find work based off of it. I respond here in three parts, the first general, the second more specific and about linear algebra, and the third about statistics. Really, in school, you still have to learn the stuff. And, there a class might help but won't be enough; so, right, again, during the course and in the hours not in the class, you still have to study and learn the stuff. Or for the class, "mathematics is not a spectator sport". That means you still have to study the stuff, get it between your ears, understand it. Eventually you can conclude that mostly college and its courses are more for certification than education. For the education, that's heavily up to you. But there are some dangers in self learning: Not all the ideas and learning materials are good; the really good ones are only a small fraction of all the ones you will likely encounter. So, in praise of college and profs, they can (1) get you on a good track with good ideas and learning materials and (2) get you unstuck and keep you on track. In such study, it's possible to do too much or too little -- from some experts you can see about what is the right amount to do. I said "college"; revise that to read "one of the world's best research universities", say, in the US, 1-2 dozen. The ideas and materials you will see in such a university really do stand to be better than nearly all you will encounter otherwise. Such learning is where there's not much substitute for quality. But, still, just to learn the material, you don't really have to enroll in such a university and, instead, just borrow from their course descriptions and materials. Indeed, some of the best such universities are working hard to make their learning materials available to all for free over the Internet. Why? Because those universities want to concentrate on pushing forward with research. Here's a way: Show up at such a university and appropriate department, in your case, applied math, mathematical sciences, operations research, statistics, whatever. Maybe show up at some public department seminars. Talk with some of the students. Say you have a career going, for your career are interested in what the department is doing, and want to learn more about the program and the mathematical content. So, get some of the students to talk and explain. Then for some of the courses you are interested in, see who the profs are and look at the course materials, say, texts, handouts, on-line files, etc. Then after looking at the materials and, say, have made some progress with them, try to get 15 minutes to chat with a prof. Then take what you just got from that department for free -- broad directions, what they regard as more/less important, texts, course materials, etc. -- and go off and study on your own. When you think that maybe you have some course studied well, try to get a copy of the course final exam or Ph.D. qualifying exam, work through it, and, if it appears you did well, ask a prof to check your solution to a few of the most difficult questions. If your solutions look good, then you will start to look good and may get asked if you would like to apply as a student in the department. So, here you and the prof and department are interviewing each other. Such things worked for me: (A) In my career I kept running into the work of John Tukey at Princeton and Bell Labs. So, it was stepwise regression, exploratory data analysis, power spectral estimation, convergence and uniformity in topology, his statement equivalent to the axiom of choice, etc. So, I wrote him at Princeton asking about graduate study, mentioned those topics, and got back a nice letter from the department Chair basically inviting me to apply. (B) I applied to Cornell and got rejected. But largely independently I visited a prof there to discuss optimization, asked about being a grad student, and soon got another letter accepting me to grad study. (C) At least at one time, the Web site of the Princeton math department said, "Graduate courses are introductions to research by experts in their fields. No courses are given for preparation for the qualifying exams. Students are expected to prepare for the qualifying exams on their own." or some such. Lesson: In grad school at Princeton, are still expected to learn the qualifying exam materials on your own. Well, to do that, don't have to be in the high rent area around Princeton, NJ. When I did go to grad school and got my Ph.D., what really saved my tail feathers was what I had done and did on my own as independent study. Some of the courses helped in providing high quality directions and materials, but the real work was nearly all independent. And, one of the crucial inflection points was when I took a problem in a course but not solved in the course, did some research, and found a solution. The solution was novel, and word spread around the department quickly. My halo got a high polish, and that greatly eased my path through my Ph.D. That is, I had proven results on the most important research academic and Ph.D. bottom line -- I'd done good, novel, "new, correct, significant" research. Then my hair cut or lack there of, sloppy hand writing, occasional upchuck at some bad course material, etc. no longer mattered. My research looked publishable, and it was -- I did publish it later, in one of the best journals, easily, no revisions. So, lesson: That inflection point was from independent work. So, don't feel that your independent work is inferior to enrolling as a student. Instead, in the best universities, as a student, nearly all the work is for you to do independently anyway. Still, I'd repeat -- try to pick the brains, for free, without hurting your present career, of the courses, profs, and materials at a world class department in a world class research university. Why a research university? World class research is a very high bar and some of the best evidence of good expertise, insight, and judgment in the field -- and you don't want the opposites.