# How much math to study?

1. I have an interest to improve problem solving ability
2. I would like to finish a 4 year degree in math/ math related field
3. I want to start a career where I grow and improve, and I would like to start it ASAP
4. Before I go back to finish school, I want to improve my problem solving ability because I feel that I will be more prepared and things will be easier for me to manage.
5. Am I wasting my time?

Feedback?

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"I want to build valuable skills that will make me employable." In terms of subject areas you might want to look into: probability, statistics, stochastic modelling & general mathematical modelling, operations research, optimization –  user18921 Mar 1 '13 at 21:05
And perhaps some game theory. EDIT: P.S. Good luck!!! –  user18921 Mar 1 '13 at 21:06
My opinion on the matter: The big hardback textbooks used in curriculums are crap. And, I know I used the Susanna Epp one last semester (didn't read it, just did the practice problems I needed for class). Get something like "How to Prove It" by Velleman. Half the size, twice the worth! Plus there are actually DECENT practice exercises in Velleman. The Epp book might have 120 practice problems with 2 decent ones, whereas the Velleman one just gives 10 great problems. doing 2 great problems is far more worthwhile than 20 bad ones. Also e-mail me for programming. Learning takes a while though. –  NeuroFuzzy Mar 1 '13 at 21:30
I actually have the Velleman book! I started out with that, then I switched to Epp, because I liked the explanation better, but I will go back to Velleman for the problems and further clarification. Also, thanks for offering help on programming, I hope to contact you in the near future =) –  Jesse Mar 1 '13 at 22:55
I converted this soft-question to CW. –  robjohn Mar 2 '13 at 8:51
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Just a few notes: You're YOUNG in the whole scheme of things, have already accumulated a significant number of undergraduate credits, and you are motivated. As I see it, you're not at all in a "bad" place to be, in terms of "making a go of it."

One suggestion: being employable is a good thing. So is doing what you love to do. Try to find an area of concentration that will satisfy both. But don't spread yourself too thin. You listed a whole host of possible directions. So do explore a bit, perhaps before re-enrolling in college, but try to hone in on area of concentration (e.g., major/minor) - that may combine a few areas of interest you've listed - but not too many that you don't develop depth and mastery of what you are learning.

Good luck!

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Couple of things:

First, you talk about the "foreign students." Based on your use of language, I surmise that you're American and the students in question were probably from Korea, Taiwan, etc. Look, we all somehow got this inferiority complex about how we can't do math as well as they can. It's a universal fear, in America anyway, and it's bunk. They were doing better in your classes because they were tracked into college-bound curricula when they were like 10 years old or something and they had seen the stuff you were studying already. That's all there was to it. You shouldn't let that bother you.

Second, I understand perfectly about being able to learn from reading, but not from listening to a lecture. I could learn from a book, but I can't count how many hours I spent in lectures thinking, "Would someone remind me why I am here again?" Nothing wrong with learning from a book. I would strongly suggest, though, that you try to study at least two books on whatever subject you're trying to learn. It's not just that one book will have some info that the other one doesn't. There is just something about getting two different perspectives on a topic that somehow really cements the stuff in your head far better. I think it's a subjective thing, in that it's part of a personal experience of learning that can't easily be put into words, but it is still an objective thing in that it is very real.

I admire you persistence and the fact that you have kept up the studying even without formal classes. But you've got to get back in there at some point because you're just going to have to get that degree, whether it means you've learned more or not.

I don't advise the jump to the problems approach. In my experience, that will make your learning too "procedural". You will maybe get a list of steps in your head to solve a particular problem, but your understanding of what is going on and your ability to move beyond the problems you have already seen will be stunted.

Finally, if you really want to study math and even enjoy it, I think you've won 75% of the battle. (BTW the spell checker here tells me that "math" is incorrect but "maths" is correct. Want some chips with that fish?) What comes next, then? I don't know, honestly. Take a good look at what your limits are and don't overload in a semester. Get yourself a tutor, or find a good study group. Do what I didn't do and make sure you go to your prof's or your TA's office hours when you have questions. That's what you're paying tuition for and they will often be more comprehensible one on one than they are in a lecture hall.

Apologies for the length.

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Maths is also correct. No need to be xenophobic –  user50229 Apr 9 '13 at 12:35
My complaint is not the "maths" is treated as correct, but that "math" is treated as incorrect. –  bob.sacamento Apr 10 '13 at 23:17
For self-study, the most important part of learning anything is practice. If you are reading a book that has exercises, do as many of them as you can stand, if not all of them. If you are working with a source that does not have exercises, make them up for yourself. Ask yourself questions about what you're reading and try to develop or find the answers. When learning to program, it is important to write programs. If you have a smart phone you can download the appropriate development tools for free for Android (I think) or $5 for iPhone and start writing silly apps that test your skills. As you read and do exercises and practice, you will start to learn how to best read, exercise and practice. The process that works for you is one of the primary benefits of practice. Everyone's mind is different which is why we can't simply just tell each other things and have that work for everyone. Each of us must repeatedly work through examples of ideas to integrate those ideas into our own way of thinking. When you get stuck (when, not if) you can look in the book or go online. Anyone with enough motivation and dedication can teach themselves almost anything with the assistance of the Internet. In addition: I have a friend who has been an actuary for 15+ years. He has a maxim that I believe is true: If you learn math, you can learn to program, but if you just learn to program, you still don't know math. - add comment A professor I know usually says that "our brain, just like any other muscle, needs to be regularly exercised". I strongly agree, as I've experienced the best results when I moved from studying hard in a short timespan, to studying (and practicing, with exercises) one to two hours a day. Of course, this period would be extended if the subject was difficult to grasp, or if some relevant event (e.g.: exams) were to take place. As of the studying technique itself, it will mostly come down to what works best for you. Say, a particular subject you're studying is composed of two main topics. You can either • study both topics today, keep a good sleep schedule, let it settle down, and tomorrow grab some exercises on those topics; or • study the first topic today, practice right after it, and let the remainder for tomorrow, so that it isn't too much to take in at once. On to programming, I have reasonable experience with Java, and I quite like it. It is the language I mostly use(d), in my day to day activities. However, having a background in math and computer science (which you also want -- at least the former), I'm finding functional programming and abstract modelling more and more appealing. Functional programming takes a declarative approach to software development, abstracting the how, in favour of the what, which resembles maths. Abstract modelling usually revolves around logic (first order predicate logic, temporal logic, ...) and/or relational algebra (preferably in a pointfree style), two beautiful (and useful!) areas, that will, for sure, make good use of your discrete maths knowledge. - Keeping a right pace and motivation are two absolutely essential steps in the right direction. Diet, sleep, and physical activity also stimulate the mind. About programming, as you're still a beginner, you can choose any route (imperative, declarative, ...). Maths, logic, algebra, and more, will apply anyway. However, independently of the language, I strongly recommend statically typed languages, as opposed to dynamic. – afsantos Mar 2 '13 at 12:04 add comment At one point in time I was a life insurance actuary. This was a few years ago and the studty program has changed a bit, but I would guess the same basic principals still apply. Advancement and salary grade are intimately related to passing exams toward becomong a fellow of the Society of Actuaries. The math-related exams do have some theoretical basis; however passing the exams entails a great deal of practice to develop a proficiency in working through the problems. What I mean is during the study period (around six months) you familiarize yourself with the material and then do endless practice problems from past tests always looking foe the most efficient way to solve them. This is not without merit as a mental exercise, and it serves the professional purpose of indicating who can set up a model or a compliant accounting structure for, e.g., a new product line of business. The other aspects of the exams deal with the legal, accounting, operative aspects of the insurance business. These are quite important since the key functions of an actuary is to validate that the companies reserves to pay claims are adequate, and that the investments are structured that payments are well-funded. All of this is on a self-study basis, which seems to be conducive to you. You definitely will not get very much if anything of what constitutes "pure math," as you typically find evident here. But that is just a statement of reality: not an endorsement in either direction. Being an actuary is a rewarding career. As a practical matter they are held in high esteem in their companies and it usually entails a high degree of job security. I would tend to agree with your friends comment at the end, and in particular as it applies to an actuarial career, yet programmers do go on to do great things in math - check out William Stein at the Univ. of Washington for one that readily comes to mind. I would encourage you to carefully weigh the practical aspects of a career path, along with what you love, and where you think you might thrive at a professional level. - @Jesse Where I worked, you were assigned to one of the main areas - typically financial reporting or product development. You will become familiar with their activities and the various aspects of their operations: their reports, how they model business lines, heir computer activities. In that regard, you will find application of your programming skills as they always need to generate new reports or set up programs to test a potential new line of business. Eventually you will become familiar with what they do and where things are (not so trivial) And then you will be given some responsibilities – 96 Tears Mar 2 '13 at 16:57 ...maintain a monthly report or check other peoples' work. It must be flawless - after all they are actuaries. Usually you are given one hr. a day for study time - they want you to pass exams. It's to their advantage as you will know more of the business side of things from exams in those areas and to yours as you pay scale is intimately tied to exam results. You just have to pass - but it's not like school. The exams can be quite demanding in their own fashion - memorization and mechanical proficiency of calculations. But it is a collegial work environment. Good luck. – 96 Tears Mar 2 '13 at 17:02 add comment For learning programming I would concentrate on the intro course then do questions on project euler website, google it, it has lotd of quedtions to do which can be solved by coding or some with your mathmagic. If you dont get much from the lectures, I feel the exact same, have the confidence to teach yourself it. If there is a particularly hard problem you cant solve ask on here and you'll probably get an answer quickly. In trying to understand things$\textbf{hard} \$ problems are your friend. In trying to solve them you inevitably use a lot of the material in a guven chapter and they are more fun.