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I am on track towards a B.S. in math or actuarial science. From what I have gathered looking at the answers, it sounds like statistics, probability, and programming are the valuable math skills to go after. I think that is where I will direct my focus.

Since I am equally close to finishing either major, which one would be better to go after? I think I could put equal energy into either one (I don't plan on going to graduate school in math).

For people who majored in either math or actuarial science, what job did you end up going into? I am under the impression that a degree in actuarial science is only for a job in that field (false?). I haven't passed an actuarial exam yet, so I am on the fence about that. I remember several of my classmates failed the P and FM exams a few times. I know I need to pass one to get a job, so I am worried about that a little. What happens if you only pass one, and fail to pass more down the road? Can you stay employed with one passed exam? How close is the work that you do related to the exams?

Finally, when going into the internship or starting out, what are you expected to know? Sometimes I am totally lost on some new concept, and it takes me a while to learn or understand it. I have this fear that I won't be smart enough or quick enough to pass the training. I am totally in the dark about what is expected from someone going into their first career out of college.

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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
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And perhaps some game theory. EDIT: P.S. Good luck!!! –  user18921 Mar 1 '13 at 21:06
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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 converted this soft-question to CW. –  robjohn Mar 2 '13 at 8:51
    
Read a course of higher mathematics by Smirnov –  metacompactness Jun 29 '13 at 19:21
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9 Answers

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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I think you have something very important here, that beyone maths and across all sectors many secondary school students don't pay attention to; there are lots of jobs out there, involving all sorts of skills, but you only get one degree (usually) so most of all pick something that you're gonna enjoy studying. You can worry about jobs when it's all over! –  Flint72 Apr 10 at 2:23
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It was a long six-year fight for me to get my undergraduate degree in Mathematics. Just having a degree in (pure) math made me more "employable" than others with less technical degrees or no degree. I think you should give earning a degree another try. Find a school that will help you earn a degree in a way that works for you. You could start with an Associate's Degree, which at least gives you some post-secondary credentials and is a smaller amount of work to commit to. Associates are also usually very affordable.

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.

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I second that maxim in one direction, I can't comment from the other, but I can certainly attest to the fact if you learn maths, you will be able to learn to program, so don't get too worried about this. –  Flint72 Apr 10 at 2:21
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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
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Where does anyone talk about "foreign students.", sorry!?!?? –  Squirtle Apr 9 at 19:49
    
Yes, I too am very confused where there are comments of "foreign students". And maths is indeed the correct spelling. –  Flint72 Apr 10 at 2:19
    
I gave this answer a year ago, as you might notice. It looks like someone has edited the question in the mean time. And "maths" is the British spelling for sure, but not everybody is British, in case you haven't noticed. "Math" is correct in several other countries. As I said, I do not object to "maths" being correct, but to "math" being marked incorrect. And you guys apparently take this far more seriously than I. –  bob.sacamento Apr 10 at 3:46
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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.

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@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 –  Andrew 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. –  Andrew Mar 2 '13 at 17:02
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It doesn't really look like anyone has answered your question, "What job did you get?", so I will attempt.

Also, some of the answers are from people who said they graduated a while ago.

Firstly, what country are you in? This probably makes quite a difference.

I graduated in Maths-Physics from the top university in my country (not where I am located now) two years ago, and got straight into a job as a derivatives trader (banker) in a big finance city on a very high salery.

Of the 23 people who graduated in my year, at least half went into working in some sort of banking/ actuary/ financial consulting etc. Our degree had no Stats or Probability classes, except for Statistical Mechanics (but this is not like a Stats or Probability course), and a very basic amount of computer programming.

Of those who graduated in Pure-Maths, of which there were about the same number, the numbers who went into financial type work are about the same.

The point being, from someone who recently graduated, once you have any degree in Maths (very broad!) people will want to pay you lots of money to make them lots more money in the world of high finance!

So I would not be too worried about it.

Just pick whichever you enjoy more, and whichever you feel that you will do best at.

To your final question, I should add that I never did any industry internships while in my undergrad (I found research ones far more fun, and far less stressful! re. the poor guy who dropped dead while interning in London last summer).

Many others in my class had done this, and it helped them they reckoned.

I was absolutely thrown in the deep end! I remember feeling very very very stupid for the first number of months (maybe I still do!), but you learn quickly, like anything else. It was not much different from moving from secondary school Maths to University Maths.

So again, you can rest assured that many of the other newbies around you in the office will be finding it tough too. It took some time before anyone would admit it to each other (if you think people are very compeditive in university, wait til you see what people will do when theres a promise of a big bonus at the end of the road!) but eventually everyone let on that they were in the same boat. The empolyer will know that you're fresh out of college, and won't be expecting you to run the place within two weeks! They are aware that it takes time.

As a final point, those who neither went into further study (another large fraction) nor finance and related areas, I think teaching was also a popular option. A few people did that, but I actually think the three that I am currently in contact with absolutely dispise it, and aren't getting paid very well for it, relative to finance. Something to bare in mind.

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I am in the United States. –  Jesse Apr 11 at 1:32
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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.

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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
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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.

And remember that you do this because you enjoy maths!

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There are a lot of answers here and I haven't read them all, so what I say may echo some preceding sentiments.

If you go into any graduate student office you will see a lot of unhappy, disheveled people. There are many reasons which don't all pertain to your circumstance (since you only want to do a B.S.) but often those graduates are forced to ask themselves why they want to do what they are doing. I assume that it is true generally that, if you don't really enjoy/love what you are doing, it will slowly eat at you and erode your happiness.

That's the primary thing, your happiness. It sounds to me that if you don't finish what you've started, it will start to eat at you, and you will always have some regret. But make sure that you choose to pursue something that you genuinely enjoy, keeping an open mind about things that you don't immediately enjoy however.

Employability is definitely a concern, but I don't recommend giving it a higher priority than liking what you do. As someone above mentioned, stats and data mining are big topics now, so if you find those areas interesting look into them a bit more.

As for debt, I don't know what tuition is like where you are, or whether you are living with your parents or friends, but if you can manage it working on the side can be good for you in terms of building time management skills and responsibility (don't mean to suggest you don't have those skills though). Of course, don't let it interfere with school.

My final suggestion is to go and talk to some professors in the math department at your university. Ask them what kind of material you would be learning in different courses, ask them to tell you about areas you might find exciting and might want to pursue as a career. My experience has been that they would love the opportunity to share their passion (and perhaps prosthelytize) about mathematics. You should get a feel for what awaits you down that path.

Good luck, and come back in a few years to tell us how it all worked out!

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Focus on Probability, statistics, modelling, and programming. These things are ubiquitous in industry and can get you jobs in areas that aren't specified as for math grads (for instance, a knowledge of python could get you in as a software engineer or web developer).

Try and stay away from pure math. I doubt field theory or real analysis is used as heavily in industry as the things I have mentioned.

Also, remember that the world is not always continuous. Focus on some discrete mathematics and data analysis. A course in numerical analysis is always good for something.

My advice is to go on a job crawler, like indeed.com, and search mathematics. Look for what people are looking for and focus on learning these skills.

Best of luck.

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Probability is a subset of real analysis. Also, field theory is useful in cryptography and so is very widely used in industry. –  Jair Taylor Apr 11 at 4:25
    
Yeah, but how many people actually implement cryptographic protocols at the level to care about field theory? Most people simply use existing cryptographic libraries, which is better. People that aren't crypto experts shouldn't be implementing cryptosystems for industrial systems. –  ml0105 Apr 11 at 5:21
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