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#21




It’s still worth taking the benefit. Just plan your taxes accordingly. It’s basically counted as taxable income above the IRS cap of ~6k/year (iirc).
Last edited by nonlnear; 07062018 at 12:05 AM.. 
#22




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The MIT OR degree is solid. The others have yet to be proven but are likely quick and dirty popups due to the data science craze. However, nothing is free as this will be a substantial time commitment. I can imagine many scenarios where what is being learned is not worth the time investment. I stopped taking actuarial exams because Riley 
#23




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Changing my course schedule isn't an option, here's what I'm doing to sort this out on my own. I've started reading How to prove it, definitely not rigorous but I'm trying to start easy since I'm going through it myself. I have these two calculus texts that are more rigorous than the standard books at the university today. I'm hoping with the aid of the previous text I can work through these books in their entirety on my own. Book 1: Calculus, Vol. 1: OneVariable Calculus, with an Introduction to Linear Algebra Book2: Calculus, Vol. 2: MultiVariable Calculus and Linear Algebra with Applications to Differential Equations and Probability Lastly, I'm going to pick up A Course of Pure Mathematics which I'm hoping will cover some topics missing from my two calc texts. For example a more detailed explanation of limits and real numbers. I also have been making use of the great courses to supplement my studies, there's are a course on proofs that I've been thinking about picking up. I really like the professor, I've used his calculus videos extensively. Prove It: The Art of Mathematical Argument I haven't started looking into Abstract Algebra or Topology. That being said do you think those courses are vital to my success in a Business Analytics or Data Science focused program? Quote:
I don't think waiting until I've attempted exams to pursue either of these schools is really an option though. I'll need to be involved in extracurriculars by about a year from now if I want to present myself as a serious candidate. This post is to help me decide if taking on all that extra work would be worth it. I understand admissions isn't guaranteed but with the chance at going that otherwise wouldn't exist for me, should I go for it? Quote:
Is Analysis really the subject or method of thinking mathematically I need to focus on here? In other words, if I had to pick 1 additional area to study without changing my current course plan, is analysis it? Thanks again for all the feedback everyone.
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#24




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If I were to decide to go to grad school and get admitted, I would need to restructure my work schedule to accommodate for it but that shouldn't be an issue. I could, in theory, take an analysis course during the day I suppose as well. I'm just trying to avoid veering off the standard schedule until I absolutely have to (program requires it) while doing some selfstudy to fill in gaps. Yeah, the time commitment is huge and that's my main hesitation. With the exception of direct career pros/cons, it's a more personal question in regards to the "is it worth it?" question. I need to figure that out. I do intend on sticking with actuarial through to retirement so maybe I should just put all my effort into studying that as you've said.
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#25




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I don't have Apostol and haven't read it, but given the questions that I've answered from people who have, it isn't an easy read for a first try. How to Prove It, I do recommend for a first treatment of proofs, but it doesn't provide good overall context as to why this stuff is important. I would recommend supplementing Apostol with either Spivak's Calculus or Bartle's Introduction to Real Analysis, but note: it will be very timeconsuming and it will require a lot of patience if you're learning this stuff on your own. In my experience, progress isn't anywhere as fast as what you would get from reading a study manual for an actuarial exam, for example. I think you're looking at the right sources, but you're approaching them in the wrong order. I would recommend doing How to Prove It first, then try the Prove It videos that you've linked, and then approach Apostol. One thing that may be difficult for you to adjust to is that real analysis and higherlevel texts can be extremely terse and will often take leaps in their work without any motivation or further explanation. This is why higherlevel math is often difficult to learn on one's own. This is a huge contrast from what are typically larger Calculus and Diff. Eq. texts with solutions manuals and thousands of exercises.
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#26




Also, I want to point out one thing that Riley said:
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#27




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Also, do you think math stack exchange could be a good resource for those times when I can't see the step being taken, enough for me to get through mostly on my own at least?
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#28




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There are some places that might take you in with a career in lieu of the master's; but having the masters will make it a shoein to get an adjunct position if you also have lots of experience.
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#29




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As for the whole real analysis bit, analysis is the subject area where most people get their first real exposure to systematic proofs that don't have the appearance of being intuitive (until you master them). Geometry is a setting where many people learn proofs, but there is an intuitiveness about it that simultaneously makes it approachable but can also make it feel confined. You get to your result by constructing things you intuit specific purposes for. Want to show something about those angles? Construct a line segment, etc. In real analysis you prove relationships between different entities by just conjuring up statements about a bunch of stuff that doesn't have an obvious reason for being in the discussion ("for all , there exist..."). Something else that feels very counterintuitive about analysis proofs is that the way they are stated is often the opposite of the order in which you figure them out. You start by looking at the delta that gets you your result, and work backwards to the relationship with epsilon. So real analysis is a good subject area within which to learn certain things about how proofs are built and how they work. It is also the only subject area in which many people do any proofs beyond geometry, so lots of people think of it nostalgically as the place where "real" mathematics happens (pun intended). So, to answer your question, yes, working through real analysis rigorously would be a very useful exercise if you want to see if any higher math is for you. That said, I think linear algebra is probably the most important content area to master as deeply as possible for a career in analytics. Absolutely everything a computer does is algebra. It is only by approximation that it relates to the continuous constructs of real analysis. The important thing is to learn enough analysis that you can see the bridge between the two for what it is (numerical analysis, approximation theory, etc.) 
#30




From a practice stand point, I agree with nonlnear that linear algebra is the most important content to master.
However, numerical analysis has its support from real analysis. That is, real analysis gives the theoretical support of why it's fine to find an answer to an "acceptable error" value within numerical approximation techniques.
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