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  #21  
Old 07-06-2018, 12:01 AM
nonlnear nonlnear is offline
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Also, I'm really surprised this hasn't been mentioned yet, but be careful about unlimited caps on tuition. Most companies have caps because once you exceed a certain level, it will be reported to the IRS as income, for which you will be taking taxes.
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; 07-06-2018 at 12:05 AM..
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  #22  
Old 07-06-2018, 12:35 AM
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Here's the program I'm considering at Harvard It's a new data science program they launched this year.
Full-time in-person. I doubt they would have night classes but don't have the time to research it.

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Also one other detail that may help my chances, my father and his wife both work at Harvard so I may have some leverage there.
Not worth much unless they work in those specific departments.

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For MIT there are two programs I would consider, Masterís in Operations Research or Master of Business Analytics.
Didn't check but pretty sure these are full-time on-site as well.

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The Harvard program I believe is more technical, MIT is more business. Either way I think for free either would be ok, they're both broad but also relatable to Actuarial. At least that's what I'm thinking, you guys are a better judge of that.
Sure, but studying actuarial material more deeply on your own might be more beneficial if you're single-sighted on that type of work.

The MIT OR degree is solid. The others have yet to be proven but are likely quick and dirty pop-ups 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 I couldn't pass them I could learn more investing my time elsewhere. Really just comes down to what you want to learn/do.

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  #23  
Old 07-06-2018, 08:52 AM
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...More specifically, you need real analysis, abstract algebra, and topology...
Yeah, I've heard that as well. And the grad students I've met clearly have a deeper understanding of the material than I do.

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: One-Variable Calculus, with an Introduction to Linear Algebra
Book2: Calculus, Vol. 2: Multi-Variable 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?

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It is good to think ahead, but the following statement is quite irrational given the non-zero possibility that MIT, Harvard, and actuarial exams all prove to be too difficult for you.
This is fair and I am really early on this. The exams I'm going to pass, if I fail on my first attempts I'm just going to take them again and keep taking until I pass. In that situation, grad school would be out the window. Hopefully, it doesn't come to that though. I'm going to do everything I can to make sure I'm well prepared for them.

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?

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But to your point, I agree that the OP should stop thinking about grad school for at least a year and focus on doing the hardest math content that he can do well at.
I'll start working on that. I like the idea of sitting in on a graduate course or looking for graduate students to work with, I'm actually studying with a grad student this weekend maybe he knows some people who can help me with Analysis.

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  
Old 07-06-2018, 09:00 AM
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Full-time in-person. I doubt they would have night classes but don't have the time to research it.

Not worth much unless they work in those specific departments...

Didn't check but pretty sure these are full-time on-site as well...

Sure, but studying actuarial material more deeply on your own might be more beneficial if you're single-sighted on that type of work...

The MIT OR degree is solid. The others have yet to be proven but are likely quick and dirty pop-ups 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 I couldn't pass them I could learn more investing my time elsewhere. Really just comes down to what you want to learn/do.

-Riley
The full-time requirements are ok, technically I don't have to take evening courses, I have a pretty flexible schedule. It's most beneficial to my team if I'm here on a 9-5 basis though so that's how I've structured my studies at the moment.

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 self-study 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  
Old 07-06-2018, 09:04 AM
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Yeah, I've heard that as well. And the grad students I've met clearly have a deeper understanding of the material than I do.

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: One-Variable Calculus, with an Introduction to Linear Algebra
Book2: Calculus, Vol. 2: Multi-Variable 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?
I was looking at the perspective from you doing an "Applied Mathematics" program. That said, I looked at Harvard's program in slightly more detail. Some analysis would be helpful.

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 time-consuming 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 higher-level texts can be extremely terse and will often take leaps in their work without any motivation or further explanation. This is why higher-level 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  
Old 07-06-2018, 09:16 AM
clarinetist clarinetist is offline
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Also, I want to point out one thing that Riley said:

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The MIT OR degree is solid. The others have yet to be proven but are likely quick and dirty pop-ups due to the data science craze.
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  #27  
Old 07-06-2018, 09:24 AM
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I was looking at the perspective from you doing an "Applied Mathematics" program. That said, I looked at Harvard's program in slightly more detail. Some analysis would be helpful.

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 time-consuming 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 higher-level texts can be extremely terse and will often take leaps in their work without any motivation or further explanation. This is why higher-level 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.
Thank you for this, I'll stick with that order. Spivak has been referenced quite a bit actually on https://math.stackexchange.com/ when people are recommending textbooks, I had already purchased Apostol at the time of finding this website though. If you think it's a good idea I'll pick up Spivak once I get to working through Apostol as a reference text.

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  
Old 07-06-2018, 09:32 AM
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I'm also semi-interested in a career in academia, possibly teaching in the evenings later in my life, or participating in industry research, academic volunteer work etc.
The bolded will be difficult to get/do w/o at least a masters degree.

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 shoe-in to get an adjunct position if you also have lots of experience.
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  #29  
Old 07-06-2018, 09:39 AM
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I'll start working on that. I like the idea of sitting in on a graduate course or looking for graduate students to work with, I'm actually studying with a grad student this weekend maybe he knows some people who can help me with Analysis.

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.
If you're 3.5 years from graduation you might not be ready to sit in on grad courses yet. Learning rigorous (i.e. real) mathematics is not osmosis but actual work. The osmosis angle exists, but only if you are actually competent to remain afloat. It doesn't work if you are way over your head. What I meant was to start looking for more exposure towards the end of your undergrad program, when you already have a sufficient foundation that it's not an untenable stretch.

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.)
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  #30  
Old 07-06-2018, 10:29 AM
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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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