Broad ask for recommendations for online, heavily quantitative masters programs

I’m looking for recommendations for a masters program.

Here’s some background, which may be too verbose or a little self obsessed, so I’ll “small it” and you can skip if you like:

In the last ten years, through a pragmatic but wandering course, as a software engineer with a passable computer science background, supplemented with lightweight but math non-intensive coursework, I’ve learned the “applied” side of machine learning.

More recently, thanks to resources suggested from this community, I have begun a self study Bayesian statistics, probabilistic programming, calculus and linear algebra.

I’m following my intellectual curiosity, which includes differential equations, symbolic computing, modeling and simulation, economics and finance - of which I’m learning the math prerequisites.

Coming to my ask:

I’d appreciate recommendations for rigorous online masters programs that are heavily quantitative.

Obviously, in-person on-site would be ideal, but I’m a middle aged father, so pulling up stakes isn’t an option. So, I’m constraining my ask with the “online” qualifier but keeping the area of study deliberately wide.

Thanks in advance.

With Gratitude,


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If you want it to lean towards finance (and why wouldn’t you!?), maybe you could check out WorldQuant University which is fully online.

I’m sure if you were looking for something more in the realm of data science (not a specific field like finance), there would be even more options.


After reading it twice, it is still not clear to me what field we are talking about. Economics, finance, CS?

At least in econ, MA/MSc programs usually have very limited funding, as opposed to PhD.

Do you actually need the diploma? If not, you could just follow online courses and do the work.


Tamas, yep, that’s a fair reaction. I asked the question without specifying a field.

As before, the context that can be skipped:

There’s a popular science book called, “Range: Why Generalists Triumph in a Specialized World” that introduced me to a term called “late specialization”.

I’ve worked within a range of adjacent specialties within the broader umbrella of software. While doing that, I’ve been an individual contributor, the founder of the company, and an executive.

Despite the premise of the book, neither the private sector nor academia like late specialization. This means that, because of my age and stage of career, what I can do to support my family has narrowed to “CTO”.

But, intellectually, I still am broadly curious, and there are a set of academic areas that make use of the math and statistics I mentioned in my first post. In other words, there are areas of study that are adjacent to one another (at least in one sense) that use similar methods - you can see this represented by the diversity of fields that show up in each individual domain in this Discourse.

When I want to do something seriously, I find it helpful to have a goal. E.g., I wanted to lose some weight so, despite never running before, I trained for and ran a marathon. So, I want to learn more deeply, and having a goal, some structure, and peers would support that. A masters program would do that.

I’d hoped that people, drawing from their own experience, would hear my broad ask, interpret it from their own experience, say, “I loved doing a masters in XYZ from ABC” and that, because so many of the “Domains” here share math and statistics that interest me that something would stand out.

Ending where I began, yep, it was a weird and overly broad ask. I’m frankly grateful that you tried - twice! - to be able to answer it. That’s a great example of why I love this Discourse and this community. I love that when someone asks, “Why is statistics so hard?!?” it gets a dozen thoughtful replies. :slight_smile:

A post-script: I got a DM from someone expressing a similar sentiment and asking how old I am (47).

I responded 1:1 and am referencing the message here because, as evidenced by this message and some other posts from others, I think there’s a group of people who fit between the bachelors-professional and the PhD-academic. Julia seems to be a bit of a beacon for those of use who are trying to “level up” from bachelors-professional, possibly because of its origin a language for scientific computing. People in this scenario will tend to have constraints that people in either other populace won’t have.

My message was an attempt to craft a problem statement within these constraints that would let me move forward more rigorously. I wrote it knowing I’d feel embarrassed, but deciding that a little embarrassment was a worthwhile risk.



One thing you will have to “overcome” is that many of these programs will focus heavily on Python. It might even be required at times. Perhaps that won’t be an issue for you though.

That’s no problem at all. I was glad to learn (some of) Bayesian Modeling in the book Statistical Rethinking using R. The language is a means to an end.

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In your position, I would could focus on a FOSS project (ie a Julia package, or a set of related packages) used for academic research that you find interesting, read up on the related bibliography, and just contribute code, starting with the minor issues and working your way up to bigger ones.

Code reviews from experts will be educational, and you can ask them for references and interesting research ideas (researchers usually have a ton of ideas that they want to explore, but haven’t for lack of time). I have seen people eventually become coauthors on papers doing this, but I admit that it takes a lot of dedication.


That’s a neat idea. Thanks, Tamas!

Hi Dan/All,

I wonder what kind of progress you might gain by observing or sharing in the self-directed learning journey of someone who had already done or was doing something similar to what you’ve mentioned and has been proposed in the responses.

If someone took this ‘unschooling college’ route, both covering theoretical fundamentals and more practical endeavours as Tamas has suggested, how much of them sharing what they were doing and how they were doing it would be of help to your own path?

Are there specific formats that you think would be well suited - e.g. would following some study sessions/marathons on twitch be of interest/insightful? Would just seeing somebody else’s curricula outline be all the input you were interested in? Or would you be interested in the detail of how they went about it, and what would be the most meaningful aspects for you to follow or observe, or could you imagine yourself becoming participative in?

Interested to know where you’ve come with this question now six weeks later, and in your (and others!) insight to the above.


As a father on this “unschooling college” route, it would be quite interesting if any of your children have an interest to join you in this “homeschooling/unschooling” approach and take a broad based approach to curiosity in life!

Sure, glad to share an update. I’ll break this into three parts:

Part-0: Wha?

People (understandably) had a “Wha?” reaction to my initial post because I didn’t narrowly specify a field of study. The curse of having a wide range of interests, most of which can be explored with similar tools in math, statistics and science. I’ve narrowed to economics and finance, which is two (or N, depending on how you combine them) fields. So, narrower but not narrow yet.

Part-1: Self-study

My on-ramp to this at all was working through Richard McElreath’s “Statistical Rethinking”. If you’re interested in modeling real world phenomena, start there.

Prior to my initial post, I had gone back to re-learn the one semester of university level calculus I had while at school. I chose Morris Klein’s “Calculus: An Intuitive and Physical Approach (Second Edition)”and supplemented it with James Stewart’s “Calculus”. I could read the former (mostly) straight through, and found the latter better as a reference. I’ve supplemented further by learning how to partially differentiate equations with multiple variables.

At about the time of my post, I’d started learning linear algebra. I’d done practical work with matrices and vectors, but had never studied linear algebra itself. I found Gil Strang’s MIT Open Courseware lectures, which are available on YouTube, to be a good way to begin. I supplemented it with Sheldon Axler’s “Linear Algebra Done Right”, which is good, but is still above my level.

Also at about the time of my post, I’d written Petre Caraiani to ask him about his book “Introduction to Quantitative Macroeconomics Using Julia”. Petre provided a two very very helpful suggestions:

He suggested that I start with “Intermediate Macroeconomics” by Eric Sims and others, which is available for free here. This book is, for me, at the “Goldilocks Just Right” level. It’s intended for an early graduate school student, It is quantitative and the math is at a level of derivatives, integrations and partial differentiation that my earlier study prepared me for. I’m about 40% of the way through the book.

He suggested that I continue onto Fundamental Methods of Mathematical Economics, by Alpha Chiang, which I’ve ordered but not yet received.

In addition to the Bayesian modeling mentioned above, I’m also interested in models expressed in linear programming. So, I’ve purchased but not yet read “Optimization Methods in Finance” by Gérard Cornuéjols and Reha Tütüncü.

Truth be told, this is a subset of the books I’ve picked up, but this is the set that’s helped the most (or which I expect to help the most when I get to them).

Part-2: Professional

I have a non-academic background that has some skills (software engineering, data, machine learning) that are applicable to the finance industry. So, I’m changing jobs to use those skills at a company in the “asset management” segment of the finance industry.

Part-3: Graduate Program

I intend to start a graduate program in either the fall or in January. I have not determined which program. I am informed (by people in this thread, among others) that most economics graduate programs are to earn a PhD. I haven’t surveyed the options too deeply yet. In a cursory check, I found a number of programs that were intended for people who want to make a career change to, say, data science. For me, after a lifetime of experience, I want something a little more academic.



FWIW, I think the admissions deadlines are well past for 2021 fall at this point. So you may have to wait another year.

That said, with the books above you are on an excellent course. After you finish them, you may be interested in working through

in Julia. This should give you an excellent background on par with a PhD student having completed their coursework (albeit in a narrow subfield). At that point, you may also want to reach out to federal reserve banks, they are always looking for competent RAs. You would program models, work with data, and get on the job training for everything.

Best of luck, and keep us updated!


Congrats! It sounds like you’ve made good progress and are comfortable with the options on the horizon.

Thanks also for the recommendations and references. Would you recommend Kline’s text unreservedly the same way you suggest McElreath?

Thanks, Tamas, for the book suggestion. I’ve ordered it. A friend recently introduced me to a Japanese word for “stack of books”. I have a healthy tsundoku of economics, finance and math books :slight_smile:

Fair point about fall enrollments. In my cursory search for masters programs, I’d noticed that there were a number that had both fall and January starts but, now that I think about it, those were mainly of the career-change/skill building masters variety.

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Would you recommend Kline’s text unreservedly the same way you suggest McElreath?

McElreath’s is a fine book that, at least to my knowledge, doesn’t have much competition. That’s with the caveat that it is for an audience that looks like me - I think it’s probably more common that people learn Bayesian modeling as part of a course of study. So, for me, who wasn’t coming up through a graduate program, it was a very straightforward way to start to learn.

I share all of that because, in the case of calculus books, there are a lot of alternatives. I originally picked it because I thought the emphasis on the “physical approach” would be best for me, but ended up appreciating the “intuitive approach”.

Two other points in its favor:

It was written, or maybe updated, in 1967. That it’s still in print, and still used all these years later is an endorsement.

It’s $21USD for the paperback. Spending that for a 1000 page textbook is a bargain.

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Cool to hear it was a good fit, I wonder if this ‘intuitive’ approach isn’t the one that a lot of successful self-study resources manage to work through!

Those last couple of points hit home :+1:

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There seems to be an audience of sorts for this topic, so while it feels weird to write to have so much autobiography, here’s an update:

Tamas and others are absolutely correct that there are few economics masters programs. It’s either zero or maybe one when you are looking for a distance learning program.

There are online applied economics masters programs. For me, the math isn’t as deep as I was looking for, so I’m not likely to pursue that.

There are a few masters in quantitive finance or financial engineering. In these, there are some classes that look interesting, but a lot of it is materials that are covered in the book “A Primer For The Mathematics of Financial Engineering”. I have that book and its solution manual, so this is something I can do as a self study.

I have found three masters programs in applied mathematics that can be done online that interest me. One is at Johns Hopkins, one at Columbia, and one is at the University of Washington.

The applied mathematics programs include topics in modeling and simulation and other topics that are of interest to me. Completing any one of them would teach me things I’m interested in and provide me with a credential that (should I need it) provides a sort of shorthand of what I know how to do.

On that last part, I’m mid-to-late career, so this is /mostly/ for me because I want to learn it. That said, it was difficult to start this career change because my resume and my experience don’t tell the whole story, so a masters would be a door opener if I need it.

Related, I will almost certainly have to go back and formally complete at least the rest of an undergrad calculus 1-3 series. My self study is insufficient; I have the first on my transcript, but need 2 and 3 on a transcript to get accepted to a program.

I’m undaunted, well maybe a little daunted because of the prerequisite coursework, but I am undeterred.


I would have guessed that if you show them a good quant GRE score then they probably wouldn’t care about you doing undergrad calculus or not.

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Thanks for the suggestion! Prompted by your post, I asked and, at least at Columbia, it’s a no. If I find a path that avoids back filling my transcript I’ll post a follow up.