Statistics vs Mathematics major + international nuances

[louis_jb]

I'm a student from New Zealand. I have just finished high school and would love to work in quantitative finance in the future. My current plan is to begin my Bachelor of Advanced Science with Honours next year, majoring in Mathematics. I have selected my courses in such a way that I can very easily switch to a statistics major in my second year if it is necessary, taking all the required courses and pre-requisites for any second year statistics or mathematics program at my university.

The typical route - from what I understand - is a bachelors degree in some quantitative field (mathematics, statistics, physics, engineering, etc.) into a MFE program. My first issue with this is that in New Zealand, our bachelor degrees are only three years long. Most courses require a '4 year US bachelor or equivalent'. Is this as simple as completing a New Zealand MSc (one extra year), meaning I have a four year degree? Does anyone who works with recruitment / any other international students know how to deal with this?

However, if I find throughout my time in university that I become very passionate about my major, I will choose the PhD route. This will again be either a PhD in Mathematics (with a focus in stochastic calculus, numerical methods, computational mathematics and modelling) or a PhD in Statistics. I would like to attend a US school for this too - ideally somewhere like Stanford. Again, this comes with another problem. As I apply to these schools, my 'masters' only comes out to four years total education, whereas other US applicants will have five. I have no doubt I will be as equally capable as other applicants through self study, though 'self-study' is hardly a credible qualification for a top PhD program unless proven academically. Again, are there any other international students who faced a similar issue?

Finally, in your own opinion, would a mathematics or statistics major contribute more value to a quantitative firm? My current mentality is that through specialisation and rigour, both PhD statisticians and mathematicians will be of equal value (or at least close enough as to where it is not worth sacrificing personal preference in my major). Firms may require specialists in stochastic modelling, but they may also require specialists in machine learning. Would it be best just to follow the route of which I have the most passion for?

There is literally zero 'quant finance' culture in my country, so I hope someone can be of help. Thank you for your time.

 

[Qui-Gon]

Math. Take statistics courses as electives. You see very view stats undergrads doing math PhDs however stats PhDs welcome math undergrads with open arms. Take all the advanced analysis and linear algebra courses offered along with one in probability and one in mathematical statistics. I'm of the mindset that machine learning can wait -- learn things rigorously first and the applied stuff ends up looking like a truncated weighted average of analysis, linear algebra, and probability.

 

[louis_jb]

Math. Take statistics courses as electives. You see very view stats undergrads doing math PhDs however stats PhDs welcome math undergrads with open arms. Take all the advanced analysis and linear algebra courses offered along with one in probability and one in mathematical statistics. I'm of the mindset that machine learning can wait -- learn things rigorously first and the applied stuff ends up looking like a truncated weighted average of analysis, linear algebra, and probability.

So a mathematics undergraduate, focusing on rigour and pure mathematics with electives in statistics? Then, with a strong base in pure mathematics, I can easily self-teach applications - i.e. modelling, neural networks, etc. - as to avoid wasting courses throughout my formal education?

 

[Qui-Gon]

So a mathematics undergraduate, focusing on rigour and pure mathematics with electives in statistics? Then, with a strong base in pure mathematics, I can easily self-teach applications - i.e. modelling, neural networks, etc. - as to avoid wasting courses throughout my formal education?

Yes — and you can always take statistical/machine/deep learning as elective courses.

 

[louis_jb]

Yes — and you can always take statistical/machine/deep learning as elective courses.

Thank you for the input. One final question - of which I should have asked in my original post - do you consider computer science electives 'worth it'? Things like data structures and algorithms. I am yet to begin tertiary education though I have an understanding of low-level programming (C, C++, assembly), memory management, and some basic knowledge on data structures. This is purely out of self-interest and my own hobbies, such as reverse engineering.

I lay more on the side that as a quant with a PhD, I will work more on the research than implementation, meaning computer science would be of lesser importance. I also believe that courses at university are better spent on more complex fields within mathematics or statistics, with relation to my career goals. Though these are simply guesses based off some reading - and maybe ignorant guesses at that. It would be great to hear your opinion on the matter.

 

[Andy Zhang]

do you consider computer science electives 'worth it'? Things like data structures and algorithms.

Hope I'm not intruding here. I'd definitely say so. I've been asked about binary search trees (BST), dynamic programming (DP), and even graph theory in quant interviews--it's assumed you've studied those. Since you're majoring in math, I would assume you got some exposure to DP and graph theory maybe through an optimization course. An algorithms course should cover BST and other stuff that they ask in interviews but that you'll never use on the job......

 

[louis_jb]

Hope I'm not intruding here. I'd definitely say so. I've been asked about binary search trees (BST), dynamic programming (DP), and even graph theory in quant interviews--it's assumed you've studied those. Since you're majoring in math, I would assume you got some exposure to DP and graph theory maybe through an optimization course. An algorithms course should cover BST and other stuff that they ask in interviews but that you'll never use on the job......

You're not intruding in the slightest. Any help is massively appreciated. There is a lack of mathematics/statistics courses in my first year, basic algebra/calculus/computational mathematics, so I have three spare electives. I was curious whether these should be dedicated to computer science, or to finance. It sounds as though computer science would then be the better route. Would you say courses in finance are of value relative to the more science based subjects? I see schools like Baruch require at least one finance course to be taken.

 

[Andy Zhang]

You're not intruding in the slightest. Any help is massively appreciated. There is a lack of mathematics/statistics courses in my first year, basic algebra/calculus/computational mathematics, so I have three spare electives. I was curious whether these should be dedicated to computer science, or to finance. It sounds as though computer science would then be the better route. Would you say courses in finance are of value relative to the more science based subjects? I see schools like Baruch require at least one finance course to be taken.

For quant interviews, I strongly say stick to computer science courses. Maybe take one finance course to have knowledge of basics such as bonds, stocks, etc. Most top quant firms expect that they can teach you the finance.

 

[Qui-Gon]

I took a course in data structures but (regretfully) not one in algorithms. I think you can probably stop here, but like @Andy Zhang is alluding to usually the concepts covered in these courses are just part of your interview prep and are relatively straightforward to learn on your own. Join your university’s finance club (assuming your school has one) and that combined with macroeconomics/microeconomics (try to take econometrics if you have room) should be sufficient.

 

[Andy Zhang]

I took a course in data structures but (regretfully) not one in algorithms.

I've (regretfully) taken neither . I learned a bit via Leetcode and quant interview books...

I think you can probably stop here, but like @Andy Zhang is alluding to usually the concepts covered in these courses are just part of your interview prep and are relatively straightforward to learn on your own.

Yeah, since @louis_jb is majoring in math, it'll probably be easier to pick up via self-study. Just be wary of the tricks, e.g., solving BST via recursion. I would suggest maybe taking a computer science course that has a large project component--large project where you can showcase your coding style, commenting, etc that can be uploaded onto Github. You can then use this as sample work to show hiring managers.

Join your university’s finance club (assuming your school has one) and that combined with macroeconomics/microeconomics (try to take econometrics if you have room) should be sufficient.

If @louis_jb plans to go to buy-side quant research, econometrics / time series analysis is good to have.

 

[WorkofArt]

I've (regretfully) taken neither . I learned a bit via Leetcode and quant interview books...

Yeah, since @louis_jb is majoring in math, it'll probably be easier to pick up via self-study. Just be wary of the tricks, e.g., solving BST via recursion. I would suggest maybe taking a computer science course that has a large project component--large project where you can showcase your coding style, commenting, etc that can be uploaded onto Github. You can then use this as sample work to show hiring managers.

If @louis_jb plans to go to buy-side quant research, econometrics / time series analysis is good to have.

You've got great advice here, just giving my thoughts. This is brilliant advice by @Andy Zhang . Implementation is key. Get comfortable being able to work on large projects. While it can be intimidating at first, being good at writing code will be essential in your job search and on the job itself. Being able to read and understand code is as important as being able to write clean, readable code. The earlier you pick up programming, the more practice you will get.

Most, if not all, good companies will screen you based on a coding round. If you don't meet their bar, they won't even look at your resume, no matter how good it is. Data Structures and Algorithms are a major part of these coding rounds and Leetcode will be your best friend. While self study is possible, I recommend taking a college course to get a strong foundation in these topics. This two part course by Princeton on Coursera is a great introduction to algorithms. It covers the basics and teaches advanced concepts as well. Leetcode can also be quite overwhelming to start off with, this curated list of "must do" questions is a good first step.

If @louis_jb plans to go to buy-side quant research, econometrics / time series analysis is good to have.

Yes, absolutely. These electives are crucial and again, a programming component would be ideal, if not , absolutely necessary. Pick up Python, get your hands dirty by working with large amounts of data. Data cleaning, manipulation, visualization, modelling - the whole nine yards - is something you want to be comfortable with. Even if the course you take doesn't mandate a project component, try to implement models on your own. Kaggle projects are a good alternative.

Some of my advice might not be relevant now, but something to keep in mind. Expose yourself to the "practical" side of things as much as possible.

 

[Qui-Gon]

I think it’s important to keep in mind that not all quant jobs are created equally. Ones with a heavier emphasis on leetcode-type questions in the interview process are in my opinion not likely to constitute true quant research roles. Just because the job title is “quant research” does not mean it is really quant research — in fact, the majority are hybrid data science/analyst/software engineer positions in disguise. Given OP is going into undergrad, and has expressed interest in a math/stats PhD, I’m of the mindset that the hard math/stats is more important to learn than programming. Don’t neglect programming or working with data, but I think it’s equally important to not prioritize it too early on in one’s technical education. Just something to keep in mind.

Take a look here: Five ways to improve quantitative finance curricula
I think there is a lot of wisdom in this.

 

[Andy Zhang]

Implementation is key. Get comfortable being able to work on large projects. While it can be intimidating at first, being good at writing code will be essential in your job search and on the job itself. Being able to read and understand code is as important as being able to write clean, readable code. The earlier you pick up programming, the more practice you will get.

Unless you join a start-up, generally the codebase is already established--could be very messy--and most likely in OOP. Part of your responsibilities may include maintaining it. This is where @WorkofArt's advice above is absolutely crucial.

Most, if not all, good companies will screen you based on a coding round. If you don't meet their bar, they won't even look at your resume, no matter how good it is. Data Structures and Algorithms are a major part of these coding rounds and Leetcode will be your best friend. While self study is possible, I recommend taking a college course to get a strong foundation in these topics. This two part course by Princeton on Coursera is a great introduction to algorithms. It covers the basics and teaches advanced concepts as well.

One example is Akuna Capital. Think Citadel and Two Sigma, among others, also do it if I recall correctly. Generally, you can select your preferred programming language out of options like C++, Java, and Python.

Leetcode can also be quite overwhelming to start off with, this curated list of "must do" questions is a good first step.

Couldn't agree anymore!

Pick up Python, get your hands dirty by working with large amounts of data. Data cleaning, manipulation, visualization, modelling - the whole nine yards - is something you want to be comfortable with. Even if the course you take doesn't mandate a project component, try to implement models on your own. Kaggle projects are a good alternative.

One thing school does a rather crappy job at is getting you sufficient exposure to data cleaning and even large amounts of data (not really a fault though since large data sets can be super, super expensive). Without good data, any model--think of the most fancy deep neural network that took hours to optimize for example--will be completely useless.

I think it’s important to keep in mind that not all quant jobs are created equally. Ones with a heavier emphasis on leetcode in the interview process are in my opinion not likely to constitute true quant research roles. Just because the job title is “quant research” does not mean it is really quant research — in fact, the majority are hybrid data science/analyst/software engineer positions in disguise. Given OP is going into undergrad, I’m of the mindset that the hard math/stats is much more difficult to learn than programming. Don’t neglect programming or working with data, but I think it’s equally important to not prioritize it to early on in one’s technical education. Just something to keep in mind.

Agree with this. Focus on math/stats in school and possibly add some computer science electives on the side. Out of school, It would still be good to at least work on some hands-on coding projects--maybe start once you've taken some data structures/algorithms course--so you can slowly build a portfolio.

 

[auroreaborealis]

I think if you grind 300-500+ LCs, you should be able to cut through most of the leetcode interviews with no problem except for a few companies. The current industry expectation in tech is around 1 hard per 45min, easy/med/med-hard in 45min or 2 med/med-hard in 45min I think. Highly recommend Python for LC, it will make things like LRU/LFU actually doable within a coding session. I think the only big thing C++ has over Python for coding interviews is using multiset.

The thing is, most of the algos/ds in leetcode arent actually that hard by themselves. Its usually about knowing a novel way to apply it. Leetcode usually dont make you figure out an eulerian path or max flow or something so I think its usually better to just dive in.

The mediums usually dont require anything fancier than binary search, dfs/bfs, sliding window, prefix sum, shortest path, monotonic stack, or DP by itself so its probably better to just kinda memorize the patterns. For the actual leetcode hards, just do the high-frequency ones.

On the other hand, requiring FANG style SDE bar for quant is a bit excessive unless its an actual HFT job or something.