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Ask HN: What bachelor program is best to focus on mathematical modeling?
Note: I graduated a master in CS in 2018. So I am by no means a new student.
I was thinking of studying an applied mathematics degree at the Technical University of Delft [1]. So I contacted a student who graduated from it and he told me that the program is very proof-based and not much about mathematical modeling (it has a few courses on it but that's it). I find this odd since I had the (perhaps naive) impression that when you apply mathematics, then it means you are using mathematics to model something.
So my question is: which bachelor program comes closest to getting a lot of experience in mathematical modeling? I kind of have the feeling that a bachelor of applied physics has more mathematical modeling in it, but also a lot of IRL experimentation (which I do not feel like learning, I just want to model a phenomenon or a bunch of data).
Has anyone done a program that had a lot of mathematical modeling in it?
[1] https://www.tudelft.nl/en/education/programmes/bachelors/tw/bachelor-of-applied-mathematics/the-curriculum
- spekcular 5y agoCan you give more details on why you want to learning about mathematical modeling? And what do you want to model? Given your educational background, there are probably more time- and cost-efficient ways to learn the same material (which is likely highly application-specific). Also, applied mathematics programs teach proofs because they want to show that their applied methods are guaranteed to work, as opposed to being fragile, ad hoc guesses.
- mettamage 5y agoI guess that's a fair point. I'd like to learn about: * Machine learning / deep learning in particular * Modeling financial data * Game development, creating a physics engine I've done all three in a humble amount. So definitely calculus, probability/stats and linear algebra. Maybe I'm missing something. I've been able to get by without calculus and linear algebra somehow.
- spekcular 5y agoThese are fairly disparate things that each require a separate degree to do well. I don't think any single degree would cover all of them, and any program is going to cover other things you're not interested in. My recommendation would to pick the one you're most excited about and focus on it. You mention in another comment that you prefer to work with other people and not do books/MOOCs alone. In this case I suggest that you find a graduate student in the relevant area and ask him/her to tutor you (i.e. give you an independent course in the topic). This might cost $50 to $100 USD per hour if you shop around (perhaps more). The goal would be to learn enough of the basics that you can pick up the more advanced things yourself. Good luck.
- fuzzfactor 5y ago>So definitely calculus, probability/stats and linear algebra. I would just take these 3 courses then, starting with linear algebra. See how much less humble you can proceed after that.
- lallysingh 5y agoStatistics or applied physics. But really, just get a tutor
- goethes_kind 5y agoSuch a program cannot exist. "Modelling" is just a catch all term. But in practice nobody learns "modelling". They just get deep in one field and learn how to model problems in that field. Those people are often not mathematicians, but engineers working on applied problems. What you need to do is to get interested in something cool. Then contact research groups in that field and ask them if there is a place for you. You will no learn modelling. But you will be doing modelling of one very specific problem.
- chaosbutters314 5y agoI do modeling in the sense of computational fluid Dynamics (cfd) or finite element analysis (fea) or just basic physics-based models and my background is in chemical and mechanical engineering. if you want to get into the field doing it though, you'll ideally need a PhD. It takes a lot of time to understand all the nuances of how to model a system and reading and practicing are the best ways. If you don't want to do a PhD, the best way to break into the field in industry is develop your own EASY TO USE open source copy cat of the commerical software. By easy to use I mean no command line, no OS or hardware dependent implementations (best to assume all users are on windows), and doesn't rely heavily on any programming. Most people doing modeling in industry have backgrounds in engineering, math, or physics, not software. Most of us code but it heavily varies.
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- GoodJokes 5y ago
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- trthatcher 5y agoWhile I'm not clear why you would want to go back to an undergrad given your education, I would look for programs with names like "Computational Mathematics" or "Computational Science". I earned a Bachelor of Mathematics in Computational Mathematics. The first two or three years were heavily focused on the mathematical foundations (eg. non-linear and discrete optimization, combinatorics and CS fundamentals, statistics and applied mathematics). The latter half of third year and all of fourth year were basically a "create your own adventure" where you could focus on subject areas that interested you (ex. econometrics, computational biology, industrial engineering, computational statistics + machine learning, etc). We had a breadth requirement t that often pushed people to obtain a minor from a different faculty (eg. Arts or Sciences). The program overview for my school might give you an indication of what content to look for [1]. You might also find graduate level programs that are similar in aim; my school also offers an MMath in Computational Mathematics [2]. 1. http://ugradcalendar.uwaterloo.ca/page/MATH-Computational-Mathematics1 http://ugradcalendar.uwaterloo.ca/page/MATH-Computational-Ma... 2. https://uwaterloo.ca/computational-mathematics/future-masters-students/masters-program https://uwaterloo.ca/computational-mathematics/future-master...
- mettamage 5y agoA couple of reasons: * Building CRUD apps lack depth, when they don't lack depth, they lack timeless knowledge (in many cases). A well picked bachelor/master does not have that. There are programming jobs out there that don't have that but they are in the minority and I am bad at getting to the interview stage, despite having a master in CS (my cv is ragged, I had a terrible start and don't know how to recover from it other than just by moving on and hoping for the best). * A university provides fellow students and TAs. In some cases I prefer heavily to study with them rather than doing a MOOC on my own. A study group is harder to setup. Getting a tutor is definitely an alternative for the TA part.
- blablabla123 5y agoI'm not 100% sure about Mathematical Modeling. But given you checked out TU Delft you might as well check out Utrecht University. They have a very cool and hands on Math department and offer 2 week Summer schools to take a look - possible to get a cost reimbursement if that's an issue. Once you're there you can just ask what they recommend. Edit: https://www.uu.nl/en/organisation/mathematical-institute/research/mathematical-modelling https://www.uu.nl/en/organisation/mathematical-institute/res...
- mettamage 5y agoAh, well I also checked it out in part because Dutch people only have to pay around 2K. This is even the case if you've done multiple masters/bachelors.
- cl42 5y agoI completed an MSc in Mathematical Modelling and Scientific Computing at Oxford[1]. You mentioned in some of your replies that you're interested in financial time series models, deep learning, and game development. I recommend you clarify whether you want to get good at mathematical modelling as a *general skill*, or *do* mathematical modelling in a specific subject area. Mathematical modelling in academia will focus on theory, proofs, etc. because it has to teach students the entire toolkit for building models. This means understanding how to frame real-world problems (weather forecasting, structural models for buildings, etc.) into a mathematical problem that can then be solved analytically (i.e., by using theorems/functions) or numerically (i.e., by estimating a solution through various 'guesses' and algorithms). As such, a mathematical modelling expert needs to have a deep mathematical toolbox, and the "applied" work then becomes easy. A pure "mathematical modelling" program will rarely touch on AI, deep learning, etc. That would be covered in computer science programs. Unless you find more focus, I'd suggest you study pure math or applied math. Any advanced AI, math modelling, etc. will require you to understand algorithm design, generate proofs (e.g., to show that your models will converge to solutions), and ultimately represent the world mathematically. An applied math program with a few courses in comp sci will get you there. Most of the folks I know who pivoted into AI or build models in specific industries have a strong mathematical background that they can leverage to learn everything else. It's why you see physics Phds working in AI, or math PhDs working in finance. They learn the industry-specific details on the job. Also, a lot of this is grad-level stuff... If you already have an undergraduate degree, you might want to consider a program like the one I completed. It took only a year and was very, very technical. Much faster + more focused than 3-4 years of undergrad. [1] https://www.ox.ac.uk/admissions/graduate/courses/msc-mathematical-modelling-and-scientific-computing https://www.ox.ac.uk/admissions/graduate/courses/msc-mathema...
- beerandt 5y agoIndustrial Engineering. It's a fairly math-heavy curriculum (without getting much into the "pure" proof type math courses you mention) that goes into both systems modeling and various logistics and process optimization domains. And being engineering, it's obviously focused on real world applications. You start with the typical engineering theoretical and/or empirical framework, then you start stating assumptions to simplify/ modify/ apply your formulas to the situation at hand. And there's methods for evaluation and verification, etc. Side Note- Most IE curriculums include more hours of computer science/ programming courses than comparable engineering and science degrees, which could be a pro/con depending on the school and your circumstances. Taking classes you already know can lighten your load, or the school might let you skip and sub credits and take a few more advanced/ interesting/ specialized courses.
- mettamage 5y agoA topic begins to become interesting when there is an "it's not possible" answer and a "oh yea, here is an example of your question" style answer, especially when they are both quite convincing answers! I think it depends on where you studied it. I know nothing about Industrial Engineering, but when I typed "Industrial Engineering" bachelor into google, the University of Eindhoven popped up and I wouldn't call it math-heavy [1]. So I wonder which Industrial Engineering program you're talking about. The program does look interesting, but I don't think I could commit to this particular one (I am searching for a program allows for self-studying, either formally or informally by being able to skip a lot of stuff). [1] It is by no means low on math though: https://assets.studiegids.tue.nl/fileadmin/content/Faculteit_IEenIS/Bachelor_College/TBdk/Curriculum/2021/Major%20IE%202021.pdf https://assets.studiegids.tue.nl/fileadmin/content/Faculteit...
- beerandt 5y agoIt's math and theory heavy relative to other engineering and applied science fields, because most of it's first principals are based more on lots of data, abstract* math, and optimizations than on physical phenomenon. But probably not heavy as compared to any degree offered by the math department. But it is one of those newer fields that can vary in how it's evolved locally. Environmental engineering, you would think involves engineering the environment, but in the US evolved into a field dominated by regulatory compliance. And now Ecological Engineering has popped up as a replacement for what environmental engineering was originally intended to be. [0]Check the curriculum at some US schools. Your local equivalent degree might be named something else, like process or systems engineering. [0]https://www.isye.gatech.edu/academics/bachelors/industrial-engineering/curriculum https://www.isye.gatech.edu/academics/bachelors/industrial-e... *It's often jokingly called imaginary engineering for its relative lack of physical products.
- vemodalen 5y agoLook into Operations Research & <mathematics>. The degree name varies between countries. Here is a bachelor program in the Netherlands [0] "Groningen teaches you all about econometric modelling." Look at this mathematics and modelling program (masters program) [1]. There are other types of specialisations; I saw you mentioned financial, which is why I linked this one. [0] https://www.rug.nl/bachelors/econometrics-and-operations-research/ https://www.rug.nl/bachelors/econometrics-and-operations-res... [1] https://lnu.se/en/programme/mathematics-and-modelling-master-programme/specialization-mathematical-statistics-and-financial-mathematics-vaxjo-international-autumn-f1523/ https://lnu.se/en/programme/mathematics-and-modelling-master...