Maths modules to choose from  advice appreciated

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Maths modules to choose from  advice appreciated
I am doing a BSc in Maths and Stats, now 2nd year of a 3year course. In October 2022 I will have to choose one elective and I am starting to wrap my head around what to choose. Figured people here would be willing to give some advice. Maybe there are some particularly EREcongruent choices.
Some academic background: I did Psychology and PolSci (and one year of Acoustics) before. Since half of the course is statistics, I had to choose between pure maths and applied maths module this year and chose the applied maths one (mathematical methods, models and modelling).
Each module is 300h of work. Modules to choose from (and my thoughts in brackets) are:
* Mathematical methods and fluid mechanics  Learn about modelling simple fluid flows, ordinary and partial differential equations and mathematical methods that can be used to solve fluidflow problems. (I thought about this one from the perspective of the yields and flows thread here, as a sort of parallel or analogy that could be explored in depth.)
* Deterministic and stochastic systems  concentrated around three themes: fundamental concepts of dynamics, deterministic dynamics, stochastic processes and diffusion. (Frankly, I don't know what to make of this module.)
* Complex analysis  this module develops the theory of functions of a complex variable, emphasising their geometric properties and indicating some applications. (Though I read that complex analysis is important in engineering, I very much like that they touch upon Mandelbrot set in this module. But I read some reviewers of it saying that it might be a bit tricky for those who have not taken the 'pure math' course earlier, which indeed I have not taken).
* Graphs, networks and design  This module is about using ideas from discrete mathematics to model problems, and representing these ideas through diagrams, showing anything from chemical bonds to transport systems. (this was my choice from the beginning of studying the degree. The course is described as 'broad rather than deep', and by the description sounds like it examines some fun problems of no immediate heavy bearing, such as the Königsberg bridges problem)
* Optimization  Examine techniques used in numerical analysis and operational research to represent real optimization problems as mathematical models, to be solved with a computer. (This is described as a natural progression from the applied maths module I am doing now, and good for applied maths enthusiasts. I am okay with applied maths but naturally more P than J, but maybe then it is good to hone the skill).
* Mathematical thinking in schools  This module will develop your knowledge and understanding of the teaching of mathematics, with an emphasis on Key Stage 3, and broaden your ideas about how people learn and use mathematics. (I think this gets a bit into psychology of learning maths, it could be interesting but I would be least inclined to take it.)
Thank you for taking the time to read the above and I appreciate your comments!
Some academic background: I did Psychology and PolSci (and one year of Acoustics) before. Since half of the course is statistics, I had to choose between pure maths and applied maths module this year and chose the applied maths one (mathematical methods, models and modelling).
Each module is 300h of work. Modules to choose from (and my thoughts in brackets) are:
* Mathematical methods and fluid mechanics  Learn about modelling simple fluid flows, ordinary and partial differential equations and mathematical methods that can be used to solve fluidflow problems. (I thought about this one from the perspective of the yields and flows thread here, as a sort of parallel or analogy that could be explored in depth.)
* Deterministic and stochastic systems  concentrated around three themes: fundamental concepts of dynamics, deterministic dynamics, stochastic processes and diffusion. (Frankly, I don't know what to make of this module.)
* Complex analysis  this module develops the theory of functions of a complex variable, emphasising their geometric properties and indicating some applications. (Though I read that complex analysis is important in engineering, I very much like that they touch upon Mandelbrot set in this module. But I read some reviewers of it saying that it might be a bit tricky for those who have not taken the 'pure math' course earlier, which indeed I have not taken).
* Graphs, networks and design  This module is about using ideas from discrete mathematics to model problems, and representing these ideas through diagrams, showing anything from chemical bonds to transport systems. (this was my choice from the beginning of studying the degree. The course is described as 'broad rather than deep', and by the description sounds like it examines some fun problems of no immediate heavy bearing, such as the Königsberg bridges problem)
* Optimization  Examine techniques used in numerical analysis and operational research to represent real optimization problems as mathematical models, to be solved with a computer. (This is described as a natural progression from the applied maths module I am doing now, and good for applied maths enthusiasts. I am okay with applied maths but naturally more P than J, but maybe then it is good to hone the skill).
* Mathematical thinking in schools  This module will develop your knowledge and understanding of the teaching of mathematics, with an emphasis on Key Stage 3, and broaden your ideas about how people learn and use mathematics. (I think this gets a bit into psychology of learning maths, it could be interesting but I would be least inclined to take it.)
Thank you for taking the time to read the above and I appreciate your comments!

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Re: Maths modules to choose from  advice appreciated
I would personally go for dynamic systems or graphs. If you're interested in permaculture etc. then modeling a setup as a dynamic system is very powerful. I've been to a few talks by conservationists where they found that predator/prey relationships effectively formed a chaotic system that revolved around an attractor. If you have a permaculture setup where there are multiple stages of resource transfer without intervention it would likely behave the same way. It could be useful for designing a system that minimizes or optimizes your labour/resource input.

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Re: Maths modules to choose from  advice appreciated
My comments based on what can be learned in 300 hours and where I think it would be most useful.
 Mathematical methods and fluid mechanics  Learn about modelling simple fluid flows, ordinary and partial differential equations and mathematical methods that can be used to solve fluidflow problems. (Mathematical insight into common engineering practices with heat, water, pipes, chemical reactions, aerospace, ...)
 Deterministic and stochastic systems  concentrated around three themes: fundamental concepts of dynamics, deterministic dynamics, stochastic processes and diffusion. (Making predictions. Data science. Very applicable to options trading. Finance.)
 Complex analysis  this module develops the theory of functions of a complex variable, emphasising their geometric properties and indicating some applications. (Fucking useless, I hate it Seriously, though, it has some applications in electrical engineering if you can stand the pain. By "some" applications, they probably mean 2 or 3 This is mostly math for its own sake and the pursuit of beauty which is attractive to P brains.)
 Graphs, networks and design  This module is about using ideas from discrete mathematics to model problems, and representing these ideas through diagrams, showing anything from chemical bonds to transport systems. (Very business friendly. Lots of show and tell. Yields and flows, web of goals.)
 Optimization  Examine techniques used in numerical analysis and operational research to represent real optimization problems as mathematical models, to be solved with a computer. (Also very business friendly. Teaches how to solve the otherwise intractable problems posed in complex analysis. E.g. substitute a onescreen piece of code for 27 pages of derivations).
 Mathematical thinking in schools  This module will develop your knowledge and understanding of the teaching of mathematics, with an emphasis on Key Stage 3, and broaden your ideas about how people learn and use mathematics. (This seems to be for teachers. Also makes you less flabbergasted when realizing that 20% of the population doesn't understand how a 1/3 pound burger can be bigger than a 1/4 pounder when 4 is clearly more than 3.)

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Re: Maths modules to choose from  advice appreciated
Thank you both, this already clarifies some things.
@basuragomi, I appreciate the comment, that module was the most obscure of all for me. I looked at the detailed syllabus, it seems to link to the other part of my degree i.e. stats.
@jacob, this was informative about complex analysis. I know that many people struggle to count, I made peace with it by now. I shall add that the 300h of study is in the context of 3600h of studying maths and stats, with a (pomodoro) watch. Not completely out of context.
At this point I' d probably be narrowing the choice to dynamic systems, graphs or optimization. Deterministic and stochastic systems  something that could work in permaculture and in data science? Impressive, will read more about it.
For those who'd like to check it out (don't feel obliged to read it) I show detailed study lists for dynamic systems and graphs. (ETA: added also the optimization one). Lots of it makes no sense to me now, but perhaps some of you will be able to write something useful after having a glimpse.
@basuragomi, I appreciate the comment, that module was the most obscure of all for me. I looked at the detailed syllabus, it seems to link to the other part of my degree i.e. stats.
@jacob, this was informative about complex analysis. I know that many people struggle to count, I made peace with it by now. I shall add that the 300h of study is in the context of 3600h of studying maths and stats, with a (pomodoro) watch. Not completely out of context.
At this point I' d probably be narrowing the choice to dynamic systems, graphs or optimization. Deterministic and stochastic systems  something that could work in permaculture and in data science? Impressive, will read more about it.
For those who'd like to check it out (don't feel obliged to read it) I show detailed study lists for dynamic systems and graphs. (ETA: added also the optimization one). Lots of it makes no sense to me now, but perhaps some of you will be able to write something useful after having a glimpse.

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Re: Maths modules to choose from  advice appreciated
I did MT365 as part of my degree, it was pretty good. Most of the other units I studied have been superseded since so I can't help on those (and I leaned towards the pure side).

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Re: Maths modules to choose from  advice appreciated
Thanks for it @ducknald_don. I see a recurring word 'algorithm' in the description of MT365. I know you have been working in IT for a bulk of life, any particular connection between MT365 and IT (yes yes I know there is generally a fundamental connection between Maths and IT)?

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Re: Maths modules to choose from  advice appreciated
Not to any great extent with MT365. The number theory and mathematical logic course probably changed my thinking more than MT365.

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Re: Maths modules to choose from  advice appreciated
Interesting. I taught myself something like MT365 as a quant. It forms a much greater part of my mental structures than number theory or logic. This may be an INTP (Ti dominant) vs INTJ (Ni dominant) difference. I definitely lean "applied".ducknald_don wrote: ↑Thu Nov 25, 2021 9:28 amNot to any great extent with MT365. The number theory and mathematical logic course probably changed my thinking more than MT365.

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Re: Maths modules to choose from  advice appreciated
I can see how formal logic can be fundamentally useful (in everything cognitive actually). Anyway, that crossroad is gone for me now.
I am reading about deterministic and stochastic dynamics (as in, skimming through wiki). Looks like this might complement well 'applications of probability', 'applied statistical modelling' and 'mathematical statistics' (the other three I'll be taking).
There is quite some time, I think I will be needing to choose in January.
I appreciate your input here, this thread will not serve anyone else nearly as much as me. Thanks.
I am reading about deterministic and stochastic dynamics (as in, skimming through wiki). Looks like this might complement well 'applications of probability', 'applied statistical modelling' and 'mathematical statistics' (the other three I'll be taking).
There is quite some time, I think I will be needing to choose in January.
I appreciate your input here, this thread will not serve anyone else nearly as much as me. Thanks.
Re: Maths modules to choose from  advice appreciated
Some qualifications, it depends on what you want to do in your future. Almost all the courses have applied to one or more positions I've had and will be valuable in the world going forward. If you want to become a data analyst, you will basically have to learn to teach yourself everything as usually the reason someone is paying you to analyze something is they don't know anyone else who can do the job.
I would say the below classes have the widest application today and could be used in any number of business applications. One caveat with all stats classes is to know if the prof is empirical or theoretical as any of these classes could be 100% proofs or 100% application with the same exact course descriptions.
* Optimization  Examine techniques used in numerical analysis and operational research to represent real optimization problems as mathematical models, to be solved with a computer. (This is described as a natural progression from the applied maths module I am doing now, and good for applied maths enthusiasts. I am okay with applied maths but naturally more P than J, but maybe then it is good to hone the skill).
* Graphs, networks and design  This module is about using ideas from discrete mathematics to model problems, and representing these ideas through diagrams, showing anything from chemical bonds to transport systems. (this was my choice from the beginning of studying the degree. The course is described as 'broad rather than deep', and by the description sounds like it examines some fun problems of no immediate heavy bearing, such as the Königsberg bridges problem)
I would say the below classes have the widest application today and could be used in any number of business applications. One caveat with all stats classes is to know if the prof is empirical or theoretical as any of these classes could be 100% proofs or 100% application with the same exact course descriptions.
* Optimization  Examine techniques used in numerical analysis and operational research to represent real optimization problems as mathematical models, to be solved with a computer. (This is described as a natural progression from the applied maths module I am doing now, and good for applied maths enthusiasts. I am okay with applied maths but naturally more P than J, but maybe then it is good to hone the skill).
* Graphs, networks and design  This module is about using ideas from discrete mathematics to model problems, and representing these ideas through diagrams, showing anything from chemical bonds to transport systems. (this was my choice from the beginning of studying the degree. The course is described as 'broad rather than deep', and by the description sounds like it examines some fun problems of no immediate heavy bearing, such as the Königsberg bridges problem)

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Re: Maths modules to choose from  advice appreciated
Thanks for commenting @WFJ.
Looking at the 'graphs...' course recently, I wonder if the fact that it is three different themes (graphs, networks, design) would play out  would it be just a hodgepodge of ideas or is there a good structure to it. What do you think?
[ETA1.0] regarding data analyst, surely there are, perhaps more mundane, jobs where qualified workforce is needed (probably less paid). I tend to think of a data analyst as a statistician + some computer skills these days. You don't know until you're there, but the idea of working as a statistician (or with statistics) feels good.
I have a brief past experience (0.5 year) of working as a market research analyst for one very large FMCG player, sadly it was mostly testing my Power Point skills which probably made me leave.
[ETA1.1]
Dug deeper and found out that graphs, networs and design are under the 'pure mathematics' branch of the course while the 'deterministic and stochastic dynamics' under the 'applied mathematics' branch. Also looked at the syllabi of two of the other three courses on the cooker next year: mathematical statistics and applications of probability which share some topics with the latter of the two. The last course that I am going to take ('applied statistical modelling') is now being written and is designed for data science students.
I lean towards taking the Deterministic and Stochastic Dynamics. I feel like I over analyz it by quite a stretch but then again it will be 300h+ of focused work.
Looking at the 'graphs...' course recently, I wonder if the fact that it is three different themes (graphs, networks, design) would play out  would it be just a hodgepodge of ideas or is there a good structure to it. What do you think?
[ETA1.0] regarding data analyst, surely there are, perhaps more mundane, jobs where qualified workforce is needed (probably less paid). I tend to think of a data analyst as a statistician + some computer skills these days. You don't know until you're there, but the idea of working as a statistician (or with statistics) feels good.
I have a brief past experience (0.5 year) of working as a market research analyst for one very large FMCG player, sadly it was mostly testing my Power Point skills which probably made me leave.
[ETA1.1]
Dug deeper and found out that graphs, networs and design are under the 'pure mathematics' branch of the course while the 'deterministic and stochastic dynamics' under the 'applied mathematics' branch. Also looked at the syllabi of two of the other three courses on the cooker next year: mathematical statistics and applications of probability which share some topics with the latter of the two. The last course that I am going to take ('applied statistical modelling') is now being written and is designed for data science students.
I lean towards taking the Deterministic and Stochastic Dynamics. I feel like I over analyz it by quite a stretch but then again it will be 300h+ of focused work.

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Re: Maths modules to choose from  advice appreciated
Heck, I do this degree mostly for personal enjoyment with a side effect of it likely generating some sort of money. No point being too instrumental about the module choice. I am going to go for the deterministic and stochastic dynamics and deal with some chaos and randomness.
I mean, learning about 'the edge of chaos'? Gives me goosebumps.
Thank you all very much for your input.
ETA a day later: man this is such a tiring choice, would be good to have an algorithm for making it. If past experiences are any indicator, I might end up going with my initial choice of graphs after all.
I mean, learning about 'the edge of chaos'? Gives me goosebumps.
Thank you all very much for your input.
ETA a day later: man this is such a tiring choice, would be good to have an algorithm for making it. If past experiences are any indicator, I might end up going with my initial choice of graphs after all.
Last edited by guitarplayer on Mon Dec 06, 2021 4:52 am, edited 1 time in total.

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Re: Maths modules to choose from  advice appreciated
If you are just interested in the subject then the OU is great but from a career perspective I don't think it is regarded that highly in the employment market. If I'd been doing it to increase my employability I would probably have done the first few maths units then jumped to a "real" university.guitarplayer wrote: ↑Sat Dec 04, 2021 2:20 pmHeck, I do this degree mostly for personal enjoyment with a side effect of it likely generating some sort of money.

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Re: Maths modules to choose from  advice appreciated
I think at this point I can't complain about employability. If you recall, the OP was more directed at 'ERE', not 'FIRE' or 'money making potential'. That being said, I am probing searching for different things to do with the acquired skills, hence querying about IT work here and there, or teaching etc. But optimizing mostly for things broader than just career.
The OU may be regarded as a 'working class' uni (I recently was part of a conversation about how classes are still a big thing in the UK), it has though to be the most convenient form of studying, and skills learned are all the same I would think.
Actually my PolSci degree was from a uni with PolSci dept in top 20 worldwide I think they were bragging (it's 25 in 2021 after checking).
The OU may be regarded as a 'working class' uni (I recently was part of a conversation about how classes are still a big thing in the UK), it has though to be the most convenient form of studying, and skills learned are all the same I would think.
Actually my PolSci degree was from a uni with PolSci dept in top 20 worldwide I think they were bragging (it's 25 in 2021 after checking).
Re: Maths modules to choose from  advice appreciated
I am also planning on doing more math studies for fun now that I am tutoring as one of my gigs. In the U.S., not having a full teaching license is somewhat limiting to some paths of employment and not having a Master's degree is somewhat limiting to other paths of employment. Still, as an independent contractor with the skills, it is pretty easy to make $25/$30 hr. on parttime basis, and the work doesn't require the "classroom cop" skills needed for teaching. The teaching of math elective might come in handy if it helps with different methods of approach for students who are blocked. The majority of people who need math tutoring are going to be stuck at levels waaaaay below what you (or I) might find fun to study recreationally. So, typical challenge might be trying to come up with one more real world example that might help a student grok the multiplication of two negative integers.
Re: Maths modules to choose from  advice appreciated
If you are taking the classes for fun, ask the profs is you can audit their classes. Many Universities allow anyone, with some approvals, to audit classes for free if credits/graduation is not the goal. Most data analysts' jobs begin with some kind of case study/tests and regardless of academic backgrounds/achievements, those who provide the best solutions in the shortest time period will usually be preferred. In some fields, meritocracy is alive and well, but dwindling.

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Re: Maths modules to choose from  advice appreciated
Which ones? I spend a nonnegligible amount of time researching this question actually!
I don't pay for the uni (well yes, the bursary is from public funds so I recover some tax money), it is also a distance learning uni so there are no physical classes/commuting/other inconveniences. It basically boils down to lots of reading, practicing, learning software and handing in work for others to assess. I am free to talk to tutors at length, but I rarely contact them as have a 'selflearner' style of acquiring info. Still, good to have them when needed and I use their forum especially for clarifying mathematical proofs.
Think of it as a super well structured online training with knowledgeable tutors that is for free and gives a uni paper at the end, the only thing that is left is to hone the skills and absorb the knowledge.
ETA: They also send a bunch of books every year and I do appreciate it as I don't have to gaze at the screen all the time. Good quality of writing, I learned LaTeX based on the handbooks.
Re: Maths modules to choose from  advice appreciated
@guiterplayer  We can get bursaries?

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Re: Maths modules to choose from  advice appreciated
Scotland is SD greener than the rest of the UK in (not only) this respect.