Full Time OU While Working Full Time

Mason-

Mason-

Mason-

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Has anyone done this?

I start a new job on the 11th of September. It's a 37.5 hour a week salaried position, like most contracts these days it stipulates that when required it is expected that you do some unpaid overtime. Some companies enforce this more than others. As such I'm going to hold off from starting my OU course until the February intake as then I will have more of a feel for the demands of my job.

I'm planning to study Mathematics, this will be my second degree. It's something I've always wanted to do and regret taking the degree subject I did previously. As of right now I do want to go further with it, Masters and potentially a PhD. But that's quite some way away.

I will be commuting 1hr 10 minutes each way to my job, so that's 2hr 20 gone. As well as the 8 hrs at work. Add another 30 minutes for 'other stuff' that's 11 hours in my weekdays gone. Which leaves 5 for eating/studying/relaxing. On the weekends I could treat it as full time i.e. 9-5 on sat + sun.

This is a subject I know I will enjoy so it shouldn't be too arduous to motivate myself to study it, I study it in my own time as it is.

I'd just like some experience of people who have done OU while working full time.

Cheers.
 
IF you commute by train (single long journey where you can usually get a seat) then that can provide a window for study. I did a (not full time) MSc with the OU and used to work on my dissertation on the train.

In a previous job where I wasn't as busy I also used to study in my lunch break at work, but if you are only spending 8hrs at work then I assume you only get 30mins for lunch which kind of rules that out.
 
I study part time at the open uni while working full time, but the degree is related to my career so a lot of it is really stuff I'm already familiar with and it doesn't take up much time. Doing full time study in a different field and full time work will surely consume your entire life for 3 years, is there really a need to study at such a fast pace when you're in stable employment and already have a degree? I would suggest starting studying at a slower pace and see how you handle it, then maybe ramp it up to full time, sure it will take 4 years that way but it's more important to ensure you get a good grade than anything else.
 
Would you not consider PT studying alongside FT working?

For a Bachelors degree, i seem to recall being told as a minimum you should be doing 2 hours self-study for each 1 hour of lectures etc. Typically having 10-15 hours of lectures in a week would equate to an additional 20-30 hours of self-study, making total study time between 30-45 hours.

Unless you're naturally gifted in mathematics and won't require anywhere near that much study time, i fear that you'll be trying to cram in way too much.

You also need to take into account other "life admin" tasks - shopping/cleaning/visiting the dentist. What happens if you feel ill for a week?

Just going on your own calculations, if you awake and leave by 07:00 (+11 hours) and return by 18:00. 5 hours would push you to 23:00, so that's maybe 4 good hours of studying. Even if you cram in 8 hours on both sat/sun, that would put you around 36 hours of study time, but that's really not giving you much breathing space.
 
well you could certainly study on your commute, why not do 90 credits per year and complete it in 4 years?

I guess another option is to do 120 credits for your 1st year modules, same again for your second year modules and then split the third year into two years as the difficulty level ramps up.

The thing with the OU is that the first year modules will be a bit easier than at a regular university as there are no entry standards for the degrees, this means the second and third year modules then need to play catchup so you'll likely find the difficulty level ramping up rather quicker.

Previously for an OU maths degree I think there was only one compulsory 30 credit 1st year module the others were optional if you needed them, so you could actually make up the required 360 credits for the degree with additional 2nd and 3rd year modules. These days, due to funding changes, you're forced to take 120 credits at each level so can't do this anymore... I guess therefore that you perhaps could risk doing the first year full time (especially if you have the relevant A-level) as it isn't really even degree level or at best perhaps overlaps slightly with 1st year at a regular uni, basically it should be revision and as it is maths, if you know it, then it doesn't need to take up much time.
 
Just some answers to some other questions. My commute is by car so I can't study while commuting.

Yeah I am cutting it fine with time - I'm single but yes there are other things that 'pop up' so maybe full time isn't the way to go.

The naturally gifted at maths question, when I was at school I was told I was. I got 100% at GCSE with no revision - but I tried that tactic at A-Level through stupid arrogance and funnily enough it didn't work that time. I got a B in Maths and a D in Further Maths. I studied computer science, at a 'not great' university that didn't even require A-Level maths to get on the course. There were bits of maths in my degree but really not much. My university was much more focussed around gearing you up for industry rather than classical Computer Science, not that that's a bad thing.

dowie said:
well you could certainly study on your commute, why not do 90 credits per year and complete it in 4 years?

I guess another option is to do 120 credits for your 1st year modules, same again for your second year modules and then split the third year into two years as the difficulty level ramps up.

The thing with the OU is that the first year modules will be a bit easier than at a regular university as there are no entry standards for the degrees, this means the second and third year modules then need to play catchup so you'll likely find the difficulty level ramping up rather quicker.

Previously for an OU maths degree I think there was only one compulsory 30 credit 1st year module the others were optional if you needed them, so you could actually make up the required 360 credits for the degree with additional 2nd and 3rd year modules. These days, due to funding changes, you're forced to take 120 credits at each level so can't do this anymore... I guess therefore that you perhaps could risk doing the first year full time (especially if you have the relevant A-level) as it isn't really even degree level or at best perhaps overlaps slightly with 1st year at a regular uni, basically it should be revision and as it is maths, if you know it, then it doesn't need to take up much time.
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Yeah they have some test on their website for one of the first year modules and the first question in the test was something like how many metres in a kilometre. And then another test for one of the other modules which was more like A-Level maths. I think I'll be fine in the first year but like you say it may ramp up a lot in the 2nd/3rd.

I think I'll do 90 credits a year, seems like a good balance.

Thanks for the input guys. Ultimately I'm going to see what my work load is like. It would also benefit my career so I might be able to ask them to help out a bit. But I don't want to start asking above and beyond within my first 6 months of work.
 
You might be able to count some of your credits towards the degree - especially at level 1.

From your background it sounds as if MU123 could be skipped and you would have covered a lot of the material in MST124 and 125 from your maths and further maths A-level.

I'd agree with what Dowie has said regarding level 2, the difficulty and volume of work does ramp up and I've heard that there is a similar jump between level 2 and 3 so some flexibility in your plan might be a good idea.
 
I found that on top of full time work, doing 60 credits a year was ok at level 2, but nigh on impossible at level 3 (I tried it once and decided never again and gave up one of the courses).

As Sheff says, there really was a step change in difficulty from level 2 to 3.
 
Cheers for the input guys.

I did see that I could apply for credit transfer, however it's been quite a while since I've done some things so I wouldn't mind going over them again that's why I'm reluctant to do a credit transfer.
 
Ah, a topic close to my heart. What you considered originally - f/t job and f/t OU - is the beginner distance learner's trap, and although doable (the Devil's triple: 30 creds intro module, 60 creds core module and 30 creds final module; L1/2/3, respectively; say for pure maths parts alone connects up quite nicely, but that's three exams close together unless staggered, plenty to soak up and plan, and not all later modules can be staggered for comfort) is not advisable. The OU, to its credit, has subtle pushes in its literature and advice against this route for your average 40 hour week worker (and not so subtle, studying at full tilt has to be authorised beforehand). To avoid rehashing in depth what's common knowledge on the student forums there and the OU's own study advice, I'll summarise:

*Get a taste for the format (try one 30 cred module, say M140/Basic Stats - no exam, but not too boring and gets you up and running with regards to tutors, student forums, courseware, etc; if Graphs, Networks and Design is still running, it's an L3 module you can easily do as a CS grad also, for extra initial challenge - discrete maths and elementary combinatorics, mostly algorithmic); you can also skim through some OU literature secondhand or at their regional centres, iirc, to get a better idea; do try the quizzes
*Pick the right course and path through it (quite hard, even with some years behind you, but generally: if you don't like the materials and your first serious core module, it's a hint)
*Pick your fights
*Don't cram
*You don't have as much time as you think you have
*Yet commute is not an obstacle - audio materials
*Let the specimen and past exam papers guide your focus
*The minimum pass requirement on certain modules is low, but people still miss it! (A way around this is to take modules as you see fit, but link them to a qualification later to progress; still the requirements must be met eventually.)
*Consider credit transfer for the optional first year bits, if speed is important (to review foundation level material, you'll only need Essential Maths 1/2; the optional M140 stats and random choice option 2 can be safely skipped via a transfer, unless you want to try out the OU as per point 1)
*First year is review stuff and doesn't affect your final classification for the degree, but if you can't recall most of it when L2 starts, you're in trouble (more re volume and exams rather than overall difficulty of content)
*Use your tutors; tutorials are sparse but most are readily reachable by phone and increasingly digitally
*Peer support, student societies and counselling are also available

Now, there are some reasons people do load up 120+ credits, come rain or shine:

*You need a degree quick, and largely for non-academic reasons
*You do not work full time or at all
*You're doing it for fun only, and have the money for this hobby
*You're completing a degree transferred from elsewhere or otherwise formalising knowledge that's already there (say, you'd studied maths on your own for the past X years or worked in an analytic field, which relies on non-trivial modelling).
*They think 60 creds per year is too slow, and base their time estimates on year 1 courses
*The degree shadows your job
*School leavers doing OU as their primary post-secondary education
*OU is life; that is, outside work and OU you don't do anything else for three or four years, and I mean running out on the dot from work and having OU's audio in the background as you shower and eat

If the above does not apply, don't do it at f/t pace. You'll burn out and you may even end up 'hating' mathematics, which would be a great shame, as it's a deep and enriching subject and a very creative human art!

As for going at the 90, let's look at the practical matters of that approach, given the degree pathway (assuming you aren't going Maths/Phys or Maths/Stats):
Year 1: 30/30/30/30 (or L1 60, such as S104 or its successor module, which must be counted as a 30 cred option and linked after you complete all other prerequisites for L1 - you have to call them to do this, as the system won't let you, but it's possible and legit)
Year 2: 60/60; yep, after the initial rewrite of the course, modules got merged, and this is a trend with the OU overall; to do 90 optimally, you'll need to take an L2/L1 combo - fractionally taking some courses, dropping out and completing/deferring later is an admin nightmare and is regulated tightly - you will need to present good reasons beyond wanting to take 90 creds and L2 only offering a 60/60 split.
Year 3: 60/30/30 (the difficulty here varies, from plain-sailing combinatorics, which are more applied and L2 or lower to some pretty meaty applied maths and competent delivery of essential pure material; some people manage to talk themselves into grabbing a few masters modules, but this is harder now (the department is strong in diff. geometry, stats, complex and applied complex analysis, PDEs, and likes its number theory well enough, with aforementioned combinatorics brought in by new blood in the staff roster. So unless you have L1 options still left to do on your list, taking L2/3 or L3/3 double whammy is asking for a panic attack)

Above all else, discipline and perseverance gets the prize in this game. Should you choose to climb the 'mountain' - the very best of good luck! :)
 
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Thanks Jack, if possible I wouldn't mind doing credit transfer to skip the two modules in the first year: http://www.open.ac.uk/courses/qualifications/q31 - Discovering Mathematics (this module is clearly for people who haven't gotten more than a GCSE in maths) and the Stats one.

I guess I'll just do 60 credits a year (with 60 from transfer) and see how that goes, that's 5 years which isn't all that bad.

I want to do Essential Maths 1 + 2 even if it is going over stuff I did at A-Level. It was a while ago and a lot of it I haven't used in a while.

I do know what subjects I'd like to study.

In stage 2 I'll do the 2 60 credit modules. Pure Maths + Mathematical methods, models and modelling.

In stage 3 I'll do:
Further Pure Maths (60)
Complex Analysis
Optimization
 
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Speak to the course team. It looks like you're looking at the 'gentle pathway'. There has always been a normal one too, which is: EM1/2; M140; Free Choice (30 creds). Like Dowie said, there's once a time when you could whack a level three or even a postgrad module as your free choice options, but now it's more restricted on named degrees (before 2008/9, I think you could even do an MMAth degree; alas it only survives in bits and bobs and the MSc now, see my note about L3). If you want more freedom in your choices, the OU now recommends doing an Open Degree. There are pros and cons to it, namely you'll always have to explain what you have done to whatever admissions you'd be facing in future, unless you wish to go on to the OU's MSc, in which case it would be fine.

Your choices are fine too. Deterministic and Stochastic Dynamics and whatever is replacing Graphs, Networks and Design would also be fun. Although that Optimization module would work equally well with any other analytical course covering PDEs/ODEs, and as it ties in numerical analysis, it'll have discrete and continuous parts as they appear in applications. For me the great shame is the lack of options in modern abstract algebra and probability beyond the necessary prerequisites (which I'm hoping nerfing GND in favour of a more focused combinatorics course would at least partially address), but you can't have it all (from what I've experienced over the years, hard modules with high failure rates get merged or cut eventually). Still, you can cover any slight gaps via MIT's open courseware for a very rounded education. (Even elite American universities start on the whole one year behind their UK counterparts (most people don't take honours classes, etc), plus they act a lot like sixth forms in the earlier/general years; hence their resources are quite a boon to an OU student! Example: http://ocw.abuad.edu.ng/courses/mathematics/ [get the degree pathways from the departments website, so you know which codes to look up for which course/level])

You may also want to consider doing EM1 + MMM, and then EM2 + PM, to leap a year, but I wouldn't push it with 90 creds beyond that unless you're flying through the material and find its retention - alongside work - straightforward. Again, doing 60 creds per year is what both the pathways and materials were designed around, so you'll encounter the least stress/friction by going down that route. You will find some early review on either the PM or MMM course, as these modules serve as standalone core maths units on their various pathways, and only really appear together on the general maths degree which you're thinking of taking, so there is some overlap, with most people finding MMM easier and more computational (ie more problem solving vs proof). But, whichever route you choose, good exam prep is key. I think if you can balance it right, do some maths for enjoyment outside the syllabus and notch up those early modules as easy wins, you'll enjoy it more than a harried cram run! :D Tutorials can be fun, if you can make it to them. They are crammed for basic science, but for Maths, especially in latter years, you'll often find yourself in 1-to-1 lessons, as people drop out or don't turn up. The Maths soc is worth a shout too: http://m500.org.uk/. They do regular events, one of which is dedicated to revision.
 
datalol-jack said:
Speak to the course team. It looks like you're looking at the 'gentle pathway'. There has always been a normal one too, which is: EM1/2; M140; Free Choice (30 creds). Like Dowie said, there's once a time when you could whack a level three or even a postgrad module as your free choice options, but now it's more restricted on named degrees (before 2008/9, I think you could even do an MMAth degree; alas it only survives in bits and bobs and the MSc now, see my note about L3). If you want more freedom in your choices, the OU now recommends doing an Open Degree. There are pros and cons to it, namely you'll always have to explain what you have done to whatever admissions you'd be facing in future, unless you wish to go on to the OU's MSc, in which case it would be fine.

Your choices are fine too. Deterministic and Stochastic Dynamics and whatever is replacing Graphs, Networks and Design would also be fun. Although that Optimization module would work equally well with any other analytical course covering PDEs/ODEs, and as it ties in numerical analysis, it'll have discrete and continuous parts as they appear in applications. For me the great shame is the lack of options in modern abstract algebra and probability beyond the necessary prerequisites (which I'm hoping nerfing GND in favour of a more focused combinatorics course would at least partially address), but you can't have it all (from what I've experienced over the years, hard modules with high failure rates get merged or cut eventually). Still, you can cover any slight gaps via MIT's open courseware for a very rounded education. (Even elite American universities start on the whole one year behind their UK counterparts (most people don't take honours classes, etc), plus they act a lot like sixth forms in the earlier/general years; hence their resources are quite a boon to an OU student! Example: http://ocw.abuad.edu.ng/courses/mathematics/ [get the degree pathways from the departments website, so you know which codes to look up for which course/level])

You may also want to consider doing EM1 + MMM, and then EM2 + PM, to leap a year, but I wouldn't push it with 90 creds beyond that unless you're flying through the material and find its retention - alongside work - straightforward. Again, doing 60 creds per year is what both the pathways and materials were designed around, so you'll encounter the least stress/friction by going down that route. You will find some early review on either the PM or MMM course, as these modules serve as standalone core maths units on their various pathways, and only really appear together on the general maths degree which you're thinking of taking, so there is some overlap, with most people finding MMM easier and more computational (ie more problem solving vs proof). But, whichever route you choose, good exam prep is key. I think if you can balance it right, do some maths for enjoyment outside the syllabus and notch up those early modules as easy wins, you'll enjoy it more than a harried cram run! :D Tutorials can be fun, if you can make it to them. They are crammed for basic science, but for Maths, especially in latter years, you'll often find yourself in 1-to-1 lessons, as people drop out or don't turn up. The Maths soc is worth a shout too: http://m500.org.uk/. They do regular events, one of which is dedicated to revision.
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The free choice doesn't appeal to me. I've done a degree, I had a 'free elective' on that. I don't care for anything other than maths, especially as I'm funding this myself now I just want to do what I want to do. I have been studying a bit in my spare time. But it's going in and out of things and never too much in depth. I've watched quite a few of the MIT lectures, they're a fantastic free resource.

I do plan to do the Masters afterwards. I didn't do a masters the first time around in my degree so I can (I believe) still apply for Student Finance for that. I might take a year out and study my masters full time and hopefully at a good uni if possible. After that I like the idea of doing a PhD, whether I will or not is another question. The optimization module and the methods module in year 2 seem quite related to my work so it would be beneficial. I'd like to get into Formal Verification via Formal Methods (hardware, not software), currently I do Verification without the Formal :p. As of right now though Number Theory is the thing that interests me the most. But I haven't formally studied it other than what I've read online and some videos I've watched.

I wasn't aware you could mix L1/L2 modules. That might be something I consider. But I feel as though I haven't used so much of the maths that I haven't done now for 4-6 years that I really should go back to basics somewhat. I should nail those modules really.
 
Mason- said:
The free choice doesn't appeal to me. I've done a degree, I had a 'free elective' on that. I don't care for anything other than maths, especially as I'm funding this myself now I just want to do what I want to do. I have been studying a bit in my spare time. But it's going in and out of things and never too much in depth. I've watched quite a few of the MIT lectures, they're a fantastic free resource.

I do plan to do the Masters afterwards. I didn't do a masters the first time around in my degree so I can (I believe) still apply for Student Finance for that. I might take a year out and study my masters full time and hopefully at a good uni if possible. After that I like the idea of doing a PhD, whether I will or not is another question. The optimization module and the methods module in year 2 seem quite related to my work so it would be beneficial. I'd like to get into Formal Verification via Formal Methods (hardware, not software), currently I do Verification without the Formal :p. As of right now though Number Theory is the thing that interests me the most. But I haven't formally studied it other than what I've read online and some videos I've watched.

I wasn't aware you could mix L1/L2 modules. That might be something I consider. But I feel as though I haven't used so much of the maths that I haven't done now for 4-6 years that I really should go back to basics somewhat. I should nail those modules really.
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That's fair enough, and yes, you'll qualify for SLC funding for your postgrad course. It's a loan up to 10K, I think, and the conditions are pegged to what's now known as Student Loan Plan 2. Easy enough to find out from their website. From 2018 there was also a move to make STEM degree funding exempt from the standard equal level qualification rule that applies now. So, you may start off paying for it yourself, but end up getting students loans, if that's what you want to do. Things are up in the air as far as domestic things like higher education are concerned, given the political situation, but they are trudging along.

As for mixing, see my advice: do the modules first, in whatever order, link later. You have 16 years to complete your degree under the current rules (hence you can leave a shell registration for a BSc hanging on its own, whilst accumulating standalone modules to be linked later). This of course only applies for self-funded students. If you do want to claim SLC funding, should it become available in 2018, I think they will force you onto a named STEM degree and that particular pathway (one reason those were developed in the first place).

Afterwards, you can progress as far as your ability will take you, up to and just after the PhD; the rest is pot luck, networking and well, on many occasions, money to carry on (which is always easier in applied fields, though not by much). If you're following an applied route, then industry, this is less of a concern, though after a point you will hit age discrimination in one form or another (but don't lose heart, there's a lack of quantitative and analytic talent in the country, so eventually that too gives). The trouble with carrying on via the OU, however, is that the department isn't very large, hence very focused on their pet areas of the subject, and the MSc is designed to stretch over at least 3 years, so you'll lose some years. It's possible to just about do in 2 years, but you hit the same out-of-order difficulty as with their undergrad, so there would be a need to self-study to ensure you can take things in odd/even years. Having said that their PhDs appear to be standard part-time and full-time options.

As for masters at a brick uni, it's a very wide sweep: some unis, say, Durham, want you to have at least two solid years of undergrad fundamentals under your belt before going on to their MSc in Mathematical Sciences (they also run a discretionary assessment, so if they're unsure about you, you will get some problems to do over two weeks during your application - do them well, and their doubt vanishes); Nottingham looks much the same minus the test bit; expect to be interviewed for some courses; Warwick and MAst at Cambridge you would struggle to just walk into after the OU, not so much on material but the way it's presented - there's very little 'book learning' and independent work utilising it - that is, the OU's materials strictly speaking combine everything you would get in lectures + what you would have in your notes + what you need to do to reinforce the material. It's excellent as far as distance learning is concerned; it can be a shock going from this excellence to your bog standard lecture/notes/library/assessment or dissertation mill. Still, there are ways to compensate: do independent study as you're doing; go via an intermediate option like a Postgrad Diploma in Mathematics at say Leeds or KCL, or even MAst at Warwick (they may suggest this if you don't meet the MSc cut). Indeed, whatever your mathematical ambitions and goals, there's always a way to get at them. :)

One final note, keep an eye on what the Russell and 1994 groups do going forward re online and distance learning. You may well find the above does not apply in five years, and you may be able to gain a credible MSc from a 'brick' uni in the standard time of 1 year, either by research or taught without attendance. The pressure and demand is certainly there, plus the financial incentive from the Government loans being available for part-time courses; particularly pressing for London unis, which are being hit with the fact that high rents are pushing out people towards their regional competitors. The latter is somewhat obscured by well to do or foreign government-backed students drafted from abroad on the strengths of their brands, but it has been happening for years. In fact, I'm pretty sure that if Imperial had stayed in the UoL federation, or merged with UCL, you'd have had a very comprehensive maths programme via International Programmes (ie UoL distance learning and outreach) by now, including an MSc.

Sadly prestige wars, since maths is often used as a prescreening tool for all and sundry industries these days, do mean that there's inertia, moaning and lots of myths about why this can't be done. But it'll come.
 
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Cambridge would be ideal as my new job is in Cambridge haha. Maybe my company has some ties with Cambridge that could help? I think they hire a lot of people from there.

Wishful thinking!

Thanks for all the advice, a lot to think over.

Also have you read Disquisitiones Arithmeticae, I wanted to read up on Number Theory. I read around and people say it's a great place to start. It is expensive though. I'm probably already sold on it... but wondered if you'd read it?
 
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Mason- said:
Cambridge would be ideal as my new job is in Cambridge haha. Maybe my company has some ties with Cambridge that could help? I think they hire a lot of people from there.

Wishful thinking!

Thanks for all the advice, a lot to think over.
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No worries. Oxbridge is always worth a punt at postgrad, more for their resources than anything else. Bear in mind also that you can comfortably do a Masters elsewhere and then apply for a PhD at Cambridge on the strength of your MSc research or dissertation on a taught course. There's also the catch that they often ask you to demonstrate how you'd support yourself on the course (crudely: have 20K in savings, and you're in :p I'm only partially joking!). Expect to be interviewed. Having said that, Cams are always good with feedback, so the worst you can do is apply, with a good reference from your tutors and work, and get a polite 'no' with useful advice on how to improve your application. OU students certainly got in in the past, in the MMath years. Further, scanning through the current crop of Oxbridge postgrads, I spied a chap from Swansea U (tbf, he must be the pride of Wales, but still)! And as for international students they pick, they too often come with a wide range of preparation levels. Ignore the marketing guff on their recruitment pages - the actual documents from the department are far more down to earth and helpful. Don't be intimidated either: Oxbridge is literally three colleges per institution providing the laurels for the rest, through wise recruitment, plenty of cash and well, by sheer dint of being around for donkeys years - their internal standard does vary, though this is less of a thing at postgrad as you move over to a more sane department level of organisation. Though the breadth and volume of content is exceptional on the Maths Tripos, the OU still manages to hit most of the topics, roughly 2/3 or so, probability and abstract algebra being the noted areas of weakness. They also offer more lab hours for mathematical programming, modelling and numerics, with software suites and electives the OU simply can't match, but, once more, these are gaps not impossible to bridge. For example, I have a student licence for Mathematica thanks to my OU dabblings, and the net is replete with assignments, solutions and lab demos. Just needs a bit of creativity on the student's part. The OU tutors are more than happy to advise where you could improve/do more too.
 
Mason- said:
Also have you read Disquisitiones Arithmeticae, I wanted to read up on Number Theory. I read around and people say it's a great place to start. It is expensive though. I'm probably already sold on it... but wondered if you'd read it?
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Gauss was an animal, but there are probably better (and cheaper) introductory texts out there, unless you're keen on the history of mathematics too. Could be useful to get a taste for classical problems and his quirks. I've read some left field things, but not this particular book. A level revision, some STEP stuff (https://maths.org/step/), then something like Basic Mathematics by Serge Lang could be quite a bracing intro. A Concise Introduction to Pure Mathematics also leans heavily on elementary examples from number theory, iirc, and pops up on pre-uni lists often enough. Have a skim.

There's words to be said about diving in head first, but likewise it's pointless hitting a brick wall from the word go. I'd say, get good and then get original.

Also, if you've got an itch:
https://www.dpmms.cam.ac.uk/study/IA/Numbers+Sets/

And the reading list to go along with it (not all books are required
  • [*]R.B.J.T. Allenby Numbers and Proofs. Butterworth-Heinemann 1997 (£19.50 paperback)
    [*]R.P. Burn Numbers and Functions: steps into analysis. Cambridge University Press 2000 (£21.95 paperback)
    [*]H. Davenport The Higher Arithmetic. Cambridge University Press 1999 (£19.95 paperback)
    [*]A.G. Hamilton Numbers, sets and axioms: the apparatus of mathematics. Cambridge University Press 1983 (£20.95 paperback)
    [*]C. Schumacher Chapter Zero: Fundamental Notions of Abstract Mathematics. Addison-Wesley 2001 (£42.95 hardback)
    [*]I. Stewart and D. Tall The Foundations of Mathematics. Oxford University Press 1977 (£22.50 paper-back)
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That's from Part IA of the Tripos syllabus from a few years back. A more up to date list is to be found on the department's website (but it's likely to be almost identical). Do look up their module guides, as only bits within those books would be applicable to an intro course; they don't expect you to read them cover to cover, as said above, unless you really enjoy getting the same ground covered from different angles and want to push yourself.

Also one note about style: the more advanced texts won't really have that many examples or problems to do (hence why Cambridge runs examples sheets for its students to do). The trick is to think about the layout of the topic, its definitions and their interactions in theorems, which are formal ways of verifying (aha!) that a mathematical relationship that is non-trivial and thus general holds true through argument. You may need to think up of your own examples for the objects and mathematics presented, and indeed create your own problems to test your understanding. This is not easy, but is an acquired skill. Finally, if you encounter a monster, the book may have skipped ahead too far and is relying on some result expanded on elsewhere, which may in turn rely on bags of other previous knowledge, that is assumed (elementary does not mean 'basic'). So some things can indeed be left for later, and there's no shame in that. There are normally references to guide you to the needed material, unless the author is a complete fiend.
 
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john_s said:
I found that on top of full time work, doing 60 credits a year was ok at level 2, but nigh on impossible at level 3 (I tried it once and decided never again and gave up one of the courses).

As Sheff says, there really was a step change in difficulty from level 2 to 3.
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My experience at L4 was that studying multiple units at a time was tough, so I only did it once. The problem with multiple units is you get conflicting deadlines for TMAs, exams very close together which splits your revision etc. When in FT education that is kind of manageable, but when working FT not so much. I'd rather do a single 30pt unit than two 15pt units for example.
Of course the flipside to my approach is that it takes a lot longer to quality PT, it took me 3.5 years to complete my PGDip, then another year later on for the dissertation.
 
Yeah, it's a logistic pita. Again, mostly due to the size of the department and the number of part time staff on it. Over the years, I've kept flinging the following suggestion at them: merge modules in 60 cred blocks (considering how little choice there now is anyway), but keep multiple exams and add extra 20% of content to the syllabus, which you can then stagger throughout the academic year and topic. Same goes for TMAs. Looking at how they went about converting the old MMath degree, it's the logical next step. At the final year mark, have 60 creds of Further Methods and Applications extending from MMM at L2 for the generalists and theoretical physicists, and perhaps Further Abstract Mathematics and Advanced Topics for the pure route (Logic, Combinatorics, Abstract Algebra; certainly bits of Alg. Geo and Topology, or just more Group theory in general, beyond the current FPM at L3 offering; Gallois Theory at the end, at least). The rest of the mathematical pathways like sciences, tech and engineering can just have the cut up version of the bigger block (hence saving cash), like they currently have with MMM, which has a 30 cred methods extract at L2. But student pressure on this is getting us nowhere for the time being. I think the current administration is more concerned with getting more youngsters in on whatever programmes are already in play, and getting a slice of the vocational pie/apprenticeships links. They are pushing big on marketing, atm. Admirable, but a touch of a snub to the academic side of the uni. :p

Update:

OP: If you want the most flexibility outside a qualification, don't register for one and take individual courses/module according to the pathway. Then register for the qual at the end and link all of your completed modules to it (you can still credit transfer at the end, I believe, but do check). It appears they are tightening up the software, so my original approach may no longer apply. Though it may still be possible to override this on the phone. Cheers.
 
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