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I am not sure if this is the right StackExchange to post this kind of question. If not, I apologize.

I currently have a problem in choosing a undergraduate program to study. I am mainly interested in software engineering, life sciences and mathematics. As a result of this, I have bought multiple undergraduate text books for these subjects to teach myself all basics of these fields. This includes things like programming, theoretical computer science, data structures, algorithms, ... , set theory, linear algebra, real analysis in one and several variables, complex analysis, abstract algebra, ... , zoology, chemistry for biologists, genetics and so on.

Now, when I look at those many different degrees available, I am kinda stumbled. Because all degrees have kind of 'nothing to offer', as I see it. By this I mean that I feel like I already know 66% of the course's content, especially in mathematics. Of course, such programs can offer more things like help from tutors (which kinda became irrelevant due to the internet), field works, expensive laboratory experiments and so on. But I don't think that programs like for mathematics or software engineering have much of such things. And I am not sure if I really want to pay 9000£ a year for such a degree then. So a degree in biology would be the best.

But then again, I am just afraid of taking a biology degree, because I fear people (both in industry and academia) will deny me because this particular degree I have pursued did not include a programming course or fundamental mathematics, even though I did teach such things myself.

Now I have no experience in how people might react when I write in a CV things like 'I might have a degree in biology and not your desired degree in computer science or mathematics, but I do think that I fit your job as statistician very well, because I taught myself modern mathematics, methods of statistics and programming. (even though I do not have a certificate proving any of the listed skills, just believe me.)'


Edit 1 'To the Dunning-Kruger effect':

Well, you can often view course structures and syllabus' for the courses included in your degree online. Let's take for instance the Bsc Mathematics (G100) program from the Imperial College. Under 'Structure' you can read what you'll learn in during this degree and you can even see all the syllabus' for all individual courses, such as for 'Mathematical Methods I'. When you now have different books covering the topics listed plus other sources from the internet (like videos, papers, articles), I do think that you can teach yourself a lot of the degree. You even have people on StackExchange you could ask for help. Despite all of that there is even a list 'Appropriate books' in which the Imperial College recommends you books to read for that course!

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    I gave an up-vote to this question because I think it's worth while asking. But, I am not clear about "low academic standards". Please clarify what you mean by that. You cannot say a course is low standard just because you already know 66% of it. The other 34% may be more difficult than the 66%. – scaaahu May 20 '16 at 5:12
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    "help from tutors (which kinda became irrelevant due to the internet)" - I strongly disagree. – O. R. Mapper May 20 '16 at 5:42
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    Are you getting any feedback? Is a mathematician looking at your proofs and telling you they are valid and well written? Is another programmer testing your programs and reviewing them for readability and maintainability? – Patricia Shanahan May 20 '16 at 7:52
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    The difference between a good and a less good place is not just the lectures/education, but also your peers. There may be brilliant people who have nothing to gain from university education, but my experience is that top locations, say, for math, Cambridge, Princeton, Bath, Warwick etc. will provide you what books do not do: not only material, but direction. – Captain Emacs May 20 '16 at 8:38
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    @AE My mathematics B.Sc., awarded in 1970, was from Imperial College. At the time, the rumor was that the Mathematical Methods course was added after they found they had a student with a USA high school education who had a deep understanding of the theory of integration, which they had taught, but who had no idea how to do practical integrations, which they had not taught. They had been counting on students having a "firm grounding" in such topics on entry. – Patricia Shanahan May 20 '16 at 12:50
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Since the sentiments already appear in your question, let me make this extremely clear:

Modern university degree programs serve at least two distinct purposes: education and certification

I entirely agree with you that a if you already know the material, for the education purpose of the degree it seems redundant to take a course on a subject you have already mastered. But as you have already indicated in your question, employers, graduate schools, and other agencies may choose to use your university transcript as evidence of said mastery. (Though, in some fields, the professional society provides their own certification function. For example, the society of actuaries have their own pathway toward membership. Those fields may be more "friendly" to someone without a formal degree.)

But I do wonder how you came to the assessment that you already know most of the material in offer for the degree programs. The Dunning-Kruger effect is a well-documented phenomenon in which practitioners of low expertise tend to overestimate their competency. While I am not saying that this necessarily apply to you, frequently in a classroom scenario one of the most difficult things is to first break down the students' existing misconceptions before actually teaching the material.

That said:

From your post I gather you are based in Britain. One option for you is to pursue a degree outside the United Kingdom. The liberal arts type education in the United States, for example, give greater flexibility in the choice of coursework toward a degree program, and frequently you can make special placement arrangements to participate in higher/graduate level coursework in lieu of the introductory courses. Additionally, given you interest, maybe you should investigate degree programs in mathematical biology. Modern math bio tend to combine theoretical and computational mathematics (which involve a good deal of programming and simulations) with life sciences.

  • Well, a graduated student probably would also say he/she knows most of the material in offer for the undergraduated degree program, but not due to the Dunning-Kruger effect. Biomathematics may be an option, however in a 3-year program one cannot teach the same amount of biology/mathematics that would have been taught in a single-degree program for biology/mathematics. So how do I certificate the extra knowledge I might will gather on my own? It's kinda hard to finance a U.S. undergeraduate degree for me, so this might be an option for later graduate degrees. – ClassicEndingMusic May 20 '16 at 7:30
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    @ClassicEndingMusic how do I certificate the extra knowledge I might will gather on my own? You can elect to take upper level/graduate level courses and receive good grades. Those good grades will show up in your transcript and certify that you do have good knowledge in those fields that are not usually taught in the 3 year degree program. – scaaahu May 20 '16 at 8:35
  • @ClassicEndingMusic: let me just give an anecdotal answer to your question about the DK effect. When I started graduate school I was certain I have mastered the material on offer for my undergraduate degree program. Now that I've held my PhD for seven years, I know I was wrong. // 3 year BSc degrees is also a British/European thing: North American degree programs typically last for 4 years. To summarize my advice: a good portion of your discomfort seem to stem from the structure of the traditional British-style University education. I would argue that what's best for you is to find a place – Willie Wong May 23 '16 at 13:59
  • ... which has the structural support for the type of education you want/need. This doesn't have to be outside the UK, as Matt's answer indicates. – Willie Wong May 23 '16 at 14:03
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You're likely aware of this option, but I thought I'd flag it up just in case. Have you considered taking a dual honours degree?

Although in theory taking a degree is two subjects leaves you a specialist in neither, your dispensation toward teaching yourself suggests you'd be more than capable of making up the shortfall. And besides, the knowledge you miss out on as part of the syllabus tends to be more the cutting edge material, more relevant to specialist research.

If this worries you, perhaps take a look at Keele University. They specialise in dual honour degrees and offer the option to switch to single honours part way through your course if you so wish. Biology and Mathematics are one of the combinations they offer.

Finally, as someone who is themselves a biologist who eventually became interesting in statistics and computing, take a look for universities with active research interests in areas that combine the two like population genetics. It's not a particularly popular topic but if memory serves Trinity College in Dublin and Nottingham University both had a high profile in this area. Other areas of biology with a high amount of crossover into maths and software include Crystallography and Biophysics.

You will likely find that biology degrees at these sorts of institutions have the options to take modules in relevant areas of maths and computing, and you will find staff sympathetic to helping with your broad-based learning interests.

Finally, don't underestimate how much there is to learn. I'm sure you're very clever and competent but modern science is terrifyingly rich in knowledge. You will certainly benefit from learning in a structure, supportive environment such as a university course and you may be surprised how much material there is to get through. It's certainly worth considering, especially given the certification angle that others have mentioned.

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I don't have enough reputation for a comment, hence the answer.

I'd like to address this comment of the OP:

Biomathematics may be an option, however in a 3-year program one cannot teach the same amount of biology/mathematics that would have been taught in a single-degree program for biology/mathematics. So how do I certificate the extra knowledge I might will gather on my own?

In software engineering, it's actually relatively easy to show your expertise, namely by having a portfolio in GitHub/GitLab/BitBucket/etc. Not only that, but also on most job interviews for positions where there is coding involved, you will be asked to show your coding skills. But to get these job interviews, you need a degree.

In mathematics and biology, you typically mention any extra knowledge in your CV, cover letter, statement of purpose, etc. And then, if that knowledge is pertinent to the position you are applying for, you will often be given a chance to demonstrate that knowledge in interviews. But again, without a degree, you most likely wouldn't reach the interview phase anyway.

There are also many advantages to going to university, even if you "know" the material.
For example, in university you often make connections (be it with other students, people from academia, people from industry) that greatly expand your options.
You also get opportunities that you otherwise wouldn't be able to get, e.g. internships and such, which are specifically for university students, and these internships not only provide amazing boost to your CV, but often give you invaluable experience that is hard to get otherwise.
And finally, something that a lot of people don't realise, in university you get exposed to many different ideas and points of view, many (I'm actually tempted to say most) of which you wouldn't be able to think of by yourself. And this can be really important.

My advice to you: go to university, even if you think you "know your stuff".

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