As I've mentioned recently, I'm trying to write an undergraduate abstract algebra textbook that's readable by humans,1 because I think that somebody should.
Your "what level have you studied to" is missing a few options.
Ex: I did a Maths O-level in 1981. I gather it covered stuff that's A-level today. I then took supplementary courses that covered some elements of the 1981-period A level syllabus (I was doing Physics), and then more at university, then yet more on a different university course (and where exactly do they start first order predicate calculus these days?).
So I have no idea what level I've studied mathematics to.
Oh, and I've forgotten how to do long division ...
For that matter I studied further maths at A Level, and my first year engineering MEng covered a lot more maths, plus some very mathsy stuff in transformations etc as we went through signal processing and quantum mechanics (bleh)
Yes, I realised after I'd posted it that that question wasn't terribly useful or helpful. I guess what I'm really trying to ask is whether respondents have heard of, briefly met or studied in detail the concepts in question, so (as is often the case) educational qualifications are perhaps not the best way to judge that. I'll try to quickly swap in a poll without that question.
Now that I think about it, I'm not sure what's actually in the GCSE or A-level syllabuses these days. I was the second year to do GCSE, so the syllabus was pretty much the same as O-level but in a slightly more readable font. And I did A-level (maths and further maths) some years before modularisation came in, and was taught by teachers who threw loads of extra stuff in because it was interesting and they knew we could cope with it. Occasionally my first-year students say things like "We did complex numbers, but it's only in FP3 so not everyone did it" and I nod sagely as if I know what they're talking about.
We teach the first year students a bit of symbolic logic (truth tables and the like) in the first term "Foundations" module, and there's an optional "Introduction to Logic" module run by the philosophy department that the maths students traditionally do quite well at.
I can do long division with polynomials, but it's probably a couple of decades since I last did it with numbers.
Well part of the motivation for writing the book is that there are lots of abstract algebra books out there that seem to have been written for people who either already understand this stuff very well already (the Éléments de mathématique series by the Bourbaki collective are some of the most extreme examples of this type) or for confident students who are prepared to hack away at something until they understand it. I think it's probably fine to expect PhD students to put a bit of work in to understand something (although that still doesn't excuse overly terse or opaque exposition) but there are a lot of students who get turned off entire branches of mathematics because their confidence gets damaged by unsympathetic or unclear lectures or books
( ... )
I ticked bachelors level, as although I have an MMath it was all in fluids and quantum physics, and it was all so long ago that I might quake if you asked me to define a group...
[x] snowflake - I've been to some undergraduate (NatSci Maths, Quantitative Biology) and postgraduate maths (Part III Medical Statistics) lectures, but in fact have probably forgotten most of what I did at A-level.
As I said to despotliz, the main target audience is mathematics undergraduates, but I'm aware that group theory has applications in other disciplines as well, so I'm keen that this book be at least partly useful for, say, computer scientists, physicists, chemists or biologists who want to learn a bit of group theory. So any constructive comments you might have would be welcome.
Similar to the above, I have a maths A-level with some patchy undergrad and postgrad-level courses in stats, so for algebra it's safe to assume I know nothing past A-level. But I am trying to learn a bit more maths, so I can take a look and see if this is at all comprehensible to me.
The main target audience for the book is mathematics undergraduates, but I'm also keen that it be at least partly useful for non-mathematicians (particularly computer scientists, physicists, chemists and biologists) who want or need to learn a bit of group theory in a hurry. So any insights you could offer would be very welcome.
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Ex: I did a Maths O-level in 1981. I gather it covered stuff that's A-level today. I then took supplementary courses that covered some elements of the 1981-period A level syllabus (I was doing Physics), and then more at university, then yet more on a different university course (and where exactly do they start first order predicate calculus these days?).
So I have no idea what level I've studied mathematics to.
Oh, and I've forgotten how to do long division ...
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We teach the first year students a bit of symbolic logic (truth tables and the like) in the first term "Foundations" module, and there's an optional "Introduction to Logic" module run by the philosophy department that the maths students traditionally do quite well at.
I can do long division with polynomials, but it's probably a couple of decades since I last did it with numbers.
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