For people looking to do Maths (at Uni).

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zetamcfc
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Not sure where to put this, so I'll put it here.

If people would like to look at some maths textbooks for free without having to buy them. Then springer have a few introductory books available for free for a while on their website,

https://link.springer.com/search/pag...1_AD_MathBooks

With Real Analysis, Linear Algebra, Probability, etc they might bee good for those of you about to go to university, or planning on going next year.
Last edited by zetamcfc; 4 days ago
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Totoro50
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You can also clear the Maths filter to find a few awesome ones on other topics like Astrophysics or other topics the cool kids are reading these days.

The free book Understanding Analysis by Stephen Abbot has been referred to as a gentler and helpful introduction to Analysis by a few American folks.
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artful_lounger
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Hmm, I've heard good things about Linear Algebra Done Right but never used and just opened it... and was surprised to find the formatting is very nearly identical to the OU module materials for maths module I did last year! Obviously whoever did the OU materials was a fan
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Totoro50
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(Original post by artful_lounger)
Hmm, I've heard good things about Linear Algebra Done Right but never used and just opened it... and was surprised to find the formatting is very nearly identical to the OU module materials for maths module I did last year! Obviously whoever did the OU materials was a fan
Sheldon Axler gets a fair number of positive reviews for that text. I am starting over after a long hiatus from Maths so I cant be as precise as I would like. Which modules did you complete last year if I may ask?
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artful_lounger
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(Original post by Totoro50)
Sheldon Axler gets a fair number of positive reviews for that text. I am starting over after a long hiatus from Maths so I cant be as precise as I would like. Which modules did you complete last year if I may ask?
Oh it was just one of the introductory maths modules (MST124), I'd been on an engineering course previously (and before that briefly on the first year of a maths degree), but I'd been out of education for a few years for health reasons so I wanted to familiarise myself with some of the calculus etc I'd become rusty with. The module itself was just sort of AS/A-level calculus, trig, etc. It didn't cover any content that would usually be considered "uni level", although the sequel module (MST125) does have a section on number theory (albeit not proof based). I'm not doing that module though and have sort of shifted to exploring other subjects

MST124 might be a good starting point to refamiliarise yourself with the a range of A-level topics if you're a bit rusty on those but have covered them before, or haven't done them before but are confident in GCSE Maths topics. I would note though, although it covers roughly similar material, the actual assignments and exam are a lot easier than A-level Maths is and the problems are quite straightforward and routine. It probably wouldn't be suitable preparation alone for mathematical courses at brick unis(e.g. maths, physics, engineering etc), is my point (although not a bad starting point, you'd just probably need to do 2-3 maths modules at the OU before you were at a comparable level to someone with a good result in A-level Maths, since they do start very much from scratch and the structure of assessment doesn't test you so much on applying stuff to unfamiliar problems).
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Totoro50
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I have the MST124 and M140 books already for my planned start. What is interesting to me is the acceleration between the OU years. When one looks at the US programs (at least distance ones that are reputable) the coverage seems to end sooner than what OU has on offer. I have the books for M210 and M208 and it was obvious about the step up in "ask" of the student. I am trying to find the pdfs for those two classes too so I can include them in free time reading without having to carry a book. I was impressed with the breadth and depth of options at the OU. For distance, they really offer some great choices. The way math and maths vary between countries is really interesting. I cannot, and would not if I could, talk about better between systems. There is a great discussion on the website math with bad drawings on the differences if you are interested. While I am working through MST124 and 125 I will be running a parallel sequence with a few key texts to create more understanding in depth. Happy to share some time.
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Totoro50
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I am reading through the modules starting July to begin prepping and also working though a secondary track of texts ending with finish Apostol or Spivak (both limits) plus Keisler (infinitesimals like Robinson) by the time I finish MST125.
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artful_lounger
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(Original post by Totoro50)
I have the MST124 and M140 books already for my planned start. What is interesting to me is the acceleration between the OU years. When one looks at the US programs (at least distance ones that are reputable) the coverage seems to end sooner than what OU has on offer. I have the books for M210 and M208 and it was obvious about the step up in "ask" of the student. I am trying to find the pdfs for those two classes too so I can include them in free time reading without having to carry a book. I was impressed with the breadth and depth of options at the OU. For distance, they really offer some great choices. The way math and maths vary between countries is really interesting. I cannot, and would not if I could, talk about better between systems. There is a great discussion on the website math with bad drawings on the differences if you are interested. While I am working through MST124 and 125 I will be running a parallel sequence with a few key texts to create more understanding in depth. Happy to share some time.
Many distance learning programmes aren't attempting to offer a full degree in mathematics though; so it's quite typical for them to just offer a calculus sequence and maybe linear algebra/differential equations for would be physicists/engineers/computer scientists etc. The stuff on analysis, abstract linear algebra, abstract algebra etc is mostly unique to mathematics degree programmes at undergrad level (and also less palatable to the general public, as it were, who might otherwise resign themselves to "suffering" through calculus with the aim of doing other things with that).

Also in the US it's quite common for colleges to have general education requirements in math which are typically satisfied by a semester or two calculus, and some students might just fulfill that requirement by distance learning (particularly if they aren't thinking of majoring in math heavy STEM majors), so there is more of a market for those more introductory topics. Similarly it's rare to find courses in even linear algebra in community colleges in the US.

MST210 and M208 represent really what first (and sometimes depending on uni, second) year students at UK universities studying mathematics cover, and certainly the latter topics are a significant departure from the style of mathematics done in A-level (which is more in line with the content of MST124/5). This can be a bit of a shock, as I found (in terms of the maths degree I started at a brick uni) But for any prospective mathematics degree student, in the UK or abroad, there is a point in their education where there is a significant "changing of gears" as they begin the much more rigorous style of university mathematics (typically in "pure" maths courses/topics in analysis and algebra).

However I don't know how the OU structures the exam for M208 and similar "pure" modules, as in MST124 certainly and I believe MST125 they are multiple choice based, which is in some respects easier. For proof based mathematics I'm not really sure how that would work so much, and not having to write the proofs yourself might avoid some of the harder aspects of getting started in those topics (as just learning how to write and structure proofs is a topic unto itself, usually covered in an introductory analysis module or similar...).

You would cover more or less the breadth of "core" topics a maths degree student would be expected to have covered in the UK with the OU though, by all accounts; it is possible though that you won't necessarily go into the same level of depth, especially if you only focus on assessed/examinable content and preparing for the exams and assignments specifically. Of course that isn't to say you couldn't spend time working on some stuff in more detail, just that you can get good marks without doing so necessarily!
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