Uni maths textbook/international textbook which are relevant to the HSC syllabus (1 Viewer)

[eyeseeyou]

R there any uni maths textbooks, which have content relevant to the HSC (with questions being harder)?

Also are there any for...say like Vietnamese maths textbooks or chinese maths textbooks?

Thanks

 

[Silly Sausage]

For challenging calculus questions I always recommend Micheal Spivak's 'Calculus'. Other then that I don't really recall many uni level math textbooks with HSC relevant subjects.

You can also search online for some Soviet-era Russian mathematics textbooks which are apparently extremely challenging.

 

[Drongoski]

Not only Spivak, but 1st Year "Calculus" texts by James Stewart, G B Thomas & Finney, Howard Anton et al etc etc - they all contain material which can be helpful for 3U and 4U. Their diagrams are excellent and their worked examples are spelt out in detail.

 

[porcupinetree]

+1 for Spivak. Read some of it during my HSC year, found it really good/interesting. (And am currently using (and loving) it now that I'm actually doing uni maths)

 

[leehuan]

My calculus lecturer gets a ton of his info out of Spivak. And one of my colleagues brings it up quite frequently to me.

(I would read it tbh, but I'm just lazy to)

 

[seanieg89]

Spivak is comfortably the best book I have seen to learn single-variable calculus properly for the first time, but it's probably not that suitable a thing to work on in HS. (His "Calculus on Manifolds" is also a gem imo, and his differential geometry series is classic although I have not read much of it.)

By this I just mean that the {improvement in HSC exam/assessment performance}/{time spent} ratio will be relatively low with reading Spivak and doing its exercises vs just crunching through the insane number of available past questions from HSC exams.

If your aim is simply to start learning calculus properly on the side and you are willing to work reasonably hard, then it is excellent. My first encounter with calculus was Stewart (which would probably have a higher value of the aforementioned ratio), but Spivak is much better if you really want to understand how things work and I would rather have learned calculus from there. (I still picked up a bunch of stuff from it when I eventually read it).

 

[davidgoes4wce]

James Stewart textbook + Worked out solutions (you wont be able to purchase the solutions in a shop or library but you can order it from the US), helped me get 98% for a 2nd year Engineering maths units. (Particularly good for multivariable calculus- alot of students seem to struggle with 3D calculus )The maths book is the best for tertiary study.

 

[davidgoes4wce]

Just my opinion also but its kind of pointless doing maths , especially as a student, if you don't have the step by step worked out solutions. I think for me, with maths, is its got to a stage now where, I can read the question like an essay, I can pick up the little errors, the flow and the structure.

I think I once tutored a Physics students , and I told their parents that I also provided the step by step worked out solutions as homework to the exercises and they blasted me. I was only trying to help the student, in case they didn't understand the question. Of course you should be able to do a question independently after seeing numerous examples or throughly understanding the concepts.

 

[seanieg89]

The maths book is the best for tertiary study.

That's pretty subjective. I wouldn't recommend Stewart for anyone planning on majoring in mathematics (or certain areas of physics). The emphasis is on using calculus as a tool to solve problems. (Generally fairly routine applications of the included theorems, but there are some ones that can capture a student's interest.)

Spivak is a stepping stone to real analysis, and (imo of course) gives you a much more detailed understanding of why/how calculus works. Books like Spivak are the sort of thing that could inspire a young student to pursue mathematics further, whereas I definitely wouldn't claim the same of Stewart.

Everyone has their own requirements of a book though, especially if self studying.

Just my opinion also but its kind of pointless doing maths , especially as a student, if you don't have the step by step worked out solutions.

I think the temptation (especially for a new student with an patchy understanding of the material) to look at completely worked out solutions rather than banging their head against the problem for a little longer would be far too much.

Imo numerical/symbolic final answers to the routine calculus exercises are fine, and solutions to "proof" exercises should probably not be provided at all (or at least be published separately).

 

[davidgoes4wce]

To be honest I have heard of Spivak but never had the chance to do any questions from there.

I will definitely make an effort to get that book from the library if I get the chance. Seeing that most of you guys know your maths well, I'll take your word.

In terms of high school, I think the best maths books are the Adelaide based company 'Haese' which prepares the IB maths books.

 

[Drongoski]

Spivak is a mathematician of high order, writer of serious work on differential geometry,etc, whereas the late James Stewart is a popular expositor of calculus. Stewart made a lot of money from his calculus textbooks and built a unique house called "calculus ?" - but I guess is not a mathematician of Spivak's order. Incidentally, Spivak also wrote one of the early primers on TeX called "The Joy of TeX" (the guy has a sense of humour, generously sprinkled in this primer)

 

[seanieg89]

Stewart made a lot of money from his calculus textbooks and built a unique house called "calculus ?" - but I guess is not a mathematician of Spivak's order. Incidentally, Spivak also wrote one of the early primers on TeX called "The Joy of TeX" (the guy has a sense of humour, generously sprinkled in this primer)

Yes, reprinting a large and expensive book so frequently with trivial additions is one way to get rich.

 

[InteGrand]

Yes, reprinting a large and expensive book so frequently with trivial additions is one way to get rich.

What was the reason he did such frequent reprinting? Was it to get mainly just to get rich??

 

[seanieg89]

What was the reason he did such frequent reprinting? Was it to get mainly just to get rich??

Who knows his motivations? But it is clear from the outset that frequently reprinting a book that is used by many university courses will earn you a lot of money.

The actual changes from version to version are very slight from what I have seen. There is even a separately printed version with just the "single variable" topics floating around somewhere.

 

[davidgoes4wce]

Who knows his motivations? But it is clear from the outset that frequently reprinting a book that is used by many university courses will earn you a lot of money.

The actual changes from version to version are very slight from what I have seen. There is even a separately printed version with just the "single variable" topics floating around somewhere.

Agree I'd actually like to know what differences there are between the 4th edition, 5th edition and 6th edition. (I used the 4th edition in my undergrad). It would be akin to 'Where's Wally?" .......

 

[Drongoski]

What was the reason he did such frequent reprinting? Was it to get mainly just to get rich??

Maybe the publisher, more than the author, is more the culprit. Of course the author can be accused of being complicit.

By producing a new edition, you hope to render all earlier editions "obsolete" so you can sell more books. Like clothing fashion - you keep coming out with radically new trends so you can retire your old wardrobe and buy new clothes, thus keeping the clothing/fashion industry going.

 

[eyeseeyou]

Thanks guys

HAven't been here for the last few days