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Higher Math for Beginners (1987)

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Re: Higher Math for Beginners (1987)

#41

Post by shimonabi »

codetrotter wrote: post #33
shimonabi wrote: post #27

Earlier quoted context omitted.

Look closely. The first half of the letter on each line is faded. (I'm the refering to the pages of the book, not the pages of the PDF)

Here's a screenshot of what I see when I look at page 358 of the updated link, which looks fine to me: https://snipboard.io/OwvDXH.jpg I don't see the fading that you are talking about. Meanwhile, here is a screenshot of the way that page 358 of the book in the original link is broken when I look at it both on desktop https://snipboard.io/G9ohqg.jpg and on mobile https://snipboard.io/VXYHC0.jpg

The top of the page is fine. The fading starts in the lower half of the page.

Are you trolling?

Re: Higher Math for Beginners (1987)

#42

Post by 29athrowaway »

k__ wrote: post #39

My experience with learning math is that the first months are all about backtracking. You have to fill all your holes. It's basically one big graph of concepts. The tricky part is, most beginners simply don't know how to navigate that graph. They see complex numbers with their exponentials and cos/sin forms and shut down. They can learn all these concepts no problem, but finding what they need to learn defeats them.

Like this?

https://cognicull.com/en/f5q2jl62

Re: Higher Math for Beginners (1987)

#43

Post by hdjjhhvvhga »

bitcharmer wrote: post #40
Throwaway1311 wrote: post #34

Reading the foreward > These de­finitions, which are not at all simple for the > beginner, came to be used in the wrong context. > Textbooks presented them before any explanation was > given of the theory and its applications, there­ > by complicating an understanding of things that > were intuitively clear. hear hear! This problem is like most of the Wikipedia pages that I come across on 'complex' topics of not just…

Fully agreed. Maths topics pages on Wikipedia are useless for 99.9% of population. They just bombard you with alien phrases and concepts with zero explanation of what's what. It's pretty useless if you want to learn anything

Having read numerous books on various aspects of mathematics written by the academia, my pet theory is that there are two kinds of people who write incomprehensible math books:

- Senior professors who actually suffer from the curse of knowledge and really forgot how it is not to know certain things, so they make tons of assumptions that are obvious to them.

- Junior profs who could actually explain the topics in an accessible way but do not feel secure enough and engage in a strange game of showing off. I know the same people could do a good job in the classroom, but once they get down to writing, they start to be afraid of being judged by their Senior colleagues so they follow the trodden path.

I gather the books that don't fail into these two categories for my daughter so when she grows enough to be able to grasp these concepts, she won't have to do dig through tons of crap.

Re: Higher Math for Beginners (1987)

#44

Post by hdjjhhvvhga »

BossingAround wrote: post #11

The crucial question is, is the text any good? My bias tells me it's next to impossible (but not actually impossible) for a text from 1987 to be 2021-beginner friendly, especially in a field like mathematics.

"Higher math" is a very broad concept now, you would need thousands of pages to cover it. This books is basically calculus with applications written in an accessible way by known experts and without confusing mistakes.

Re: Higher Math for Beginners (1987)

#45

Post by TheFreim »

k__ wrote: post #39

My experience with learning math is that the first months are all about backtracking. You have to fill all your holes. It's basically one big graph of concepts. The tricky part is, most beginners simply don't know how to navigate that graph. They see complex numbers with their exponentials and cos/sin forms and shut down. They can learn all these concepts no problem, but finding what they need to learn defeats them.

Last time I took math courses was high school, algebra 2 or geometry. Do you have any resources you can suggest for not only going forward but also filling in the gaps that I've forgotten or never filled?

Re: Higher Math for Beginners (1987)

#46

Post by pid-1 »

BossingAround wrote: post #17
qsort wrote: post #15

Earlier quoted context omitted.

Why would you say that? The kind of mathematics that book presents has barely changed in the last 200 years. I would doubt there's much difference to speak of at all.

Because while the field of mathematics has probably not changed, the field of didactics has changed drastically, and the student expectations in 1980s and 2021 will be also drastically different.

Most modern textbooks I used in university are complete garbage. A lot of concept vomiting without intuition building or real world insight.

Re: Higher Math for Beginners (1987)

#47

Post by gyam »

hdjjhhvvhga wrote: post #43
bitcharmer wrote: post #40

Earlier quoted context omitted.

Fully agreed. Maths topics pages on Wikipedia are useless for 99.9% of population. They just bombard you with alien phrases and concepts with zero explanation of what's what. It's pretty useless if you want to learn anything

Having read numerous books on various aspects of mathematics written by the academia, my pet theory is that there are two kinds of people who write incomprehensible math books: - Senior professors who actually suffer from the curse of knowledge and really forgot how it is not to know certain things, so they make tons of assumptions that are obvious to them. - Junior profs who could actually explain the topics in an a…

Would you mind sharing the names of the books that you’ve gathered for your daughter?

Re: Higher Math for Beginners (1987)

#48

Post by BrandoElFollito »

Context: I have a PhD in physics (many years ago), work in industry since then and have two high-schoolers I help in maths.

I clicked on the link, the book opened on page 500-something and I said "oh fuck" loud when I saw the mess of equations. I actually thought that the rendering failed.

I then moved back and the book has some down-to-earth approach but I could not stand the block of text page after page. It is truly a horrible book to learn from.

Re: Higher Math for Beginners (1987)

#49

Post by AnonymousPlanet »

cardanome wrote: post #26
BossingAround wrote: post #11

The crucial question is, is the text any good? My bias tells me it's next to impossible (but not actually impossible) for a text from 1987 to be 2021-beginner friendly, especially in a field like mathematics.

I haven't worked through the book yet but looking at the authors, Yaglom wrote some great Math books and Zeldovich was an absolutely genius in the field of theoretical physics, so it probably is. As a German living in the Western part, my math teacher would always rant how much better the East German math books were. Math and science education in the Soviet Union and the Eastern Bloc was and still is vastly superior…

Having the same background, I often heard this praise too, though mostly for Soviet works. But every time I followed up on it, I found that even the introductory level books dug right into the depths without much explanation. They might have been good in rigor or depth, but I found them very lacking didactically.

Maybe I looked at the wrong ones. Your link seems to suggest that it's different for textbooks aimed at young children.

Can you give me some examples of good East German higher math or physics books? I'd like to have another go at it.

Re: Higher Math for Beginners (1987)

#50

Post by ivansavz »

k__ wrote: post #39

My experience with learning math is that the first months are all about backtracking. You have to fill all your holes. It's basically one big graph of concepts. The tricky part is, most beginners simply don't know how to navigate that graph. They see complex numbers with their exponentials and cos/sin forms and shut down. They can learn all these concepts no problem, but finding what they need to learn defeats them.

> It's basically one big graph of concepts

True that. I have created a bunch of concept maps for my books in order to show readers this graph. It's really useful to find your way in a new field, to keep track of your progress, and also to look ahead into the the concepts that are coming up. Here are the links to the concept maps:

High school math: https://minireference.com/static/conceptmaps/math_concepts.p...

Mechanics and calculus: https://minireference.com/static/conceptmaps/math_and_physic...

Linear algebra: https://minireference.com/static/conceptmaps/linear_algebra_...

For an even better UI, there is the browsing interface in metacademy.org, which dynamically hides nodes and shows you only the prerequisites needed to learn a concept: https://metacademy.org/graphs/concepts/complex_vectors_and_m... This project is not actively maintained anymore, but it has a wealth of info and it is open source https://github.com/metacademy/metacademy-application so hopefully someone will pick up the torch.

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