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Higher Math for Beginners (1987)

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Re: Higher Math for Beginners (1987)

#91

Post by alexchantavy »

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.

A professor once told me that math isn't a spectator sport - if you can't get your hands dirty and do it then you don't understand it - and it stuck with me and encouraged me to always find examples to learn.

Re: Higher Math for Beginners (1987)

#92

Post by chris_wot »

ivansavz wrote: post #50
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... Mechan…

I bought your book some time ago, really good - thank you!

Re: Higher Math for Beginners (1987)

#93

Post by rmdashrfstar »

jodrellblank wrote: post #85
gopher_space wrote: post #79

Earlier quoted context omitted.

I work alongside different industries and a hobby of mine is getting the people I work with to break down their domain for me. You've given me some good examples for organization, I have a lot of different media but everything would translate to concept maps, but I don't understand the 'graph' term you and OP are using. I found two definitions, neither of which seem like a perfect match. Is this an analogy? Would I b…

The study is graph theory, and I won't link Wikipedia because its math pages are always overwhelming, other blog posts are likely more readable. 'Graph' in this sense does not mean these: https://royalsocietypublishing.org/cms/asset/ac7c91c1-a95b-4... but like this: https://upload.wikimedia.org/wikipedia/commons/thumb/5/5b/6n... or this: https://lh3.googleusercontent.com/proxy/l31aliLTy0BqoatXyi7K... It's what the ge…

Fantastic dive into the applications of graphs, thank you.

Re: Higher Math for Beginners (1987)

#94

Post by ivansavz »

nefitty wrote: post #90
ivansavz wrote: post #50

Earlier quoted context omitted.

> 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... Mechan…

Holy crap. Thank you for this. Not only the math reference, but the great examples of knowledge visualization. It's something I've been obsessing over recently.

Thanks. The concept maps were created using CmapTools, in case you're interested: https://cmap.ihmc.us/

It's a GUI tool for drawing, but the underlying format is some sort of XML so it could potentially be computer generated (I haven't tried).

Re: Higher Math for Beginners (1987)

#95

Post by amai »

If you want to spend some money instead on a modern book:

Riley, Hobson, Bence: Mathematical Methods for Physics and Engineering: A Comprehensive Guide

It has a whopping 1300 pages, but it has everything you need. And if that is not enough for you get

Cahill: Physical Mathematics

This will give you advanced topics like differential forms, path integrals, renormalization group, chaos and string theory.

Re: Higher Math for Beginners (1987)

#96

Post by France_is_bacon »

ivansavz wrote: post #50
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... Mechan…

Looking at these maps makes my eyes roll back in my head so far.

Re: Higher Math for Beginners (1987)

#97

Post by gopher_space »

jodrellblank wrote: post #85
gopher_space wrote: post #79

Earlier quoted context omitted.

I work alongside different industries and a hobby of mine is getting the people I work with to break down their domain for me. You've given me some good examples for organization, I have a lot of different media but everything would translate to concept maps, but I don't understand the 'graph' term you and OP are using. I found two definitions, neither of which seem like a perfect match. Is this an analogy? Would I b…

The study is graph theory, and I won't link Wikipedia because its math pages are always overwhelming, other blog posts are likely more readable. 'Graph' in this sense does not mean these: https://royalsocietypublishing.org/cms/asset/ac7c91c1-a95b-4... but like this: https://upload.wikimedia.org/wikipedia/commons/thumb/5/5b/6n... or this: https://lh3.googleusercontent.com/proxy/l31aliLTy0BqoatXyi7K... It's what the ge…

So busy digging into this that I forgot to thank you. Profusely. I really appreciate the time you put into this, and I'm just incredibly happy.

Re: Higher Math for Beginners (1987)

#98

Post by handrous »

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

"Hover to define" on all terms in formulae on Wikipedia would go a long way toward fixing that problem.

Not completely, because they'd still all read like they were written by a math grad student who's trying to impress their peers rather than communicate clearly. But it'd help a lot.

Re: Higher Math for Beginners (1987)

#99

Post by jodrellblank »

gopher_space wrote: post #97
jodrellblank wrote: post #85

Earlier quoted context omitted.

The study is graph theory, and I won't link Wikipedia because its math pages are always overwhelming, other blog posts are likely more readable. 'Graph' in this sense does not mean these: https://royalsocietypublishing.org/cms/asset/ac7c91c1-a95b-4... but like this: https://upload.wikimedia.org/wikipedia/commons/thumb/5/5b/6n... or this: https://lh3.googleusercontent.com/proxy/l31aliLTy0BqoatXyi7K... It's what the ge…

So busy digging into this that I forgot to thank you. Profusely. I really appreciate the time you put into this, and I'm just incredibly happy.

Thanks! That's nice to hear.
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