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Higher Math for Beginners (1987)

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Re: Higher Math for Beginners (1987)

#51

Post by ivansavz »

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…

I recognize your two categories of bad math books and would like to add a third: commercial textbook publishers "padding" the pages with filler. It seems every book made for first-year undergraduate students is 10x thicker than it needs to be: there are these huge color images and lots of repetition, which makes students just tired and not want to read the book.

It's completely artificial padding and unnecessary: you can teach calculus in 100 pages, you don't need 1000 pages (cf. Silvanus Thompson book on calculus or my books). I think the padding is done to make the exorbitant price tags seem more reasonable, so this is why I'm optimistic about this book since it's coming from the Eastern Block (no padding).

Re: Higher Math for Beginners (1987)

#52

Post by medo-bear »

TheFreim wrote: post #45
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?

in your case i would suggest khan academy - https://www.khanacademy.org/math

Re: Higher Math for Beginners (1987)

#53

Post by hasmanean »

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.

Yup. It’s not about taking the quickest route from a to b, like textbooks try to do (no doubt to save paper) but to “fill in” the mental graph in your head as fully as you need.

If that means solving the same problem multiple times using different methods no matter how useless or inefficient, trying things without knowing if they’ll work, and adding to your bag of tricks for later problems.

You know, like life itself.

Re: Higher Math for Beginners (1987)

#54

Post by [deleted] »

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

[deleted]

Re: Higher Math for Beginners (1987)

#55

Post by medo-bear »

BrandoElFollito wrote: post #48

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 tru…

> It is truly a horrible book to learn from

given your lengthy experience and qualification i am surprised that typesetting is such an issue for you. perhaps the book might be helpful to you as a teacher to draw some material from. me personally, trying to recall my attitude and focus during high school, i don't think i would have minded this book at all

Re: Higher Math for Beginners (1987)

#56

Post by rfrey »

29athrowaway wrote: post #42
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

I love that! What's its story?

Re: Higher Math for Beginners (1987)

#57

Post by hdjjhhvvhga »

gyam wrote: post #47
hdjjhhvvhga wrote: post #43

Earlier quoted context omitted.

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?

Sure. I feel that many contemporary undergraduate/college textbooks are actually fine in this regard (like Topics in Contemporary Math by Bello, Britton, and Kaul). As for the rest, some of my favorites:

- Warner, Pure Mathematcis for Beginners

- Devlin, Introduction to Mathematical Thinking

- Stewart, Concepts of Modern Mathematics

- Herrmann, Sally, Number, Shape, and Symmetry

- Baylis, What is Mathematical Analysis?

- Feil, Krone, Essential Discrete Math for Computer Science

- Rotman, A First Course in Abstract Algebra with Applications

- Banjamin, Chartrand, Zhang, The Fascinating World of Graph Theory

- Zou, Mult-Variable Calculus: A First Step

- Hubbard, The World According to Wavelets

- Sayama, Introduction to the Modeling and Analysis of Complex Systems

- Darst, Introduction to Linear Programming: Applications and Extensions

- Sourin, Making Images with Mathematics

- Gallian, Contemporary Abstract Algebra

And many others. Of course, all such lists are completely arbitrary. Once I get familiar with a certain topic, elaborate explanations seem redundant and I feel like shouting, "Get to the point already!" - whereas the same explanations can be extremely helpful for a beginner.

Re: Higher Math for Beginners (1987)

#58

Post by codetrotter »

shimonabi wrote: post #41
codetrotter wrote: post #33

Earlier quoted context omitted.

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?

I scrolled down and looked closer there and see it now. It was more subtle so I didn’t notice.

Re: Higher Math for Beginners (1987)

#59

Post by hdjjhhvvhga »

ivansavz wrote: post #51
hdjjhhvvhga wrote: post #43

Earlier quoted context omitted.

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…

I recognize your two categories of bad math books and would like to add a third: commercial textbook publishers "padding" the pages with filler. It seems every book made for first-year undergraduate students is 10x thicker than it needs to be: there are these huge color images and lots of repetition, which makes students just tired and not want to read the book. It's completely artificial padding and unnecessary: you…

I appreciate your No Bullshit guides a lot! Especially the fact that you provide the solutions to the exercises so that they're perfect for self-studying. I can imagine someone might like to have hundreds of color images - the assumption is they can help in absorbing certain concepts by linking imagery with abstract ideas.

Re: Higher Math for Beginners (1987)

#60

Post by syntaxfree »

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.

Math is “regular” enough that you can get away with using math at a higher level than one understands. All “practitioners” are using fringes of math they barely understand, which is ok — book says Theorem XYZ guarantees. But that’s also where your mathematical growth is stunted. Learning “higher math” is always standing back a little.

The epitome of this is the feared Real Analysis class where many people realize they’re pretty much incapable of understanding high school calculus. But it keeps happening.

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