The Hard Truth About Reading Math Books

In this video I talk about reading math books. We also take a look at an abstract algebra book written by Dan Saracino.

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[curtiswfranks]

I always had fun telling my friends in the humanities, who often read hundreds of pages per week, that I spent an equal amount of time reading maybe twenty pages from math and physics added together. The looks of horror on their faces was priceless.

[swordofstrife]

Yeah I had to learn this the hard way throughout my University career. Sometimes it's better to accept that you don't get something initially and move on and hope that you end up understanding from the context provided later. Math is difficult and learning to accept that you don't understand something is just as important as trying hard to understand things

[amydebuitleir]

I used to find it *extremely* difficult to move on if I didn't understand something. But I figured out a strategy that helps me: I write down a very precise description of what I'm having trouble with. This helps in two ways: 1) it forces me to articulate what's confusing me, so when I do encounter the "missing piece" of insight or knowledge, I'll recognise it immediately, and 2) I can easily return to the problem and pick up where I left off.

[jbbentley]

Wizard, I’m happy to say that my classes are going swimmingly. Let’s keep up the motivation and stay ahead.

[jakobwachter]

I just spent six hours yesterday with a differential topology book. In that time, I think I made it through about 10-12 pages, and did eight exercises. But, looking back on those 10-12 pages and being able to reflect on the contents inside and the pride gained from grasping the new mathematics is an experience that is rarely rivalled by any other kind of didactism.

[DnBComplex]

As a guy graduated in Social Sciences ( i'm from Brazil), and entering the mathematical field, i got to say that the approach of most of the books you show in your channel are VERY similar to philosophy and sociology, anthropology etc... (other areas of social sciences). And the cool thing of it all is that one REALLY does complement the other; even in terms of semantics. Humanities + Maths is truly a beautiful thing and i don't have words to describe it.
I love your channel and you're one my firsts inspirations to finally get into math, a field and subject that i loved without realizing. Thank you! I can better understand who am i.

[TheMathSorcerer]

I misspoke at 3:49, the binary operation is associative, not the set:)

[jimbobago]

One of the main problems I had after calc was that proof as its own teachable branch of math wasn't taught. It was something the student was somehow expected to know anyway. I would have given my left kidney for Daniel Solow's "How to Read and Do Proofs".

[myhandlehasbeenmishandled]

I'm 42 now. Back in highschool I just didn't understand any of the text unless someone explained it to me in depth. Sometimes it feels like in math books a lot of info is just missing. It makes assumptions about a reader. Granted if you are reading something like math book perhaps the point is not to repeat info you should already know.

I just wanna learn math to feel better about myself. I have no intention of pursuing it as a career. I just feel i missed out a lot in highschool because i came to the states unable to speak English. Most of my courses were ESL classes. Everything else they have me take was just a bare minimum just to meet graduation requirements.

No one really took a time to help me with anything outside of English.

[guillotinechophead]

Hey math sorcerer. Im a college student from singapore. Been watching your content for a while. And really thanks to you i been getting really interested and even liking mathematics. Which is something i never thought I say, because all my life I have always been told that im not that smart on the subject of math because i always get a bad grade on a test. And I was told to never study STEM subjects because im not smart a student.

But during the pandemic because I was bored. I found one of your videos on learning mathematics from start to finish and how to study mathematics. And well I just did it, start off with basic algebra, and really try to understand the concept and do a lot of practices question. And well i like it. I started seeing Math as a pattern recognition game with rules to abide to solve a puzzle. And now I have been getting really into writing proof and calculus. Math is still quite hard for me but the feeling accomplishments is very rewarding and I hope I get progressively better at it. So thank you for inspiring me to self-teach myself mathematics.

Anyway I want to hear your thought on what the possible impact for AI on the education system and the teaching of mathematics.

[mallk]

One of the hardest things I see a lot of math students have trouble with is connecting new math back to old math they already learned. A lot of things taught are kinda just shown, and then we move onto the next thing and the old thing is never mentioned again, even if the new thing is just the exact same concept, just written a different way and used for a different thing. Like how square roots are just exponents but instead of whole numbers, the exponent is a fraction; so it plays by the exact same rules.
or how factoring and factor by grouping are the literal exact same thing except one skips steps.
I want a math class that doubles back on old math before it moves to the new math. or even just goes "for this chapter you will need to have learned... " because whenever I helped my friends with this stuff, it always ended with us just talking about old math things like logarithms and how to divide fractions. Sure, this isn't the ONLY reason that people have trouble with math, but darn it if just answering the question "When will we use this?" doesn't clear up like 40% of the confusion about some of the math.

[DavidGonzalezSamudio]

I mention this book in the first lecture of all my CS courses. For me, this book was like watching the Matrix, the real one. Not only I knew how most math we need for programming was made, but it is homomorphic to source code. And, source code is isomorphically transformed into machine code, as stated on the Red Dragon Book (Aho). Beautiful, indeed.

[stevenfallinge]

Everything becomes much clear with a rudimentary introduction to mathematical logic. Sentences, formulas, validity, and proofs. You don't actually need to know these in-depth, but a basic understanding of these things goes a long way.

[vtron]

Me han dicho que lo mejor que puedo hacer son dos cosas:
1. Tratar de crear una intuición en la mente, usualmente geométrica si es posible. Esto se me hace muy fácil.
2. Hacer anotaciones de los teoremas, sus pruebas, ejemplos, y ejercicios. Mi problema con esto es que usualmente termino copiando el libro y no siento que estoy haciendo nada, simplemente escribiendo hasta que haga “sentido”. Ósea, puedo entenderlo lo más seguro, pero el asunto cae en el mismo proceso de tomar notas.

[gabrielascencio]

I had been seeing your videos for weeks, and today I found your spanish yt channel. This was amazing because I'm a spanish native and hear you speaking spanish blow my mind.

Thanks a lot Math Sorcerer for share your knowledge in both language.

[kv]

I'm a retired Physicist and I find your site quite enjoyable. I always taught my students something similar to you and often found that instead of writing in the margins I actually made my own notes including examples from the text and usually worked most of the problems included in texts. I have a couple notebooks that go with each old textbook that I passed on to a younger faculty member and some students when I retired. Love the Channel!!

[davidfrancknkotnguene]

Your videos are so motivating. At times I really feel lazy to do maths but when I just watch one of your videos the motivation pop in me! Thanks!

[nunoalexandre]

The most common dificulty to all students.. is understanding the language!!! the subjects are pretty simple...but the language is Encrypted...

[coffeeconfessor]

This has been me with reading an entire book on Fuchsian groups along with papers on the subject...except I've managed to cobble together a Rosetta stone of sorts with a few textbooks on fractal geometry and hyperbolic geometry. The Princeton Companion to Mathematics has also been helpful.

[ashwinbalaji]

your advice is really good. i am a physics student doing msc and i find myself wanting to learn a lot of math that is either assumed to be known or just shown off to believe that they are true. reading books is difficult, esp math, but without solid reason, it is impossible to go through for me. a word of advice: it is a little annoying that the audio for the video is recorded in mono channel(left channel), it would be nice if it was recorded in stereo, or perhaps it was missed during edits. else great video.