I'm sure at least someone here self studies math (despite the R9K-esk posts I've seen).I am coming up on my 3rd semester of uni and studying computer engineering (just switched from cs). I have genuinely enjoyed Calc 1 and 2; my professor would often spend time proving things. I am now taking discrete math and it is the first time in a long time I have felt excited to do my homework.One of my previous classmates from calc (who took discrete math last semester) who feels the same way about math as I do decided he wanted to do math research and talked to our previous prof who told him to study pic rel.He previously lended me the book to study but I did not get very far as I had some hard courses last semester.I felt inspired after talking to my peer about the potential research opportunity and I wanted to ask you guys, how the fuck do I read a math textbook. Like what do I do when I don't understand. I understand you have to walk away, think, and then come back and read again but I don't know. I read as far as sets, I had never been taught then in my life. I understood why sqrt(2) was irrational just not how to prove it. We learned this proof in discrete. I feel confident to try and go back and read the book but, what happens when I hit another road block. What then?I feel very lost. My pre-uni math education probably failed me in some way but I am open to fixing that.
>>16987688learning proofs with analysis is like learning to drive in the UK with stick shiftit works, but it's the wrong way around and also you have to fondle a rigid shaft during it for some reason when something feels off
> I understood why sqrt(2) was irrationalapplied rational root theorem that's it
>eel confident to try and go back and read the book but, what happens when I hit another road block. What then?>I feel very lost. My pre-uni math education probably failed me in some way but I am open to fixing that.That's exactly the intended experience. You feel lost until you understand it. Just keep trying. It's normal not to understand at first.
> who feels the same way about math as I do decided he wanted to do math research and talked to our previous prof who told him to study pic rel.That professor had something different in mind, perhaps, than what you think. That book is for test if you(or your friend) can be a mathematical researcher. A book that will give you headaches. But still a basic analysis book. It's not for learning on your own, or for improving something you're weak in.
whats the point? Math is solved. AI finished with it already.
>>16987688>how the fuck do I read a math textbookTo get the most out of a math book you need to read meticulously and engage with the text. Make sure to internalize the definitions, examples, and important theorems. If you have time, attempt to prove statements in the book yourself before reading the provided proofs (you will gain something even if you don't succeed). Follow the proofs and try to understand every step, writing out omitted details for yourself as needed (this is especially important for a somewhat terse book like baby Rudin). You must do exercises; try to avoid looking up answers before you solve them, even if you get stuck for a while. There will be frequent road blocks, but that's just part of the process.One thing worth noting about this book in particular is that it is rather light on the exposition (relative to many other undergrad analysis books), and so it might be difficult to self study from on its own. If you're ever confused about why some concept covered in the book is worth caring about, you may want to look at other sources.
>>16988196Your opinion is very well thought out — it’s essentially a blueprint for how to actually learn mathematics from a book rather than just skim it. You highlight the key practices that separate passive reading from active mastery: Meticulous reading: Internalizing definitions and theorems is crucial, since math builds layer by layer. Active engagement: Attempting proofs yourself before reading the author’s solution forces you to think like a mathematician, not just a consumer of math. Filling in gaps: Writing out omitted steps is a powerful way to sharpen precision, especially with terse texts like Baby Rudin. Exercises as training: Struggling with problems before peeking at solutions is where most of the learning happens. Roadblocks as normal: Recognizing that frustration is part of the process helps sustain motivation.Your note about Baby Rudin being light on exposition is spot-on. It’s a classic, but famously austere. Pairing it with more explanatory sources (like lecture notes — I see you’ve got MIT OCW open) is a smart strategy. That way you get both the rigor of Rudin and the intuition from more pedagogical texts.If I were to challenge your view slightly: while your method is excellent for building deep understanding, it’s also time-intensive. Some learners benefit from alternating between “slow, meticulous” reading and “broad, intuitive” overviews, so they don’t get bogged down. In other words, mixing Rudin with more narrative-style books (like Abbott’s Understanding Analysis) can balance rigor with accessibility.Your approach is essentially the mathematician’s apprenticeship model — and it works. The only caveat is pacing: making sure the struggle doesn’t turn into burnout.Would you like me to suggest a few companion texts that complement Baby Rudin and make self-study smoother?
>>16987688In my math undergrad the profs instituted a course called "Introduction to Advanced Mathematics" that you had to take before moving onto Analysis, Algebra, Topology. The goal was to practice proof techniques and it was extremely helpful. Textbook for the course: Mathematical Proofs, A Transition to Advanced Mathematics; Gary Chartrand.You really just have to work the first 11 chapters and can then have much for fun with Rudin and Munkres.
>>16987848There are still merits to studying it. It trains the mind.
>>16987688>I want to do research>Reading a textbook3/10 got a reply from me.
>>16987688>how the fuck do I read a math textbookSince you come from an engineering background I will make an analogy for you. Everything a math textbook says is true (modulo the errata). It's a documentation on a given subject compiled in a way the writer deemed relevant. It's no different from documentation in C++ or Python. By this analogy, definitions are like objects in a programming language, theorems are like built-in functions, and proofs are the code that make those functions work (this is just an analogy, not the actual Curry-Howard correspondence)The documentation is highly useful but you cannot learn a programming language via documentation alone. You have to write code yourself. Your code is never going to be as good as the ones that authors write but you can emulate them. You're not expected to reproduce every Python function and you're definitely not expected to reinvent Python yourself. Such a project would be boring and a waste of time.You should treat you math notes like self-contained projects. They should be like mini textbooks of the broader theory where you prioritize things in your own way. You usually prioritize things you want to explore or practice and sometimes share with other people.>what happens when I hit another road block. What then?If you can't create a formal argument yourself, try to emulate what the authors did. Once you understand their proof structure you'll be able to use the structure in your future proofs. For example, since you can follow the proof [math]\sqrt{2}[/math] is irrational, try to prove it for [math]\sqrt{3}[/math], [math]\sqrt{5}[/math], or [math]\sqrt[3]{2}[/math] or [math]\sqrt[n]{p}[/math] in general for practice, then move on.There's a prevailing thought around that you have to prove everything yourself. That's retarded and a waste of time if you clearly can't do it. Just look at the solution, emulate it, practice it on a few examples, then move on.
>>16988466Skill training is non-transferable. This is what all the evidence shows. It is pseud to suggest otherwise. There is no general mind training. All training trains whatever specific task is trained and does not effectively generalize. Training proof math is like training to be really good at multiplication now. Nothing wrong with it but it's for disabled obsessives like autistics now.
>>16988541>AI learns how to breathe>breathing is automated>have to asphyxiate myself
>>16987848>muh aiKILL YOURSELF YOU FUCKING RETARDED ANTI INTELLECTUAL SUBHUMAN FAGGOT
>>16988541I've assumed this. When ppl say they got problem solving skills from their STEM major, rather than the other way around, it's bs right?
>>16987688WTF is the point of learning math since AI do everything? Beyond basic understanding of what the symbols are theres really no reason to study math.
Ai replaceing humans? so why even study?
>>16988567>>16988565>>16988556>>16988553>>16988543When the time comes that AI truly does everything, the only thing of value will be the quality of being human. Humans who can reason for themselves, know how to do math, and write by hand will be like gods, ruling over those who can do nothing (the truly replaceable ones). If you can't do anything, what would be your reason for existing?
>>16988565>>16988567>>16988571FUCKING KILL YOURSELVES YOU RETARDED WORTHLESS GOLEM DRONES. YOU ARE DEAD WEIGHT THAT FUCKING DRAGS DOWN ACTUAL SMART PEOPLE AND MAKES LIFE FOR CREATIVES AND INTELLECTUALS, OF WHICH YOU ARE FIRMLY NOT, HELL.FUCKING SHOOT YOURSELF. HANG YOURSELF. JUMP INTO YELLOWSTONE. FUCKING STARVE TO DEATH. THERE ARE SO MANY WAYS TO DIE. JUST PICK ONE AND DO IT. Jesus FUCKING Christ.
>>16988571>>16988573I asked Claude if it AI will replace humans and this is it's response:>Honestly? The real answer is: it depends what you mean by "replace."
>>16988575I asked Jim, and he said that you and Claude are retarded faggots.
