/sci/ - Science & Math » Thread #10962830

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Anonymous Wed 11 Sep 00:52:32 2019 No.10962830 View Reply Original Report

Quoted By: >>10962849 >>10962970 >>10962976 >>10963046 >>10963049 >>10963176 >>10963218

I’m studying philosophy at Cambridge but am a pleb at math who wants to get into math, but /sci/ disagrees over the books I should read, so there are several contrasting lists of “how to get into math.” I only have a semester off and want to use this time as best as possible to get into math, so how should I do it? Btw I currently have a physical copy of Spivak’s Calculus (4th edition)

Anonymous

Anonymous Wed 11 Sep 2019 00:56:40 No.10962843 Report

Quoted By:

Are you perhaps a nignog?

Anonymous

Anonymous Wed 11 Sep 2019 00:57:57 No.10962847 Report

Quoted By: >>10962899

Read Spivak's calculus. Really spend your time with it (if I were you, I would spend the entire semester on it). If you really work through this textbook (like basically every problem), you will have the mathematical skills to quickly read your way up to more difficult texts.

Anonymous

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Anonymous Wed 11 Sep 2019 00:59:00 No.10962849 Report

Quoted By: >>10962899 >>10963594

>>10962830
the chances are very high that you're not cut for it. So why even bother. There is little use anyway in anything mathematical beyond arithmetics and calculating interest rates.

Anonymous

Anonymous Wed 11 Sep 2019 01:25:54 No.10962899 Report

Quoted By: >>10962935 >>10963163 >>10963166 >>10963218

>>10962847
Thanks, although when reading the book, I feel that my lack of experience with math (basically nothing after high school geometry) makes it so that a lot of the book is going over my head. It isn’t so much that I’m “not getting it” as much as it is that I’m afraid I’m not getting it. For instance, at the beginning of each problem set, I have to glance at the answer of the first problem before answering the rest in order to know what form the question is looking for in its answer. It feels like I’m supposed to have some knowledge going into the book that I lack
>>10962849
I agree with pic related, and it’s a focus of the philosophy I’ve written so far. Still, to be credible with those kinds of claims, I feel I need a background in math in order to make claims that can be taken to mean stuff like “the abuse of mathematical concepts is what causes the majority of society’s problems”

Anonymous

Anonymous Wed 11 Sep 2019 01:38:55 No.10962935 Report

Quoted By: >>10962954 >>10962980

>>10962899
First, those charts are not as helpful as they may seem. If you're already doing Spivak, you don't have to read any of the other Analysis books because they will just repeat most of what you have already learnt. You should by then specifically look out for a Calculus book dealing with multiple variables. If you're primarily interested in the philosophy of mathematics, you should get yourself acquainted with Wittgenstein, Russell, Cantor and the foundations of predicate logics and Boolean Algebra. Munkes' Topology is to be recommened but the topic itself is of little interest for philosophy. Serge Lang's Algebra may be of use since the treated concepts there are of worth when dealing with Logics.

Anonymous

Anonymous Wed 11 Sep 2019 01:44:54 No.10962954 Report

Quoted By: >>10962980 >>10962985

>>10962935
If you're specifically interested in Mathematics, you should follow this schedule:
Trigonometry, Basic Algebra (which I assume you have completed)
Basic single variable Calculus, Linear Algebra (an introduction will suffice)
Multivariable Calculus, Ordinary differential equations
Partial differential equations, Complex variables
At that point, you have more or less covered what most non-mathematics STEM students learn mathematics-wise
Further studies would lead you to:
Complex calculus, Topology
Algebra (Group and field theory)
Fourier series and Hilbert spaces
Differential geometry and differential topology
Numerical mathematics and methods
Mathematical methods in physics.

Anonymous

Anonymous Wed 11 Sep 2019 01:49:46 No.10962970 Report

Quoted By: >>10962980

>>10962830
Why do you want into math? You could be better off getting into Mathematical Logic and maybe Algebra rather than making Calculus your goal.

Anonymous

Anonymous Wed 11 Sep 2019 01:52:00 No.10962976 Report

Quoted By: >>10962985

>>10962830
Kahn Academy, unironically.

Anonymous

Anonymous Wed 11 Sep 2019 01:56:04 No.10962980 Report

Quoted By: >>10963017

>>10962935
>>10962954
Thank you very much for all of the recommendations and for the roadmap you’ve given me. Would you advise something else, like khan academy, on top of going through books on these subjects?
>>10962970
Thanks for the recommendation. I’m interested in math because my understanding is that the STE of STEM is basically all just math and it feels wrong to philosophize without having any knowledge of these disciplines

Anonymous

Anonymous Wed 11 Sep 2019 01:57:07 No.10962985 Report

Quoted By:

>>10962976
Khan Academy isn't a particularly good resource but it is convenient and easy to use. It'll only get you to a very rudimentary level though.
>>10962954
It's best to start with proofs if you're going to do any maths above middle school level.

Anonymous

Anonymous Wed 11 Sep 2019 02:14:00 No.10963017 Report

Quoted By: >>10963736

>>10962980
>Would you advise something else, like khan academy, on top of going through books on these subjects?
Khan Academy is only so good and then it stops. It's definitely a good option for someone who's unsure with the material. Usually, I recommend it for those who are still in High School. It's not rigorous however.
Beyond that, the path is hard. After all, it's you who needs to understand the content and applying them to different situations more often than not requires a proper understanding of how all these things relate to each other.

Anonymous

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Anonymous Wed 11 Sep 2019 02:27:06 No.10963046 Report

Quoted By: >>10963736

>>10962830
Come to the CMS some time. 3rd year puremo here. It depends what you want to get out of maths; there's Logic & Set theory in Lent which might tie in with philosophy, but otherwise all the courses are generally very maths-y

Linear Algebra is fundamental to progress to a lot of areas of maths, as is undergrad Analysis, so I'd recommend getting those two nailed first.

Anonymous

Anonymous Wed 11 Sep 2019 02:28:06 No.10963049 Report

Quoted By: >>10963736

>>10962830
It would be redundant to read Apostol’s Calculus after Spivak, and a linear algebra text on the level of H&F should prepare you to bypass the introductory algebra texts

Anonymous

Anonymous Wed 11 Sep 2019 03:38:22 No.10963163 Report

Quoted By: >>10963736

>>10962899
That's understandable. A lot of the problems in the text are not only hard, but you don't even know where to start. My recommendation would be to know the content like the back of your hand. If you don't understand something in the chapter, you must look it up and thoroughly understand it.

I'm gonna be honest though, many of the problems in the text use 'tricks' (like in ch.1 with problems concerning the triangle inequality: you add and subtract the same number). These are tricks that you can only get by playing around with the problem and thinking about them for a long time. It can get frustrating and even pointless but it genuinely does get easier over time.

This is one of the marks of becoming proficient in mathematics so I highly suggest you get used to the process.

Anonymous

Anonymous Wed 11 Sep 2019 03:41:18 No.10963166 Report

Quoted By: >>10963736

>>10962899
Also, I should have mentioned that Spivak is a unique book in that your lack of experience is not an issue at all. You build up all the experience you need to be successful in the book by doing the problems.

Good luck Anon. You must persevere. I believe in you.

Anonymous

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Anonymous Wed 11 Sep 2019 03:47:07 No.10963176 Report

Quoted By: >>10963736

>>10962830
>I only have a semester off and want to use this time as best as possible to get into math, so how should I do it?

Anonymous

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Anonymous Wed 11 Sep 2019 04:35:01 No.10963218 Report

Quoted By: >>10963230 >>10963736

>>10962830
>I only have a semester off and want to use this time as best as possible to get into math, so how should I do it?
First off, a semester won't be nearly enough to really understand much math. As others have already said in this thread, you must ask yourself what is it that you really want out of math. Are you more interested in the foundations and the philosophy of mathematics, or do you care more about the actual application of mathematics? In a post you've said:
>>10962899
>“the abuse of mathematical concepts is what causes the majority of society’s problems”
If you're interested in the truth or falsity of statements of that sort, then maybe you should focus more on symbolic logic and set theory rather than calculus. Though my two cents on the matter is that most people don't really have a good understanding of mathematical concepts, so I don't see how they could've influenced society at large (except possibly in some very indirect way). As Nicolas Gomez Davila said, the issue with technology is that the one who uses it doesn't have to be as smart or knowledgeable as the one who invented it. Math may be at the root of technological society, but the actual problems related to technology have more to do with psychology and sociology than math. Most people who use technology have no understanding of math beyond basic arithmetic; even the people who built it are usually specialized in a relatively narrow field of math and know very little about the actual foundations of "mathematical concepts". More likely, the issue with technology is that it is a self-perpetuating monster that has almost taken a life of its own beyond our understanding of it (like AI being able to deisgn things that work even though we humans have no idea why they work). Whether you want to welcome that monster like Nick Land or you want to slay it like Unabomber doesn't really matter: the fact is that you can't understand it; it has become too big and far too complicated.

Anonymous

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Anonymous Wed 11 Sep 2019 04:47:48 No.10963230 Report

Quoted By: >>10963736

>>10963218
(continued)
On the other hand, if by “the abuse of mathematical concepts is what causes the majority of society’s problems” you want to refer to the proliferation of "soft sciences" that try to emulate the methods of the hard sciences like a cargo cult, then maybe you should study statistics and probability and the way in which they're (often erroneously) applied in the soft sciences. But you won't be able to get very far in one semester, so my advice to you is that you should really focus on symbolic logic and set theory first of all. You can try to pick up more mathematical knowledge on the side as you go, instead of trying to cram it in a limited time frame.

Even if it may not help you directly in your attempt to understand applied math and technology, there might still be some value in learning about logic and set theory (since these subjects are very much related to philosophy in general from the get-go, especially the analytic tradition).

Anonymous

Anonymous Wed 11 Sep 2019 09:37:01 No.10963594 Report

Quoted By: >>10963597 >>10963736

>>10962849
That pic is pretty inspiring as a CS student. Time to lead the downfall of humanity and the rise of our mechanical overlords.

Anonymous

Anonymous Wed 11 Sep 2019 09:38:32 No.10963597 Report

Quoted By: >>10963602

>>10963594
> Time to lead the downfall of humanity and the rise of our mechanical overlords.
You're dumb.

Anonymous

Anonymous Wed 11 Sep 2019 09:42:57 No.10963602 Report

Quoted By:

>>10963597
I would feel offended but you haven't given me any reasons or evidence to back up your claim.

Anonymous

Anonymous Wed 11 Sep 2019 12:10:00 No.10963736 Report

Quoted By:

>>10963017
>>10963046
>>10963049
>>10963163
>>10963166
>>10963176
Thanks for the advice!
>>10963218
>>10963230
Thanks for the clarification. At this point I care more about the application of math itself, but like you said, philosophy of math, logic, and set theory will probably better benefit my goals. I’d describe what I’ve written so far as anti-accelerationist, however, it feels like I run the risk of being wildly erroneous while reasoning around the immoral application of math when I know nothing of math itself. An idea I have in the back of my head is that some of the overarching problems in modernity can be understood once people realize that their field of study is a body of concepts meant to metaphorize aspects of reality, as opposed to a depiction of reality itself: this includes philosophy, but I want to focus on STEM for the proliferation of technology and the demiurgical AI you mention. To properly apply this to STEM, I feel I need a good grasp of the limitations of mathematics. To my knowledge, Nick Land himself is versed in math, and I have no doubt that his knowledge of math combined with his beliefs that the philosophical “outside” is accessible to people (when he went crazy on drugs and performance art in the attempt to reach this) is partially what creates his pessimistic outlook. He’s a positivist who’s mistaken concepts for reality, and sees those concepts as being negative, whereas in reality, there’s nothing that allows us to factually claim we can’t stop the acceleration of technology — at the end of the day, it is people deciding to accelerate it, as opposed to a self-propagating AI god. However, to properly make someone like Nick Land consider an argument like this, I feel part of my case would require needing to show him the limitations of math
>>10963594
You should read Nick Land and ask if that’s what you really want to contribute to

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