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how i relearned erry mathsz by Lydia Lightshit - Fri, 05 Feb 2016 02:37:19 EST ID:mVsq12K/ No.15040 Ignore Report Quick Reply
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Everyday before work, I woke up 2 hours early and forced myself to read/do exercises of the following books. (this later became 3 hours). I averaged 3 books per month if they were survey books, and about 1-3 months for a rigorous book. This became an easy routine after the first week, and I'm still doing this.

>1) Daily Rituals by Mason Currey
This is where I got the idea of making a routine from, it's a survey of historical artists, philosophers, scientists ect who all had a routine in order to get work done consistently. Franz Kafka would split his sleep up into 2 section in order to fit in work beside his regular office job.

>2) Basic College Mathematics by M. Lial et all
As mentioned before in here this covers elementary school and Jr. High math basically. You can just survey this for the most part (not do any exercises) unless you don't understand something, then do the exercises. Took 3 days to survey this. When I later took Harvard's CS50 computer science course, the first lecture about Binary numbers directly was related to this book's first chapter on whole numbers. I torrented this book.

>3)Basic Mathematics by Serge Lang
I got out the notepaper and did most of the exercises by hand. This was all focused on reasoning, why is this true, how do we prove this is true, ect. This book teaches you so well that applied calculus is your bitch afterwards. I torrented this book too since author dead, copies are like $80 on amazon.

>4)Introduction to Mathematical Reasoning by Eccles
Pretty much essential book, this should be required reading for anybody going to university. I downloaded this from libgen.io (library genesis, domain often changes due to copyright lawyers). At the same time as reading this, I watched the following:

A supplemental MIT lecture that explains wtf calculus actually is
https://youtu.be/UcWsDwg1XwM Calculus: Big Picture.

18.01 Single Variable Calculus lectures
https://youtu.be/jbIQW0gkgxo which I breezed through since Serge Lang's book + Intro to Mathematical Reasoning prepared me so well for this. I didn't do any exercises except for whatever following a long with the lectures which I often solved myself by pausing the video, doing them then watching him work out the answer. I finished this in a week doing it every morning.

Continued .........................
Lydia Lightshit - Fri, 05 Feb 2016 03:05:44 EST ID:mVsq12K/ No.15041 Ignore Report Quick Reply
>5) A Course in Pure Mathematics by Hardy
Free http://www.gutenberg.org/files/38769/38769-pdf.pdf
Best Math book I have ever read. No applied math whatsoever, all theoretical analysis of single variable calculus which is what I was missing from the MIT lectures. Did this in LaTeX.

>6)Advanced Calculus - Shlomo Sternberg and Loomis
Free off his university page http://www.math.harvard.edu/~shlomo/
Very rigorous treatment of single and multi variable calculus, analysis, some classical mechanics and linear algebra which is perfect since I wanted to do LA for computer science later. This teaches you every which possible way you could ever conceive on the calculus of differentiable manifolds. This is a reference book I continually go back to. Afterwards I grabbed the final exams for MIT 18.02 and MIT 18.03 and audited them without even watching the lectures, full pass no problem. I also used Polya's "How to Solve it" to help complete a lot of the exercises and still use Polya's book as a reference for the books I"m currently doing.

This covers general math, I went on to specialize in my interest (compsci) like Feller's books on Probability which I'm still doing. You can also use Spivak's Calculus/Calculus on Manifolds. I had to read Spivak's Manifolds book for his views on modern mathematical notation, as it was a pre-req for some Sussman books I was doing and enjoyed how to the point he is. He defers everything to exercises.

This all took about 5 months to do from start to finish, as on weekends I would do a lot of work during the day as well (6 hrs at least). Advanced Calculus took the longest, a little more than 3 months but I was also reading other books like Polya's to help me through it.
Clara Bambleweck - Thu, 11 Feb 2016 11:52:46 EST ID:4hU7+JsY No.15043 Ignore Report Quick Reply
The entire highschool common core for math should just be replaced by Serge Lang's book. First chapter in you are proving why (-1)(-1)=1 instead of the magic they teach you of just assuming two minus signs equal positive.
Molly Blablingtack - Sun, 13 Mar 2016 21:06:03 EST ID:Ayxv8mCh No.15070 Ignore Report Quick Reply
I like his mathematical work as much as the next guy but he was a total crank outside of mathematics and he shouldn't be promoted due to this flaw.
Barnaby Pockford - Mon, 28 Mar 2016 17:36:13 EST ID:eS3khjIT No.15071 Ignore Report Quick Reply
He was, but personal politics aside that's the best Basic Math book I've found, unless you know of another book written by an actual mathematician for other mathematicians. I don't honestly care about personal political views, just like I can listen to Wagner without worrying about his extreme politics.

Update to this, finished Feller's An Introduction to Probability Theory Vol 1 and a few chapters out of Vol 2. To my delight, it turns out Harvard has an open course for this http://www.math.harvard.edu/~ctm/home/text/class/harvard/154/11/html/index.html so I followed their course notes as well as the texts. This was absolutely the most thought provoking mathematics I've ever done, you are presented with paradox after paradox. The only other similar material I could find in my league (in other words, not advanced graduate level probability I can't understand) was The Art of Computer Programming 4b (draft on Kuth's site) which covers Random Walks and Probabilistic Satisfiability. Besides whatever I come across in TAOCP I'm pretty much done my self-learning math experiment as I've run out of spare time to do it in (girlfriend, job, programming side projects). If you're sitting around doing nothing definitely try some of this because your spare time will get less and less as you get older.
Eugene Pogglewadge - Mon, 28 Mar 2016 20:26:50 EST ID:3PN7sFx7 No.15072 Ignore Report Quick Reply
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Thanks for introducing me to Daily Rituals

Not mine. But I felt it was save worthy when I saw it.
Emma Menkindod - Wed, 30 Mar 2016 11:00:49 EST ID:HXm2gRCi No.15073 Ignore Report Quick Reply

Interesting, many of those books are in the new Math 55a/55b Harvard course too http://math.harvard.edu/~ctm/math101/www/home/text/class/harvard/55a/08/html/syl.html and http://math.harvard.edu/~ctm/math101/www/home/text/class/harvard/55b/10/html/index.html

The "Advanced Calculus" book was written by profs of Math 55 to cover their 2 semester course before it was split so has much of the same curriculum as Harvard's modern 55a/55b but distills it into a sophisticated treatment like their linear algebra chapters, since the authors when possible don't assume that all spaces are finite-dimensional.

Incredible book, I would say you could replace half the books in that pastebin with just Advanced Calculus if your goal was to gain mathematical maturity which essentially was my goal. It also has no official pre-reqs you only use single-variable calculus in a few of the exercises but they expect you have done proofs before and understand basic notation.

The main difference I've notice between undergrad/intro texts and graduate level texts like Feller's Intro to Probability Theory Vol 2, or research papers I've come across, is everything is defined and constructed abstractly. You could definitely spend a few years in just one graduate text thinking about how many layers you can abstract from whatever constructions are in the book.
Emma Menkindod - Wed, 30 Mar 2016 11:46:28 EST ID:HXm2gRCi No.15074 Ignore Report Quick Reply
>Also, re: that pic

Sussman has another Physics book https://mitpress.mit.edu/books/functional-differential-geometry

Much like SICM, you translate equations into programs, abstract them, test them for approximate correctness to make sure you're on the right path, debug them if something goes wrong, ect. The tensor product is constructed in incremented abstractions which is what graduate level texts on multi linear algebra do. Totally mind blowing book.

Sussman and Wisdom concentrate in problems with math notation which Spivak also covers in Calculus on Manifolds (the book I wrote about earlier having to read in order to do this book). By simplifying the notation into scheme you get an ah-ha moment and can now start tearing equations apart and abstracting them with ease.

The basic theory of ordinary differential equations, tensor product, and classical mechanics (Lagrange equations) are all covered in Advanced Calculus by Sternberg and Loomis in order to do SICM or Functional Differential Geometry. nb
Hannah Pashhood - Sat, 16 Apr 2016 14:28:02 EST ID:v0g4AmIN No.15094 Ignore Report Quick Reply
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thank you for this. I skipped a grade of math when I was a kid because I was pretty smart, but it really just fucked me over when I had to play catch up with all the other kids on some really basic shit. As a result I pretty much fucked off during math for the rest of my education and completely avoided it in college. More and more I see what I was missing and this sort of collection is a godsend - some other dude confirming it's possible to relearn on your own time.

Fuck Crinningnig - Fri, 20 May 2016 12:29:49 EST ID:RHLOntyV No.15125 Ignore Report Quick Reply

Here's something else I found today
Shit Benningbury - Sat, 06 Aug 2016 02:49:47 EST ID:ijd+nKqH No.15179 Ignore Report Quick Reply
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OP here, some other books I've been reading lately

>Algebra: Chapter 0 by Aluffi
Graduate text in Abstract Algebra, writing style is incredible. Totally explains category theory, and other advanced topics then shows how they can all be unified and relate to each other. Focuses on 'why', beautifully written, machine learning applications galore here. Contains review of undergrad material like set theory, and then proceeds to teach you what real abstract linear algebra is.

>Naive Set Theory by Paul Halmos
Set theory is the “machine language” of mathematics, abstract math stripped away and you are working with bare primitives in first-order logic. Proofs are somewhat informal, with the details left as exercises to the reader which is why it's called 'naive'. There's paradoxs in here that will twist your brain. I still haven't finished this, since it takes me so long to grok just one page of this book, even after reading Aluffi's treatment on set theory. This book completely relates to computer security as you can combine it with satisfiability logic to break shit (see below).

>Introduction to Mathematics of Satisfiability by Victor W. Marek
Modern computer security, you open a program's control flow graph and use satisfiability to find errors you can exploit. The look on your face when you discover lthere's almost infinite branches of errors for a basic C program because they do not satisfy correctness.

After talking to a professor during a Satisfiability lecture here at a local university (free drop in, I don't go to university), he told me why it's important to study abstract mathematics as a computer scientist, because compsci is all about abstract thinking and the theoretical abstract math you do changes your thinking. Education isn't about filling a bucket, it's about expanding your mind to be able to perform complete wizardry. All that math I did, all it did was reshape my brain I won't ever use 1/4 of it.

>tfw I altered my brain with math
Fucking Gaddleware - Fri, 26 Aug 2016 13:35:07 EST ID:lrmxwgCP No.15183 Ignore Report Quick Reply
>details left as exercises to the reader which is why it's called 'naive'
No, it's called naive set theory because it is not formal axiomatic set theory. You are just learning our first, primitive version of it which has many uses but is also fundamentally flawed.
Eliza Chabberkotch - Tue, 13 Sep 2016 07:03:07 EST ID:9vmmdAPm No.15196 Ignore Report Quick Reply
they tried teaching math from the proof up, and it was a disaster
Basil Blatherfoot - Tue, 20 Sep 2016 12:17:53 EST ID:ijd+nKqH No.15207 Ignore Report Quick Reply
There's a new 'Proof School' in SF that attempts to teach middle highschoolers proofs using Ring fields (Linear Algebra). It's apparently been quite successful.

Anybody interested in Math education, or how math supposedly goes from 'elementary' to 'advanced' should read this Princeton book http://press.princeton.edu/titles/10697.html it also has a ton of interesting historical information while still being a short book. For example Abraham Lincoln lamented his lack of formal education so taught himself Euclid's Elements books 1 through 6, enough so that he could effortlessly prove anything out of the books. Since book 5 has some extremely advanced number theory going on it's safe to say Lincoln was a mathematician.

Yes, It is naive in that the language and notation are those of ordinary informal (but formalizable) mathematics. Most 'axiomatic' proving these days is done by a computer in gigantic outputs that nobody can visually verify, with the justification being 'trust the software' being that it's logic can be verified as it's X amount lines of code, whereas verifying the formal proof would take your entire life and life of your children.
Shit Hommerbanks - Tue, 20 Sep 2016 13:08:56 EST ID:2x1g2XF0 No.15208 Ignore Report Quick Reply
This is a nice history of the "new math" that I found recently:
Fanny Fammerhare - Sun, 30 Oct 2016 21:39:49 EST ID:yxQzbAra No.15257 Ignore Report Quick Reply
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I have failed most of my exams in mathematics because depression and no motivation/interest, however I want to learn mathematics now so I just want to thank you and the other posters for this thread.
Also, how "much/long" do you need to study before you get good at this shit? History and politics is easier to learn since it is pretty straightfoward, how does mathematics compare?
Martha Sottingdodging - Sun, 30 Oct 2016 22:02:40 EST ID:FFd5rNZG No.15258 Ignore Report Quick Reply
It takes about a year to do everything done through the end of high school in the US. Then 3 to 6 years of full-time study will make most math books/papers at least somewhat comprehensible. Mastering a modern field of math may take decades.
Fanny Fammerhare - Mon, 31 Oct 2016 07:10:21 EST ID:yxQzbAra No.15259 Ignore Report Quick Reply
Aw shit, well I'm not talking about a doctorate in it, I'm talking more about getting a solid base of mathematical knowledge. So a couple of years? Doesn't seem that bad. I think I'll read a lot of the recommended books in this thread
James Turveyfield - Sun, 06 Nov 2016 16:09:28 EST ID:AvE/EBRJ No.15264 Ignore Report Quick Reply
>History and politics is easier to learn since it is pretty straightfoward
I'm going to disagree, but cannot form logical conclusions outside of axioms so will leave it there.
Eugene Worthinggold - Wed, 09 Nov 2016 20:34:35 EST ID:Kybqo6e7 No.15267 Ignore Report Quick Reply
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they thanks for teaching me a new word there!
Cyril Fuckingham - Thu, 10 Nov 2016 07:44:26 EST ID:A03XOBvv No.15268 Ignore Report Quick Reply
Which one of those words did you not know?
George Honningham - Sat, 14 Jan 2017 20:50:27 EST ID:pPw7QUKx No.15324 Ignore Report Quick Reply
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>3 books per month
How do you do that? I've been reading A book of set theory by Charles C. Pinter for about six months and have only read the first 70 pages. Some of the excerces took me days to solve them, and after two months i could finally understand the resolution of the Russell's paradox. However, I've reading it over and over again until being pretty sure my proofs of every single problem are indeed proofs.
Frederick Wicklesadging - Wed, 18 Jan 2017 12:25:37 EST ID:bkgMqk62 No.15326 Ignore Report Quick Reply

That's a slow pace, but good. I think if you are reading three math books in a month you are missing a lot of details. It took me a year to read Shoenield's mathematical logic and I have been reading Kunen's set theory for a year nearly and I'm only half way through. Shit takes time.
Emma Drundlestock - Mon, 06 Feb 2017 13:38:21 EST ID:0v0QG0m/ No.15330 Ignore Report Quick Reply
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>That's a slow pace,
Yes, I know it. That's because I got my bachelor degree in maths but never studied it seriously until now, that I have noticed my lack of foundations; and it's because of that that I don't go on unless I'm pretty sure I have solved and understood every single part of the text and the problems, specially set theory and logic, wich are basic for all mathematics. Solving all the doubts arising when studying mathematics is a very important part of our study routine if one really wants to understand them... and it's probably the most tedious part.

>Shoenield's mathematical logic
I'd swear it was a model theory book. I remember I didn't buy it due to that, and bought Richard E. Hodel's An Introduction to Mathematical Logic instead.
Jarvis Pessledale - Tue, 14 Mar 2017 17:19:17 EST ID:ueMHQ1BO No.15419 Ignore Report Quick Reply
sick, now read a Math physics textbook and become a god
George Blatherbanks - Sat, 18 Mar 2017 16:35:05 EST ID:ck7N7PYR No.15422 Ignore Report Quick Reply
Frankel's The Geometry of Physics: A very good way to learn what modern geometry tastes like.
Albert Bivinghall - Tue, 22 Aug 2017 03:01:37 EST ID:OVoqDNaY No.15550 Ignore Report Quick Reply
Ernest Claystone - Mon, 21 May 2018 10:51:24 EST ID:hr6uWBv0 No.15658 Ignore Report Quick Reply
im gonna make use of this one day
Sophie Dicklestone - Tue, 29 May 2018 17:55:46 EST ID:sR7kJ2DP No.15661 Ignore Report Quick Reply
Honesty self-learning is the only way to learn math.
Coming from a guy who has an MS in math, you can only get so much out of taking a class on anything quantitative. It’s still you who has to work the homework and read the book.
I’m currently studying for my actuary exams and gotta study hours a day for it. It gets easier and easier over time.

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