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How to choose a textbook that is optimal for oneself?

251 points by JustinSkycak 2y ago

yjkk 2y ago
[flagged]
Olesya000 2y ago
[dead]
cultofmetatron 2y ago
This echoes my own experience. I made an attempt at andrew Ng's revised machine learning course last year. I could understand well enough at a high level how gradient descent worked but its been 20 years since I did any calculus and the level to which my ability to even do algebra had atrophied greatly. To their credit, they derive the equations for you but I did't see how I was going to be able to really apply any of what I learned when the caclulus "handwaiving" is probably the most crucial step. I'm a fulltime CTO so finding textbooks that can fill in the gaps and finding endless problem sets to solve was just not going to work. Luckiy, A good friend of mind from hack reactor clued me in to mathacademy. I would argue thats its probably one of the biggest underated resources for getting back in mathematical shape. I've been setting aside an hour a day to just grind through the lessons and problem sets that it throws at me. it uses spaced repetition along with an inital placement test to figure out what you're weak at and just hits you with those problems as you improve. echoing the sentiment in the article, you'll get better just grinding though different problem sets consistently each day with the occasional metaphorical boss battle. Once you realize that, actually getting better at math is more of a logistical challenge (having to track down skill appropriate problems to cut your teeth on) Mathacademy basically automates that completely for you. I've gone from giving up on ever getting into this machine learnign stuff to looking forward to spending next year taking on deep learning. PS: not paid by mathacademy.com. just an incredibly pleased custoner Also PS: didn't realize you worked at math academy. any plans on expanding into physics problems? would LOVE these ideas to delve back into phsyics. (especially circuits.)
- gabrielsroka 2y ago
  The OP is Chief quant at mathacademy.com
  - cultofmetatron 2y ago
    omg.. that explains a lot.
- JustinSkycak 2y ago
  Wow! Love running into MA users. Your comment totally made my day. Thanks for the kind words and I'm so happy that the system is working out for you. After all the work we've put into building this thing, it's the best feeling ever to hear about positive impact it's having on people's lives. > any plans on expanding into physics problems? would LOVE these ideas to delve back into phsyics. (especially circuits.) Our grand plan is to completely fill out out math courses, then expand to other related fields such as computer science and physics.
  - Booleans 2y ago
    I've been wanting to read books like Algorithms for Optimization (https://www.amazon.com/gp/product/0262039427/ https://www.amazon.com/gp/product/0262039427/) and Probabilistic Machine Learning (https://www.amazon.com/gp/product/0262046822/ https://www.amazon.com/gp/product/0262046822/) but when I open them up I immediately think "wow I really need to refresh my calculus because I have no idea what's going on." It sounds like I should look into Math Academy for relearning old Calculus and learning some new stuff as well.
    - JustinSkycak 2y ago
      Definitely! Three things I'd like to bring to your attention, that are particularly relevant to your situation: 1. Our Mathematics for Machine Learning course: https://www.mathacademy.com/courses/mathematics-for-machine-learning https://www.mathacademy.com/courses/mathematics-for-machine-... 2. We designed a Mathematical Foundations course sequence specifically for adults who want to get up to speed or relearn math skills they have forgotten as preparation for Mathematics for Machine Learning and other university math courses. More info here: https://www.mathacademy.com/adult-students https://www.mathacademy.com/adult-students. 3. When you start on the system we assess not only your knowledge of the course you're placing into, but also lower-level foundational topics. If we detect that you have any gaps in your foundations (most learners do, especially adults who have been out of the game for a while), then we'll automatically add them to your learning plan and make sure you learn them before we give you any more advanced topics that depend on them. More info here: https://www.mathacademy.com/how-our-ai-works#diagnostic-algorithm https://www.mathacademy.com/how-our-ai-works#diagnostic-algo...
davikr 2y ago
I download the most textbooks I can, for evaluating which appeal to me, and then use that one. If I don't like a chapter on it, I look for another one.
markus_zhang 2y ago
My credentials for textbooks for self learning: 1. Must explain stuffs in a clear way. 2. Must give enough examples. 3. Must have many exercises AND a solution book for at least some of them. Context: prepraing to study all undergraduate Math and Physics courses to get a holding of General Relativity. Since I graduated as a Math Master but forgot most of it, I have to start from Calculus and Linear Algebra. I count about 8-10 courses for the journey.
grepLeigh 2y ago
I recently learned about mathematical maturity: https://en.wikipedia.org/wiki/Mathematical_maturity https://en.wikipedia.org/wiki/Mathematical_maturity Previously, I thought certain math topics were "hard" (e.g. category theory) while others were supposed to be "easy" (e.g. Calc I). I beat myself up for struggling with the "easy" topics and believe this precluded me from ever tackling "hard" topics. I was thirty-something years old when I finally realized math has a well-documented maturity model, just like emotional maturity or financial maturity. This realization inspired me to go back and take a few math classes that I had previously labeled as "too hard," with the mindset that I was progressing my math maturity. My point is that choosing an "age-appropriate" (in terms of math maturity, not actual calendar age) textbook is important. I also find it extremely helpful to chat with people who are more mathematically mature than I am, in the same way it's helpful to seek advice from an older sibling.
- 4ad 2y ago
  I am not sure what you are trying to say because your message and your posted link seem to be an odds with each other. Mathematical maturity has all to do with practice and experience and nothing to do with age. Category Theory is easy because it starts from nothing, literally. You can learn it at any age and with no almost no prior education. Same with various formal logics. You can't study or use in any way the theory of Calabi–Yau manifolds unless you have mastered all of its prerequisites. Certainly the advice of not choosing textbooks you don't understand is spot on, however. Unfortunately (?) most textbooks assume quite a bit of background, so you don't often have much choice in this regard.
  - CamelCaseName 2y ago
    Is there a map of this? Would love to see which topics branch of each other and which start from scratch
    - plonk 2y ago
      Big schools' curricula? Look at some top school's math undergrad courses and graph them
Frieren 2y ago
If you look for optimal you are going to spend more time looking for that textbook than learning. The optimal solution is to find a good enough textbook and start as soon as possible to learn and tonstop procrastinating.
- magnio 2y ago
  Yeah, this is it. A year ago if I tried to find the perfect textbook to learn Linear Algebra, I would still be looking. There are certainly good and bad textbooks, and a book good for many people might be unsuitable for your style, your goals, and your background. But there are plenty of good enough textbooks, trudging through any of them will yield far more benefits than getting that ideal book.
  - blopker 2y ago
    If you're still looking, Gilbert Strang makes the best introduction book I know of: https://math.mit.edu/~gs/linearalgebra/ila6/indexila6.html https://math.mit.edu/~gs/linearalgebra/ila6/indexila6.html
    - plonk 2y ago
      I like that he leaves determinants to a later chapter and doesn't _start_ with them, I never understood why they were useful or made sense. His view, represented on the cover, is great for learning
      - lupire 2y ago
        I don't understand the anti-determinant brigade. Many linear algebra books don't don't start with determinants.
        plonk 2y ago
        They're fine where they are useful, I guess, but my undergrad put way too much emphasis on them when they're not intuitive, don't help (me) much with comprehension, and aren't useful in that many cases compared to the other techniques.
aranchelk 2y ago
For a business I had to learn how to design parts for mass production injection molded plastic. It’s simple in concept but the devil is in the details, of which there are a great many. I couldn’t find a general non-fiction book with the information I needed, so I found and ordered the best textbook I could find on the subject. Teaching yourself from textbooks, I think you just have to be prepared for a serious grind, involving lot’s of looking up math and other terms that you either forgot or never knew, trips down the Wikipedia rabbit hole, etc. Those books are, for the most part, designed as teaching tools to accompany classroom learning — sometimes the whole class is going to come and not have a clue what they’ve read, and it’ll be via class or office hours they figure out WTF is going on. These books are not designed for autodidacts. I could be less charitable and talk about a lack of competitive pressure and perverse incentives for selection of academic books, but I’ll leave it at that. Worked out for me and the manufacturer I was working with said we were the most professional part designers he’d worked with (we were helped tremendously by software I’d written), he wasn’t a bullshitter generally, so I’m inclined to believe it. You can be successful but it’s going to take a lot more energy than it would with a nice trade book with an animal on the cover.
- marai2 2y ago
  "... I couldn’t find a general non-fiction book with the information I needed, so I found and ordered the best textbook I could find on the subject." Which textbook did you get?
  - aranchelk 2y ago
    Plastic Part Design for Injection Molding 2E: An Introduction 2nd Edition
- VeryDevy 2y ago
  Not sure if it's needed for you anymore, but I'll post it anyways, here are some links to documents from Bayer MaterialScience I have collected for designing injection molded parts. Pretty good general resources for the subject: * https://web.archive.org/web/20240531004633/https://kompozit.org.tr/wp-content/uploads/2021/11/A_Design_Guide_Part_and_Mold_Design_Engi.pdf https://web.archive.org/web/20240531004633/https://kompozit.... * https://web.archive.org/web/20230816100057/https://fab.cba.mit.edu/classes/S62.12/people/vernelle.noel/Plastic_Snap_fit_design.pdf https://web.archive.org/web/20230816100057/https://fab.cba.m... * https://web.archive.org/web/20230602222325/https://techcenter.lanxess.com/scp/americas/en/docguard/Joining_Guide.pdf?docId=77016 https://web.archive.org/web/20230602222325/https://techcente...
behnamoh 2y ago
IMO textbooks are dead and they were never a great source of knowledge to begin with. The idea of reading some piece of text written by someone, then edited by someone else, and expressed in an "appropriate" style and language (think formal language which uses fancy jargon), and then having to robotically solve some end-of-chapter problems is just absurd. My experience tells me the "gems" of knowledge are often found when authors and experts just say whatever the fuck they want on a forum or in personal discussions. That obviously presumes those authors actually know what they're talking about. So many math, physics, engineering, etc. books are written by people who had no business talking about those topics.
- aio2 2y ago
  i fw this
- klyrs 2y ago
  Is this parody?
rhelz 2y ago
There is no optimal textbook. This is a constraint satisfaction problem, not an optimization problem. ANY textbook you sit down and read, and solve its problem sets is infinitely better than ANY textbook you don't. Stop bike shedding and start studying!!!
- anthomtb 2y ago
  100%. The best time to start studying mathematics was when you were 4, with multiple private tutors and supportive-yet-not-overbearing parents who are also math educators. The second best time is right now, with whatever materials you have in front of you.
- cubefox 2y ago
  This is the wrong way to look at it. If a textbook is bad, or is good but too difficult (i.e. bad) you will stop reading it. The alternative to self-studying a good textbook isn't studying a bad one, but studying none.
max_ 2y ago
I thought it was just me but 2 mathematicians I look up to. The guy behind Stat Quest & Harry Crane. Both have explicitly said that there is simply no good book for their maths fields (statistics & probability). This really needs to be fixed. Since I alot of people think they are "not gifted" at maths when the real problem is that there is simply very bad study material.
- plonk 2y ago
  Don't machine learning books kind of fill that gap? e.g. Bishop uses probabilistic reasoning, Elements of Statistical Learning seems to be heavy on frequentist stats (haven't read it though), etc.
- brennanpeterson 2y ago
  But there are great books in this area? https://www.statlearning.com https://www.statlearning.com https://www.stat.cmu.edu/~cshalizi/ADAfaEPoV/ https://www.stat.cmu.edu/~cshalizi/ADAfaEPoV/ There are other fine ones, but these are very good.
  - max_ 2y ago
    Why isn't there a text book that explains math content as simply as Stat Quest? Also, thanks for the resources, they look really good.
    - constantcrying 2y ago
      >Why isn't there a text book that explains math content as simply as Stat Quest? Because you can't explain a complex concept simply and completely at the same time.
Vaslo 2y ago
I avoid any book that have complicated equations on the first few pages. There is a place for that but in this case the author is just trying to show everyone how smart and complex they are rather than trying to teach people.
- constantcrying 2y ago
  Maybe the equations are there because they are important and instructive?
cubefox 2y ago
Exercises in textbooks usually focus on proofs, but mathematics isn't just about proving theorems. Mathematics is also about: 1. Understanding mathematical concepts (e.g. what is an "acyclic" relation? What is KL divergence?) and theories (several interrelated concepts, e.g. decision theory). This also includes knowing why those concepts are important in the first place, which is often neglected. 2. Knowing the meaning of mathematical notation and technical terms, e.g. to be able to read papers in some field. Papers are often full of mathematical and other jargon while otherwise not necessarily being difficult to follow. 3. Learning mathematical formulas (e.g. Bayes' rule) and algorithms (e.g. differentiation), in order to solve specific problems by calculation or computation (mostly in applied mathematics, more rarely in pure mathematics) 4. Proving conjectures (mostly in pure mathematics, less often in applied mathematics) 5. Learning how to formalize informal problems using mathematical concepts and theories (by applying conceptual understanding gained by 1) in order to understand the problem better, or to make it easier to solve, e.g. by employing calculation (2). (This is often done in engineering and science) Problem sets in textbooks often focus on proofs (4) or some more difficult algorithms (3) but less on the other applications of mathematics. They could also check conceptual understanding (1) by asking the reader to explain some concept in their own terms, or how two different concepts relate to each other, or which concepts various example cases have in common, or how the cases differ on a conceptual level. Though verifying the answers might require a human teacher. 5) could be taught by coming up with word problems from a scientific or engineering (or economics etc) example, where the solution is easy once the correct formalization is known. Unfortunately it is hard to come up with such artificial word problems in which the correct formalization is unique, non-trivial, and doesn't require technical background knowledge from engineering/science etc. Moreover, in the real world, the difficulty with formalization is often to recognize in the first place that there is some problem that could be formalized, which can't be replicated in an artificial word problem. Overall, coming up with good exercises, especially for 5, but also partly for 1, might require the writer of the textbook to know a lot of possible practical applications. Writers of math textbooks are often mathematicians, so they probably don't know a lot about engineering, computer science, empirical science etc in order to come up with good word problems.
ziroshima 2y ago
There needs to be more resources for self-learning. Solutions need to be provided for problems, with clear explanations. It's a different mindset from a formal academic setting, where there's a strong focus on cheating prevention.
- Booleans 2y ago
  I hate when I buy an interesting math book and then it's like "oh wait, no solutions." And then I end up going on GitHub hoping for community-worked solutions.
- constantcrying 2y ago
  A Textbook is good enough for self learning. Almost all university learning is "self learning", at least that has been the case for my mathematical training. > It's a different mindset from a formal academic setting, where there's a strong focus on cheating prevention. What? Who cares about cheating prevention, most of my classes had oral exams, you can't cheat there.
  - ziroshima 2y ago
    I agree with you. It's been my experience though that tracking down solutions manuals for textbooks is very hard. Presumably because they want them out of the hands of students (to prevent cheating).
    - danielmarkbruce 2y ago
      100%. This is the missing piece in many cases.
    - SoftTalker 2y ago
      Maybe for specific textbooks, but if you just want e.g. introductory calculus with solutions those books are all over eBay. Or use Wolfram.
  - ralphc 2y ago
    I never had an oral exam. How is that feasible with class sizes, how many questions are asked? What's it like in general?
mvdwoord 2y ago
I found the text and workbooks for my mathematics courses at the Open University in the Netherlands absolutely fantastic. They are created / supervised by a famous (educational) mathematician in NL named Jan van de Craats. The method was designed for self study, and the absolute best I had ever worked through. Perhaps material from other similar institutes are of similar quality? https://nl.m.wikipedia.org/wiki/Jan_van_de_Craats https://nl.m.wikipedia.org/wiki/Jan_van_de_Craats
coffeemug 2y ago
I'm currently working through calculus. I picked up Spivak's and Apostol's books-- probably the most recommended calc books on the internet. Aaaand... they're ok. There are many parts that are confusing, not because calculus is "hard", but because the authors didn't do any user testing. If they actually reworked the books to minimize real students struggling, the books would have been much much easier to self-study from. I eventually found David Galvin's calculus notes[1] from University of Notre Dame. He basically follows Spivak closely, but reorganized the material a bit in response to user testing. The notes aren't perfect, but much much easier to follow. Same experience with Terence Tao's linear algebra notes[2]. I think book authors, even very highly respect ones, often kind of suck because they optimize for writing a beautiful book, not for minimizing student confusion. Once you struggle through the confusing parts, yes, the book is beautiful. But it's supposed to be written for people to learn, not for experts to appreciate! Notes written by professors who teach smart kids, optimize for minimizing confusion, and do real user testing are often much better than the best books, in my experience. [1] https://www3.nd.edu/~andyp/teaching/2020FallMath10850/GalvinNotes.pdf https://www3.nd.edu/~andyp/teaching/2020FallMath10850/Galvin... [2] https://terrytao.wordpress.com/wp-content/uploads/2016/12/linear-algebra-notes.pdf https://terrytao.wordpress.com/wp-content/uploads/2016/12/li...
- cubefox 2y ago
  Exactly. It's very hard to judge how hard it is to understand something when you already understand it. This is also why video games with puzzles need extensive play testing. Because the puzzle designer, already understanding how to solve the puzzle, is terrible at judging how hard it is to understand the puzzle. It seems that our counterfactual reasoning ability largely breaks down when it comes to understanding. For some reason we can't evaluate the question "what would I think if I didn't already understand this?" > Notes written by professors who teach smart kids, optimize for minimizing confusion, and do real user testing are often much better than the best books, in my experience. Yeah. Though smart kids get confused less easily, which means lecture notes written to teach dumb kids are even less confusing.
Jeff_Brown 2y ago
Don't! Faithfulness to a single source is the biggest reason I see for failure In students. Be promiscuous. If a page, chapter, or even whole book bores you, scan ahead, put it on trial for a bit, and if it doesn't redeem itself quickly, replace it. The same goes (to the extent possible) for courses, teachers and even whole media. Only once you've tried the whole universe do you have reason to lower your standards and try something again from that universe that didn't meet your earlier ones. A book isn't a friend. There are no brownie points for completion. Also most subjects are like that too. If you really want to know a natural language and hate the verb rules, focus on the rest of the language. If you soak up the verbs more slowly you'll still be hnderstandable, and you'll have fun, and most importantly you won't give up. And programming languages are especially like this. Don't like class methods? Good! They suck anyway. Keep your functions pure. Don't like generics? Well that's a shame but it didn't stop the first many generations of Go programmers who couldn't use them if they wanted to. Etc.
- fsckboy 2y ago
  because the topic, textbooks, is pedagogic, when i read your "Don't like class methods?" I thought the follow on was going to be "find a new professor!"
- 6keZbCECT2uB 2y ago
  In all seriousness, this seems to carry risk of never doing anything deep or hard. In particular, I've been programming for long enough, that I can be casual about many programming languages until I hit something which is actually new, such as in Rust or Prolog. Promiscuous doesn't have to mean having a low tolerance for difficulty, but everything else you wrote seems to support that. So, are you saying that enduring difficulty is unnecessary, or did you mean something different?
  - mcdow 2y ago
    Not the person you responded to, but I actually take a similar approach as them so maybe I can explain. Firstly, difficulty and fun are not always directly correlated. Something can be difficult but fun, or difficult and unfun. Following on my first point, different activities or goals usually have aspects that are more or less fun. It’s better to start with the easy and fun stuff. You don’t have to swallow the ocean. Now this last part really is dependent on the type of person you are. For me, once I’ve gotten into a subject, I just become more curious about it. The aspects of the subject that were unfun at first are now interesting. I’m more invested and I’m more curious. And if I’m more curious, it’s more fun. To sum it up, it’s not that one can avoid enduring difficulty. It’s more about harnessing your own strengths and curiosity.
RheingoldRiver 2y ago
My 2 cents on the topic is that for the most part I've had a lot of success choosing what to be interested in based on good book recommendations on the internet rather than looking for good book recommendations on the internet based on what im interested in If you're learning for fun, probably every topic in the history of the universe can be interesting given the right approach
spoonfeeder006 2y ago
Ahhh, the good old gym analogy... We use it We love it And it is our mainstay for understanding all things personally growth related Where would we be without it? We would be lost in darkness and ignorance
vouaobrasil 2y ago
I have a PhD in math and read many textbooks. The tried and true approach: gather 20 books on the subject and read the first couple pages of each. It should jump out to you right away which one is the best for you.
- elric 2y ago
  Unless you have access to a particularly mathy library, are fond of piracy, or have an exceptionally well stocked second hand bookshop nearby: that's going to be an expensive undertaking. (Says the guy who has dozens of untouched maths books lying around)
  - vouaobrasil 2y ago
    Library genesis. Nothing wrong with it.
sn9 2y ago
Some books that meet some of the described criteria: * the books of RP Burn: https://www.amazon.com/stores/author/B001HP60DI/allbooks?ingress=0&visitId=281469ea-239e-4309-bb14-f68c9b444e36 https://www.amazon.com/stores/author/B001HP60DI/allbooks?ing... * the abstract algebra text by Dos Reis and Dos Reis: https://www.amazon.com/gp/product/1539436071?psc=1 https://www.amazon.com/gp/product/1539436071?psc=1 * the books by AOPS: https://artofproblemsolving.com/store https://artofproblemsolving.com/store
BobbyTables2 2y ago
I also realized that a lot of specialized areas in Engineering are just preoccupied with a few specific concepts —- most are not incredible wizards. I was weak in matrix/linear algebra. All the graduate students seemed obsessed with matrix decomposition, eigenvalues, and Hermetian forms. After taking an optimization course (heavily matrix based) I realized they were just using the same small bag of tricks for everything.
BarbaryCoast 2y ago
Use the darknet. Get a list of possible texts, then download them. Figure out which one teaches the way you need to learn, then go buy that one. Used.
begueradj 2y ago
My experience with ex-USSR published books in mathematics and physics was very pleasant -and maybe the most pleasant ever. They rather provide simple examples and easy to solve exercises which thing always boosted my confidence psychologically to the point when I faced exams I was thinking: "This is just another set of exercises which I will succeed to solve, like I did multiple times". I also had the same experience with the American published Schaum's books. Apart from these, I almost got PTSDs with other publishers: they give you very hard to solve exercises to the point you would feel you are useless and incompetent to face even the easiest exams.
- graycat 2y ago
  The track record of math teaching in Russia has been impressive, Kolmogorov, Dynkin, etc. Too much in the US, there is secret culture: Math teaching is to filter, and the students have to prove themselves against challenges presented and deliberately constructed to cause a significant fraction of the students to fail. Eventually I had enough in accomplishments just to quit making an effort to prove myself again. Then when people started to attack me, I'd let them go too far and then use some accomplishment, old or new, to shoot them down. One of the best ones: At the end of 8th grade arithmetic, the teacher pulled me aside, alone, and with care and trying to be good, gave me a D in her class, said I could take High School Arithmetic, and should take no more math. It's true: I was no good in much of her course, the part that needed careful writing for the arithmetic, say, 1234 times 5678. Why? I was an 8th grade male with not so good manual dexterity -- the girls were MUCH better (standard). My 6th grade teacher saw the same. But as a senior, the SAT scores came back, and the 6th grade teacher read them to me: For the verbal score, trying to be nice, and with her low expectations, said "Very good". Not really! Then for the Math SAT she stopped. Afraid. "There must he something wrong." Yup, there was, and had been for 12 painful years. Of 1-2-3 in the class, I was #2. #3 was voted "Most Intellectual" and went to MIT. Right, since there was no Yeshiva in town, 1 and 3 were Jewish!!! It continued that way: Get attacked and attack back with some accomplishment and win. But, net, a dumb situation. Solution? Own a successful startup! Working on it!
- will1am 2y ago
  An important aspect of effective educational materials: the balance between challenge and accessibility
Horffupolde 2y ago
Just study all of them.

251 points by JustinSkycak 2y ago

yjkk 2y ago

[flagged]

Olesya000 2y ago

[dead]

cultofmetatron 2y ago

This echoes my own experience. I made an attempt at andrew Ng's revised machine learning course last year. I could understand well enough at a high level how gradient descent worked but its been 20 years since I did any calculus and the level to which my ability to even do algebra had atrophied greatly. To their credit, they derive the equations for you but I did't see how I was going to be able to really apply any of what I learned when the caclulus "handwaiving" is probably the most crucial step. I'm a fulltime CTO so finding textbooks that can fill in the gaps and finding endless problem sets to solve was just not going to work. Luckiy, A good friend of mind from hack reactor clued me in to mathacademy. I would argue thats its probably one of the biggest underated resources for getting back in mathematical shape. I've been setting aside an hour a day to just grind through the lessons and problem sets that it throws at me. it uses spaced repetition along with an inital placement test to figure out what you're weak at and just hits you with those problems as you improve. echoing the sentiment in the article, you'll get better just grinding though different problem sets consistently each day with the occasional metaphorical boss battle. Once you realize that, actually getting better at math is more of a logistical challenge (having to track down skill appropriate problems to cut your teeth on) Mathacademy basically automates that completely for you. I've gone from giving up on ever getting into this machine learnign stuff to looking forward to spending next year taking on deep learning. PS: not paid by mathacademy.com. just an incredibly pleased custoner Also PS: didn't realize you worked at math academy. any plans on expanding into physics problems? would LOVE these ideas to delve back into phsyics. (especially circuits.)

gabrielsroka 2y ago
The OP is Chief quant at mathacademy.com
- cultofmetatron 2y ago
  omg.. that explains a lot.
JustinSkycak 2y ago
Wow! Love running into MA users. Your comment totally made my day. Thanks for the kind words and I'm so happy that the system is working out for you. After all the work we've put into building this thing, it's the best feeling ever to hear about positive impact it's having on people's lives. > any plans on expanding into physics problems? would LOVE these ideas to delve back into phsyics. (especially circuits.) Our grand plan is to completely fill out out math courses, then expand to other related fields such as computer science and physics.
- Booleans 2y ago
  I've been wanting to read books like Algorithms for Optimization (https://www.amazon.com/gp/product/0262039427/ https://www.amazon.com/gp/product/0262039427/) and Probabilistic Machine Learning (https://www.amazon.com/gp/product/0262046822/ https://www.amazon.com/gp/product/0262046822/) but when I open them up I immediately think "wow I really need to refresh my calculus because I have no idea what's going on." It sounds like I should look into Math Academy for relearning old Calculus and learning some new stuff as well.
  - JustinSkycak 2y ago
    Definitely! Three things I'd like to bring to your attention, that are particularly relevant to your situation: 1. Our Mathematics for Machine Learning course: https://www.mathacademy.com/courses/mathematics-for-machine-learning https://www.mathacademy.com/courses/mathematics-for-machine-... 2. We designed a Mathematical Foundations course sequence specifically for adults who want to get up to speed or relearn math skills they have forgotten as preparation for Mathematics for Machine Learning and other university math courses. More info here: https://www.mathacademy.com/adult-students https://www.mathacademy.com/adult-students. 3. When you start on the system we assess not only your knowledge of the course you're placing into, but also lower-level foundational topics. If we detect that you have any gaps in your foundations (most learners do, especially adults who have been out of the game for a while), then we'll automatically add them to your learning plan and make sure you learn them before we give you any more advanced topics that depend on them. More info here: https://www.mathacademy.com/how-our-ai-works#diagnostic-algorithm https://www.mathacademy.com/how-our-ai-works#diagnostic-algo...

davikr 2y ago

I download the most textbooks I can, for evaluating which appeal to me, and then use that one. If I don't like a chapter on it, I look for another one.

markus_zhang 2y ago

My credentials for textbooks for self learning: 1. Must explain stuffs in a clear way. 2. Must give enough examples. 3. Must have many exercises AND a solution book for at least some of them. Context: prepraing to study all undergraduate Math and Physics courses to get a holding of General Relativity. Since I graduated as a Math Master but forgot most of it, I have to start from Calculus and Linear Algebra. I count about 8-10 courses for the journey.

grepLeigh 2y ago

I recently learned about mathematical maturity: https://en.wikipedia.org/wiki/Mathematical_maturity https://en.wikipedia.org/wiki/Mathematical_maturity Previously, I thought certain math topics were "hard" (e.g. category theory) while others were supposed to be "easy" (e.g. Calc I). I beat myself up for struggling with the "easy" topics and believe this precluded me from ever tackling "hard" topics. I was thirty-something years old when I finally realized math has a well-documented maturity model, just like emotional maturity or financial maturity. This realization inspired me to go back and take a few math classes that I had previously labeled as "too hard," with the mindset that I was progressing my math maturity. My point is that choosing an "age-appropriate" (in terms of math maturity, not actual calendar age) textbook is important. I also find it extremely helpful to chat with people who are more mathematically mature than I am, in the same way it's helpful to seek advice from an older sibling.

4ad 2y ago
I am not sure what you are trying to say because your message and your posted link seem to be an odds with each other. Mathematical maturity has all to do with practice and experience and nothing to do with age. Category Theory is easy because it starts from nothing, literally. You can learn it at any age and with no almost no prior education. Same with various formal logics. You can't study or use in any way the theory of Calabi–Yau manifolds unless you have mastered all of its prerequisites. Certainly the advice of not choosing textbooks you don't understand is spot on, however. Unfortunately (?) most textbooks assume quite a bit of background, so you don't often have much choice in this regard.
- CamelCaseName 2y ago
  Is there a map of this? Would love to see which topics branch of each other and which start from scratch
  - plonk 2y ago
    Big schools' curricula? Look at some top school's math undergrad courses and graph them

Frieren 2y ago

If you look for optimal you are going to spend more time looking for that textbook than learning. The optimal solution is to find a good enough textbook and start as soon as possible to learn and tonstop procrastinating.

magnio 2y ago
Yeah, this is it. A year ago if I tried to find the perfect textbook to learn Linear Algebra, I would still be looking. There are certainly good and bad textbooks, and a book good for many people might be unsuitable for your style, your goals, and your background. But there are plenty of good enough textbooks, trudging through any of them will yield far more benefits than getting that ideal book.
- blopker 2y ago
  If you're still looking, Gilbert Strang makes the best introduction book I know of: https://math.mit.edu/~gs/linearalgebra/ila6/indexila6.html https://math.mit.edu/~gs/linearalgebra/ila6/indexila6.html
  - plonk 2y ago
    I like that he leaves determinants to a later chapter and doesn't _start_ with them, I never understood why they were useful or made sense. His view, represented on the cover, is great for learning
    - lupire 2y ago
      I don't understand the anti-determinant brigade. Many linear algebra books don't don't start with determinants.
      - plonk 2y ago
        They're fine where they are useful, I guess, but my undergrad put way too much emphasis on them when they're not intuitive, don't help (me) much with comprehension, and aren't useful in that many cases compared to the other techniques.

aranchelk 2y ago

For a business I had to learn how to design parts for mass production injection molded plastic. It’s simple in concept but the devil is in the details, of which there are a great many. I couldn’t find a general non-fiction book with the information I needed, so I found and ordered the best textbook I could find on the subject. Teaching yourself from textbooks, I think you just have to be prepared for a serious grind, involving lot’s of looking up math and other terms that you either forgot or never knew, trips down the Wikipedia rabbit hole, etc. Those books are, for the most part, designed as teaching tools to accompany classroom learning — sometimes the whole class is going to come and not have a clue what they’ve read, and it’ll be via class or office hours they figure out WTF is going on. These books are not designed for autodidacts. I could be less charitable and talk about a lack of competitive pressure and perverse incentives for selection of academic books, but I’ll leave it at that. Worked out for me and the manufacturer I was working with said we were the most professional part designers he’d worked with (we were helped tremendously by software I’d written), he wasn’t a bullshitter generally, so I’m inclined to believe it. You can be successful but it’s going to take a lot more energy than it would with a nice trade book with an animal on the cover.

marai2 2y ago
"... I couldn’t find a general non-fiction book with the information I needed, so I found and ordered the best textbook I could find on the subject." Which textbook did you get?
- aranchelk 2y ago
  Plastic Part Design for Injection Molding 2E: An Introduction 2nd Edition
VeryDevy 2y ago
Not sure if it's needed for you anymore, but I'll post it anyways, here are some links to documents from Bayer MaterialScience I have collected for designing injection molded parts. Pretty good general resources for the subject: * https://web.archive.org/web/20240531004633/https://kompozit.org.tr/wp-content/uploads/2021/11/A_Design_Guide_Part_and_Mold_Design_Engi.pdf https://web.archive.org/web/20240531004633/https://kompozit.... * https://web.archive.org/web/20230816100057/https://fab.cba.mit.edu/classes/S62.12/people/vernelle.noel/Plastic_Snap_fit_design.pdf https://web.archive.org/web/20230816100057/https://fab.cba.m... * https://web.archive.org/web/20230602222325/https://techcenter.lanxess.com/scp/americas/en/docguard/Joining_Guide.pdf?docId=77016 https://web.archive.org/web/20230602222325/https://techcente...

behnamoh 2y ago

IMO textbooks are dead and they were never a great source of knowledge to begin with. The idea of reading some piece of text written by someone, then edited by someone else, and expressed in an "appropriate" style and language (think formal language which uses fancy jargon), and then having to robotically solve some end-of-chapter problems is just absurd. My experience tells me the "gems" of knowledge are often found when authors and experts just say whatever the fuck they want on a forum or in personal discussions. That obviously presumes those authors actually know what they're talking about. So many math, physics, engineering, etc. books are written by people who had no business talking about those topics.

aio2 2y ago
i fw this
klyrs 2y ago
Is this parody?

rhelz 2y ago

There is no optimal textbook. This is a constraint satisfaction problem, not an optimization problem. ANY textbook you sit down and read, and solve its problem sets is infinitely better than ANY textbook you don't. Stop bike shedding and start studying!!!

anthomtb 2y ago
100%. The best time to start studying mathematics was when you were 4, with multiple private tutors and supportive-yet-not-overbearing parents who are also math educators. The second best time is right now, with whatever materials you have in front of you.
cubefox 2y ago
This is the wrong way to look at it. If a textbook is bad, or is good but too difficult (i.e. bad) you will stop reading it. The alternative to self-studying a good textbook isn't studying a bad one, but studying none.

max_ 2y ago

I thought it was just me but 2 mathematicians I look up to. The guy behind Stat Quest & Harry Crane. Both have explicitly said that there is simply no good book for their maths fields (statistics & probability). This really needs to be fixed. Since I alot of people think they are "not gifted" at maths when the real problem is that there is simply very bad study material.

plonk 2y ago
Don't machine learning books kind of fill that gap? e.g. Bishop uses probabilistic reasoning, Elements of Statistical Learning seems to be heavy on frequentist stats (haven't read it though), etc.
brennanpeterson 2y ago
But there are great books in this area? https://www.statlearning.com https://www.statlearning.com https://www.stat.cmu.edu/~cshalizi/ADAfaEPoV/ https://www.stat.cmu.edu/~cshalizi/ADAfaEPoV/ There are other fine ones, but these are very good.
- max_ 2y ago
  Why isn't there a text book that explains math content as simply as Stat Quest? Also, thanks for the resources, they look really good.
  - constantcrying 2y ago
    >Why isn't there a text book that explains math content as simply as Stat Quest? Because you can't explain a complex concept simply and completely at the same time.

Vaslo 2y ago

I avoid any book that have complicated equations on the first few pages. There is a place for that but in this case the author is just trying to show everyone how smart and complex they are rather than trying to teach people.

constantcrying 2y ago
Maybe the equations are there because they are important and instructive?

cubefox 2y ago

Exercises in textbooks usually focus on proofs, but mathematics isn't just about proving theorems. Mathematics is also about: 1. Understanding mathematical concepts (e.g. what is an "acyclic" relation? What is KL divergence?) and theories (several interrelated concepts, e.g. decision theory). This also includes knowing why those concepts are important in the first place, which is often neglected. 2. Knowing the meaning of mathematical notation and technical terms, e.g. to be able to read papers in some field. Papers are often full of mathematical and other jargon while otherwise not necessarily being difficult to follow. 3. Learning mathematical formulas (e.g. Bayes' rule) and algorithms (e.g. differentiation), in order to solve specific problems by calculation or computation (mostly in applied mathematics, more rarely in pure mathematics) 4. Proving conjectures (mostly in pure mathematics, less often in applied mathematics) 5. Learning how to formalize informal problems using mathematical concepts and theories (by applying conceptual understanding gained by 1) in order to understand the problem better, or to make it easier to solve, e.g. by employing calculation (2). (This is often done in engineering and science) Problem sets in textbooks often focus on proofs (4) or some more difficult algorithms (3) but less on the other applications of mathematics. They could also check conceptual understanding (1) by asking the reader to explain some concept in their own terms, or how two different concepts relate to each other, or which concepts various example cases have in common, or how the cases differ on a conceptual level. Though verifying the answers might require a human teacher. 5) could be taught by coming up with word problems from a scientific or engineering (or economics etc) example, where the solution is easy once the correct formalization is known. Unfortunately it is hard to come up with such artificial word problems in which the correct formalization is unique, non-trivial, and doesn't require technical background knowledge from engineering/science etc. Moreover, in the real world, the difficulty with formalization is often to recognize in the first place that there is some problem that could be formalized, which can't be replicated in an artificial word problem. Overall, coming up with good exercises, especially for 5, but also partly for 1, might require the writer of the textbook to know a lot of possible practical applications. Writers of math textbooks are often mathematicians, so they probably don't know a lot about engineering, computer science, empirical science etc in order to come up with good word problems.

ziroshima 2y ago

There needs to be more resources for self-learning. Solutions need to be provided for problems, with clear explanations. It's a different mindset from a formal academic setting, where there's a strong focus on cheating prevention.

Booleans 2y ago
I hate when I buy an interesting math book and then it's like "oh wait, no solutions." And then I end up going on GitHub hoping for community-worked solutions.
constantcrying 2y ago
A Textbook is good enough for self learning. Almost all university learning is "self learning", at least that has been the case for my mathematical training. > It's a different mindset from a formal academic setting, where there's a strong focus on cheating prevention. What? Who cares about cheating prevention, most of my classes had oral exams, you can't cheat there.
- ziroshima 2y ago
  I agree with you. It's been my experience though that tracking down solutions manuals for textbooks is very hard. Presumably because they want them out of the hands of students (to prevent cheating).
  - danielmarkbruce 2y ago
    100%. This is the missing piece in many cases.
  - SoftTalker 2y ago
    Maybe for specific textbooks, but if you just want e.g. introductory calculus with solutions those books are all over eBay. Or use Wolfram.
- ralphc 2y ago
  I never had an oral exam. How is that feasible with class sizes, how many questions are asked? What's it like in general?

mvdwoord 2y ago

I found the text and workbooks for my mathematics courses at the Open University in the Netherlands absolutely fantastic. They are created / supervised by a famous (educational) mathematician in NL named Jan van de Craats. The method was designed for self study, and the absolute best I had ever worked through. Perhaps material from other similar institutes are of similar quality? https://nl.m.wikipedia.org/wiki/Jan_van_de_Craats https://nl.m.wikipedia.org/wiki/Jan_van_de_Craats

coffeemug 2y ago

I'm currently working through calculus. I picked up Spivak's and Apostol's books-- probably the most recommended calc books on the internet. Aaaand... they're ok. There are many parts that are confusing, not because calculus is "hard", but because the authors didn't do any user testing. If they actually reworked the books to minimize real students struggling, the books would have been much much easier to self-study from. I eventually found David Galvin's calculus notes[1] from University of Notre Dame. He basically follows Spivak closely, but reorganized the material a bit in response to user testing. The notes aren't perfect, but much much easier to follow. Same experience with Terence Tao's linear algebra notes[2]. I think book authors, even very highly respect ones, often kind of suck because they optimize for writing a beautiful book, not for minimizing student confusion. Once you struggle through the confusing parts, yes, the book is beautiful. But it's supposed to be written for people to learn, not for experts to appreciate! Notes written by professors who teach smart kids, optimize for minimizing confusion, and do real user testing are often much better than the best books, in my experience. [1] https://www3.nd.edu/~andyp/teaching/2020FallMath10850/GalvinNotes.pdf https://www3.nd.edu/~andyp/teaching/2020FallMath10850/Galvin... [2] https://terrytao.wordpress.com/wp-content/uploads/2016/12/linear-algebra-notes.pdf https://terrytao.wordpress.com/wp-content/uploads/2016/12/li...

cubefox 2y ago
Exactly. It's very hard to judge how hard it is to understand something when you already understand it. This is also why video games with puzzles need extensive play testing. Because the puzzle designer, already understanding how to solve the puzzle, is terrible at judging how hard it is to understand the puzzle. It seems that our counterfactual reasoning ability largely breaks down when it comes to understanding. For some reason we can't evaluate the question "what would I think if I didn't already understand this?" > Notes written by professors who teach smart kids, optimize for minimizing confusion, and do real user testing are often much better than the best books, in my experience. Yeah. Though smart kids get confused less easily, which means lecture notes written to teach dumb kids are even less confusing.

Jeff_Brown 2y ago

Don't! Faithfulness to a single source is the biggest reason I see for failure In students. Be promiscuous. If a page, chapter, or even whole book bores you, scan ahead, put it on trial for a bit, and if it doesn't redeem itself quickly, replace it. The same goes (to the extent possible) for courses, teachers and even whole media. Only once you've tried the whole universe do you have reason to lower your standards and try something again from that universe that didn't meet your earlier ones. A book isn't a friend. There are no brownie points for completion. Also most subjects are like that too. If you really want to know a natural language and hate the verb rules, focus on the rest of the language. If you soak up the verbs more slowly you'll still be hnderstandable, and you'll have fun, and most importantly you won't give up. And programming languages are especially like this. Don't like class methods? Good! They suck anyway. Keep your functions pure. Don't like generics? Well that's a shame but it didn't stop the first many generations of Go programmers who couldn't use them if they wanted to. Etc.

fsckboy 2y ago
because the topic, textbooks, is pedagogic, when i read your "Don't like class methods?" I thought the follow on was going to be "find a new professor!"
6keZbCECT2uB 2y ago
In all seriousness, this seems to carry risk of never doing anything deep or hard. In particular, I've been programming for long enough, that I can be casual about many programming languages until I hit something which is actually new, such as in Rust or Prolog. Promiscuous doesn't have to mean having a low tolerance for difficulty, but everything else you wrote seems to support that. So, are you saying that enduring difficulty is unnecessary, or did you mean something different?
- mcdow 2y ago
  Not the person you responded to, but I actually take a similar approach as them so maybe I can explain. Firstly, difficulty and fun are not always directly correlated. Something can be difficult but fun, or difficult and unfun. Following on my first point, different activities or goals usually have aspects that are more or less fun. It’s better to start with the easy and fun stuff. You don’t have to swallow the ocean. Now this last part really is dependent on the type of person you are. For me, once I’ve gotten into a subject, I just become more curious about it. The aspects of the subject that were unfun at first are now interesting. I’m more invested and I’m more curious. And if I’m more curious, it’s more fun. To sum it up, it’s not that one can avoid enduring difficulty. It’s more about harnessing your own strengths and curiosity.

RheingoldRiver 2y ago

My 2 cents on the topic is that for the most part I've had a lot of success choosing what to be interested in based on good book recommendations on the internet rather than looking for good book recommendations on the internet based on what im interested in If you're learning for fun, probably every topic in the history of the universe can be interesting given the right approach

spoonfeeder006 2y ago

Ahhh, the good old gym analogy... We use it We love it And it is our mainstay for understanding all things personally growth related Where would we be without it? We would be lost in darkness and ignorance

vouaobrasil 2y ago

I have a PhD in math and read many textbooks. The tried and true approach: gather 20 books on the subject and read the first couple pages of each. It should jump out to you right away which one is the best for you.

elric 2y ago
Unless you have access to a particularly mathy library, are fond of piracy, or have an exceptionally well stocked second hand bookshop nearby: that's going to be an expensive undertaking. (Says the guy who has dozens of untouched maths books lying around)
- vouaobrasil 2y ago
  Library genesis. Nothing wrong with it.

sn9 2y ago

Some books that meet some of the described criteria: * the books of RP Burn: https://www.amazon.com/stores/author/B001HP60DI/allbooks?ingress=0&visitId=281469ea-239e-4309-bb14-f68c9b444e36 https://www.amazon.com/stores/author/B001HP60DI/allbooks?ing... * the abstract algebra text by Dos Reis and Dos Reis: https://www.amazon.com/gp/product/1539436071?psc=1 https://www.amazon.com/gp/product/1539436071?psc=1 * the books by AOPS: https://artofproblemsolving.com/store https://artofproblemsolving.com/store

BobbyTables2 2y ago

I also realized that a lot of specialized areas in Engineering are just preoccupied with a few specific concepts —- most are not incredible wizards. I was weak in matrix/linear algebra. All the graduate students seemed obsessed with matrix decomposition, eigenvalues, and Hermetian forms. After taking an optimization course (heavily matrix based) I realized they were just using the same small bag of tricks for everything.

BarbaryCoast 2y ago

Use the darknet. Get a list of possible texts, then download them. Figure out which one teaches the way you need to learn, then go buy that one. Used.

begueradj 2y ago

My experience with ex-USSR published books in mathematics and physics was very pleasant -and maybe the most pleasant ever. They rather provide simple examples and easy to solve exercises which thing always boosted my confidence psychologically to the point when I faced exams I was thinking: "This is just another set of exercises which I will succeed to solve, like I did multiple times". I also had the same experience with the American published Schaum's books. Apart from these, I almost got PTSDs with other publishers: they give you very hard to solve exercises to the point you would feel you are useless and incompetent to face even the easiest exams.

graycat 2y ago
The track record of math teaching in Russia has been impressive, Kolmogorov, Dynkin, etc. Too much in the US, there is secret culture: Math teaching is to filter, and the students have to prove themselves against challenges presented and deliberately constructed to cause a significant fraction of the students to fail. Eventually I had enough in accomplishments just to quit making an effort to prove myself again. Then when people started to attack me, I'd let them go too far and then use some accomplishment, old or new, to shoot them down. One of the best ones: At the end of 8th grade arithmetic, the teacher pulled me aside, alone, and with care and trying to be good, gave me a D in her class, said I could take High School Arithmetic, and should take no more math. It's true: I was no good in much of her course, the part that needed careful writing for the arithmetic, say, 1234 times 5678. Why? I was an 8th grade male with not so good manual dexterity -- the girls were MUCH better (standard). My 6th grade teacher saw the same. But as a senior, the SAT scores came back, and the 6th grade teacher read them to me: For the verbal score, trying to be nice, and with her low expectations, said "Very good". Not really! Then for the Math SAT she stopped. Afraid. "There must he something wrong." Yup, there was, and had been for 12 painful years. Of 1-2-3 in the class, I was #2. #3 was voted "Most Intellectual" and went to MIT. Right, since there was no Yeshiva in town, 1 and 3 were Jewish!!! It continued that way: Get attacked and attack back with some accomplishment and win. But, net, a dumb situation. Solution? Own a successful startup! Working on it!
will1am 2y ago
An important aspect of effective educational materials: the balance between challenge and accessibility

Horffupolde 2y ago

Just study all of them.