[HN Gopher] How to choose a textbook that is optimal for oneself?
___________________________________________________________________
How to choose a textbook that is optimal for oneself?
Author : JustinSkycak
Score : 244 points
Date : 2024-07-20 14:13 UTC (1 days ago)
(HTM) web link (matheducators.stackexchange.com)
(TXT) w3m dump (matheducators.stackexchange.com)
| cultofmetatron wrote:
| 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 wrote:
| The OP is Chief quant at mathacademy.com
| cultofmetatron wrote:
| omg.. that explains a lot.
| JustinSkycak wrote:
| 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.
| cultofmetatron wrote:
| >it's the best feeling ever to hear about positive impact
| it's having on people's lives.
|
| you guys deserve it! its a great product. admittedly its a
| bit spartan/plain in terms of ui but I respect that you guys
| focus on substance over useless shit that emphasizes
| edutainment over actual actionable knowledge _cough_
| brilliant _cough_
| JustinSkycak wrote:
| Yeah, we realize the UI is a bit spartan. No disagreement
| there; it's a valid critique. As you say, we're focusing on
| functionality and content first since that's what really
| moves the needle on people's learning -- but yes, we're
| also going to be adding some bells and whistles in the
| future.
| amun_dev wrote:
| I signed up for mathacademy and I'm extremely overwhelmed by
| the courses. I'm not exactly sure what course I am supposed to
| start with. I went with Linear Algebra and I'm going through
| the diagnostics but I'm struggling with all the questions so
| far.
| JustinSkycak wrote:
| Hey! So, sometimes adult learners sign up for a university-
| level math class not realizing how serious our courses are or
| how much foundational knowledge is necessary (or how much of
| it they never actually learned during school, or how much of
| it they've forgotten since then).
|
| That's totally fine and all it means is you may need to start
| off in a lower course to shore up your missing foundations
| [1].
|
| There have been so many people in this situation that we
| actually designed a Mathematical Foundations course sequence
| specifically for adults who want to get up to speed or
| relearn math skills they have forgotten (from fractions
| through calculus) as preparation for upper-level university
| math courses. More info here:
| https://www.mathacademy.com/adult-students.
|
| Please do let me know if you have any follow-up questions
| about that or if anything is unclear. I'm always happy to
| chat with people who are serious about learning math.
|
| ---
|
| Footnotes
|
| [1] Note that we do check for missing foundations during
| diagnostics, and any that we find we'll add to your learning
| plan -- but currently there's a limit to how far we look
| back. For Linear Algebra, we only look back to the beginning
| of Algebra 2. So if you're rusty on any Algebra 1 stuff --
| factoring, quadratic equations, systems of linear equations,
| etc. -- or arithmetic stuff like working with
| fractions/exponents, then you'll need to drop back to a lower
| course to shore up those foundations.
| amun_dev wrote:
| That makes sense, I'll try out Mathematical Foundations I
| and go from there.
| JustinSkycak wrote:
| Sounds like a plan! If you run into any issues at all,
| feel free to ping me on X/Twitter
| (https://x.com/justinskycak) or shoot me an email
| (justin@mathacademy.com). The first piece of the puzzle
| to learning math is just getting on the rails at the
| appropriate level and I want to make sure we help you get
| over that hump.
| throwaway81523 wrote:
| Why not work with a tutor? Also I found the fast.ai videos good
| for explaining stuff like gradient descent.
|
| I don't see spaced repetition being useful for theoretical math
| though maybe it is ok for calculation. Main thing as you say is
| grind out problem sets, and that's more a question of logistics
| and motivation than finding the right textbook.
|
| I've always been skeptical of sites like mathacademy but I'll
| take a look at it.
| cultofmetatron wrote:
| I had considered working with a tutor. but honestly, its not
| hard to understand math from the textbooks. The main value of
| the tutor is that they figure out what you're weak at.
| however cost and time come into the equation. with a tutor,
| you have to plan ahead. you also can't have a tutor by your
| side everytime you practice math.
|
| > I don't see spaced repetition being useful for theoretical
| math though maybe it is ok for calculation.
|
| what Ive learned over the years over multiple disciplines is
| that really understanding theory is built on a strong
| intuition and a strong intuition is built on LOTS of
| practice. if you're solving the problem a lot, you are
| engaging with it on multiple levels which is going to force
| your brain to understand it on a level you will simply not
| get from simply watching a video on the subject. In much the
| same way that watching a video on react does not make you a
| web developer.
| fn-mote wrote:
| A tutor can give you an opinionated approach to a subject.
| They can offer you what they believe are the best (well,
| good) references. They can give you intuitive explanations
| for why things are true - the kind of explanation that is
| missing in a typical "rigorous" book. They can tell you
| what lines make sense to explore at your level and what
| things you should save wondering about for later. A tutor
| is another name for a professor, if you expect enough.
|
| Studying statistics / ML, I absolutely found that there
| were "truths" from the text that I would try to prove with
| simulations and ... couldn't really reproduce. Having
| somebody tell you that "that chapter is good but those
| particular statements are controversial / wrong / not
| exactly saying what you think they are saying" is really
| valuable.
|
| In the end, my opinion is that if you find it easy to learn
| from a text, probing the boundaries of your understanding
| could be good. Some stuff is easy. Other stuff just sounds
| easy but there is a deeper understanding to acquire.
| sonabinu wrote:
| I take classes at community college to up/revise skills in
| foundational mathematics. What I love is the small class sizes,
| the presence of adult students and the teacher engagement. This
| alongside the need to finish hw, keeps me on track
| davikr wrote:
| 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 wrote:
| 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 wrote:
| I recently learned about 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 wrote:
| 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 wrote:
| Is there a map of this? Would love to see which topics branch
| of each other and which start from scratch
| plonk wrote:
| Big schools' curricula? Look at some top school's math
| undergrad courses and graph them
| 4ad wrote:
| I am not aware of any good one, but I realized you could
| probably mechanically extract such a map from Lean's
| mathlib[0][1].
|
| Since Lean builds everything from scratch, this should be
| doable, albeit Lean builds everything on top of type theory
| which is not the only choice possible. Different
| foundations will result in a different graph.
|
| Also the best way to learn math is probably not by
| following this sort of graph, it would be far too abstract
| and disconnected from both the real world and usual
| practical applications.
|
| [0] https://leanprover-community.github.io/mathlib4_docs/
|
| [1] https://github.com/leanprover-community/mathlib4
| nextos wrote:
| Garrity's _All the Math You Missed_ book, mentioned
| elsewhere in the comments, draws a nice map of subjects,
| along with little introductions and book recommendations.
| The map is good for continuous mathematics, but IMHO fails
| to consider logic and type theory, which is a bit odd given
| the separate chapter for category theory. It also does not
| do proper justice to computation and clumps everything
| together under the label "algorithms".
|
| Good alternatives are _The Princeton Companion to
| Mathematics_ by Gowers and _Mathematics: Its content,
| Methods and Meaning_ by Alekxandrov, Kolmogorov, et al.
| Those present much more detailed maps so YMMV.
| throwaway81523 wrote:
| While beginning calculus students often pick up derivatives
| and integrals (and the associated formulas) easily, the
| delta-epsilon definitions of limits and continuity are a well
| known stumbling block for many. I've been told that the
| difficulty stems from that being the first place math
| beginners really see nested quantifiers: (forall
| epsilon)(exists delta)(...). In logic though, nested
| quantifiers are fundamental. I don't know what happens if
| someone tries to study logic without first having studied
| calculus. Maybe it's a good idea, but few people do it that
| way.
| lupire wrote:
| Delta epsilon is just an annoying unenlightening
| technicality, not the essence of real analysis. Surreal
| numbers (infinitesimals)solve the problem more elegantly.
| tnh wrote:
| To each his own, but epsilon-delta is my go-to example of
| formalizing an intuitive concept ("gets closer and
| closer"), which is a high-level mathematical skill.
|
| The intuition and the formalism are presented together
| (at least, they should be!). To learn the role of epsilon
| and delta, the student needs to jump back and forth,
| finding the correspondences between equations and the
| motivation. This is a skill that needs practice; this was
| one of the first places I found the equations dense
| enough that I couldn't just "swallow them whole".
|
| (The earlier I remember is the quadratic formula, which I
| first painfully memorized as technical trivia. It took me
| a couple of years to grasp that it was completing-the-
| square in general form. Switching between the general and
| the specific is another skill that you develop)
| throwaway81523 wrote:
| Surreal analysis is sort of a thing but it is quite far
| out there (e.g. you can have transfinite series instead
| of merely infinite ones). Maybe you meant nonstandard
| analysis (NSA), which is real analysis done with
| infinitesimals, but the machinery justifying it is way
| outside of what you'd see in even a theory-oriented intro
| calculus class. There was an intro calculus text
| (Keisler, 1976) that used infinitesimals and NSA. I don't
| know how it dealt with constructing them though.
|
| https://en.wikipedia.org/wiki/Elementary_Calculus:_An_Inf
| ini...
| will1am wrote:
| Rather than viewing delta-epsilon and infinitesimals as
| opposing methods, they can be seen as complementary tools
| I think
| LudwigNagasena wrote:
| It's very enlightening. Math was formalized for a reason.
| Now you don't have to argue what something was supposed
| to mean and whether it is a correct or a false
| interpretation, eg:
| https://hsm.stackexchange.com/questions/6867/what-is-the-
| cor...
| chucksmash wrote:
| > I don't know what happens if someone tries to study logic
| without first having studied calculus.
|
| When I was in college, the Philosophy department offered
| this course. It was considered an easy way to get a general
| education math credit without needing to be good at math.
| It was a really enjoyable course[0] that put me on the path
| to becoming a computer programmer. It occasionally comes in
| handy[1].
|
| [0]: https://news.ycombinator.com/item?id=37655058
|
| [1]: https://news.ycombinator.com/item?id=23412641
| Onavo wrote:
| The problem is that epsilon deltas have very little
| practical use outside of theoretical proofs in pure
| mathematics. Even for cutting edge CS/statistics fields
| like high level machine learning, most of the calculus used
| are existing formalisms on multidimensional statistics and
| perhaps differential equations. Aside from Jensen's
| inequality and the mean value theorem, I have never seen
| any truly useful epsilon delta proofs being used in any of
| the ML papers with significant impact. It's perhaps
| mentioned once in passing when teaching gradient descent to
| grad students.
| throwaway81523 wrote:
| > Even for cutting edge CS/statistics fields like high
| level machine learning, most of the calculus used are
| existing formalisms on multidimensional statistics and
| perhaps differential equations.
|
| If you mean experimental work, then sure, that's like
| laboratory chemistry. You run code and write up what you
| observe happens. If you're trying to prove theorems, you
| have to understand the epsilon delta stuff even if your
| proofs don't actually use it. It can be somewhat
| abstracted away by the statistics and differential
| equations theorems that you mention, but it is still
| there. Anyway, the difficulty melts away once you have
| seen enough math to deal with the statistics,
| differential equations, have some grasp of high
| dimensional geometry, etc. It's all part of "how to think
| mathematically" rather than some particular weird device
| that one studies and forgets.
| ghufran_syed wrote:
| I agree, and including delta-epsilon proofs in calculus 1
| seemed like a way for the curriculum authors to feel good
| that they were "teaching proof techniques" to these
| students, when in reality they are doing no such thing. I
| later did an MS in math, and _loved_ the proofs,
| including delta-epsilon proofs...after taking a one
| semester intro to proofs class that focused just on
| practicing logic and basic proof techniques
| zozbot234 wrote:
| If you want to do "exact" computation with real numbers
| (meaning, be able to rigorously bound your results) you
| just can't avoid epsilon-delta reasoning. That's quite
| practical, even though in most applied settings we just
| rely on floating point approximations and try to deal
| with numerical round-off errors in a rather ad-hoc way.
| xanderlewis wrote:
| > Category Theory is easy because it starts from nothing,
| literally.
|
| It has virtually no prerequisites, at least in classical
| mathematics. But I wouldn't call it 'easy' (indeed, many
| proficient in elementary calculus and so on find it very
| hard). If you study category theory with no knowledge of any
| of the concepts it's designed to abstract it's not going to
| make any sense and the whole exercise is pointless. You may
| be able to follow it and complete exercises, but you won't
| actually grok it.
| mhh__ wrote:
| It's sufficiently general as to be approachable from all
| angles but to actually understand _why_ anything is being
| discussed I think category theory requires a certain amount
| of background material.
| sn9 wrote:
| > Mathematical maturity has all to do with practice and
| experience and nothing to do with age.
|
| That's OP's point.
|
| "Age-appropriate" was put in quotes because it was referring
| to a metaphorical "mathematical age" to tie it to the concept
| of mathematical maturity.
|
| And, indeed, certain books require more mathematical maturity
| to get through than others, even though the prerequisites may
| be minimal. You'll see this often explicitly described in the
| preface of textbooks and reviews of those textbooks.
|
| They mentioned studying certain books to _develop_
| mathematical maturity because that 's where the practice and
| experience happen. Calculus is one such course used as part
| of this process, as are many courses intended as a first
| exposure to proofs like linear algebra and discrete math.
| Some might use the Moore Method with point-set topology.
| runald wrote:
| > 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.
|
| I disagree, you need to have capacity for abstract thought
| for abstract topics, most especially with category theory.
| Normal people have quite difficulty understanding
| abstractness, you either have the aptitude for it, or work
| your brain hard enough that it becomes somewhat easier.
| Children and younger people especially have difficulty
| understanding non-concrete topics.
| landosaari wrote:
| Thomas Garrity discussing mathematical maturity [0]
|
| Author of _All the Math You Missed: But Need to Know for
| Graduate School_
|
| [0] https://inv.tux.pizza/watch?v=zHU1xH6Ogs4
| kccqzy wrote:
| This was very much my experience with computer science. When I
| first studied computer science in middle school at age 13, I
| could only understand simpler algorithms like quicksort. I
| simply couldn't grasp dynamic programming. When I studied it
| again at age 19 (after having learned a couple of more
| programming languages like C++ and Python and Haskell, as well
| as taken some classes in mathematical proofs), it became much
| easier to understand. And then it was around age 22 when I
| could solve competition-style dynamic programming problems with
| ease.
| graycat wrote:
| Yes, _mathematical maturity_ is a consideration, but working
| carefully through just one mid-college math book that is based
| on theorems and proofs is a reliable cure. The consideration is
| not really big since the main goal remains: Just prove the
| theorems.
| llm_trw wrote:
| This is quite immature.
|
| Proving theorems is the easy part. Getting an intuition on
| which theorems you need to prove and which you can assume are
| true is the hard part.
| aquova wrote:
| This sounds somewhat similar to my experience in mathematics. I
| realized part way through college that I would only gain an
| innate understanding of a topic about two semesters into a
| harder one - ie I only had a firm grasp of Calculus I once I
| took Calculus III. I would still do well in those courses, but
| I would have to follow the motions at times. Alas, this meant
| the tail end of my education was doomed to some courses I only
| sort of understood. Fortunately I didnt major in it.
| Frieren wrote:
| 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 wrote:
| 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 wrote:
| If you're still looking, Gilbert Strang makes the best
| introduction book I know of:
| https://math.mit.edu/~gs/linearalgebra/ila6/indexila6.html
| plonk wrote:
| 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 wrote:
| I don't understand the anti-determinant brigade. Many
| linear algebra books don't don't start with determinants.
| plonk wrote:
| 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.
| zozbot234 wrote:
| > A year ago if I tried to find the perfect textbook to learn
| Linear Algebra, I would still be looking.
|
| You know, there is a textbook for Linear Algebra that's
| literally titled "Linear Algebra Done Right". It's pretty
| much what it says on the tin.
| apocadam wrote:
| Equally there is also a text called "Linear Algebra Done
| Wrong"
| lupire wrote:
| Not equally, better. It's intended as a book for learning
| the concepts of Linear Algebra intuitively and with some
| introductory rigor, before doing it "right" in a
| professional way.
| lupire wrote:
| And it is strongly discouraged as a first book, by the
| author himself!
|
| https://linear.axler.net/
|
| > This best-selling textbook for a second course in linear
| algebra is aimed at undergraduate math majors and graduate
| students.
|
| > No prerequisites are assumed other than the usual demand
| for suitable _mathematical maturity_.
| ghostpepper wrote:
| This seems a false dichotomy to me.
|
| Surely the optimal solution would be to spend a few hours /
| days in the first week picking the textbook, then 51 weeks
| studying it, as opposed to literally picking the first one
| you see and studying it for 52 weeks.
| mbivert wrote:
| It's a common issues with self-learners, mathematics or not:
| there is no perfect course out there, and switching from
| courses to courses can be wasteful.
|
| In my experience, focusing on a single, good-enough course
| (when in doubt, go for a famous/respected author/field
| contributor) and looking for other sources once in a while, has
| been the best approach.
| rochak wrote:
| Applies the same to job search too. Find one that is good
| enough and then work from there for future prospects. Often,
| the definition of "good" changes over time as priorities in
| life change.
| ghostpepper wrote:
| Sort of related
| https://en.wikipedia.org/wiki/Secretary_problem
| iamsaitam wrote:
| And if you pick up the wrong one, you might just end up
| dropping the whole ordeal. It's not so black and white, it
| makes sense to spend a bit of time and figuring out a good
| resource. At the least you'll get a sense of the domain's main
| trunk of knowledge, get into the jargon, etc.
| lupire wrote:
| If you pick up one knowing you can try a different one,
| putting it down isn't dangerous.
| will1am wrote:
| An important principle in learning
| patrick451 wrote:
| We do this with all demanding endeavours. Circling around the
| tactical perimeter is easier than knuckling down and getting it
| done. But it's close enough that we can fool ourselves into
| thinking we are being productive.
|
| Many examples:
|
| - It's easier to research the "best textbook for me" than it is
| to study and do problems.
|
| - It's easier to read about the optimal periodization cycle
| while sitting on the couch than it is to go sweat in gym.
|
| - It's easier to read about dieting (it must be the best diet
| for meee!) than it is to just stop ordering pizza.
|
| - It's easier to order business cards and redesign your logo
| than it is to find customers.
|
| - It's easier to fiddle with your vim config than it is sit
| down and write code.
|
| Unless you are already in top 10%, focusing on optimality is a
| distraction.
| aranchelk wrote:
| 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 wrote:
| "... 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 wrote:
| Plastic Part Design for Injection Molding 2E: An Introduction
| 2nd Edition
| VeryDevy wrote:
| 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....
|
| *
| https://web.archive.org/web/20230816100057/https://fab.cba.m...
|
| *
| https://web.archive.org/web/20230602222325/https://techcente...
| behnamoh wrote:
| 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 wrote:
| i fw this
| klyrs wrote:
| Is this parody?
| rhelz wrote:
| 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 wrote:
| 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.
| max_ wrote:
| 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 wrote:
| 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 wrote:
| But there are great books in this area?
|
| https://www.statlearning.com
|
| https://www.stat.cmu.edu/~cshalizi/ADAfaEPoV/
|
| There are other fine ones, but these are very good.
| max_ wrote:
| 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 wrote:
| >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 wrote:
| 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 wrote:
| Maybe the equations are there because they are important and
| instructive?
| cubefox wrote:
| 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 wrote:
| 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.
| constantcrying wrote:
| 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 wrote:
| 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 wrote:
| 100%. This is the missing piece in many cases.
| SoftTalker wrote:
| 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 wrote:
| I never had an oral exam. How is that feasible with class
| sizes, how many questions are asked? What's it like in
| general?
| constantcrying wrote:
| These were master and late Bachelor courses, so 30 people
| at most. Exams lasted around 60 minutes, of which around 45
| were questions.
|
| >how many questions are asked?
|
| Totally depends on the subject and how the exam goes.
|
| >What's it like in general?
|
| Your professor is poking you with questions. Usually he has
| prepared some general questions and then asks follow ups.
| It might go something like this. "What is X Theorem? What
| does it represent geometrically? Does conditions Z need to
| be true for the Theorems to hold? Can you name a counter
| example? How does the proof (discussed in lecture) look
| like? How exactly do you construct that part? Where do you
| need that condition? Here is a similar theorem (not
| discussed in class), can you outline a proof for this?"
| mbivert wrote:
| I'd go a bit deeper: as we developed, in particular with the
| advent of the Internet, we went from scarcity of information to
| spectacular opulence. This demands different studying habits
| that what we had 30 years ago or so.
|
| For example, we need to find ways to filter out noise from
| signal, or to connect scattered bits of knowledge from various
| sources to get intelligible solutions to problems (most
| problems can be solved by googling around, especially in
| maths/physics, because people of all levels have been
| asking/answering questions for Internet points e.g. on Stack
| Exchange & cie for many years now, but -- take it as a feature
| -- you have to work a little to get there).
|
| EDIT: regarding solutions, it's not just about preventing
| cheating, it's because teachers wants you to do the work. The
| point isn't necessarily to succeed in solving problems, but
| more to have you try, get creative, etc.
|
| Perseverance is crucial to move forwards. But they could still
| provide clear and/or progressive solutions, I fully agree.
| joshlemer wrote:
| Funny you say that. I recently picked up a textbook on
| Corporate Finance for self-learning purposes. Going through the
| problem sets, it's not really that useful if you have no idea
| if you got the answer right or not. Looked all around online
| for where to buy the solutions manual, ended up just calling
| the publisher to ask. Turns out they refuse to sell the
| solutions manual to anyone not a registered instructor at a
| University.
|
| It took like 5 minutes on the phone to even explain to them
| that I'm reading the book for self learning purposes. Like
| they'd never encountered such a thing. Even after explaining,
| they wouldn't let me have the solutions.
|
| I ended up just going on the black market, and finding some
| anonymous person to sell me the solutions on WhatsApp for $25.
| ghodith wrote:
| Now would be a good time to upload the solutions to libgen so
| other people can skip the black market
| mi_lk wrote:
| How does one access the said black market? I might adventure
| myself to acquire similar things
| owenpalmer wrote:
| If you have to ask, you'll never know.
| joshlemer wrote:
| I just googled, and by the way when you want to google for
| something with qustionable legality, it's best to use
| search engines not based in western countries, such as
| Yandex. There ended up being a lot of sites advertising the
| solutions manual for sale. But also, there are entire
| subreddits where these people post threads advertising that
| they have whatever ebook/solutions for sale with a whatsapp
| phone number included in the content. I messaged on
| Whatsapp and sent a paypal payment (yes, I had no recourse,
| it was a leap of faith) but it's not that much a risk since
| it's only $25.
| burnished wrote:
| Had a similar experience with an engineering text, contacted
| the author and he gave me the same shit.
| ZoomerCretin wrote:
| I'd really like a Khan Academy-like site, maybe with
| explanations from different textbooks for each concept. Of
| course then you'd need a good set of diverse problems or a way
| to generate such problems.
| elric wrote:
| It's a shame that Khan has gotten less diverse in subjects.
| They used to have medicine and bio stuff among others, but
| now it's mostly maths. The maths lectures and exercises are
| still great, but even those seem limited (still no discrete
| maths last time I looked).
| spoonfeeder006 wrote:
| I'm trying to find a calculus book that goes incredibly deep
| into integration techniques
|
| Still searching, so if anyone has any tips I'd love to hear
| cevi wrote:
| Have you tried to read any of the literature on the Risch
| algorithm? If you haven't, you might want to get started by
| taking a look at the paper "Integration in Finite Terms" by
| Rosenlicht [1] and chasing down some of the references
| mentioned in [2].
|
| Of course, in the real world we don't give up on integrals
| just because they can't be expressed in terms of elementary
| functions. Usually we also check if the result happens to be
| a hypergeometric function, such as a Bessel function. If you
| want to get started on understanding hypergeometric
| functions, maybe try reading [3] (as well as the tangentially
| related book "A = B" [4]).
|
| [1] https://www.cs.ru.nl/~freek/courses/mfocs-2012/risch/Inte
| gra... [2] https://mathoverflow.net/questions/374089/does-
| there-exist-a... [3]
| https://www.math.ru.nl/~heckman/tsinghua.pdf [4]
| https://www2.math.upenn.edu/~wilf/AeqB.html
| ExciteByte wrote:
| These might of interest to you:
|
| https://link.springer.com/book/10.1007/978-3-030-43788-6
|
| https://link.springer.com/book/10.1007/978-3-031-24228-1
|
| https://link.springer.com/book/10.1007/978-3-030-02462-8
|
| https://link.springer.com/book/10.1007/978-3-031-21262-8
| linearrust wrote:
| > Solutions need to be provided for problems
|
| Agreed. It's frustrating to solve a problem and being unable to
| check if it is correct. It's even more frustrating knowing that
| if you had the answer, it would help you to solve the problem.
| Sometimes the answer pushes you in the right direction to
| figure out how to solve the problem.
|
| > with clear explanations.
|
| Hopefully separate from the answers.
|
| For programming exercises, we should be given datasets so that
| we can tests whether our code works or not. Heck books should
| provide links to unit tests.
| mvdwoord wrote:
| 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
| coffeemug wrote:
| 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/Galvin...
|
| [2] https://terrytao.wordpress.com/wp-
| content/uploads/2016/12/li...
| Jeff_Brown wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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)
| sn9 wrote:
| Some books that meet some of the described criteria:
|
| * the books of RP Burn:
| 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
|
| * the books by AOPS: https://artofproblemsolving.com/store
| BobbyTables2 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| An important aspect of effective educational materials: the
| balance between challenge and accessibility
| Horffupolde wrote:
| Just study all of them.
___________________________________________________________________
(page generated 2024-07-21 23:16 UTC)