[HN Gopher] Higher Math for Beginners (1987)
___________________________________________________________________
Higher Math for Beginners (1987)
Author : mindcrime
Score : 277 points
Date : 2021-11-13 03:03 UTC (19 hours ago)
(HTM) web link (archive.org)
(TXT) w3m dump (archive.org)
| amelius wrote:
| Why is this called "higher math"? It mostly covers high-school
| calculus and physics. And how would you call more advanced math?
| mpalmer wrote:
| Maybe it has a different relationship to the average math
| curriculum at the time versus that of the present day.
| mindcrime wrote:
| There really isn't any universally accepted definition of what
| "higher math" means. To mathematicians it seems to be something
| of a synonym for "proofs based maths", but for the rest of us,
| plenty of people use "higher math" to refer to Calculus and up.
| But in that sense, "higher" will always just be relative to
| where you already are, so honestly it's not a particularly
| useful term. But personally I don't think it's anything worth
| getting to worked up about.
| The_suffocated wrote:
| I think in the Soviet bloc, "higher mathematics" referred to
| mathematics taught at higher institutions (i.e. universities or
| technical institutions at the same level). This usage is a bit
| different from that in the Commonwealth of Nations (see
| https://en.wikipedia.org/wiki/Further_Mathematics for
| instance). As for the current text, while it does mostly cover
| high-school calculus, some portions of it (e.g. contour
| integration, analytic functions and Dirac delta function) are
| definitely outside high-school curricula. As the authors
| indicated in the preface, the intended audience of this book
| include high-school students, high-school teachers and first-
| year college students.
| [deleted]
| Throwaway1311 wrote:
| Reading the foreward
|
| > These definitions, which are not at all simple for the >
| beginner, came to be used in the wrong context. > Textbooks
| presented them before any explanation was > given of the theory
| and its applications, there > by complicating an understanding of
| things that > were intuitively clear.
|
| hear hear!
|
| This problem is like most of the Wikipedia pages that I come
| across on 'complex' topics of not just maths but anything
| remotely intersting technically. I just give up in the end. Life
| is too short to be bothered with some editor's 'dick measuring'
| competition about how clever they.
| mananaysiempre wrote:
| Hm. No. Wikipedia pages on advanced mathematical concepts are
| _intensely_ useful, frequently more so than any other single
| text you could find on the topic, because the only other way to
| obtain the same information would be to scavenge it paragraph
| by paragraph from a dozen or so textbooks, some of which are on
| apparently unrelated and /or even more advanced topics. (I've
| had to do this, multiple times, and it can take months and an
| absolutely unreasonable tolerance of frustration fueled by
| either youthful naivety or sheer boneheaded arrogance.)
|
| But that's provided your general mathematics education is
| something like one or two semester-long courses away from the
| thing you want to learn. Otherwise, they'll frequently be
| useless, and you're better off turning to gentler
| introductions.
|
| Wikipedia is not unique in this; many other technical reference
| books are the same, including the _Springer Encyclopedia of
| Mathematics_ (a rebranded and somewhat expanded version of the
| Russian-language _Matematiceskaja enciklopedija_ ), probably
| the best general reference on university-level mathematics ever
| (unsurprisingly, as a lot of it has been written by then-
| current or -future stars of Soviet mathematics, that being one
| of the few legal ways to earn additional money while holding a
| job in academia). Few references are good introductions. You
| don't learn C from the ISO standard--or even Scheme from RnRS,
| as wonderfully written as the latter is.
|
| I am quite literally furious over an accusation of a cleverness
| contest in a source the quality of mathematics Wikipedia ...
| But to direct this fury at you would be both wrongheaded and
| useless. Only, any environment where this kind of behaviour
| exists at all, in any way, is best exited as soon as possible
| and forgotten about. It's just that if you happened to suffer
| such an environment previously (possibly unwillingly, such as
| in school), you may see signs of this even where there are
| none. The best way to avoid this false impression is probably
| to look not at whether some people (appear to) flaunt their
| knowledge, but whether others are scorned for _not_ having such
| (to be distinguished from scorn for being unwilling to learn).
|
| Pure mathematics departments are generally among the
| friendliest places I've been to, if you just show up with a
| question (and display signs of having tried to find an answer
| by yourself, even if the result is a completely arse-backwards,
| mangled parody of the subject). Applied mathematics departments
| too, by and large, but there's a small minority of them where
| people are jaded by having to teach unwilling students and
| justify their existence to narrow-minded bureaucrats, so
| unfortunately I can't just recommend them unreservedly.
| bitcharmer wrote:
| Fully agreed. Maths topics pages on Wikipedia are useless for
| 99.9% of population. They just bombard you with alien phrases
| and concepts with zero explanation of what's what.
|
| It's pretty useless if you want to learn anything
| [deleted]
| hdjjhhvvhga wrote:
| Having read numerous books on various aspects of mathematics
| written by the academia, my pet theory is that there are two
| kinds of people who write incomprehensible math books:
|
| - Senior professors who actually suffer from the curse of
| knowledge and really forgot how it is not to know certain
| things, so they make tons of assumptions that are obvious to
| them.
|
| - Junior profs who could actually explain the topics in an
| accessible way but do not feel secure enough and engage in a
| strange game of showing off. I know the same people could do
| a good job in the classroom, but once they get down to
| writing, they start to be afraid of being judged by their
| Senior colleagues so they follow the trodden path.
|
| I gather the books that don't fail into these two categories
| for my daughter so when she grows enough to be able to grasp
| these concepts, she won't have to do dig through tons of
| crap.
| scythe wrote:
| My objection to this argument is that it seems to present
| "comprehensible" as the default outcome, and then derive
| confusion as a result of problematic thinking.
|
| Anyone who has actually tried to teach students knows this
| is false. Merely trying to be understood fails with high
| probability. The average math or physics grad student _upon
| entering_ already knows more than they have any chance of
| explaining thoroughly; distinguishing between senior and
| junior professors puts that line much further away than it
| really is.
|
| It's plausible that a sort of follow-the-template dynamic
| entrenches bad pedagogy, but I would think that the reason
| authors defensively stick to the old patterns is not
| because they worry about being judged, but rather the
| concern that they will do students a disservice if they are
| not "better than the Beatles":
|
| https://pubmed.ncbi.nlm.nih.gov/22378269/
|
| In other words, rather than risk being blamed for using a
| progression that works poorly, it's safer to follow the old
| patterns, so that tradition is blamed instead -- nobody
| ever got fired for teaching IBM^W the geometry sandwich.
| hdjjhhvvhga wrote:
| OK, a fair point. Let me be specific. What I consider a
| good math book for undergraduate students should have the
| following:
|
| - Explain the reason first instead of jumping into the
| definition straight away. I'm not taking about
| applications in physics etc., just a simple sentence
| like, "We have to learn series first in order to
| understand limits, and limits are necessary for
| understanding differentiation." Just one short sentence
| is enough to create a map in my mind and actually give me
| a decent reason to learn the topic. Seems obvious? Most
| math books chapters start with a definition.
|
| - Give examples. Really. How am I going to even remember
| the topic if you have failed to give even one example?
|
| - Give exercises for self-study. This is where the actual
| learning happens: at this point I can text whether I
| understood the theory or not. Moreover, it is through
| exercising that retention happens. Without exercises I
| can force myself to learn 50 pages and have only a vague
| memory of it the next day.
|
| - Provide the solutions to the exercises. I get it, if
| it's a textbook, you want to separate them - that's fine.
| But not providing them at all means the books is only
| half-useful for self-study.
|
| If a book has all these, I already consider it decent
| enough. Additional points for explaining particularly
| difficult points in more detail (good profs know well
| where their students are lost most often). If it makes
| sense, providing examples of practical application in
| sciences is always useful as it gives me some mental
| anchors connecting ideas and helping them to stick.
| gyam wrote:
| Would you mind sharing the names of the books that you've
| gathered for your daughter?
| hdjjhhvvhga wrote:
| Sure. I feel that many contemporary undergraduate/college
| textbooks are actually fine in this regard (like Topics
| in Contemporary Math by Bello, Britton, and Kaul). As for
| the rest, some of my favorites:
|
| - Warner, Pure Mathematcis for Beginners
|
| - Devlin, Introduction to Mathematical Thinking
|
| - Stewart, Concepts of Modern Mathematics
|
| - Herrmann, Sally, Number, Shape, and Symmetry
|
| - Baylis, What is Mathematical Analysis?
|
| - Feil, Krone, Essential Discrete Math for Computer
| Science
|
| - Rotman, A First Course in Abstract Algebra with
| Applications
|
| - Banjamin, Chartrand, Zhang, The Fascinating World of
| Graph Theory
|
| - Zou, Mult-Variable Calculus: A First Step
|
| - Hubbard, The World According to Wavelets
|
| - Sayama, Introduction to the Modeling and Analysis of
| Complex Systems
|
| - Darst, Introduction to Linear Programming: Applications
| and Extensions
|
| - Sourin, Making Images with Mathematics
|
| - Gallian, Contemporary Abstract Algebra
|
| And many others. Of course, all such lists are completely
| arbitrary. Once I get familiar with a certain topic,
| elaborate explanations seem redundant and I feel like
| shouting, "Get to the point already!" - whereas the same
| explanations can be extremely helpful for a beginner.
| fzil wrote:
| > - Gallian, Contemporary Abstract Algebra
|
| That is an amazing book. I will also recommend "A walk
| through combinatorics" by Miklos Bona for simple
| explanations and well made exercises with solutions
| present in the book itself.
| ivan_ah wrote:
| I recognize your two categories of bad math books and would
| like to add a third: commercial textbook publishers
| "padding" the pages with filler. It seems every book made
| for first-year undergraduate students is 10x thicker than
| it needs to be: there are these huge color images and lots
| of repetition, which makes students just tired and not want
| to read the book.
|
| It's completely artificial padding and unnecessary: you can
| teach calculus in 100 pages, you don't need 1000 pages (cf.
| Silvanus Thompson book on calculus or my books). I think
| the padding is done to make the exorbitant price tags seem
| more reasonable, so this is why I'm optimistic about this
| book since it's coming from the Eastern Block (no padding).
| hdjjhhvvhga wrote:
| I appreciate your No Bullshit guides a lot! Especially
| the fact that you provide the solutions to the exercises
| so that they're perfect for self-studying. I can imagine
| someone might like to have hundreds of color images - the
| assumption is they can help in absorbing certain concepts
| by linking imagery with abstract ideas.
| ivan_ah wrote:
| Slightly better version here
| https://archive.org/details/ZeldovichYaglomHigherMathematics
|
| (the PDF is 20MB instead of 150MB and the text has been OCR-ed)
| dang wrote:
| We've changed to that from
| https://archive.org/details/HigherMathForBeginners. Thanks!
| bobuk wrote:
| This very book (but in russian) is the source of all my math
| skills. Academic Zeldovich was a brilliant physicist and I am
| glad to know what his works translated to English
| shimonabi wrote:
| Are pages 358, 373, 379, 396, 530 misprinted or scanned sloppily?
| codetrotter wrote:
| The book in the updated link [1] does not have the problem that
| the old link had I think, if you were talking about how for
| example on page 358 the page had become split so that the
| rightmost part of the page had been cut off and placed on the
| left side of the page. I didn't check the other pages because
| I'm on mobile, but since page 358 looks good in the new link
| the others might too.
|
| [1]:
| https://archive.org/details/ZeldovichYaglomHigherMathematics
| yuuu wrote:
| Thanks for getting me flagged by completely overhauling your
| comment without recognizing its original content.
| codetrotter wrote:
| wut?
| shimonabi wrote:
| Look closely. The first half of the letter on each line is
| faded. (I'm the refering to the pages of the book, not the
| pages of the PDF)
| codetrotter wrote:
| Here's a screenshot of what I see when I look at page 358
| of the updated link, which looks fine to me:
| https://snipboard.io/OwvDXH.jpg
|
| I don't see the fading that you are talking about.
|
| Meanwhile, here is a screenshot of the way that page 358 of
| the book in the original link is broken when I look at it
| both on desktop https://snipboard.io/G9ohqg.jpg and on
| mobile https://snipboard.io/VXYHC0.jpg
| shimonabi wrote:
| The top of the page is fine. The fading starts in the
| lower half of the page.
|
| Are you trolling?
| codetrotter wrote:
| I scrolled down and looked closer there and see it now.
| It was more subtle so I didn't notice.
| yuuu wrote:
| This sounds entitled.
| Taywee wrote:
| Sounds like a pretty straightforward question to me. There's
| no reason to be defensive about flaws in a math book scan,
| even if it's largely a cool thing.
| yuuu wrote:
| He edited his comment. Substantially. The original comment
| told people that because five pages were missing, "either
| do it right or don't do it at all." That was basically all
| he said. Great guy, getting me flagged by completely
| changing his response without acknowledging there was an
| edit.
| PostOnce wrote:
| in addition and much more importantly:
|
| if no one points out flaws, flaws can not and will not be
| fixed.
| k__ wrote:
| My experience with learning math is that the first months are all
| about backtracking. You have to fill all your holes.
|
| It's basically one big graph of concepts.
|
| The tricky part is, most beginners simply don't know how to
| navigate that graph.
|
| They see complex numbers with their exponentials and cos/sin
| forms and shut down.
|
| They can learn all these concepts no problem, but finding what
| they need to learn defeats them.
| syntaxfree wrote:
| Math is "regular" enough that you can get away with using math
| at a higher level than one understands. All "practitioners" are
| using fringes of math they barely understand, which is ok --
| book says Theorem XYZ guarantees. But that's also where your
| mathematical growth is stunted. Learning "higher math" is
| always standing back a little.
|
| The epitome of this is the feared Real Analysis class where
| many people realize they're pretty much incapable of
| understanding high school calculus. But it keeps happening.
| k__ wrote:
| Yes, this just doesn't help in the first few math lectures at
| university.
| 29athrowaway wrote:
| Like this?
|
| https://cognicull.com/en/f5q2jl62
| rfrey wrote:
| I love that! What's its story?
| 29athrowaway wrote:
| It appeared a few weeks ago in HN.
| ivan_ah wrote:
| > It's basically one big graph of concepts
|
| True that. I have created a bunch of concept maps for my books
| in order to show readers this graph. It's really useful to find
| your way in a new field, to keep track of your progress, and
| also to look ahead into the the concepts that are coming up.
| Here are the links to the concept maps:
|
| High school math:
| https://minireference.com/static/conceptmaps/math_concepts.p...
|
| Mechanics and calculus:
| https://minireference.com/static/conceptmaps/math_and_physic...
|
| Linear algebra:
| https://minireference.com/static/conceptmaps/linear_algebra_...
|
| For an even better UI, there is the browsing interface in
| metacademy.org, which dynamically hides nodes and shows you
| only the prerequisites needed to learn a concept:
| https://metacademy.org/graphs/concepts/complex_vectors_and_m...
| This project is not actively maintained anymore, but it has a
| wealth of info and it is open source
| https://github.com/metacademy/metacademy-application so
| hopefully someone will pick up the torch.
| gopher_space wrote:
| I work alongside different industries and a hobby of mine is
| getting the people I work with to break down their domain for
| me. You've given me some good examples for organization, I
| have a _lot_ of different media but everything would
| translate to concept maps, but I don 't understand the
| 'graph' term you and OP are using. I found two definitions,
| neither of which seem like a perfect match.
|
| Is this an analogy? Would I be able to apply the concept to
| my project if I dug into it?
| jodrellblank wrote:
| The study is graph theory, and I won't link Wikipedia
| because its math pages are always overwhelming, other blog
| posts are likely more readable.
|
| 'Graph' in this sense does not mean these: https://royalsoc
| ietypublishing.org/cms/asset/ac7c91c1-a95b-4...
|
| but like this: https://upload.wikimedia.org/wikipedia/commo
| ns/thumb/5/5b/6n...
|
| or this: https://lh3.googleusercontent.com/proxy/l31aliLTy0
| BqoatXyi7K...
|
| It's what the geek-famous tool graphviz is for, visualising
| these kinds of graphs: https://duckduckgo.com/?t=ffab&q=dot
| +graphviz&iax=images&ia=...
|
| The study is the connections between things, not the shape
| they make on paper. So not squares, triangles, hexagons,
| etc. but can you get from one thing to another and how many
| intermediate ones do you have to go through? Are there
| multiple paths from here to there, or just one? Which
| graphs have the same connectivity even when drawn in a
| different layout? What does it 'cost' to go from one to
| another (see below)?
|
| It's used in the classic Konigsberg Bridge problem: https:/
| /physics.weber.edu/carroll/honors_images/BarbasiBridg...
| where the nodes are places in Konigsberg, and the bridges
| are the connections between them, and the puzzle is asking
| if you can visit all the areas, cross all the bridges once
| and only once, and return to where you started.
|
| In the classic Travelling Salesman problem:
| https://cdn.optimoroute.com/wp-
| content/uploads/2020/07/Trave... where the salesman wants
| to visit all the cities, they certainly can use the same
| route more than once, but what's the most efficient route
| to visit them all without wasting time and fuel going back
| to the same one unnecessarily?
|
| Edges can have weights (numbers) on them like this:
| https://i.stack.imgur.com/ET4ny.jpg which you can use to
| represent how far the link is, or how costly it is to go
| that way (fuel cost, or travel time, or effort, or speed
| limit on the roads, or bus/train/plane ticket price) and
| then you can ask the cheapest way to visit all the places,
| or the shortest way, or the fastest way. So it can be used
| in route planning (I want to fly here to here, via
| somewhere, what are my options?)
|
| Because it's about connections, not location or shape, it's
| very general. It can talk about computer networks like
| this: https://static.packt-
| cdn.com/products/9781788621434/graphics... and you can see
| one choke point in the middle that has to be fast enough to
| take the aggregate traffic of all the computers on both
| ends. Or you can look at it for the reliability - that
| single middle link is a good place to make two links,
| because then one can fail and all the computers are still
| working.
|
| Then you can deal with different "shapes" of graph (not
| layout on paper, "shape" of connections): http://2.bp.blogs
| pot.com/-GW8bGXZNrWg/VmFGCI949QI/AAAAAAAACd... does each
| node connect to every other one? Is it sparsely or densely
| connected? How many links could we lose and leave the
| minimum spanning tree - the skeleton network where
| everything is still connected end to end by one link? Is
| there one critical link which would separate it into two
| disconnected parts? What's the worst case for any two
| nodes? What if one link fails, what happens to the best and
| worst cases?
|
| It can describe "shapes" of communication or organisation -
| military has a top-down structure, anarchy has a meshed
| everyone-to-everyone structure.
|
| Graphs can be directed, edges can be one-way, they can be
| used in project planning, nodes can be tasks and edges can
| be which task output feeds into the next task input, and
| tasks and edges can weight how long things take: https://2.
| bp.blogspot.com/-SHnStluEIPc/WkarHINi08I/AAAAAAAAQ... then
| you can ask what things you can arrange to do at the same
| time and what you can't. In the picture there's a 3 day
| task waiting on a 4 day task. No matter how quickly you do
| all the other tasks, the whole thing must take 7 days
| minimum. This comes round to computing and how quickly you
| can speed up a program by adding multiple-processors. If
| there's a chain like that, only speeding up that chain can
| help, nothing else can help.
|
| State transition diagrams are graphs: https://faculty.etsu.
| edu/tarnoff/ntes2150/statemac/states1.g...
|
| They come into computing, tree structures are connection
| graphs, regular expressions are state transition graphs,
| concurrent programming is about tasks you can do at the
| same time, the internet is a connection graph and routing
| is finding short paths between distant computers through
| other systems.
|
| Neural Networks are about connection graphs - each node is
| a neuron holding an activation value and when it triggers,
| it sends some activation out to the neurons it's connected
| to. If the combined input passes that neuron's activation
| value, it does the same. Somehow by adjusting these trigger
| values and feeding a prepared input in (pixel values from a
| photo, one value to each input neuron) it triggers a
| cascade of activation through the whole network, and it
| settles on an output high for a picture of a dog, low for
| anything else.
|
| And concept maps, knowledge graphs, can be modelled like
| this; which ideas are connected to other ideas? When
| learning something it can help to make dense connections -
| instead of trying to remember that "shoe" is "zapato" in
| Spanish as a plain word connection which will be easy to
| forget, try and have it in a sentence about how your shoes
| are pinching your feet, and one about the smell of leather
| shoes, and one about the slimy feel of shoe polish, and a
| visual memory of the nearest shoe shop. More dense
| connections give you more ways to access that memory, more
| redundant, more easily, and using the mental connections
| reinforces them.
|
| Note taking tools like Obsidian, Dendron, TiddlyWiki, and
| systems like Zettelkasten are working with the problem
| "when I've taken notes, I can never find them, and hardly
| use them", and saying you need to connect the notes to
| other notes, more connections, then you see one and it
| gives you ideas by seeing what it links to - last time you
| used this note, what else were you thinking about?
|
| Wikis are graphs, HyperText (web) links make a spider's web
| of connections between pages.
|
| This is the "graph" in Facebook's "social graph" - who
| knows each other, how do they know each other, how strong
| are the connections between people? You know one person as
| a coworker, another by being in a hobby group, another is
| an extended family member and a close friend, another your
| phones both see the same WiFi access points so you must
| live or work near each other.
|
| It's so general it comes up all over the place; how do
| decisions get through your company from the people who make
| them to the people who need to hear them? How does Google
| Maps find you a good route? How do you deliver post around
| the country moving it from regional post office to central
| sorting hub back to regional delivery office? How does an
| AI path-find a route in a computer game? Which routes do
| you send trucks and cargo ships so they avoid making a
| return journey carrying no cargo, or never go via a bridge
| they can't go under? How do you build a country-wide
| telephone network without bankrupting yourself trying to
| run a copper wire from every person to every person? How do
| you represent the connections in your supply chain from
| company to company so you can avoid a 'chip shortage' event
| and have redundant suppliers if one of them has problems?
| Where does the water in the heating system need to go to
| get to all the radiators? Who is only six degrees from
| Kevin Bacon, where people are connected by appearing in the
| same film as each other? Who has the lowest Erdos number,
| where people are connected by being named in the same math
| papers as each other? If someone watches a VSauce YouTube
| video, which channels might they be interested in being
| recommended?
|
| The study of "stuff which is connected". ok I will link
| Wikipedia
| https://en.wikipedia.org/wiki/Graph_theory#Applications
| k__ wrote:
| For example, you have the concept "complex numbers" as a
| node and it has edges to "trigonometry", "exponentials",
| "real numbers", which are other concepts that are
| represented as nodes.
| TheFreim wrote:
| Last time I took math courses was high school, algebra 2 or
| geometry. Do you have any resources you can suggest for not
| only going forward but also filling in the gaps that I've
| forgotten or never filled?
| ivan_ah wrote:
| disclaimer: self-promotion ahead, highly relevant but
| still...
|
| > RE: resources for filling in the gaps
|
| I recently published a book titled _No Bullshit Guide to
| Mathematics_ that has precisely the goal of reviewing
| concepts form high school math for adults. Context: I was a
| private tutor at university for many years, so I know how
| common it is for university students not to remember anything
| from high school and struggle a lot, even though a few weeks
| of review would bring them back up to speed.
|
| The book's websie is here https://nobsmath.com/ and you can
| see an extended PDF preview of it here https://minireference.
| com/static/excerpts/noBSmath_v5_previe... (see my other
| comment for links to the concept maps).
|
| Once you have the high school math review done and solved
| some exercises and problems, you'll be in good shape for the
| other two books in the series _No Bullshit Guide to Math &
| Physics_, which covers mechanics and calculus, and the _No
| Bullshit Guide to Linear Algebra_. You can easily find links
| if you search for them and see reviews on the amazons.
| mindcrime wrote:
| Nothing wrong with a little self-promotion now and then.
| FWIW, I appreciate it, and I just ordered a copy of your
| _No Bullshit Guide to Mathematics_.
| medo-bear wrote:
| in your case i would suggest khan academy -
| https://www.khanacademy.org/math
| TheFreim wrote:
| Thank you, I will investigate this.
| hasmanean wrote:
| Yup. It's not about taking the quickest route from a to b, like
| textbooks try to do (no doubt to save paper) but to "fill in"
| the mental graph in your head as fully as you need.
|
| If that means solving the same problem multiple times using
| different methods no matter how useless or inefficient, trying
| things without knowing if they'll work, and adding to your bag
| of tricks for later problems.
|
| You know, like life itself.
| inglor_cz wrote:
| This is a good book. It would be even better if it were typeset
| in LaTeX.
|
| I wonder if such an effort could be financed from some kind of
| microgrants. Take old Soviet maths and physics books - they were
| very good! - translate them into English, possibly with small
| alterations (e.g. a QR code link to an animation), type them in
| LaTeX or AMSTeX and release them under a friendly license.
| enriquto wrote:
| Do you think so? It looks really beautifully typeset to me.
| inglor_cz wrote:
| Maybe it is just my problem, but I have hard time studying
| from a two-column book. I am mostly used to multiple columns
| in newspapers.
| Bayart wrote:
| Wouldn't there be right-holders still around ?
| inglor_cz wrote:
| If it was a Western book, definitely, but with books
| published in the 1980s in the USSR, I am not sure how it
| works.
|
| The USSR was not a signatory to the Berne convention, so the
| original rights may be lapsed. Russia joined the Berne
| convention in the 1990s, but there were some reservations
| agreed upon that limited the retroactivity.
|
| I think only Russian IP lawyers can answer that question with
| any precision.
| VitalyAnkh wrote:
| It's not *Higher* math. It's just normal math.
| BossingAround wrote:
| The crucial question is, is the text any good? My bias tells me
| it's next to impossible (but not actually impossible) for a text
| from 1987 to be 2021-beginner friendly, especially in a field
| like mathematics.
| medo-bear wrote:
| dont judge a math book by its date. also i found math books by
| russian or ex-soviet authors to be quite good, esp those by
| vladimir arnold
| adharmad wrote:
| Gelfand's books are good too.
| hdjjhhvvhga wrote:
| "Higher math" is a very broad concept now, you would need
| thousands of pages to cover it. This books is basically
| calculus with applications written in an accessible way by
| known experts and without confusing mistakes.
| 256cats wrote:
| Maybe just open it and have a look?
|
| The text covers a lot of ground very quickly omitting a lot of
| "pure math" details.
| pfortuny wrote:
| Classical books are usually much more engineering oriented than
| modern ones, with many more applications.
|
| The thing is that most applications are just ordinary things:
| tou are not going to go much deeper than angular momentum
| and/or the Stoked-Gauss theorem for electric-magnetic fields.
| qsort wrote:
| Why would you say that? The kind of mathematics that book
| presents has barely changed in the last 200 years. I would
| doubt there's much difference to speak of at all.
| BossingAround wrote:
| Because while the field of mathematics has probably not
| changed, the field of didactics has changed drastically, and
| the student expectations in 1980s and 2021 will be also
| drastically different.
| BeetleB wrote:
| I doubt math professors who write textbooks that are not
| meant for the mass public (i.e. not part of a state
| mandated curriculum) follow the field of didactics.
|
| I've read math textbooks from the 60s onwards. I do not see
| a trend vs time.
| pid-1 wrote:
| Most modern textbooks I used in university are complete
| garbage. A lot of concept vomiting without intuition
| building or real world insight.
| Jensson wrote:
| Has it actually improved though? Every study I've seen says
| students are worse at maths today than 30 years ago, so to
| me it doesn't look like all that pedagogy research improved
| things. If things actually got better we should have strong
| evidence supporting that. Images are prettier, sure, but do
| students who study using modern books actually understand
| the material better after the course is done?
| alisonkisk wrote:
| Can you link to some studies?
| Mandelmus wrote:
| I think attention spans have shortened (which is arguably
| devastating for maths), and the materials considered
| "state of the art in modern pedagogy" are the ones that
| take that into account in ways that a book from 1987 does
| not.
| Jensson wrote:
| As someone who had a hard time focusing in school, modern
| books with lots of text actually made it harder to focus
| than books with less text and more information per word.
| I can read 20 words and then think about those, I can't
| read the same information if it is spread out and hidden
| within a 2000 words text.
|
| So maybe kids has problems focusing partially due to
| modern pedagogy? Every word you write down has a cost to
| the reader, and the less attention span the reader has
| the more that cost matters. Drown them in too many words
| and they will just zone out since their attention span
| didn't last long enough for them to reach the important
| parts of the text.
| civilized wrote:
| Like food and architecture, math pedagogy has been
| affected by the progressive diseases of modern
| civilization, so new often does not mean good.
| pfortuny wrote:
| Drill exercises require very little attention time but
| are the keybto learning a topic and understanding it.
| This is nothing new but it is usually despised because
| "boring"...
| pfortuny wrote:
| Not so much with respect to Maths: either you integrate
| volumes or you do not, and the theory is essentially
| "dumb".
|
| As long as you know what a derivative is, all integral and
| vector calculus is just a comination of "look at the
| problem with an infinite loupe and then add all those
| values ".
|
| DiffEq is more or less similar.
|
| Classical maths was very well taught: examples and
| applications galore.
| keewee7 wrote:
| Actually my view is the opposite. Older math books has a lot of
| practical examples.
|
| It seems like in the 90s and 2000s a lot of math books started
| being written by pure mathematicians who don't care about the
| applications of mathematics.
| Jensson wrote:
| My understanding is that in the 90s and 2000s publishers
| started realizing that they could sell bare bones textbooks
| and then sell those problem examples in compendiums,
| effectively double dipping on each student.
|
| Edit: For example, books like this:
| https://www.amazon.com/-/es/Gregory-Grant/dp/B08FP7SNZJ
|
| > In addition to well-explained solutions, this manual
| includes corrections and clarifications to the classic
| textbook Linear Algebra, second edition, by Kenneth Hoffman
| and Ray Kunze.
| alisonkisk wrote:
| That solution book was written decades after the main
| textbook, by different authors.
|
| Barebones texts books were common in math since Rudin in
| 1953 and probably earlier.
| BossingAround wrote:
| I think this is actually fair; even Strang, after all,
| provides answers to only select problem sets (e.g. only odd
| problem sets in Linear Algebra if I recall correctly)
| though to be fair to Strang, it seems to me that in his
| case, it's more a matter of "if you are unsure, come and
| ask me" and probably not the case of maximizing profits.
| rmm wrote:
| This so much but in mechanical engineering. I was struggling
| in my course when I happened on a book written in 1980s in
| used book store for $1
|
| It had worked examples, basic theory from foundation up, and
| was absent all superfluous info.
|
| I credit it to passing my course and getting to where I am
| today. I still have it in my office to this day.
| cardanome wrote:
| I haven't worked through the book yet but looking at the
| authors, Yaglom wrote some great Math books and Zeldovich was
| an absolutely genius in the field of theoretical physics, so it
| probably is.
|
| As a German living in the Western part, my math teacher would
| always rant how much better the East German math books were.
| Math and science education in the Soviet Union and the Eastern
| Bloc was and still is vastly superior to anything we had or
| have in the West.
|
| See also this thread:
| https://news.ycombinator.com/item?id=26849866#26850468
| AnonymousPlanet wrote:
| Having the same background, I often heard this praise too,
| though mostly for Soviet works. But every time I followed up
| on it, I found that even the introductory level books dug
| right into the depths without much explanation. They might
| have been good in rigor or depth, but I found them very
| lacking didactically.
|
| Maybe I looked at the wrong ones. Your link seems to suggest
| that it's different for textbooks aimed at young children.
|
| Can you give me some examples of good East German higher math
| or physics books? I'd like to have another go at it.
| cardanome wrote:
| Unfortunately I wasn't really that interested in math when
| I was a student, I just remembered the ranting of my math
| teacher. I think you can still get quite a few on Ebay but
| I fear that not much has been digitized. I can recommend a
| few Soviet works however that are more introductory level
| and that I have worked with myself.
|
| A good example of a introductory book with good didactic is
| Probability Theory (first steps) by Wentzel. https://archiv
| e.org/details/ProbabilityTheoryfirstSteps/mode...
|
| Also Physics of Everyone, though maybe a bit more
| difficult: https://archive.org/details/LandauKitaigorodskyP
| hysicsForEve...
|
| Link to all the Mir titles:
| https://archive.org/details/mir-titles
|
| There are books for basically every level and age there.
| TuLithu wrote:
| Awesome book. Thanks. I've been needing to get back on my
| mathematics studies. This fits the bill perfectly.
| actually_a_dog wrote:
| PDF download link for those who want to download it, but don't
| want to hunt for the link:
| https://ia801303.us.archive.org/29/items/ZeldovichYaglomHigh...
| GaryTang wrote:
| Thanks, won't be long before the woke mob starts censoring this
| BrandoElFollito wrote:
| Context: I have a PhD in physics (many years ago), work in
| industry since then and have two high-schoolers I help in maths.
|
| I clicked on the link, the book opened on page 500-something and
| I said "oh fuck" loud when I saw the mess of equations. I
| actually thought that the rendering failed.
|
| I then moved back and the book has some down-to-earth approach
| but I could not stand the block of text page after page. It is
| truly a horrible book _to learn from_.
| medo-bear wrote:
| > It is truly a horrible book to learn from
|
| given your lengthy experience and qualification i am surprised
| that typesetting is such an issue for you. perhaps the book
| might be helpful to you as a teacher to draw some material
| from. me personally, trying to recall my attitude and focus
| during high school, i don't think i would have minded this book
| at all
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