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I completely agree regarding books. I've been refreshing my university undergrad-level math, and older textbooks have been much more accessible than most writte
by ericbarrett 5y ago
I completely agree regarding books. I've been refreshing my university undergrad-level math, and older textbooks have been much more accessible than most written after (roughly) the 1990s, even though the subjects haven't changed at all—this isn't avant-garde stuff. Seems no field is exempt from the modern "churn for churn's sake" phenomenon.
- bigthymer 5y ago> older textbooks have been much more accessible than most written after (roughly) the 1990s Why? How are they different?
- hungryforcodes 5y agoIn Grade 12, I had a revelation when a good friend explained to me in 5 minutes that trigonometry was largely just ratios. I guess either it hadn't been explained to me before properly or I didn't understand it at a DEEP level, but when he laid it all out for me on the board, it was suddenly all so simple. I had three reactions: 1) I was elated to finally understand sin and cosin. 2) I was thankful for him and also amazed at how simple it was in 5 minutes to explain something that seemed to have eluded me for 5 years of highschool. It made me wonder alot what other difficult subjects could be easily taught by just a good explanation. 3) I wondered why math class had failed so specifically to give me that knowledge, or at least test me to see if I understood it and if I didn't to ensure that I did understand it. The answer I think was math class just encouraged me to use a calculator, thus short circuiting any real understanding. Anyways he went on to be a physics professor at Cambridge. I always appreciated that moment.
- dataflow 5y agoHow were sine and cosine taught to you as anything other than ratios? I just assumed they were always taught as "opposite over hypotenuse" and "adjacent over hypotenuse" etc.
- hungryforcodes 5y agoThey were clear to me intellectually, but the way he explained it made me SEE the ratios. Instead of just being abstract functions, there was a clear relationship between the angles in the triangle. After that I was able to reason about them, where as before they were just things I plugged into my calculator.
- mixmastamyk 5y agoSometimes we are not ready for specific bits of information. i.e. brains have a "limited bandwidth." It's possible back in the old days the math teacher did mention it, but we couldn't understand it at the time because we had little sense of the subject. A common take on this phenomenon is discussed here occasionally: http://habitatchronicles.com/2004/04/you-cant-tell-people-anything/ http://habitatchronicles.com/2004/04/you-cant-tell-people-an... For a demonstration, go back and watch a good movie that requires focus, say three times in a row. Every viewing should uncover details you didn't notice the first time, because we can't take them all in at once. It's also why repetition is a good learning technique. Unfortunately few people have the patience to start over from the absolute beginning.
- r00fus 5y agoThis is very true. You are not the person you were in HS - everyone is a "Ship of Theseus" [1] therefore you can only guess at what HS version of you was like based on fuzzy remembrances. At your current age, you are more capable in some ways, less in others, and thus your learning capacity is different. [1] https://en.wikipedia.org/wiki/Ship_of_Theseus https://en.wikipedia.org/wiki/Ship_of_Theseus
- mcbuilder 5y agoI was originally taught the standard SOHCAHTOA in high school, and it didn't really click for me at all until I got to my undergrad introductory functions and graphs course. Near the end we got to Euler's forumla and our professor starting graphing e^{ix} in an extended complex plane. So apparently people learn things differently, as I prefer to work with identities and conceptual understanding rather than disconnected concepts.
- L0in 5y ago> 2) I was thankful for him and also amazed at how simple it was in 5 minutes to explain something that seemed to have eluded me for 5 years of highschool. It made me wonder alot what other difficult subjects could be easily taught by just a good explanation. I didn't understand what functions are/ how they work, my brain absolutely refused to understand, until i started programming. Then i got it in 5 minutes.
- mmmpop 5y agoYep, I think CS 101 should be a coreq with engineering calculus for this exact reason.
- L0in 5y agoI was so pissed... It took me years of trying to understand why i couldn't understand something so vital. I don't know if it has to do with how my brain works. I wouldn't say i have too technical mind.
- jacquesm 5y agoConversely, I had been programming in a BASIC dialect that used DEF FN to add user defined functions to the language and that made the concept of functions in math trivial for me. Being exposed to computers at a very young age was a huge advantage in school in the 70's.
- justinlloyd 5y agoI started programming at a young age, and got introduced to enumeration, product of and functions in math, absolute value, and so forth, but they were explained in any clear and succinct way that made sense. And then I had that "Aha!" moment of "oh, those are just these computing concepts." But when I later talked to the math teacher, "no, no, those are wrong, you don't understand" he would say. We were most definitely talking about the same concepts, just with different language, and I, at that young age, didn't not understand his language, and he, not having any computing of software experience, didn't understand my language.
- 2-718-281-828 5y ago> Anyways he went on to be a physics professor at Cambridge. such a shame. sounds like a talented fellow who really could have made something of his life. maybe even a chair at Oxford :/
- 908B64B197 5y agoHad he added a "New" in front of the country of his institution he might also have tripled his impact factor and salary!
- BLKNSLVR 5y agoThe foundational reason / concept behind cubic splines "clicked" for me whilst waiting to go into the room to sit the exam. I went from "fuck I have no idea" to "this is easy" in the space of about 5 seconds. The responsibility for not knowing until that point is more likely to be on my shoulders than the lecturer's, however.
- blocked_again 5y ago> older textbooks have been much more accessible than most written after (roughly) the 1990s Explain?
- ericbarrett 5y agoI don't have an explanation; it's entirely empirical/anecdotal. And there are certainly exceptions in both directions, e.g. I have a 1978 textbook on linear algebra that never mentions the relationship between matrix determinants and area. Overall what I've found is that older textbooks (edit: not just math) are more likely to (1) explain concepts in smaller steps; (2) not bury them in symbols and abstractions; (3) introduce and explain physical intuitions for subjects when they are relevant.
- spc476 5y agoOne book I found that was incredible was _Mathematics for the Million_ (3rd edition, from 1951) that's part mathematics book, part history book. It goes over the history of mathematics from ancient Egypt going forward, showing how only how math works (geometry, trig, algebra, the calculus) but how it was discovered and evolved over time.
- GeorgeTirebiter 5y agoI think it's just familiarity. Those are the books where you learned the stuff. So their way (style) is 'what you have been programmed to like'. to learn anything, so you can teach it to somebody else (the REAL def of Learning I'd say), you have to Do The Exercises. ---- I recently went over one of my older books on Matrices and it was a curious mix of trying to be sort-of precise, with trying to bring the 'wonder' and 'magic' of the concepts to life early -- so as to maintain reader interest. Ultimately, it was the way of thinking (mathematically) that was mostly taught; the 'matrix intro' was just fodder to support the pedagogy!
- ericbarrett 5y agoMost of the advanced math I learned used textbooks from the early 2000s era, which were often junk; this was the beginning of the "new book every year" phase of universities, one which they seem to have never left. (What I did retain was usually taught by lectures or compassionate fellow students.) My multivariable calculus book was recalled by the publisher mid-semester! One of the more talented kids got so pissed off at its quality that he went through the whole thing and ended up finding several hundred calculation errors in it (not typos or typesetting).
- runnerup 5y agoAs a related side note, I'm looking for a post on HN from earlier this year which linked to a textbook from the early 1900's or late 1800's about visualizing data. If anyone can help me find it, I'd greatly appreciate it.