6 ms·

Honest question: how do you tackle 2k pages of material like this?

by jahbrewski 7y ago

rectangletangle 7y ago
Binary search.
shademaan 7y ago
Use it as a reference
george_ciobanu 7y ago
I went to high school in Romania and first two years of college as well. We did tons of theory on about 2/3 (if not 3/4) of the material here (I also covered some of it when I continued my college in Montreal, Canada). But that took about 6 years of daily (maybe there was a day in the week when we didn't do math) study. And I'm sure we didn't cover it in the same depth as they do here (for most things we did a lot of proofs and theory). So it's possible but it takes a lot of time. In addition, it was usually motivated by the next step: you need to learn how to compute the inverse matrix in order to further process it with more complex algorithms which you actually use in labs or some sort of application (even if it's made up). The interesting thing is that, for a Math student (or a college professor) this is the FOUNDATION of math you need in order to study advanced stuff. For some of the recent math proofs (think famous ones) you'd need to study a whole year (after you know most of this stuff) just to learn the theory foundations for that proof. I'm of course exaggerating a bit - most Math majors would probably go through most of the stuff in this PDF but not necessarily all (machine learning stuff for example, and possibly numerical analysis stuff) of it. And if they do they usually forget* most of it, except the areas they use in their daily research (assuming they got for an advanced degree). And when you use some of this stuff every day it becomes second nature after a certain point. My experience is mostly based on the Romanian educational system which is typically more hardcore science (Math and Physics) even for Computer Engineering degrees. *Sometimes you don't forget stuff, you just don't think about it until you see it again (concrete example for me: Schur decomposition) and then partial memories of it come back.
- adamnemecek 7y ago
  There's no way you covered 2/3 of this in hs.
  - xenihn 7y ago
    CIS nations don't fuck around when it comes to math ed. Why do you think there's so many Eastern Europeans in fintech?
    - adamnemecek 7y ago
      I have first hand experience with mathematical education in post-communist countries. There's no way they did 2/3 of this in hs.
    - deleted 7y ago
      [deleted]
thijsb 7y ago
How do you eat an elephant? Piece by piece. it sounds stupid, but start at the beginning, and pace yourself. Chapter by chapter, you'll get through it. I'm really poor at math, so I've learned to work slowly and check if I really understand something before I go to the next chapter. Most maths is based on previous work / understanding. So, when I rush or try to skip pieces, I misunderstand the next part, making my rushing completely useless.
Scarbutt 7y ago
By accepting that you will spend two years studying it.
ur-whale 7y ago
I don't think you do, in the same way no one learns the webster dictionary by rote. OTOH, this is a fairly extensive and in-depth reference, which means that if - in the course of your studies or research - you hit on a topic you need to understand better, the book is here to be consulted on that specific topic. And you won't get the "I don't understand that part" feeling when you read it because the part that's giving you a headache is likely explained somewhere else in the book.
deleted 7y ago
[deleted]
faizshah 7y ago
My process based on the book “Make it stick: the science of successful learning” and trial and error. Before you begin, have a single source of truth for your daily goals whether its a calendar, todo list etc. I like a paper agenda notebook, my favorite layout is the emergent task planner from David Seah and the roterunner on amazon. A quick note on process: you want your schedule to be flexible and fault tolerant but specific, actionable and accountable. I like to block times of day for an activity and have a general idea of my goals for that day. I keep a big weekly todo list for each activity and chip away at it each week. You want to give yourself the least possible amount of choices each hour of your day but be able to tolerate errors in estimating time for a goal. Write down a purpose, of what u want to get out of the book. Thing back to the learning objectives on a syllabus in college, these should be specific. Look at the outline, take inventory of the topics you want to cover and their chapters/sections. Now schedule some block of time in your calendar, agenda, etc each week to study the book. Now when studying a chapter/section: first survey for a summary, practice questions, exercises etc. to get an overview. Start by answering the exercises, making predictions about a section and generally pre testing your knowledge of the topic. Based on some psychological studies in the book, the more you challenge your mind the more connections your brain makes thus improving learning. Next read through the section in order to fill in the gaps identified in your pre test phase, this purpose based reading improves retention. Dont underline, copy sections into notes, highlight etc these arent worth the time. Now create a diagram, outline or other summary of the text for your notes without copying things from the book. Try to do it in your own words. Finally, go back to the exercises you didnt complete or revisit your pretest questions and answer them. This greatly increases retention. Quizzing yourself is the best way to learn. In summary the way you tackle 2k pages of material is the same way you do in school. Weekly work towards the goal with practice, clear objectives, creating study guides and outlines and testing yourself.
bigred100 7y ago
Get a math degree and take a few grad courses and then use it as a reference. Alternative route: get an advanced degree in a relatively mathematical non-math STEM field and use it as a reference. I doubt there’s 1-2 people on the planet who are going to use that kind of book otherwise.
graycat 7y ago
Regard all of math as a tree based on essentially depth. Right, this is an over simplification since really have a directed graph of dependencies. But cheat a little and get a tree. Then study the main trunk and larger branches. For the deep roots, that is, the foundations, go light on those or will get confused, discouraged, and generally stuck-o. E.g., do some axiomatic set theory if really want; see some of the axiom of choice, but go light on the latest material on model theory and forcings. Then with the trunk and larger branches, will be able, as circumstances require, get to nearly any of the leafs fairly quickly as required. For that ~2000 page PDF, there, too, try to find the trunk and larger branches and mostly skip over the leafs. Maybe 80% of that book is leafs. Finding the trunk and larger branches in that book could be challenging. So, instead, just stay close to the commonly recommended undergraduate math major texts and topics. For each such text, at least glance at the 2-3 leading competitive texts and, then, take what is in common as the trunk and larger branches. Also for each topic, pick the best looking treatment and then glance at the other treatments. If you can, find a really good math prof in a really good math department at a really good university and try to chat with him about your progress for a cup of coffee (you pay) hopefully 4 times a year. If you can find more than one such prof, even better. Some departments publish their old copies of their qualifying exams; might get some of those! One more: Don't let yourself get stuck or discouraged. It's a fact of life that not all the materials are good. So there are some actual errors. Some exercises are just too darned hard, need material presented later in the book or not at all, or are just tangential curiosities not worth the trouble. Some of the writing can be obscure. Often there is not enough motivation to let you figure out what is important and what is not: If really obscure definition X or theorem Y seems not to be used in the rest of the book, then find some good reason to study X and Y or maybe delay them or just skip them. Sometimes obscure X, Y actually are important; sometimes not. There should be motivation, but commonly there is not. If you can't after a good effort understand something or solve an exercise, don't assume that the difficulty is you or that you are leaving a dangerous hole in your knowledge. If later you decide you need that something, then return and give it another shot. Generally for a really good, mature view of a book, just need more than one pass through it; so don't seek everything on just a first pass. Even given a really thorough first pass, you will notice significantly more on a second pass, e.g., some later material on the first pass will help you better understand the real points and importance of some earlier material on a second pass. And do glance at some alternative treatments. One recommendation is to chew on a proof until you really see it thoroughly. A counter recommendation is just to notice that we are all short of time. Net, use some judgment.

Honest question: how do you tackle 2k pages of material like this?

rectangletangle 7y ago

Binary search.

shademaan 7y ago

Use it as a reference

george_ciobanu 7y ago

I went to high school in Romania and first two years of college as well. We did tons of theory on about 2/3 (if not 3/4) of the material here (I also covered some of it when I continued my college in Montreal, Canada). But that took about 6 years of daily (maybe there was a day in the week when we didn't do math) study. And I'm sure we didn't cover it in the same depth as they do here (for most things we did a lot of proofs and theory). So it's possible but it takes a lot of time. In addition, it was usually motivated by the next step: you need to learn how to compute the inverse matrix in order to further process it with more complex algorithms which you actually use in labs or some sort of application (even if it's made up). The interesting thing is that, for a Math student (or a college professor) this is the FOUNDATION of math you need in order to study advanced stuff. For some of the recent math proofs (think famous ones) you'd need to study a whole year (after you know most of this stuff) just to learn the theory foundations for that proof. I'm of course exaggerating a bit - most Math majors would probably go through most of the stuff in this PDF but not necessarily all (machine learning stuff for example, and possibly numerical analysis stuff) of it. And if they do they usually forget* most of it, except the areas they use in their daily research (assuming they got for an advanced degree). And when you use some of this stuff every day it becomes second nature after a certain point. My experience is mostly based on the Romanian educational system which is typically more hardcore science (Math and Physics) even for Computer Engineering degrees. *Sometimes you don't forget stuff, you just don't think about it until you see it again (concrete example for me: Schur decomposition) and then partial memories of it come back.

adamnemecek 7y ago
There's no way you covered 2/3 of this in hs.
- xenihn 7y ago
  CIS nations don't fuck around when it comes to math ed. Why do you think there's so many Eastern Europeans in fintech?
  - adamnemecek 7y ago
    I have first hand experience with mathematical education in post-communist countries. There's no way they did 2/3 of this in hs.
  - deleted 7y ago
    [deleted]

thijsb 7y ago

How do you eat an elephant? Piece by piece. it sounds stupid, but start at the beginning, and pace yourself. Chapter by chapter, you'll get through it. I'm really poor at math, so I've learned to work slowly and check if I really understand something before I go to the next chapter. Most maths is based on previous work / understanding. So, when I rush or try to skip pieces, I misunderstand the next part, making my rushing completely useless.

Scarbutt 7y ago

By accepting that you will spend two years studying it.

ur-whale 7y ago

I don't think you do, in the same way no one learns the webster dictionary by rote. OTOH, this is a fairly extensive and in-depth reference, which means that if - in the course of your studies or research - you hit on a topic you need to understand better, the book is here to be consulted on that specific topic. And you won't get the "I don't understand that part" feeling when you read it because the part that's giving you a headache is likely explained somewhere else in the book.

deleted 7y ago

[deleted]

faizshah 7y ago

My process based on the book “Make it stick: the science of successful learning” and trial and error. Before you begin, have a single source of truth for your daily goals whether its a calendar, todo list etc. I like a paper agenda notebook, my favorite layout is the emergent task planner from David Seah and the roterunner on amazon. A quick note on process: you want your schedule to be flexible and fault tolerant but specific, actionable and accountable. I like to block times of day for an activity and have a general idea of my goals for that day. I keep a big weekly todo list for each activity and chip away at it each week. You want to give yourself the least possible amount of choices each hour of your day but be able to tolerate errors in estimating time for a goal. Write down a purpose, of what u want to get out of the book. Thing back to the learning objectives on a syllabus in college, these should be specific. Look at the outline, take inventory of the topics you want to cover and their chapters/sections. Now schedule some block of time in your calendar, agenda, etc each week to study the book. Now when studying a chapter/section: first survey for a summary, practice questions, exercises etc. to get an overview. Start by answering the exercises, making predictions about a section and generally pre testing your knowledge of the topic. Based on some psychological studies in the book, the more you challenge your mind the more connections your brain makes thus improving learning. Next read through the section in order to fill in the gaps identified in your pre test phase, this purpose based reading improves retention. Dont underline, copy sections into notes, highlight etc these arent worth the time. Now create a diagram, outline or other summary of the text for your notes without copying things from the book. Try to do it in your own words. Finally, go back to the exercises you didnt complete or revisit your pretest questions and answer them. This greatly increases retention. Quizzing yourself is the best way to learn. In summary the way you tackle 2k pages of material is the same way you do in school. Weekly work towards the goal with practice, clear objectives, creating study guides and outlines and testing yourself.

bigred100 7y ago

Get a math degree and take a few grad courses and then use it as a reference. Alternative route: get an advanced degree in a relatively mathematical non-math STEM field and use it as a reference. I doubt there’s 1-2 people on the planet who are going to use that kind of book otherwise.

graycat 7y ago

Regard all of math as a tree based on essentially depth. Right, this is an over simplification since really have a directed graph of dependencies. But cheat a little and get a tree. Then study the main trunk and larger branches. For the deep roots, that is, the foundations, go light on those or will get confused, discouraged, and generally stuck-o. E.g., do some axiomatic set theory if really want; see some of the axiom of choice, but go light on the latest material on model theory and forcings. Then with the trunk and larger branches, will be able, as circumstances require, get to nearly any of the leafs fairly quickly as required. For that ~2000 page PDF, there, too, try to find the trunk and larger branches and mostly skip over the leafs. Maybe 80% of that book is leafs. Finding the trunk and larger branches in that book could be challenging. So, instead, just stay close to the commonly recommended undergraduate math major texts and topics. For each such text, at least glance at the 2-3 leading competitive texts and, then, take what is in common as the trunk and larger branches. Also for each topic, pick the best looking treatment and then glance at the other treatments. If you can, find a really good math prof in a really good math department at a really good university and try to chat with him about your progress for a cup of coffee (you pay) hopefully 4 times a year. If you can find more than one such prof, even better. Some departments publish their old copies of their qualifying exams; might get some of those! One more: Don't let yourself get stuck or discouraged. It's a fact of life that not all the materials are good. So there are some actual errors. Some exercises are just too darned hard, need material presented later in the book or not at all, or are just tangential curiosities not worth the trouble. Some of the writing can be obscure. Often there is not enough motivation to let you figure out what is important and what is not: If really obscure definition X or theorem Y seems not to be used in the rest of the book, then find some good reason to study X and Y or maybe delay them or just skip them. Sometimes obscure X, Y actually are important; sometimes not. There should be motivation, but commonly there is not. If you can't after a good effort understand something or solve an exercise, don't assume that the difficulty is you or that you are leaving a dangerous hole in your knowledge. If later you decide you need that something, then return and give it another shot. Generally for a really good, mature view of a book, just need more than one pass through it; so don't seek everything on just a first pass. Even given a really thorough first pass, you will notice significantly more on a second pass, e.g., some later material on the first pass will help you better understand the real points and importance of some earlier material on a second pass. And do glance at some alternative treatments. One recommendation is to chew on a proof until you really see it thoroughly. A counter recommendation is just to notice that we are all short of time. Net, use some judgment.