 So, as we talked about in the previous videos, we figured out why it is that we're studying, whatever it is that we're studying. We've figured out that it's better to sit down and study longer periods than it is to do short chunks, right? We found our happy space, which is right here, right now, sitting down, right? And we've got a to-do list and our schedule, which is going to allow us to sit down for a while and study something new. And our to-do list is to learn a little bit of linear algebra, read a little bit of physics and learn a little bit of contemporary present-day politics, okay? So what we're going to do in this video right now is take a look at how to read a textbook. What you have to keep in mind is two things about textbooks, okay? The two of the most important parts of a textbook. And those happen to be the table of contents and the index, okay? And the way you should take a look at this is the table of contents for a book is the way the thought, the information has been organized and the way it's going to be delivered to you, okay? If you've ever taken notes from textbooks, what you're really trying to do whenever you're taking notes is take a chapter and condense it into a shorter chunk, a smaller chunk, right? That's what taking notes is. And the table of contents for books is basically chapters taken down to their key words, to their key thoughts, right? And if a textbook is organized well, then from beginning of the textbook, from the beginning of the table of contents, to the end of the table of contents, the train of thought, you should be able to read the table of contents and follow that train of thought, okay? And that is what basically the book is all about. The index of a book allows you to find specific topics right away and it's extremely useful if you're using a book, if you're using a textbook, to study, okay? So keep that in mind, the most important parts of a book are the table of contents and the index. And the third most important part of some books is the bibliography, the footnotes, where they're referencing other material, okay? And that really, that comes into play for math textbooks somewhat, but it comes into play a lot in politics, economics, and non-science based textbooks a lot because they are taking ideas from different places and presenting them or they're taking data and analyzing that data, okay? Now as for these books we're going to take a look at and we're just going to sort of skim through them just to show you how, what the best way it is to read certain textbooks. The first book is a linear algebra book, okay? It's the second edition linear algebra and its applications. So what we're going to do is take a look at the table of contents right now and you can see there's a preface and the introduction is usually a preface so I do usually end up reading the preface to this, okay? Sort of allows you, gives you an idea of what the authors were trying to do, right? So it's usually a good read and gets you in the mindset of this book so it becomes more personal. And as you can tell by the table of contents here there's chapter one and each chapter is broken down into subcategories, right? And usually when it comes to math textbooks they start off with the most basic concepts for each chapter, right? And they go to more complicated concepts and each chapter usually builds on the next. So table of contents is super important and then you have the appendix where they provide additional information, okay? And a lot of textbooks, math textbooks and science textbooks have these, the appendix in the back where they provide either tables with data, where they provide graphs, where they provide additional information, right? Formulas. So take a look at what's available to you in the appendices, right? The references is the books that they're referencing. You've got exercises and solutions and you've got the index. References for math textbooks, if you're really digging down into a specific topic they're important because you can go down further, right? Read more about that stuff. The solutions and exercises are very important for any math textbook. If you pick up a math textbook and it doesn't provide you with solutions, okay? Put that book down. Go pick up another book that does provide you with solutions and exercises, okay? Because no matter what math course you're taking you're going to have to practice, right? Because what you see at the end of every chapter for any math textbook, for any good math textbook I should say, you're going to have exercises, exercises, right? Every chapter is going to have exercises that you're going to have to do because these are sort of processes that you're going to have to learn how to do, okay? And that's the table of contents. Now you get into chapter one. This is how you're going to read math textbooks and math textbooks you read differently than you do physics textbook to a certain degree and non-science based textbooks. When it comes to math textbooks always read the header. Keep in mind the header, what chapter you're in. Keep in mind the sub-headers introduction. This is just to give you a general overview, right, of what's going on, what you're going to talk about specifically in this book, in this chapter. Always look at the examples that they're presenting, extremely, extremely important. So if this is an example of Gaussian illumination, if this isn't a full example, you read this example all the way to the end because when it comes to math, one reason you're looking at the examples is because when you're solving a specific type of problem, it has a certain pattern that flows. There's, you know, when you start solving certain types of problems, there's visuals that come at you, okay? There's geometry, symmetry within the specific type of problems you're solving for, right? So if you're able to notice a certain problem and you know what the pattern, how you're going to go, how you're going to solve it, what the pattern looks like, then you already know how to do that problem, okay? I'm going to take a look at that in the next video. But basically take a look at the examples. Read the bold stuff, 100% you read the bold stuff. And if you need to understand what's going on with the bold, you read the sentence before and the sentence after. And if you still don't understand it, read the paragraph where the bold appears, okay? There's a reason that they're making text bold, because it's important they want to stand out. When it comes to science textbooks, extremely, actually economics and politics as well, extremely important to take a look at the graphs and the visuals that is provided or that are provided, okay? And read the description of the diagrams, okay? So diagrams, graphs, charts, extremely important for all textbooks. Read them, spend time on them. Make sure you understand what this visual means, because this visual is an explanation of what you just did. For math textbooks, extremely important to look at the formulas, especially formulas that number their formulas, okay? Just like, you know, numbering their figures, so this is figure 1.3, they number their formulas. And they've done it here, I guess. This is explanation, right, 1A. And this is something that you're going to have to know, right? So anything that's highlighted and numbered, keep those in mind. Know where they are. Know how to access stuff. And understand what this means. So let's flip through this a little bit and see if we come to... So that's the end of chapter 1, right? And they provide you with exercises, review exercises here. And they have the solutions in the back, right? So if we flip this, this is chapter 1, right? So exercises, and the solutions would be right here for chapter 1, solutions to exercises. And that way you can do a problem and look up the answer. And one thing you should keep in mind, if you're learning a new process for mathematics, never ever sit down and do everything in a certain section and then check all the answers, right? Always sit there and do 10 problems in a row and then check all the problems all in one shot. Not at the beginning anyway. If you're trying to learn something new, do one question, look up the answer. If you got it wrong, try to figure out why you got it wrong. If you can't, go to the next one, do the question, look up the answer, right? Because if you end up doing a whole bunch of questions in one shot and looking up all the answers in one shot. If you were doing it wrong from the beginning, then you just reinforced the wrong method for yourself 10 times, right? So it's going to take a little bit of doing to undo that. What you want to do when you're learning a new process is read, do a question, look up the answer, make sure you got it right before you move on. So math textbooks in general take a little bit longer to go through. Sometimes, if you understand the concepts, then they're very quick reads, okay? Because you end up using these things as references. Because once you learn a certain process, you don't have to keep on relearning that process, right? If you know how to do long division, you know how to do long division. You don't need to learn how to do long division. Again, every time you do long division, right? It's different. Mathematics is powers that you're obtaining. And once you know how to do it, you know how to do it. The second book we have here is a physics textbook. And this is, I think, considered to be one of the best textbooks out there when it comes to physics, mainly, I believe, I'm not too familiar with the other authors, but mainly because of Richard Feynman. And for physics books, for textbooks like this, specifically science-based textbooks, for the most part, you can dive into a certain chapter. You do need to know some of the basic stuff. For sure, you need to know some of the basic stuff. But once you learn some of the basic stuff, the concepts sort of can jump around. So very extensive table of contents, and it provides you the train of thought that they were going with, how the information is being presented, right? So before you start going through the books, you should definitely look at the table of contents and have a feel for how the information is being presented. Okay? As for the index for this, it's going to be quite extensive because they cover a lot of stuff. And you can tell it's a nice index. And this is exactly what you want. Now, how to read a physics textbook? With physics textbooks, chemistry textbooks, biology textbooks, any science-based textbooks, the columns on the side, anything appearing on those, you take a look at, you read it, and you get a feel for it. Okay? Because that stuff is extremely important. Beautifully done, always read the text that goes with the imagery, right? With the diagrams because that gives you a feel of what this paragraph is talking about. For these types of books, whenever you get into a new chapter, a new subsection, always read the first paragraph. Read the first sentence of every paragraph. And take a look at the drawings and the charts and the graphs on the side. Read the description. If you understand this and you understand the first sentence and the paragraph, jump to the next paragraph and read the next sentence. Okay? If the paragraph is small, that's all you need. If the paragraph is midsize, you read the first sentence and the last sentence. If the paragraph happens to be large, read the first sentence, read a sentence in the middle, or anything that is in bold, for sure, and read the last sentence. Okay? That's one way you can cut back on your reading. When it comes to science-based books, the formulas that you're given, after those formulas or before the formulas, they explain to you what the letters represent. Okay? So you really have to, when you look at a formula, you really have to go above and below it as well. You have to read those because you have to know what the formula says. And the way you should think about formulas presented in science is their sentences. Okay? Their relationships, their functions. So you have to understand what those are. And when an idea is being built up, all right? They give you this, they present visuals inside of the text, and 100% you have to follow this. And usually when they're building up concepts like this, you have to go back to the beginning of this and read all of this to be able to understand this concept. Because what they're telling you is they couldn't condense this information on the sides. Okay? They're telling you that this is extremely important. Read these. Again, sub-heads, sub-headers, right? And usually you end up reading the last section of a chapter. Because that sort of, in general, provides a summary of what you just talked about. Okay? So you read the introduction, so you treat a chapter just the way you would treat a large paragraph, right? You read the first introductory part of it, right? You read the last chapter, and you skim through the middle parts and read all the diagrams. If you don't have the time to go through all of this, right? But if you really want to learn the subject, you have to read this for the first time if you're learning it, right? So that's how you read, you know, more physics-based textbooks. As for non-science-based textbooks, now, if you take a look at this, Days of Destruction, Days of Revolt, by Chris Hedges and Joe Sacco, right? And this was the first printing I picked it up. So first thing I did was I read the introduction by Chris Hedges just to get a feel for what he was trying to achieve. And he had some notes here, and he's giving some stats here, right? And when you looked at this, you know, the table of contents for this is very short, right? You got acknowledgement, notes, bibliography, and the index here, right? So let's go to the bibliography and the index, 287, 293. So he's got notes here. It's sort of something that most books don't provide, but he provided it because there's a lot of info being presented, okay? From each chapter, and these are sort of the footnotes. And he, you know, provides these footnotes for people that, you know, want to dig down further. And he's got his bibliography and is an extremely well-read person, same with Joe Sacco, an extensive bibliography, right? And then he's got the index, okay? So let's go, you know, flip through this book really quickly. Introduction I read, notes, data I read, okay? Days of theft. And, you know, when I first started reading this, I wasn't sure how to take it, right? And this, the imagery is by Joe Sacco's brilliant. And you start reading it, I start reading it, start reading it. And this stuff is, it's, you know, it's not a science book. So if you want to speed read through this, you can. You can just read the first sentence of, you know, shorter paragraphs. For mid-sized paragraph, you can read the first sentence and the last sentence. For large paragraph, read the first sentence, pick a sentence in the middle, read that and read the last sentence, right? For me, I read every word. Sometimes I read certain paragraphs more than once, right? And the imagery by Joe Sacco, brilliant. And then what I started doing was starting, taking notes in a book, okay? And that's one thing I do do if I come across extremely good books. Some books, like this, I don't mock up. Certain books I do mock up, okay? I just started going ballistic with some of the stuff. Information that he was presenting, taking notes, highlighting, underlining, right? Beautiful imagery by Joe Sacco, diagrams. You know, I end up taking a lot of notes in this book, highlighting a lot of stuff for my own, my own use. And that's how I, you know, read, you know, textbooks like this, or books like this, necessarily, I don't know if this is considered textbook or not, but for me it was because it was a book I was learning from. And I use this book as a reference and I take notes in it. And this would be a keeper for me, right? And that's, you know, how I end up reading textbooks, how I end up using textbooks. And best way to read textbooks as far as I'm concerned, okay? As for the next tip I have for you, right? Tip number six, I believe, when it comes to studying, what we're going to do, we're going to take a look at how to, you know, and this is going to be very specifically math-oriented tip on how to study. We're going to take a look at how you should lay down your questions, how you should solve problems, because what happens in mathematics, certain types of problems play out in a certain way. And math is very visual, so if you end up reading a problem, right, and you're trying to solve an equation or graph a function, there are certain things you have to do to an equation, to be able to solve it, to be able to graph it, and a certain pattern emergence for specific types of problems. So what we're going to do is we're going to take a look at those patterns and what you should do whenever you're doing mathematics, whenever you're solving certain types of problems, you should remember the structure of that problem, okay? You should remember how that question, that problem, plays out and is going to play out, because if you know that, then the odds are you know how to solve those problems, you know how to answer the question, you know how to graph those functions, okay, and that's what we're going to do with tip number, that's it for now. I'll see you guys in the next video.