The Ultimate Crash Course for PLEM Majors

All right, kids. Uh, we’re going to learn how to take a look at a college algebra textbook here. I’m going to Google a couple books here. Oops. Wanted to open a new window. Just going to take a look at a couple different books here for you guys. These ones I looked at here. There’s many, many, many, many different uh books out there. Okay. When you guys are reading a college algebra textbook or any textbook, you should really be familiarizing yourself with um many different authors because their um notations and things can change. So that so in here, this book here, um I’m just this is the OpenStack one. I’m just looking at the beginning quick here to kind of see. Actually, I’m going to download these and um open them up as PDFs to show you the differences. I just want to record where I found these books so that I don’t have any issues with copyright. This person wrote they hold this book in a PowerPoint. This Sullivan one’s a pretty pretty common popular one and probably the Open Stacks one maybe as well. Uh did I download the Sullivan? No. Okay. All right. Let’s look at these three. So here here we got in comparison of the books here, what I’m looking at first is the introduction section for all of these prerequisites and review. So if you guys you guys are in a college course, math physics, it’s it’s really important that you look at multiple books. Some books are going to be easier to understand than other books. The point of your college degree is to struggle through these things to make connections. It’s kind of like lifting weights. It It’s like pointless repetitions that build into something that build into strength that come together to make you stronger. You when you when you start college, you start a new course, months, weeks before the semester starts, you should be finding books, sifting through them one way or another. You have the great advantage today of accessing the internet. But on the internet, the majority of what you find is not credible. These books are accredited books from accredited universities. If you notice where I get the where I am at here, you see this is aedu. For the most part, I’m getting books from.edu. That’s an accredited source. A.com is not a credible source. Okay? These books are at au website for education purposes. It’s fine for you to use them. Okay? If you don’t want to pay an, you know, $300 for a brand new hardcover, you can find the PDFs of old editions for free atedu websites, a legitimate source. Um, when you’re reading the So, anyways, let’s let’s talk. If you’ve watched my other videos, you know what I tell you be before you get to chapter one, you should read every single word in the book. Just have it played to you. I just I just highlight it and I have Siri read it to me just like this. Jupiter images. I just highlight everything and have it played to me. I I do that for everything leading up to the first chapter and I do that for everything after the last chapter. I go to the after the last chapter and I review everything that’s in the end of the book to know where everything is. I take a look at where everything is and then I go to like you can skip the answer part but I go to the glossery and I have all the words read to me. It is amazing what’ll happen with your education. See these words if you just have these words played to you out loud while you’re like doing dishes or something. You’ll be shocked at how much better you understand things when you get to it. How much easier it is because your brain learns in layers. First you hear the word. It uses energy to store that information. Then it heals. You come back, then you learn the definition. Then it uses energy to store the definition rather than trying to store the word and the definition simultaneously. When you guys are learning new words, you should read the words first and just memorize the words and then wait a week and then come back and know and learn the definitions because your body is a machine and it’s using an energy in a certain fashion. It’s using this energy to first store the information for that word. Then it’s using energy to store the definition. Then when you come around to applying the definition, then it will use the energy to apply the definition. If you try to learn the word, the definition, and the application of it in one shot, it’s unlikely that your brain will re will retain retain the information. Just like when you guys are listening to these videos on like three times the speed, that doesn’t help you learn faster. Your brain can only absorb information at the rate of which it absorbs information, which is trained to absorb information at the rate of which people generally talk like me at this pace. When you speed it up, it’s just shooting it in one ear and out the other at a much faster rate. I I recommend you slow down, take a deep breath, enjoy patience, enjoy the fact that you are living in society and you don’t have to stress because you have everything you need to survive as long as you’re willing not to break the law. I don’t know. Whatever. Uh anyways, just have the words have the words played to you is my point. Just look at there’s a ton of words. You’re going to learn all of these words over the next four months. If you listen to them all before the semester starts, when you first come across them, they won’t be so foreign or daunting. You’ll have already heard the word. Now you can focus on memorizing the definition. You hear the word first, then it goes into your brain, then you work on memorizing the definition. Okay? So, you familiarize yourself with everything before chapter 1 and everything after chapter 1. Have every word read to you, then you go to chapter one or the review chapter. In algebra, we’re talking about the review chapter right now. The review chapter is very important because what you’re going to see in in here is is um different notations that mean the same things from book to book. Let me see here in this book what if they’re using for the most part they’re going to be using the same notations at algebra but they’re talking in this book they’re right off the bat talking about set notation those curly braces. Um they’re trying to help you here understand irrational numbers versus rational numbers. A rational number can be expressed as the ratio of two integers. An irrational number cannot be expressed as the ratio of two integers. And they’re talking about that at the beginning here just like they are over in this book. However, in this book, they’re going to describe it a little bit differently. Do you see here? They’re talking about the same thing with this set notation as they are right here uh with with um that’s the number set. Where did I go? Where? Right. Just right here. They’re they’re talking about it right here. Now, notice the structure the structure of this versus the structure of this. You know, it’s his is his is a little bit more elaborate than this one. This is a little bit vague in comparison to the to this one. This is also talking about a um a rational number here. This is talking about an irrational number. The way they wrote this set is very different from the way you’re going to see it in like my book. So, let me show you in my book under the new book I’m writing. It’s not it’s not really different. It’s just you guys got to understand that the notations they they change course to course, subject to subject, professor to professor. And and that’s why in my book I document everything. I’m trying to my book is is meant to teach you guys how to read books. So in here I show you here they’re talking about um a rational number a over b. B is not equal to zero. See how I write it here? See how they write it here? He’s got much more writing. And then how this person’s writing it the this person’s writing an an irrational number set. My irrational number set is this right here. I is equal to R set minus Q. And that’s what they’re saying there. If you if you take away all the rational numbers from the real number set, you’ll be left with only irrational numbers. That’s what this is saying. They’re saying the same. We’re all saying the same thing with different notations as well. And this is important before you start these courses that you that you look through all multiple books to understand what notation you’re using for your course and what notation is in the books you have, what notation your professor is using, whatever. This book right here, I’m not even going to look at it because it’s kind of defective. not not the best quality. Um here here they they outlined. Now look at this. N is the set of natural numbers. See how they have N WI, Q and Q where I have double stamped C, R, Q and Z. This book he says I is the set of integers. In my book the set of integers is Z. This is generally generally used for higher math Z. In this guy’s book, he chose to use the letter I for the set set of integers. And in other math, I is the identity matrix and W and N. These things have different meanings in different books, which is what I I do in my book is I show you the difference between these things are all the same thing. They can be all the same thing. I’m even going to add in this I’m going to read in this book that I might I’m going to have to add this. Sometimes I is is the set of integers. Sometimes I’m going to do script I I’m going to do this regular I integers. So I’m just going to add that into my book as I because I I hadn’t gone through this book this guy’s book. This but this is my book is to explain to you guys how to read books. This is a this is a sample of like basically what I do when I’m writing these books. I go through the I go through other textbooks and I I learn how their notation works and I show you how to differentiate between courses and subjects on understanding notation and stuff. Um, but this is for algebra, okay? If you if you’re in algebra or if you’re in calculus or higher, if you want to understand how little you actually know about math, go to the prerequisite chapter of an algebra book and look through it because you’re going to find out that you don’t know anything about math. All you know how to do is a little bit of arithmetic. And for the most part, all of the stuff in this section, you you don’t know any of it. And and you need you need to So, here’s this guy’s this guy’s image here compared to this guy’s image that I was just looking at. Where did that go? Whatever. He had all those circles. Same same kind of thing, a vin diagram sort of deal. Um anyways uh the these so when you’re reading a when you’re reading an algebra textbook you guys need to understand that algebra is the most complicated subject there is. It starts with algebra. You go through all the applications of algebra and then you come back to algebra starting with linear algebra then modern algebra and abstract algebra. Algebra is the most complicated subject there is but it’s the easiest to do arithmetic wise. It’s very basic operations which leads us to these operations. Operation right these these things here you need to start memorizing these things. You’re never going to you’re never going to stop using these things. Every semester after every semester after every semester, you are going to continuously be applying all of these rules and and uh axioms and properties over and over and over. So, uh to recap first on how to read and take notes from the from an algebra textbook, first of all, make sure you list make sure you review everything before and before the start of the book and at the end of the book. Okay? Review all of that. Do this in increments. Do it do that over a period of like 30 minutes. then come back and uh then we’ll start at chapter one if you’re in any other book. In this case, we start at the review section. For college algebra, it is very important that everything in the review section is taken very seriously. It’s not something it’s not a chapter you want to you want to like just brush over. I in college the professors will just brush over it. They’ll just toss it to the side and just get to the thick of problem solving. But that sets you up for disaster down the road. If you have to go into calculus and higher, that’s going to set you up for disaster. You need to have a thorough understanding of this stuff. However, the professor assumes that you have already gone through this stuff before the semester started. But most of you assume that the semester starts two weeks after the semester starts. You you understand what I’m saying? Most of you guys don’t start until the second week of the semester when you’re supposed to be two weeks ahead of the semester before it starts. And then you play the blame game. You’re like, “Well, nobody told me that.” And I’m like, “Nobody’s supposed to tell you anything. You’re a scientist. You’re supposed to do research to solve these problems. I’m trying to help. I’m trying to help you guys see that that you are responsible for your own actions. And if you’re not prepared, it’s no one else’s fault but yours. Okay? It’s not my It’s not my responsibility to tell you to be prepared for something. It’s you. It’s your responsibility to decide whether or not you’re a prepared person. You understand? You’re making the choice to have integrity, punctuality or not. And being unpunctual and skipping lectures and things and then blaming somebody else for not telling you you’re supposed to do this is not mature. It’s not something a company wants working for them. You need to take ownership and be prepared. Stop whining and stop complaining. Stop blaming. Stop victimizing yourself. the college algebra textbook. If you guys most of you don’t start opening textbooks till calculus or higher and you and now with all the videos on YouTube and stuff, a lot of you can just cheat all the way through linear algebra. And then what happens is when you get to linear algebra, you can’t read a textbook. And these textbooks require 15 different textbooks as prerequisites. And now you don’t have time to fix that problem. All you know how to do is memorize solutions from fake problems from the internet. These textbooks are designed the way they are for a reason, kids. Okay? The way you think education should be is exactly why you’re in college because you don’t know anything. If college should be the way you think it should be, then you would be in charge of it. But you’re not. You’re part of the process of becoming educated and you’re going against what is what you need to do, whatever. Um, okay. So, let’s let’s get this done. You’ve reviewed everything from the beginning to the end. Now, you’re ready to start working through the chapter. What I recommend you do is before before you start taking notes and reading the chapter, I recommend you make lunch or something and highlight every word in the chapter and have it played to you. Or just if you like to read physic, if you like to actually read, sit down and just read through all of it. Skim through all of it. I like to have it played to me because it’s just it’s just kind of, you know, you’d be you’d be shocked at how much easier it is to remember things when you’re not paying attention. I’m just having it played to me while I’m cooking or doing dishes or something and it just kind of like sinks into my head. It’s amazing. So then you do that. Then you come to chapter one. Okay. Before you start reading reading it, you go through and you collect all the bold words. All right? You collect all the bold words and then you write their definitions. Any bold word there is, you write out its definition. Don’t be concerned with whether or not you understand it or not. be concerned with the physical action of typing out that definition in your own words or verbatim. When you when you verbatim it, you’re taking it, you’re processing it, you’re shrinking it down. What you’re doing is you’re storing it in your head for later. You will not understand this stuff immediately. It will take time to understand it. Some of this stuff you may not, you’ll use it, you’ll apply it, you may not understand it for five years from now. Don’t worry about understanding it. Worry about the process of embedding it into your brain cells. Okay? So, so you go through first and you collect all the bold words and verbatim their definitions. Then you go through then you go back through and you collect all the formulas and equations that are in these boxes. Anything that’s in these boxes, you go through and you do the same thing. So you first in your word document, you got a an itemized bulleted list of the bold words with their definitions. Then underneath that, you have an itemized list of all the equations and formulas. Now you’re ready to start reading the book. Now you should do this in in intervals. 15 minutes, take an hour break. 15 minutes, take an hour break. Something like that. It sounds like a lot of work, but I’m telling you, but it’s not. It’s like warming up for exercise. You do it slowly, patiently in intervals. Then you do this way before the semester starts. You do this way before the lecture on the topic. You’ll be shocked that like your your school, your degree will be so easy. College is actually really easy as long as you’re prepared and you’re punctual. It’s very easy. It makes it so much easier. It’s not a challenge. It’s just a process. College isn’t difficult. It’s challenging, but it’s not challenging if you’ve turned it into a process. Okay. So, so now you’ve collected all the bold words. You’ve gotten all the equations and formulas. You’ve typed it all out nice, beautifully in Word, you got your document right there. The way I’ve showed you guys how to do these documents. Then next, next, you go to paragraph one. This is very important. This is where the learning starts. Okay? All you’ve been doing for leading up to this is warming up. Now, this is where the learning starts. You go to paragraph one. You read paragraph one. You do not move to paragraph two until you completely understand paragraph 1. Once you fully understand paragraph 1, you then move to paragraph two and repeat. You do this until you get to example one. When you get to example one, you you you write out the solution for the example in your word document until you understand it. Then you take a break. You come back and you try to solve it with pencil and paper like you would an exam. So you’re you’re writing the professional document which gets you ready for your gets your resume ready for your job. You’re getting experience being professional. You’re enhancing your knowledge. You’re evolving. But you write with pencil and paper to take the practice exams to prepare for the exam. These example questions in the reading are the questions that are most likely to be on the exams. They’re the ones that you should be doing for the practice exams. The doing the practice practice exams is not about guessing the right questions that are going to be on the exam. It’s about getting experience with detecting where you’re at with the information because you will realize how little you know in two seconds when you sit down to do an exam. And you need to know how little you know before the exam comes so that you can overcome that lack of knowledge and know what you need to know. Practice exams. Doing homework will get you really good at doing homework. Practicing exams will get you really good at taking exams. Your exams are the bulk of the grade. Don’t waste your time on homework. Okay? Do you you do this with the textbook before the lecture, then you go home and you’ll be able to do the majority of your homework in like five hours. Like you’ll be able to do your homework really quickly. And don’t waste your time trying to solve that one really long crazy problem at the end. Leave that one alone. Just go do the practice exams. If you if you get 50s to 70s on all your homeworks and A’s on all your exams, you will get an A in the course. If you get hundreds on all your homeworks and and C’s on all your exams, you get a C in the course. Doesn’t matter what your homework is. What matters is what you get on the last exam and the final exam on average from the average school. Okay? So now you’ve gone through and you’ve worked all the example questions one at a time until you can solve them on paper without referencing anything. If you guys if you think this is too much work, you need to question whether or not this is the right degree for you. You are supposed to be able to read this stuff from memory and analyze it without using chat GPT. You’re supposed to open one of these books up by the time you graduate, go to any theorem, read it, and apply it. You’re not supposed to have it all memorized. You’re just supposed to be able to understand it. ChatBT is not accurate when it’s explaining things to you. It’s not accurate. You can’t trust it. You have to learn how to trust yourself. All right? All of these things that are in these boxes, this this stuff, you need to be able to open up any book and look at it and read it and understand it. That takes years, okay? It takes years of what? Practice. It does not happen overnight. And you guys are like, “It’s so hard to learn from a textbook.” You’re not learning from a textbook. You’re gaining experience from those who came before you by lifting weights with your brain for a long time to become strong. It takes time. It’s It’s hard because it’s hard to lift weights. It’s what makes you stronger. You guys give up and you use Chad GBT. It’s like using a wheelchair to prepare for a marathon. It’s not going to help you. It seems like, yeah, a wheelchair is less work to get around. But you’ve got to actually run a 20 mile marathon or something. You probably want to be running. And kids, you don’t cram the day before the exam. That’s like going to the gym and working out for 10 hours the day before you got to run a marathon. You got to be prepared for the exam a week before the exam. My god, will your life be so less stressful and you’ll get so much better grades and you’ll enjoy college so much better if you’re ready for that exam a week before you have to take it. You’re g your life is going to be so much better. You just have to be prepared. It’s the initial push that’s the hardest. Getting getting the momentum going and being ahead of the class is the is the hardest thing to do. But that’s also what divides the really successful people from the people that are rarely successful. Being prepared, readiness. All right. Now the other thing about the algebra books is uh that um well any basically anything look anything that is in these boxes if you don’t have these memorized by the time you get to like linear algebra I mean you’re you’re in you’re in trouble. You need to have all that stuff memorized. You get you should be carrying these books around with you and just leisurely reading these things like all day and thinking about them all day. It’s going to take years and years to get this stuff in your head. You need to have all of that memorized. Okay? you know, the process of reading the book, taking the notes, doing that, working the problems. Then there’s Easter eggs in these things. The Easter eggs can sometimes come in the worked examples, like there’s special little tricks that you need to know. But a lot of times those Easter eggs, they come in the question bank back in the back here. Like in the back of the question banks, there’s like some type of formula you need to know. probably not at the very beginning part like that, but like if I go back to some further ones back here, sometimes in the question banks, there’s formulas that are Easter eggs. Like maybe something like this would be on the test or or here’s these questions here in the back. You need to familiarize yourself with everything everything in the book everywhere it is. You’re be you’re being tested on on your knowledge of what you’ve learned from these books, kids. You’re not being tested on your knowledge from what you got from Khan Academy or ChatBT. You’re being tested on your knowledge from these books that they give you. Most of you are just, you know, doing college completely wrong. Just completely wrong. All right. Here’s here’s a here’s an Easter egg looking formula right here. Like they might give you a question like this on the test. They in the in the lecture. They might talk about this question like 76. In the lecture, they do 76. On the exam, they give you 77. When you’re in lecture, you got to pay attention to what they’re doing. It’s very important you go to lecture because what they’re doing in lecture is going to tell you what’s going to be on the exam. If they’re doing 76 in lecture, they’re going to put 77 on the exam. If they’re working example two from chapter 3, they’re going to put example three from chapter 4. You know, they’re giving you what’s on the exam in class. They are giving you what’s on the exam in class. Okay? You’ve got to go to lecture for that. Um, but the Easter eggs are important. They they’ll pop up throughout the questions in the in the question bank. There might be an Easter egg in the columns over here. Easter eggs are just like little tricks. They usually start coming more along in calculus. Uh but uh there are still some in these books that you got to pay like right here. Here’s a perfect example. Like you guys haven’t done physics yet. They might give you a physics question in algebra where you just need to know the formula. And those formulas are right here in the question bank. Look at this formula right here. That’s an Easter egg. It’s in the question bank. You’re going to need to know that for the test. You’re not going to learn that from watching Khan Academy or CHACPT. You’re going to learn that by looking in the book. that CHBT is not going to know what your professor is going to put on the book, put on the test. You’re going to know what’s on the test by going to lecture and and thinking critically, strategizing, being strategic, getting into the professor’s head. Okay. So, so anyways, this is how you read a college algebra textbook. I’m uh if you’re if you’re following my website, following my progress here, what I’m doing is I’m just starting a new um structured flow for the ultimate crash course for plum majors here where you come here and I’ll add this lesson will be here under under algebra and you come here and you can see all these individual lessons I’m doing. I’m um I’m just structuring this is a new book I’m writing that it’s a little bit more tailored to students that have to be heavily ready for uh advanced math by junior year math, physics, and engineer students. It’s it’s more for people that that need to be ready for junior year or for adults returning to college that haven’t done math in a while or people that are interested in in just learning math. Um so this video will go right here. You guys can get uh access to this website right now for life if you want by uh picking up a copy of my uh ultimate crash course book, any one of them and the big ones. And uh I’m doing a lifetime access while I’m laying out the skeleton of this website. I have a lot of work to do over the next six months. I you’ll get my fiction books, too. You got to be 18, though. But uh just just so you guys know that this video will be organized right here with this book. And every video I do, I’m just going to do a couple videos every day writing this new book. I’m writing it live. I was writing it live. I’m I’m going to do pre pre-recorded videos now. I’m not going to do live anymore because whenever I do the live videos on here, it just the algorithm just messes up and it ruins my my views and stuff. Um, so I’m just going to stick with pre-recorded videos. And uh the primary the primary focus of this book is I take a book and I will take the book and I will talk about the book in here like I just did. I will show you what I’m pointing out from the books and then after this I will take a question from the book and I will solve the question using the book to show you guys. The whole purpose of this channel is to show you guys how to use textbooks. Okay. So once a week or so we’ll do a new textbook. All right. All right. Thanks for listening. If you can pick up a copy of my book or become a member, subscribe to my site or anything, I greatly appreciate it. This uh is only possible with your guys’ support. It’s a lot of work to do this. I can only do it when you guys show support. And please subscribe, like the video, and leave a good comment if you can. Have a nice day.