Before You Start a Math Degree in College
This lesson explains one of the most important ideas for STEM students entering college mathematics:
You are in college to study the textbook assigned to you.
The lesson argues that mathematics in college is not simply a collection of random arithmetic problems or internet tricks. Instead, each textbook represents its own structured subject containing:
- Definitions
- Properties
- Axioms
- Theorems
- Notation systems
- Rules of communication
- Proof structures
- Conditions and assumptions
Students are encouraged to stop thinking of “calculus” or “algebra” as vague generic topics and instead recognize that:
Thomas Calculus, Stewart Calculus, Sullivan Algebra, Larson Precalculus, and David Lay Linear Algebra
are all separate subjects with their own internal structures and communication systems.
The Textbook Is the Subject
The lesson strongly emphasizes that students are expected to learn the assigned textbook directly rather than replacing it with random internet videos, AI generated solutions, or unrelated external materials.
If students cannot learn from textbooks, the lesson argues that they may struggle significantly in advanced mathematics, physics, and engineering courses where textbook literacy becomes essential.
Students are encouraged to:
- Read definitions carefully.
- Study theorem conditions.
- Understand notation.
- Learn the properties and rules formally.
- Recognize how chapters connect together.
- Use the assigned textbook consistently.
The Importance of Definitions and Properties
A major point throughout the lesson is that many students treat mathematics as simple arithmetic rather than a formal language system.
The lesson explains that mathematical statements rely on formally defined properties such as:
These are not “common sense” statements. They are formally defined properties within the mathematical structure of the textbook.
Students are encouraged to answer mathematical questions scientifically by:
- Identifying the textbook or subject.
- Referencing the appropriate property or theorem.
- Citing the formal mathematical structure being used.
The lesson argues that this is how professional mathematicians, scientists, and engineers communicate technically.
Why Review Sections Matter
The lesson strongly emphasizes the importance of the review and prerequisite sections of algebra and precalculus textbooks.
According to the lesson, many advanced difficulties in:
- Linear algebra
- Differential equations
- Calculus
- Physics
- Engineering mathematics
occur because students never fully mastered the foundational review material from earlier textbooks.
Examples discussed include:
- Rational numbers
- Irrational numbers
- Reflexive properties
- Symmetric properties
- Transitive properties
- Substitution principles
- Additive inverses
- Multiplicative identities
The lesson argues that these foundational ideas continue appearing repeatedly throughout advanced mathematics.
Different Textbooks Organize Material Differently
The lesson compares Sullivan Algebra and Larson Precalculus to demonstrate that even when the arithmetic appears similar, the organization, terminology, theorem numbering, and presentation style can differ significantly between books.
Students are warned not to randomly combine properties, notation systems, or theorem references from unrelated textbooks while studying a different assigned subject.
The central argument is:
You are studying the assigned textbook, not all textbooks simultaneously.
The Purpose of P.L.E.M. Academy
The lesson explains that P.L.E.M. Academy was designed to teach students how to properly use textbooks through structured examples, guided solutions, live sessions, textbook walkthroughs, and professional communication systems.
Jonathan demonstrates how problems are:
- Cited directly from textbooks.
- Worked through step by step.
- Compared against official solutions.
- Formatted professionally using LaTeX and WordPress.
- Used as communication training exercises.
The lesson explains that the goal is not simply obtaining answers. The goal is learning how to think, communicate, and study professionally.
“You are in school to study that textbook.”
Final Message
The lesson concludes with a strong reminder that advanced mathematics and physics require years of disciplined study, textbook reading, communication practice, and consistent effort.
Students are encouraged to honestly evaluate whether they are willing to dedicate themselves to the assigned textbooks and the workload required for STEM fields before committing fully to a mathematics intensive degree path.
Transcript reference: :contentReference[oaicite:0]{index=0}
Original Transcript
All right. So, this is a uh before starting math in college playlist that I’m doing here. And I just want to I want to show you guys some very important stuff before you start math in college. You guys are in college to study the textbook that is assigned to you. If you don’t have a textbook, read your syllabus. Likely you have a textbook. If you still don’t see the textbook in the syllabus and you’re using online homework, the online homework platform likely tells you where the textbook is. If for some reason you still don’t have a textbook, I would ask the professor what source they are using when they are doing their math. And if they don’t understand that, not all professors are intelligent guys. Just because they went through the motions and did an original discovery or contribution does not mean that they are know-it-alls like whatever you are in college to study the textbook that is given to you. Algebra is a topic. Calculus is a topic, not a subject. Thomas’s calculus, that’s a subject. Stuart’s calculus, that’s a subject. This person’s calculus, that’s a subject. David Lei, linear algebra versus Gilbert Strain, linear algebra versus engineering differential equations with linear algebra. Subjects, subjects, subjects. These are all subjects. You are given the book to study that subject. A lot of you will encounter the Sullivan Algebra and trigonometry textbook. This is a subject that you are studying. You are in college to study this book. If you think it’s too difficult to learn from the book, you need to leave this field because you will waste your time. I’m not saying that to shame you or judge you. I’m telling you that if you don’t want to take on the challenge of learning these textbooks, this is not the right place for you to be. That you’ll be much better off in like a business degree. You can use Khan Academy to get through your algebra and calculus courses and never have to do math again and make a lot of money as a business major. It’s a much better way to go. Okay, to do math in college as a STEM major, you have to understand how to read these books fluently. You also should understand, look at all these people that were involved in this book. This is what I do with Plym Academy. For those of you who critique the work I do in this book and join the live sessions, your name is put in my book just like this. You get credit for the book. You get the book when it’s published and you get your own website to host all your work and you get to write your own book and you get to keep the rights to your book and make all the money off of it. It’s a great service I’m offering for you guys. [snorts] But before before you start a math degree, okay, before you start a mathematics degree, you need to understand what the textbook means. The textbook is a subject that contains rules and conditions that you have to follow. Definitions. There’s properties, there’s rules, there’s axioms, there’s definitions, and there’s theorems. The theorems are comprised of the definitions, and the definitions are comprised of all the everything else. The the rules and properties and all that stuff. These are definitions. Okay, here’s your first thing. A rational number. I meet kids that are in linear algebra 10 courses down the road that still don’t know what a rational number is. And they think irregardless is a word. And they think 1* zero equals zero is because they can take apples out of magical space and put them together with no space and apples just magically disappear. It’s a problem. If you if you’re in if you’re in a junior senior level math course and you still think a rational number is um what an irrational you think an irrational number is what a rational number is, you’re in trouble. Okay. The uh the prerequisite or review section of an algebra or pre-calculus book is the most important section for you at any level of math. The majority of you would not be able to comprehend or understand any of this in the review section. You got you guys a lot of the math that you come across later on is review of the review section of an algebra book and you guys are like nobody told me this, nobody ever said this, nobody ever told me that. For example, reflexive property, symmetric, transitive, principle of substitution, blah blah blah. This is in the review section of an algebra book and you guys get to like linear algebra and you start getting mad at the professor because you chose not to read your textbooks in algebra and you want to blame them for all of your laziness. Before you start a math degree, kids, you need to understand that the review section or the pre the preface sections of the book are the what contain all the rules. Here’s the properties you’re allowed to use. These are properties. Why does one why does 1* a equal a? It’s it’s a property. It was defined that way. 0 plus a= a plus 0= a. It was defined that way. These are called multip multiplicative identities. Additive identities. Additive inverse. The additive inverse property. I ask you why does a plus I go why does a minus a equal zero? And you’re like uh that’s common sense. And I go no it’s not. Your response should be immediately to which subject are you referring? And I’ll say oh Sullivan algebra. and you go, “Oh, according to the additive inverse property, 5 a plus parenthetical negative a is equivalent to zero.” That’s the answer. You cited the source, you cited the subject, you provided the correct response. That’s how a scientist would respond to any question. First, I ask you a question, your first response is to which subject are you referring? Then I would tell you which subject. Then you would reference the property rule definition theorem and that’s how you answer the question doing arithmetic. What you guys when you get guys later on here you’re just doing a bunch of hardcore arithmetic in these in these um later on in the chapters. You guys get caught up with arithmetic and puzzle solving and you ruin your education because you think let me get a little further down here to something else. You guys think that algebra is just doing a whole bunch of arithmetic. It’s not. That’s just that’s what a calculator is for. You guys, algebra, college, math is about understanding how to use all of these things that are in the boxes. It’s about knowing all of these words that are bold. It’s about understanding how everything in the book ties together. You can’t just take questions from another book and solve them with another book. you you might get the same answer coincidentally, but all of the rules and properties and theorems are different because in this book, property 5A, that doesn’t necessarily mean that’s the same property in this book. A different book I go to um let’s take a look at uh where’s the Steuart calculus pre-calculus?
Uh that’s calculus calculus. I’ll just look at the algebra one. That’s Oh, here’s the Ron Larson pre-calculus. Pre-calculus is the same as algebra with trigonometry. Okay. So, I come here and we’ll look at um we’ll look here in the pre-calculus additive additive inverse. Okay. So, what what does their additive inverse come at here in their book? it comes as a bold word and then they tell you I don’t know let’s see furthermore the additive inverse they introduce it as a bold word situation there then they show you what it is and then here here’s your additive inverse it’s not property 5A it’s under definitions of subtraction and division and it is here multip additive inverse here property 1 2 3 4 5 6 7 8 N property nine
or did they actually hold on right here property additive inverse these are different that’s uh that’s negation inequality uh they don’t they don’t identify it as an individual property. So yes, you guys, what you need to understand is yes, the the arithmetic is is generally the same algebra course to algebra course. But when you’re actually doing these questions and you’re referencing things, if you’re referencing information from this book and you’re in the other book, you’re doing it wrong. You are in college, you are in college to study these books, not you don’t need to study all of them, but once you understand how one of them works, then it’s that much easier to understand how all of them work. So here is they got the additive inverse written differently in this book. I mean it’s the same math and everything, but the point is is that when you’re doing these books and you’re going back and referencing all the theorems and definitions, they change but book to book because it’s different subjects. You’re not at your college to study this subject. You’re at college to study this subject, the Sullivan subject. So before you start math and college kids, reality check. If you can’t dedicate yourself to the textbook that’s been assigned to you, then you’re in the wrong place because you are there to study that book and how that book works and only that book. The book, the book, the book. Okay? I’m going to walk you guys through understanding these books. That’s what Plem Academy is all about. Plem Academy is all about showing you guys how to use textbooks. I show you how to do it. This is what I do. This is an example of a series power series sequence, second semester calculus. Okay? I take the question from the book. I cite the book. I get the answer from the book. So there’s no issue with your pride and ego about getting that answer. Here’s the answer. You don’t need to have your pride. Nobody cares about the answer. A calculator can do that. I give you the question. I give you the answer. Now your job is to fill in the blank. If you can, then you compare it to my work to see if it comes out professionally. That’s one thing. I show you guys how to use the textbook. This is how this is how you should be doing your homework like this. But there’s a way to write it on exams. So I will I will show you guys that in the next video. the difference between doing your homework and writing exam solutions. All right. Anyways, so uh before you start math kids, have a reality check with yourself. If you leave the textbook or you left the subject, you’re in school to study that textbook. If it’s too hard for you, you’re in the wrong field. There’s no shame in that. Okay? No shame at all. Do not feel like you are losing pride because you leave math or physics. You’re making the right decision. This is a ton of work. It takes decades. You will not make much more money than anybody else in any other field. Okay? You’ll work really, really hard. You’ll study harder than anybody else. You’re not going to make more money. You’re going to be just as stable as anybody else with any other job. It’s about you individually that you get paid a high paying job based on you, not your education. Okay? All right. Have a nice day. Don’t forget to subscribe. If you guys can purchase one of my books, become a member to this YouTube channel, leave a donation, I greatly appreciate it. Without your support, I cannot do this. Uh the best way to support me is by joining Plem Academy research position or internship position so I can guide you through to your resume and writing your own book and everything.