Got a few questions about my long term math goals.

Burned_Follower

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Well, I got into college because I wanted to work on rocket ships at spaceX in the future some day, so my focus was going to be in mechanical engineering, but after I finish earning a bachleors degree in ME in a few years, I plan to major in physics instead because that subject seems to fascinate me even more than rocket science. From what I've been told this is very common for folks to discover something even more interesting to study while in school.

Anyway, because of this I now have a 'specific' official long term math goal: I want to ultimately reach the level of math skill needed so I can 'explore' the math that goes into general relativity and quantum mechanics and plasma physics. I have a very long journey ahead of me to get to that level of epic math skills, considering where I'm at math wise right now...but I've already accomplished a lot in the last few years, so I'm feeling confident I can reach my goals if I work hard enough. :)

This is what I've accomplished so far:
-I used google and youtube and Khan Tutoring to teach myself basic math and some pre-algebra
-I then took a pre-algebra class at a technical college
-I then started attending another college online and as of this moment, I've worked all the way to pre-calculus.

Unfortunately, I'm quickly figuring out that online college sucks when it comes to math. My math teachers don't teach me anything. They only grade. And if I email them when stuck on something, they tell me to use tutorials that are hidden in the maze that is the college's online school interface called canvas.

After the third math class in a row at this online college, I finally began to realize that I'm going into student loan debt to pay for the privilege of teaching myself math. ...and I'm paying hundreds of dollars for college level math textbooks that I can check out at my local library for free.

So I left the college and now I'm continuing my math education FOR FREE. And I'm taking the money I'm saving, and I'm spending some of it on an online tutoring service whenever youtube, google, or khan academy material can't help me get unstuck on an equation that I'm stuck on. I need to work my way to calculus 1 or 2 anyway before I can officially start a major in engineering anywhere, so I'll go back to college when I'm done doing my pre-requisite level education for free lol....but when I go back to school, it'll be on an actual college campus this time where I can go to a physical class room and have a math teacher teach me math. At least that way, I can have free access to tutors if I'm going to a community college or something.

Sorry for the long intro but needed to show you where I'm at with math so I can ask my questions:

1. After I finish pre-calculus, what is the correct order of math subjects I need to study and master so that I can achieve my long term math goals of being able to explore the mathematics that goes into general relativity?

2. Same question for quantum mechanics

3. Same question for plasma physics

4. What exactly are the types of math that go into these three subjects anyway?

5. I have a TI-84 plus in my possession, but I still haven't used it that much. How do I learn how to use this thing? I also discovered a free TI-84 app that I downloaded my phone FOR FREE after I paid over 100 bucks for the physical calculator and I see no difference between them, lol. Did I just rip myself off? lol

6. Am I correct to assume that a textbook I find at my local public library on let's say Calculus 2 for example, and the textbook is like 12 years old, that shouldn't matter right? I mean, at the end of the day, calculus 2 is calculus 2, no matter what year the book has been published in, so why should I care if it's a new textbook or not?

7. What the heck is a scientific calculator and why would I need/want to get one? What's the difference between a scientific calculator and my TI-84? At what point in my journey in math would I even need one?

Thanks in advance for any answers on my math questions. :)
 

topsquark

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1. After I finish pre-calculus, what is the correct order of math subjects I need to study and master so that I can achieve my long term math goals of being able to explore the mathematics that goes into general relativity?
Have you taken something like College Algebra? I would then suggest Calculus (I through III, or IV depending on which college you are at), Differential equations, Advanced Math (such as Fourier series, special functions, Laplace transformations, approximation techniques, etc.), and Partial Differential equations. I think that's all the highlights.

2. Same question for quantum mechanics
Pretty much the whole core: Waves and Optics, Introductory Modern Physics, Calculus based Introductory Physics (essentially Mechanics), Introductory Electricity and Magnetism, Advanced Mechanics and Advanced Electricity and Magnetism. To get to things like Special Relativity, General Relativity, and Quantum Field Theory you are going to need a lot more Math. Plan on essentially having a BS in Mathematics (though you probably won't have the time to get the degree). Group Theory, Algebra (the real thing, not what you learn in High School), and Topology will be your friends.

3. Same question for plasma physics
I can't give you a full run-down but you will need some kind of Introduction to Materials Science and add Thermodynamics and probably Statistical Mechanics.

5. I have a TI-84 plus in my possession, but I still haven't used it that much. How do I learn how to use this thing? I also discovered a free TI-84 app that I downloaded my phone FOR FREE after I paid over 100 bucks for the physical calculator and I see no difference between them, lol. Did I just rip myself off? lol
Good! The only way to learn how to use it is to sit down with the instructions and play with it. The more you use it the better you can use it. I'd strongly recommend, though, that you learn how to do everything by hand first. The calculator is a tool and a resource... it is not a way to get around learning the material.

6. Am I correct to assume that a textbook I find at my local public library on let's say Calculus 2 for example, and the textbook is like 12 years old, that shouldn't matter right? I mean, at the end of the day, calculus 2 is calculus 2, no matter what year the book has been published in, so why should I care if it's a new textbook or not?
You can get the textbooks from anywhere and probably be good. But I doubt you are going to find Differential Equations and Partial Differential equations at your local library. I'd go to Barnes and Noble (or Amazon, or something) and see what you can do to get used textbooks. All of them. Again, it'll cost but you will want the references on hand, rather than having to go to the Library and use interlibrary loan to get a book for 2 weeks.

7. What the heck is a scientific calculator and why would I need/want to get one? What's the difference between a scientific calculator and my TI-84? At what point in my journey in math would I even need one?
A scientific calculator merely has extra functions like logs and trigonometric functions. (And their inverses.) In Math? You probably won't need one. In the Sciences, however, a graphing calculator will be critical. Not so much for the graphing (for the advanced stuff you will need a computer and something like Mathematica) but for both the function capability and the processing power for the calculations. So far as I know all graphing calculators also have programming capabilities, which allows you to bring your approximation techniques on the road with you. (Though now a days you can probably get a tablet to do it for you more efficiently.)

It's great that you are trying to learn the basics on your own but recognize that you are going to miss details. I've been teaching myself the advanced Physics and Math for some 25 years now and I find that I just can't get beyond a certain point. (I keep trying because I love the work and I'm a hard-*ss about giving in.) But it is what it is. The basics are critical. Try to find some kind of tutor at a college to keep you up to speed on what your future classes are going to require. I taught myself Calcs I through III in my Senior year of High School (I thought it was all Calc I) and though I got all the basics, I missed a lot.

-Dan
 

Burned_Follower

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Oh wow, I didn't know there was any calculus to explore beyond calculus 2! cool! Ok, please let me know if I got these subjects out of order(the order in which i'd study them, whether self taught or learning at a college):

1. Finish my pre-calculus textbook that I got from the school I recently left
2. Calculus 1-4
3. Differential Equations
4. Fourier series, special functions, Laplace transformations, approximation techniques
5. Partial Differential equations
6. Introduction to modern physics
7. Calculus based introductory Physics
8. Introductory Electricity and Magnetism, Advanced Mechanics and Advanced Electricity and Magnetism.
9. Group theory and Topology
10. Materials Science and Thermodynamics
11. Statistical Mechanics

Only thing I'm worried about when self teaching myself math is when I'm done with one textbook and going to the next that I accidentally study math out of order.

There is something I forgot to ask about algebra and I'll include it in this reply:
I never went to high school. I have a GED. But I heard that people learn pre-algebra, algebra 1 and 2 in high school, and in college, it's intermediate algebra, and college algebra.

But my experience ended up being:
1. some pre algebra through google and youtube
2. a basic algebra class at a technical college that my teacher at the time told me that the class really should be called pre-algebra
3. Two classes that utilized the same textbook I now own on algebra, which was an intermediate algebra and introductionary trig textbook.
4. Pre calculus

I never personally encountered anything called college algebra or algebra 1 and 2. I find this confusing, but the algebra that I actually learned wasn't confusing. So what happened? Did the education system around algebra change or something?
 

cbarker12

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2. Calculus 1-4
3. Differential Equations
4. Fourier series, special functions, Laplace transformations, approximation techniques
5. Partial Differential equations
6. Introduction to modern physics
7. Calculus based introductory Physics
I would say first calculus 1-3, then calculus based introduction physics. then teach yourself linear algebra (here is where some proof writing will come into play which will help you in Group theory and Topology and real analysis (proof-based calculus)) and then Differential equations (will have laplace transformations and other special functions), partial differential (will have fourier series and special functions). Finally introduction to modern physics.
 
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Burned_Follower

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I would say first calculus 1-3, then calculus based introduction physics. then teach yourself linear algebra (here is where some proof writing will come into play which will help you in Group theory and Topology and real analysis (proof-based calculus)) and then Differential equations (will have laplace transformations and other special functions), partial differential (will have fourier series and special functions). Finally introduction to modern physics.

so the order would be this then? :

1. Finish my pre-calculus textbook that I got from the school I recently left
2. Calculus 1-3
3. Calculus based introductory physics
5. linear algebra(this will help you with 'group theory' and 'topology')
6. Differential Equations(will have laplace transformations and other special functions)
7. partial differential equations(will have fourier series and special functions)
8. Introduction to modern physics
9. Introductory Electricity and Magnetism, Advanced Mechanics and Advanced Electricity and Magnetism.
10. Group theory and Topology
11. Materials Science and Thermodynamics
12. Statistical Mechanics
 

cbarker12

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3. Calculus based introductory physics
There will be some introduction to electromagnetism in calculus based introductory physics.
linear algebra(this will help you with 'group theory' and 'topology')
in Group theory, yes, you have to write proofs in group theory. Special types of matrices are groups. Linear algebra gives some tools on writing proofs. Topology is about proof-writing and set theory.
 

cbarker12

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Before 8, I recommend to learn some complex analysis (using complex numbers in a calculus setting), and group theory and topology.
 

Jomo

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Why would you finish a degree in Mechanical Engineering if you want to study Physics? I do not get this at all. I think that you should get your degree in Physics!

Math courses you should take/know.
Arithmetic/Prealgebra
Algebra
Trigonometry
Pre Calculus
Calculus 1-3
Differential Equations
Linear Algebra
Real Analysis 1-2
Complex Analysis 1

You can take calculus based physics before finishing calculus 3. You can take physics 1 along with calculus 1, same with calculus 2/ physics 2

Study physics from Halliday and Resnick. Classic book.

This list is so close to being a math major!
 

Burned_Follower

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Why would you finish a degree in Mechanical Engineering if you want to study Physics? I do not get this at all. I think that you should get your degree in Physics!

Math courses you should take/know.
Arithmetic/Prealgebra
Algebra
Trigonometry
Pre Calculus
Calculus 1-3
Differential Equations
Linear Algebra
Real Analysis 1-2
Complex Analysis 1

You can take calculus based physics before finishing calculus 3. You can take physics 1 along with calculus 1, same with calculus 2/ physics 2

Study physics from Halliday and Resnick. Classic book.

This list is so close to being a math major!

Ok, first of all, I didn't know there was even such a thing as a math major. That alone might help me choose which college in my town since math is going to be my focus for a long time. :)

As for the reason why I still plan to earn at least a BS in Mechanical Engineering, and then focus on math and physics afterwards is pretty big. This is going to sound absolutely insane, but if you google what I'm about to type it'll make more sense. :)

I originally got into college because ever since I was 2 years old(I'm 35 now) I dreamed of designing starships for a living. I never took this dream seriously and even called it a pipe dream all the way until 2018 when I discovered SpaceX and what they're up to. That's when I discovered that if one were to go to school, become a mechanical engineer, and work hard enough in the trade, that I could possible build a good enough track record as an engineer to qualify as a starship mechanical engineer, which in my opinion would be the closest thing to being a real life version of Scotty from star trek. It's not every day that you discover that if you work hard enough that your very first dream can come true.

But last year, I made an even bigger discovery: I discovered that in the 1990s, Dr. Miguel Alcubierre, a physicist, published a paper that proves that warp drive is actually possible. So warp drive has graduated from being nothing more than a scifi prop, to an actual scientific theory. As I continued to fall down the 'warp drive rabbithole', I also discovered that a physicist and engineer at NASA, Dr. Harold White(also known as Sonny), continued to R&D warp drive theory. He became so convinced that warp drive can be invented within the next 100 years that he published his own paper called the Alcubierre/White warp drive. Beteen the time I learned all this and well into this year, I discovered that another scientist called Dr. Froning, also continued to develop warp drive theory and he published a paper. His work is called the Alcubierre-Froning warp drive. And I discovered another scientist called Dr. Musha who did the same thing. His work is called the Musha Jump drive. I also discovered that Dr. Harold White became so invested in interstellar R&D that he no longer works for NASA and is now part of an orginazation called Limitless Space Institute, which is an organization in Texas that exists for the purpose of R&Ding interstellar propulsion. I also learned of another organization called AsteronX that's doing the same thing.

...But my rabbithole didn't stop there. These discoveries let me to ask myself the question, "Can I research and develop FTL(faster than light) technology for a living instead of R&D rocketships at spacex?" If the answer is yes, then I would much rather do that. Elon Musk's starship will take the better half of a year just to get human beings to Mars, while a warp drive can get you to the next solar system in a matter of hours or minutes.

So I used the internet to track down Dr. Alcubierre. I found that he is teaching at a school in Mexico. I used a translator plugin on my browser to navigate the school's website and found his email. I then sent Dr. Alcubierre an email, asking the question that I asked myself. I asked him what must I study to be able to comprehend his theory on warp drive, and what must I study so I can further develop warp drive theory so it is matured enough to become an engineering puzzle to solve and not just a physics problem to solve. ...and to my surprise, he emailed me back! And he was nice enough to tell me what I needed to do. Dr. Alcubierre told me that in order to fully understand warp drive theory, I need to fully understand General Relativity. He went on to warn me that this is no small feat because most physicists don't fully study the subject out when they are in college.

I then found the 'contact us' section on Limitless Space Institute's website, and sent them an email, saying pretty much the same stuff I said and asked of Dr. Miguel Alcubierre, hoping I can get lucky and be able to communicate with Dr. Harold White. I also included in that email, telling them that I already have Dr. Alcubierre's warp drive paper downloaded on my computer and explained how Dr. Alcubierre communicated with each other over email.

A few days later, I get an email back from Dr. Sonny's secretary, saying that Dr. White wants to have a zoom meeting with me! I was so stoked over this! The next week I had an hour long zoom meeting with Dr. Harold White himself and he explained to me that warp drive R&D is in such an infant phase that there's no such thing as a trade in Warp Drive R&D. So I would basically would have to be a pioneer. I learned from him that the education he earned over the years to be able to be a Warp Drive R&D pioneer himself was a Masters in Mechanical Engineering, and advanced degrees in physics.

I then asked Dr. White this question, "I have a hypothetical question for you. Let's imagine that 50 years from now, warp drive has been invented and you have engineers who are R&Ding warp drives for a living, what kind of education/experience would you think these kind of people would need in order to be able to do their jobs?" I found it a perfectly logical question to ask him because this guy is literally the world's top mind on warp drive R&D. I explained to him the reason I'm asking him this question is because 15 years ago I didn't bother going to college, despite wanting to design starships for a living because I believed that starships would never exist in my life time. And I now see how huge of a mistake that was for me because here we are, with a shipyard in Texas, where they're pumping out and testing starship prototypes on a literal starship assembly line. I then told him that I don't believe that warp drive technology will exist in my life time right now...but since I was proven dead wrong about starships existing, then I might also be wrong about warp drive not existing in my life time. So I want to prepare myself for any opportunity in the future to research and develop warp drive technology as an occupation...even if that means that I would have to be a pioneer and not a tradesman in that field.

Dr. Sonny White's advice to me was very simple. What he advised I'd do is this:

1. Earn a bachleor's degree in Mechanical engineering.
2. When it comes time to work on a master's degree, that's when I should decide whether or not to pursue a masters in ME or physics. He said to
not make a decision on which until I'm done with the BS degree in ME because of all the little things I'll earn about math, science, physics, etc along the way, and that information will help me make my decision by the time I earn a BS degree in ME.
3. He told me that the answer to my hypothetical question is this:
"It's general relativity that tells us that it's possible to create a space warp using negative energy density, but it's quantum mechanics that gives us an idea how to do that.". He also said that this person in my future hypothetical scenario would also be educated in a scientific theory that hasn't been invented yet. He said that there are scientists all over the world trying to invent this new theory in physics right now. When he described it, he said they'll be a new theory published in the near future by someone that'll unify both General Relativity and Quantum Mechanics and it'll give us more pieces to the puzzle that'll help us invent warp drive.
4. All three of the FTL experts I talked to all told me that I won't be able to fully study general relativity or the other two subjects if I don't explore the math that goes into them, thus me diving into the deep end of math.

As for my interest in plasma physics, that's mostly due to Dr. Harold White telling me that star trek's idea of using a matter/anti-matter reaction to power a warp drive engine is a really bad idea and that a real life equivilant of a warp core will be something more along the lines of a fusion reactor. He also told me about a really be fusion reactor prototype that's being built right now and said that due to how technology evolves, it's only a matter of time that fusion reactors will become small enough to put in a starship for the purpose of powering a warp drive.

So bottom line, 15 years ago I said that starships will never exist in my lifetime and I was proven wrong. Today, I'm saying that warp drive will never exist in my life time. So I originally got into college to work on rocket ships, but now I'm continuing my education because I believe that 15 years from now, I will be proven wrong about warp drive as well. After watching SpaceX launch and successfully land humanity's first starship prototype this year, the word impossible has lost all of it's credibility with me. :)
 
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