How can I tell if Im good at "Real Math"? + Emphasis anxiety

[Roberthree]

Hello forums. I've finished my time at community college where I've finished the calculus line, differential equations, and an intro to logic class. I aced them all, and was chosen to be a math tutor for the school. In the fall, I'm transferring to a university, where I'll be taking a 300 level statistics course (I've never done an ounce of statistics in my life) and linear algebra to start off my major in mathematics.

I think I'm decent at math, but I feel like about 90% of that is me faking it. I've heard on this forum and other forums that most of what I've done isn't "real math" and that scares the hell out of me. What if I've been building up to something that I'm actually terrible at? I can explain the how and why of everything I've done (and I've had to, with the tutoring and all) but the thought of figuring it all out MYSELF sounds impossible. I've heard that I essentially have to re-prove all of calculus at some point in my major and I wouldn't even know where to start on that.

Additionally, I've been looking into statistics a bit. I've never done anything with it, but as far as I can tell it's the best emphasis for a math degree as far as jobs are concerned. The stats emphasis and the general math emphasis are only about 4 classes off and it wouldn't be very hard to major in one and minor in the other. Is there any real advantage to doing that?

Ehhh this whole ordeal confuses the heck out of me. Every time I pick a major I get convinced by someone or something that I've picked wrong. I'm really quite terrified that I'm doing the wrong thing with my life and I don't wanna be thousands of dollars in debt with a useless degree or a bunch of classes that I can't pass because I'm no good at the subject.

[gorcee]

I think I'm decent at math, but I feel like about 90% of that is me faking it.

Welcome to the world. Impostor syndrome is common, but it's (possibly increasingly) normal. The only thing you can do is try, and to periodically re-evaluate your priorities. You've been good enough so far, obviously. But you're uncertain if you're good enough to go forward. Think about it in a different way. Look forward; rather than completing an assignment to a satisfactory degree for the short term, look ahead, and see if you're learning well enough to position yourself for the future. Read the next chapter in the book. Look at the next course in the sequence. It's just a matter of perspective. You're anxious now because you're making a big step. But if you make it a habit to keep looking into uncertain territory, it becomes less intimidating.

Regarding career choices, statistics certainly has applications, so it's a valid route, but it's far from the only one. In fact, if you do go a statistics route, you somewhat limit your career options. Most companies don't casually employ advanced statistics; either they hire an expert, or they don't. Likewise, most companies aren't sitting on unsolved statistics problems. There are lots of ways to employ them, particularly in health sciences, but just be aware that having a stats background doesn't give you some kind of magical weapon that X department at Z Corp needs to succeed.

Math has lots of career potential, particularly applied math. All of the engineering sciences are built on dynamical systems, and most practical implementations of algorithms involve linear algebra to some degree. Mathematical modeling is something that can apply to every field, and having a background in math allows you to adapt easily to fields outside your area of expertise. An applied mathematician is often an asset to SMEs (subject matter experts) in other applied fields: a corrosion expert, for instance, might not understand what an L2 space is, but you will. Likewise, you might not know how the Nernst-Planck equation applies in some particular application, but you'll know the best way to develop ways to solve it.

I'm biases (pun intended), but I feel that an applied math focus with a strong coursework background in stats is a fantastic undergraduate experience that can open you up to doing real-world research, right out of the gate, in many areas: small/large business, government, post-graduate work.

Finally, don't worry about what you don't know now. You have your entire lifetime to learn. Worry about where you want to be, and figure out the path to get there. Everything else is just an obstacle that you will be able to overcome.

[Snark]

I aced things in high school and community college as you did and tutored many students as you did as well. I received my Associate in Arts degree at the same time I graduated high school. I then transferred to the University of Central Florida and majored in Statistics with a minor in Actuarial Science. I stayed away from a regular Mathematics degree because, while I love math, I didn't see any viable career options that would be available before I received at least a Master's degree (or perhaps even a Doctorate). I chose Statistics because it was close to pure mathematics, and I minored in Actuarial Science because the actuarial career sounded quite exciting. I graduated from UCF with a 4.0 GPA and my diploma in May of this year.

Before I transferred to UCF, I had only taken STA 2023 (Statistical Methods 1), one of the most basic stats class one can find. I was a little nervous about college as you are now, but as much work as it was, it was a pleasant challenge and not overwhelming. For comparison, I received a 760 on the math portion of the SAT the first time I took it.

I wish you the best of luck and encourage you to strongly consider majoring or minoring in statistics. It is close to pure math while having many practical applications.

If you have any more specific questions, please ask me! I don't want to brain-dump too much and end up being off on a tangent.

[Roberthree]

I pulled out my course catalog, the applied math and general math degrees look very similar. What are the notable differences?

[z4lis]

Hello forums. I've finished my time at community college where I've finished the calculus line, differential equations, and an intro to logic class. I aced them all, and was chosen to be a math tutor for the school. In the fall, I'm transferring to a university, where I'll be taking a 300 level statistics course (I've never done an ounce of statistics in my life) and linear algebra to start off my major in mathematics.

If you can ace an intro to logic class, you can probably deal with proofs, which seem to give the most trouble with advanced math courses. You can also probably deal with the abstraction, as well.

I think I'm decent at math, but I feel like about 90% of that is me faking it. I've heard on this forum and other forums that most of what I've done isn't "real math" and that scares the hell out of me.

I feel like I'm "faking it" quite a bit, and I'm about to go to grad school for math. It's not unique to you.

I've heard that I essentially have to re-prove all of calculus at some point in my major and I wouldn't even know where to start on that.

You don't have to! That's why you take a class with a book and a professor. You'll go through and study the foundations of calculus much more rigorously, but you don't have to come up with everything on your own. That would be absurd! Not even the most brilliant mathematician can think of everything.

[CCC]

I think I'm decent at math, but I feel like about 90% of that is me faking it.

There's a simple test that will tell you if you are, in fact, faking it or not.

Are you getting the right answers, consistently? If yes, then you are not faking it. If no, then I'd argue that you are not 'decent at math'.

Therefore, given that you are decent at maths, you can not be faking it. Maths is the process of moving, in logical steps, from the problem to the solution; if you are getting the right solution, then it doesn't matter if you're doing it the same way as the guy next to you - most, if not all, problems have many different ways to get to the solution.

I've heard on this forum and other forums that most of what I've done isn't "real math" and that scares the hell out of me.

And if you go to formula one racing forums, I'd bet you'll find people who tell you that it's not "real driving" if it's not on a race track and trying to win. Personally, I'd be dead scared of going as fast as a racing driver, but that doesn't mean that me driving down to the shops is not "real driving".

Basic arithmetic is as much "real math" as any other type of math, and I suggest you ignore any formula-one math drivers who try to tell you otherwise.

What if I've been building up to something that I'm actually terrible at? I can explain the how and why of everything I've done (and I've had to, with the tutoring and all) but the thought of figuring it all out MYSELF sounds impossible. I've heard that I essentially have to re-prove all of calculus at some point in my major and I wouldn't even know where to start on that.

Right. It's more likely that you'll be shown the proofs, they will be explained to you, and you will be expected to understand them. With the help of your professor.

Ehhh this whole ordeal confuses the heck out of me. Every time I pick a major I get convinced by someone or something that I've picked wrong. I'm really quite terrified that I'm doing the wrong thing with my life and I don't wanna be thousands of dollars in debt with a useless degree or a bunch of classes that I can't pass because I'm no good at the subject.

Every major's terrible. You need to decide what you want out of your major, and then find the major that most meets those aims and goals. For every major, someone will be able to find something bad about it; but that should be balanced against the benefits of taking that major.

[gorcee]

I pulled out my course catalog, the applied math and general math degrees look very similar. What are the notable differences?

Applied math programs generally focus on two things: methods and applications. Applied math courses teach you how to connect abstract mathematical principles to model real-world problems. They also teach you ways in which to frame, approach, and solve problems that would appear in applied domains.

Some things that applied mathematicians would do:

Uncertainty analysis (dealing with physical problems that have random, unmeasurable, or unknown quantities/parameters)
Inverse methods (taking data that was measured, say by an MRI machine, and attempting to compute the process that generated that data, even when the inverse of that process is ill-defined)
Physics modeling (modeling non-linear dynamical systems: most non-linear systems cannot be solved closed-form, and doing long-term computation of the system is computationally unfeasible, so determining the behavior of the solution, even when it cannot be found, is useful)
Algorithm development (computational power continues to increase, enabling innovation in the ways we handle models, simulations, and data)

Pure math curricula generally emphasize the abstraction and proof of concepts, including formal analysis (proving calculus from scratch, which isn't that hard), the study of the concept of spaces and their properties (aka topology), algebra, and so on.

I can't speak for your university, but it sounds like a "general math" program would likely expect you to do about 50/50 in applied/pure math, to give you a decent background in both. So you might be looking at Vector Calculus, ODEs, Real Analysis, Linear Algebra, Abstract Algebra, Complex Analysis as a typical 3rd-4th year curriculum. Sprinkle in your extra-departmental requirements, and that sounds like par for the course for an undergrad program of study.

[theodds]

I think it's promising that you aced logic, though I'm not sure what a CC logic course looks like. CC courses an be far easier than university. It wouldn't be shocking if you found out you simply couldn't do (say) abstract algebra and end up being unable to pass on multiple trys; you certainly wouldn't be the first in your shoes. For what it's worth, a popular math forum that handles math at all levels was founded by a passionate high school student that last I heard had given up on a math major because he just couldn't pass some courses.

That's the hard truth. But it doesn't have to be a catastrophe IF it comes to that. I tend to recommend either doubling up and doing both applied (or CS, or Statistics, etc) and pure math if you are passionate but want to hedge, or else just doing applied if you aren't passionate.

[Something Awesome]

Hello forums. I've finished my time at community college where I've finished the calculus line, differential equations, and an intro to logic class. I aced them all, and was chosen to be a math tutor for the school. In the fall, I'm transferring to a university, where I'll be taking a 300 level statistics course (I've never done an ounce of statistics in my life) and linear algebra to start off my major in mathematics.

I think I'm decent at math, but I feel like about 90% of that is me faking it. I've heard on this forum and other forums that most of what I've done isn't "real math" and that scares the hell out of me. What if I've been building up to something that I'm actually terrible at? I can explain the how and why of everything I've done (and I've had to, with the tutoring and all) but the thought of figuring it all out MYSELF sounds impossible. I've heard that I essentially have to re-prove all of calculus at some point in my major and I wouldn't even know where to start on that.

Additionally, I've been looking into statistics a bit. I've never done anything with it, but as far as I can tell it's the best emphasis for a math degree as far as jobs are concerned. The stats emphasis and the general math emphasis are only about 4 classes off and it wouldn't be very hard to major in one and minor in the other. Is there any real advantage to doing that?

Ehhh this whole ordeal confuses the heck out of me. Every time I pick a major I get convinced by someone or something that I've picked wrong. I'm really quite terrified that I'm doing the wrong thing with my life and I don't wanna be thousands of dollars in debt with a useless degree or a bunch of classes that I can't pass because I'm no good at the subject.

I'm halfway through grad school and I still feel like I'm faking it. All that matters is that you love it. Love math, and the rest will follow. Maybe "real math" is entirely different from what you're used to, but dive in and, if you enjoy the material, you'll figure out how to do it.

"Reproving calculus" is sort of the aim of a class in real analysis, and it'll probably be more like a "guided tour" than dumping it all in your lap at once.

Also, if you end up not loving statistics, it doesn't mean you're bad at math either. Math is like pie. There are all sorts of particular kinds of math, and to me, statistics is like... chocolate cream pie. Not really my thing, and I'm glad some people like it, but I'd rather have set theory and cherry pie.

[Roberthree]

I think it's promising that you aced logic, though I'm not sure what a CC logic course looks like. CC courses an be far easier than university.

The logic class I took started out with informal fallacies and valid/invalid arguments. Then we abstracted the arguments into a symbolic form, Then we did truth tables to prove/disprove validity and invalidity. Then we learned a bunch of logical manipulations like the Modus Tollens and Disjunctive Syllogism and a ton of others that I don't remember off the top of my head. We used those to prove the validity of some longer arguments.

[coffeesneeze]

As others in this thread have said the feeling of "faking it" is normal. You will likely have to memorize a formula here or there for a test before "really" understanding why it's true. Whenever I do this I feel like I'm faking it but that's ok, it's a temporary fix to buy myself some time to "really" learn it later.

Also, I would suggest shrugging off people who make a distinction between "real math" and other math ("fake" math??). If you are having fun learning math keep doing so, it just gets better and more interesting. Usually when people talk about fake math they are criticizing the over-emphasis of calculus in most undergrad curriculums. They are right, it is overemphasized. However, I happen to think calculus is a lot of fun, and I love it even more now that I've taken a few analysis classes and checked to see that it actually works. (spoiler: it works!)

[sam_i_am]

Every Majors Terrible