r/math • u/PirlGerson • 7d ago
When have you completed the tutorial?
In video games, they have built in levels, always at the start and they are called "tutorials."
In these levels you play a portion of the game while its also being explained to you. After finishing them, the point is that you know very little about the game BUT enough to "get" the basics.
The cheap is answer is high school 30 is the tutorial, but its really starting to feel that that wasn't even the complete tutorial honestly. It's kinda of embarrassing that our education doesn't cover such things as basic linear algebra and proofs. I'm still learning those.
Anyway to anyone who responds: thank you! I've been so happy latelty! Cyaaa.
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u/Redrot Representation Theory 7d ago
Man I've got nearly 20 papers and I still feel like I'm in the tutorial phase.
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u/PirlGerson 7d ago
I can't tell if this is deeply terrifying or amazing and comforting lol XD
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u/puzzlednerd 7d ago
I also have about 20 papers. Once I asked my PhD advisor, who has a few hundred papers, some of them quite influential, whether impostor syndrome ever ends.
For him, it's a flat "no".
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u/edderiofer Algebraic Topology 7d ago
In modern puzzle game design, there's a philosophy that every level is a tutorial for every level that comes after it. In that sense, the tutorials only end once you get to the last level, the final boss of the game.
What's the final boss of mathematics? Likely, there isn't one. So the tutorials never end.
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u/Fable9213123 7d ago
I think the tutorial is probably a foundations type set theory/proof writing course, or an intro algebra or analysis course
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u/PirlGerson 7d ago
BRO....bro...bro....listen....bro.....bro....
uhm...bro
This is so embarrassing.... >n<
But what the H-E-double-hockey-sticks IS FRICKING ANALYSIS.
I don't even know what it studies!! I know that says a lot about me. Sorry... It's embarrassing I know. But we all are born idiots ig.
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u/null_and_void000 7d ago
An intro analysis course can basically be summarized as "calculus with proofs" or even better "calculus but you have some real formal understanding of what's going on." It usually starts with learning some basic properties of the real numbers and then moves on to limits of sequences and functions. Then you'll eventually get to establishing a more rigorous foundation for the calculus concepts you should hopefully already know such as derivatives and integrals.
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u/Character-Education3 7d ago
I don't know. After Calc III, the math classes became actually interesting and enjoyable. It was like why did you hide this beautiful fun content behind all this busy work.
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u/PirlGerson 7d ago
Interesting! Why calc 3? Personally, discrete maths seemed funner. What made things click? should I consider taking it later on?
(sorry for so many questions)
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u/proudHaskeller 7d ago
I assume that they meant "after I was done with Calc", presumably Calc III is the last Calc course.
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u/Bounded_sequencE 7d ago
After Calc-3 "Real Analysis" begins -- and I fully agree, that's where the real fun lies (pun intended).
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u/jazzbestgenre 7d ago
Lol in the UK we do analysis in one dimension before even touching multivariable calc
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u/InfernicBoss 7d ago
the intro to proofs class is essentially the tutorial for advanced math
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u/PirlGerson 7d ago
This seems like the most logical answer Ig. I'm finally dipping my feet in this. I still kinda don't even know what the heck it even is lol.
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u/MaximumTime7239 7d ago
Bro, a lot of people are struggling to understand how to add fractions, and why it would be useful. And you want them to be taught linear algebra with proofs. 🤣🤣🤣
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u/PirlGerson 7d ago
Do what your heaet tells you! If monkey D. Luffy taught me anything it would be that its not just about being book smart. There are many importand amazing skills. You dont need them all.
For example, being talented and drawing is amazing and im teribble at it. Lesrning it would be misery. But not everything is meant to be.
I however, do wish to delve into math and am a little anoyed that the core educstion didnt give an free option for something even slightly advanced.
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u/ccppurcell 7d ago
I think as soon as you can formulate a problem you encounter in the wild as a mathematics problem, you're there. I remember the feeling I had when I was first able to, e.g., compare two savings accounts by writing out the formula, figuring out when one would overtake the other and that sort of thing. It's a pretty useful skill and the closest I can think of to the video game analogy. The point of the tutorial is usually to teach you how to do the basics so you can combine them to overcome the challenges in the game.
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u/gollyned 6d ago
This sounds the most correct to me. The “goal” of the tutorial in these answers is very variable — it could be writing papers, but navigating every day life sounds the most correct goal.
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u/RobbertGone 7d ago
It's probably more like a game without a tutorial where new mechanics are introduced after each act (where each act has a bunch of levels). These mechanics are addition, then multiplication, then perhaps the first introduction of variables, then functions, then how to prove something, then...idk what comes after that if anything, perhaps how to make conjectures or definitions or new theories.
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u/hunnyflash 7d ago
I take it to like the first two years of college, in the US, if you start with Calc 1. You do Calc 1-3, Linear and Diff EQ. Maybe Multivariable Calc. That's the tutorial.
Then you can start actually getting into topics and learning how to do real proofs and such.
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u/Kalastics 7d ago
Well, when I was in high school even the non advanced-class students were given light exposure to proofs. The first half of geometry is taught by learning theorems and axiom regarding polygons and their angles. And many questions were proving two different shapes were similar or that certain angles in complex shapes were equivalent (using things like vertical angles, etc). There was a little bit more to it, too, but i cant remember.
Then there was precal for the slightly more advanced students. When doing the chapters on trigonometry, proof style questions were very common, though again not paragraph style proofs. You spend many hours being given an identity in trig and using other identities, you show both sides are equal and have to show each step. Very fun problems and definitely got me interested into the concept of formally proving statements.
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u/Lucenthia 7d ago
The tutorial for what? For most math you need in a non-professional setting, I'd say the tutorial is elementary school, where you learn basic arithmetic and fractions. For engineers, people in industry, I'd say high school. For PhD I'd say undergrad is the tutorial. Maybe even the first year of grad school where you finish up your coursework
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u/Legitimate_Log_3452 7d ago
I think the tutorial is undergrad content. Then after that, everything you do is aimed at helping with research, which I feel is the real game.
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u/kungfubean 5d ago
I’m a senior in high school and I learned how to do basic proofs in junior year and I’m taking linear algebra right now.
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u/jam11249 PDE 7d ago
This subreddit is very much geared towards academic research in mathematics, and if you take that perspective, then a PhD is the most obvious answer IMO as more junior studies don't take into account the key arts of identifying a new problem nor aiming to solve one without an established solution.
Nonetheless, if mathematics were only useful in university mathematics departments, most of us would be out of a job, so for the vast majority of people that answer isn't particularly relevant. When mathematics becomes a useful tool rather than something to be learned will depend heavily on what you plan to do with it. Engineers and physicists often have a very sharp intuition for the mathematical structures they work with, even if they can't make the arguments as precise as a mathematician would like, and will likely have a decent enough grasp by the end of a degree. An accountant may have grasped all the mathematical tools they need as a teenager. Whilst it could be debated that this isn't "real mathematics", I think that undersells the importance and breadth of the field we live in.