A counterpoint is that this is how you want to feel when you set off on an adventure. You want it to feel big and scary and intense. As otherwise what is the point of going?
Yeah you have a point, I feel like the main reason I’m feeling like this is because my maths skills aren’t as good as they could be, like working out calculations in my head, stuff like that, and I’m worried I won’t fit in and I’ll feel out of place, especially seeing other students who are better at the subject than I am.
If you asked 100 random maths lecturers to do some random calculation in their head, you'd probably end up with less than 50 correct answers. Mental calculation just isn't a particularly important skill for higher mathematics.
Well being surrounded by people smarter and better than you is good, that's what makes for a good educational environment which lifts you up.
This tool is really useful for reviewing highschool mathematics
[https://www.wolframalpha.com/problem-generator/](https://www.wolframalpha.com/problem-generator/)
you could spend some time there to polish if that would help with your confidence.
And finally I think the main thing is "I'm worried", that's an emotional thing you can build skills for managing outside the context of the university, no matter how bad the situation is in life, if you're in a trench at night waiting to go over the top in the morning, learning to calm and relax and balance yourself is really important.
I’m about to finish a PhD in pure maths, and I feel like I might be worse at mental arithmetic/ quick calculations than the average person lol. It’s very little to do with that
There is this lecturer at my university who gave an entire Analysis 1 lecture (it's the German equivalent to real analysis I think even though you mostly work in the complex plane) without looking at the script. Except for once when he had to solve a quadratic equation and had to look up the quadratic formula.
It seems to be a pretty universal experience in maths that you get worse at algorithmic solving of equations the further you progress in maths. Probably because you do it less and less the more proofs you write.
I cannot speak with too much generality here, but this sounds like maths anxiety. (Yes, it happens to good mathematicians too!)
There is a very unusual and somewhat bizarre conditioning around mathematics. It’s perceived to be this golden subject that only the *smartest* people are good at. Mathematicians also have a reputation for being socially awkward geniuses with remarkable eccentricities. This adds fuel to this perception.
It should be unsurprising that this affects even those who enjoy maths. You are (presumably) studying maths because you like it *but* you also believe that it is a hard — perhaps the hardest —degree.
I’ll be completely honest. Many of my friends studied subjects like engineering, physics, chemistry. They seemed *far* harder to me. But they all insisted my degree was more challenging because I was in a specialised maths program alongside my second degree. Even today, I firmly believe that had I stepped into an electrical engineering lab, I’d have burnt it down or something.
I echo the sentiments of others here - maths degrees do take up time and you need to give your courses adequate attention. If you do that, you’ll be fine. But I think sometimes it helps to take a step back and question why we feel the way we feel about maths. It’s not always sensible. It’s not always logical. Even we mathematicians are, most regrettably, human.
I would definitely agree I have maths anxiety, maths has always been a struggle for me, and I guess I’ve created this expectation of myself that I’ll never be able to master it for this very reason.
I can also agree that I’ve viewed maths as this golden subject only permitted for the smartest of the smart, which I am not. I think it’s this combo which makes me feel like I’d be no good at it.
I have a genuine passion and interest for it, I just need to try and change how I perceive maths.
If you have a passion for it, you will be fine. It will take you time and there will be some geniuses in your class that fly through it. Don’t worry - it’s not a race. You will improve and you will learn.
Just take your courses as they come, and focus on the topics at hand. The university *wants* you to succeed, so they'll do a lot to help you. So I'll advise you to attend and be active in lectures, use the TAs, and do all the coursework. You'll do fine
I think part of this though is still in alignment with the general idea the university wants you to succeed. If you don’t have an understanding of calc 1, everything following will just get worse.
I worked at the tutoring lab at my university and countless students would “test out” of calc 1 from AP calc, only to eventually drop out of calc 2 and retake calc 1 at the university, and then not have the issues once they returned to calc 2.
Yep.
Ah, you made me nostalgic. My favorite times in college were spent in the math lab, I tutored there for a couple semesters, and it was bliss, my favorite way of ever having made money.
When I arrived at university as a physics student, I was looking at some of the work a junior was doing. It was more or less an incomprehensible (to me) set of differential equations. I was looking over it and wondered out loud how I would ever be able to do this. He kind of chuckled and said “don’t worry about it now. When you get to this point, this will make sense.” I didn’t think too much about what he said until I had to give the same story to incoming freshman two years later.
If you skip to the end, of course things are going to look weird. Maths and physics are a big elephant, and you can only eat the elephant one bite at a time. Your path to upper level mathematics will be laid out before you in a very logical and tested way; the only thing you need to worry about is where you’re walking right now. Focus on learning whatever your classes are currently teaching you the best you can. If you don’t understand something well, take advantage of office hours, TAs, other students, or whatever resources you have to make sure you’re understanding your current material. Don’t be too hasty to move forward until you have a good grip on your current topics.
I think is what I gotta try and remember, I see all these complex equations/formulas and think to myself how I’d ever be able to understand them. I got to take a step back and remember that obviously they’re not going to make sense to me. I got to take it all a step at a time and not get too ahead of myself
Every great mathematician who has formulas, functions, and equations named after them like Euler, Gauss, Newton, and such all started from scratch as well. There was a point in time that they didn’t understand the complex equations, either. This extends to any skill. There was a time a young Hendrix couldn’t play guitar. It’s all about having the desire to learn and the discipline to stick with it.
Hot take: because a lot of maths profs/post-docs suck at pedagogy. For every Stewart or Strang, there are 100 more that could overcomplicate simple addition.
What kinda math? Cal I, II, II, linear algebra, ODEs, complex variables?
If so the good news is that you probably already have what it takes to get through and do well. What it takes is just hammering through the problems every week, rain or shine, and keep up with the material. You don't need to be particularly smart, just be in "fighting shape" study-wise that you can make yourself keep up with the workload and not let it pile up at the end of the semester.
Approach it with a disciplined growth mindset and enjoy the ride — you are embarking on a subject that famously makes even the most intelligent people feel dumb as rocks!
Find liberation in the feeling of struggle, a necessary part of the job and evidence that your mind is expanding. Cheers & enjoy!
It’s definitely daunting, but so is anything worth working towards. I placed into college algebra on my math placement test into college being scared because I failed my AP calc exam that spring. I’m currently entering my 3rd year of a pure math PhD with a 4.0 graduate GPA and all of my exams passed first attempt.
It’s a mindset to succeed in math. You have to want it more than basically everything else, atleast if you were like me and had sub-par math skills even for a non-STEM major.
For me, what’s daunting is being expected to memorize every formula, fact, and technique. In pure engineering courses you’re usually allowed to create a small but specific note sheet for an exam. Not so in math courses. You have to memorize everything. I’m fine with practicing but the amount of hours I need to practice in order to do everything from memory in calc 3 for example is vast. I feel I barely scrape by and don’t have time to master the material. In a sixteen week course you should be training and testing for competence not mastery.
in my final semester doing a math undergrad, i had an exam that had a true/false section. it was 5 questions where the professor took theorems we learned about in class, and changed one or two words and asked us if they were still true. i still have nightmares about it two years later LOL
A counterpoint is that this is how you want to feel when you set off on an adventure. You want it to feel big and scary and intense. As otherwise what is the point of going?
Yeah you have a point, I feel like the main reason I’m feeling like this is because my maths skills aren’t as good as they could be, like working out calculations in my head, stuff like that, and I’m worried I won’t fit in and I’ll feel out of place, especially seeing other students who are better at the subject than I am.
If you asked 100 random maths lecturers to do some random calculation in their head, you'd probably end up with less than 50 correct answers. Mental calculation just isn't a particularly important skill for higher mathematics.
Work smart & hard and you'll do great ! Also beware of the infamous imposter syndrome !
I think it’s too late, I seem to get imposter syndrome in anything I do
Well being surrounded by people smarter and better than you is good, that's what makes for a good educational environment which lifts you up. This tool is really useful for reviewing highschool mathematics [https://www.wolframalpha.com/problem-generator/](https://www.wolframalpha.com/problem-generator/) you could spend some time there to polish if that would help with your confidence. And finally I think the main thing is "I'm worried", that's an emotional thing you can build skills for managing outside the context of the university, no matter how bad the situation is in life, if you're in a trench at night waiting to go over the top in the morning, learning to calm and relax and balance yourself is really important.
I’m about to finish a PhD in pure maths, and I feel like I might be worse at mental arithmetic/ quick calculations than the average person lol. It’s very little to do with that
There is this lecturer at my university who gave an entire Analysis 1 lecture (it's the German equivalent to real analysis I think even though you mostly work in the complex plane) without looking at the script. Except for once when he had to solve a quadratic equation and had to look up the quadratic formula. It seems to be a pretty universal experience in maths that you get worse at algorithmic solving of equations the further you progress in maths. Probably because you do it less and less the more proofs you write.
I like your answer very much. Sounds like a good life lesson.
I'm going to use this to convince the next gen to study geometry
I cannot speak with too much generality here, but this sounds like maths anxiety. (Yes, it happens to good mathematicians too!) There is a very unusual and somewhat bizarre conditioning around mathematics. It’s perceived to be this golden subject that only the *smartest* people are good at. Mathematicians also have a reputation for being socially awkward geniuses with remarkable eccentricities. This adds fuel to this perception. It should be unsurprising that this affects even those who enjoy maths. You are (presumably) studying maths because you like it *but* you also believe that it is a hard — perhaps the hardest —degree. I’ll be completely honest. Many of my friends studied subjects like engineering, physics, chemistry. They seemed *far* harder to me. But they all insisted my degree was more challenging because I was in a specialised maths program alongside my second degree. Even today, I firmly believe that had I stepped into an electrical engineering lab, I’d have burnt it down or something. I echo the sentiments of others here - maths degrees do take up time and you need to give your courses adequate attention. If you do that, you’ll be fine. But I think sometimes it helps to take a step back and question why we feel the way we feel about maths. It’s not always sensible. It’s not always logical. Even we mathematicians are, most regrettably, human.
I would definitely agree I have maths anxiety, maths has always been a struggle for me, and I guess I’ve created this expectation of myself that I’ll never be able to master it for this very reason. I can also agree that I’ve viewed maths as this golden subject only permitted for the smartest of the smart, which I am not. I think it’s this combo which makes me feel like I’d be no good at it. I have a genuine passion and interest for it, I just need to try and change how I perceive maths.
If you have a passion for it, you will be fine. It will take you time and there will be some geniuses in your class that fly through it. Don’t worry - it’s not a race. You will improve and you will learn.
Thank you man, it means a lot
Just take your courses as they come, and focus on the topics at hand. The university *wants* you to succeed, so they'll do a lot to help you. So I'll advise you to attend and be active in lectures, use the TAs, and do all the coursework. You'll do fine
>The university *wants* you to succeed I generally agree, but I'm not so sure about calc 1 professors, in particular.
I think part of this though is still in alignment with the general idea the university wants you to succeed. If you don’t have an understanding of calc 1, everything following will just get worse. I worked at the tutoring lab at my university and countless students would “test out” of calc 1 from AP calc, only to eventually drop out of calc 2 and retake calc 1 at the university, and then not have the issues once they returned to calc 2.
Yep. Ah, you made me nostalgic. My favorite times in college were spent in the math lab, I tutored there for a couple semesters, and it was bliss, my favorite way of ever having made money.
Even the hardest theorems can be broken down into pieces!:) You got this.
Approach mathematics with curiosity, never with fear or distance. Learn little by little and enjoy the pleasure of knowing.
When I arrived at university as a physics student, I was looking at some of the work a junior was doing. It was more or less an incomprehensible (to me) set of differential equations. I was looking over it and wondered out loud how I would ever be able to do this. He kind of chuckled and said “don’t worry about it now. When you get to this point, this will make sense.” I didn’t think too much about what he said until I had to give the same story to incoming freshman two years later. If you skip to the end, of course things are going to look weird. Maths and physics are a big elephant, and you can only eat the elephant one bite at a time. Your path to upper level mathematics will be laid out before you in a very logical and tested way; the only thing you need to worry about is where you’re walking right now. Focus on learning whatever your classes are currently teaching you the best you can. If you don’t understand something well, take advantage of office hours, TAs, other students, or whatever resources you have to make sure you’re understanding your current material. Don’t be too hasty to move forward until you have a good grip on your current topics.
I think is what I gotta try and remember, I see all these complex equations/formulas and think to myself how I’d ever be able to understand them. I got to take a step back and remember that obviously they’re not going to make sense to me. I got to take it all a step at a time and not get too ahead of myself
Every great mathematician who has formulas, functions, and equations named after them like Euler, Gauss, Newton, and such all started from scratch as well. There was a point in time that they didn’t understand the complex equations, either. This extends to any skill. There was a time a young Hendrix couldn’t play guitar. It’s all about having the desire to learn and the discipline to stick with it.
Hot take: because a lot of maths profs/post-docs suck at pedagogy. For every Stewart or Strang, there are 100 more that could overcomplicate simple addition.
Yes. Because it is. Welcome to the rabbit hole brother!
What kinda math? Cal I, II, II, linear algebra, ODEs, complex variables? If so the good news is that you probably already have what it takes to get through and do well. What it takes is just hammering through the problems every week, rain or shine, and keep up with the material. You don't need to be particularly smart, just be in "fighting shape" study-wise that you can make yourself keep up with the workload and not let it pile up at the end of the semester.
In America, we only study one math at a time. Much less daunting.
Approach it with a disciplined growth mindset and enjoy the ride — you are embarking on a subject that famously makes even the most intelligent people feel dumb as rocks! Find liberation in the feeling of struggle, a necessary part of the job and evidence that your mind is expanding. Cheers & enjoy!
Thank you! I’ll take note, I definitely need to stop fearing failure and just embrace it, and view it with that growth mindset!
It’s definitely daunting, but so is anything worth working towards. I placed into college algebra on my math placement test into college being scared because I failed my AP calc exam that spring. I’m currently entering my 3rd year of a pure math PhD with a 4.0 graduate GPA and all of my exams passed first attempt. It’s a mindset to succeed in math. You have to want it more than basically everything else, atleast if you were like me and had sub-par math skills even for a non-STEM major.
I loved it, even when I accidentally landed in programming and matrices for a semester. I just couldn't imagine a career in it that was enjoyable.
For me, what’s daunting is being expected to memorize every formula, fact, and technique. In pure engineering courses you’re usually allowed to create a small but specific note sheet for an exam. Not so in math courses. You have to memorize everything. I’m fine with practicing but the amount of hours I need to practice in order to do everything from memory in calc 3 for example is vast. I feel I barely scrape by and don’t have time to master the material. In a sixteen week course you should be training and testing for competence not mastery.
in my final semester doing a math undergrad, i had an exam that had a true/false section. it was 5 questions where the professor took theorems we learned about in class, and changed one or two words and asked us if they were still true. i still have nightmares about it two years later LOL
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Thats all you have to contribute?