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Do any PhD students feel like they still struggle with some fundamental mathematics?

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Defended this semester, and yeah I definitely don’t remember specific things from undergrad. But being able to solve routine problems and cram tons of concepts in our heads isn’t what a PhD is for — take some solace in that fact :)
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To answer your question: yes. I'm a 4th year student and have mostly forgotten a lot of undergraduate math because i havent really used it. That being said, you won't feel it as much after you spend a couple semesters as a TA, teaching your own classes, or running study hall. For example, I have taught multivariate calculus a couple times and now i know it like the back of my hand. I spent a semester grading analysis and had to review all of that stuff.

Don't sweat it. You might feel like you don't have a deep understanding, but most likely if you wanted to review any particular thing, you can absorb a whole semester's worth of undergraduate material in a week or two. Also you will probably have to spend two semesters taking classes. For example, you will definitely understand Jacobians and stuff like Stokes' theorem at a deep level after taking differential geometry.
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I still come across bits of maths that are fundamental but still come as a surprise to me because I never internalised them before. It’s only when a particular  mathematical area becomes just another tool in your kit to solve problems that you know you’ve got it. And you can never have enough tools.
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As someone who loves math but wasn't a math major, this post makes me feel so much better about my journey to better my math skills. I did well as an undergrad, but I feel the same  dissatisfaction with my math deficiencies. You'll get there OP.
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Of course. Forget about teachers who don’t fully grasp it themselves, or grasp it but don’t fully understand the significance; the way the curriculum is designed there’s so much to cover that inevitably you’re going to get rushed through the concepts. Simply put, there’s a lot to chew but it takes time to digest. I should say I’m not a PhD student though, just a Bachelor.
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Totally. I’m constantly trying to remember bits and pieces of courses I’ve taken and knew very well back then. It’s completely normal and is actually a good opportunity to bolster your knowledge in those areas. Whenever you need something take an hour or two to go review it and do some problems. It’s kind of like in an RTS game where you try to fortify your defenses over and over as the game gets progressively more difficult.
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If you could "just" manipulate the symbols in your Calc 2/3 course, then you were already better than 90% of your peers. Not having a firm grasp in those cram courses is incredibly common. Going back later you relearn it as you need it, faster, deeper, better.
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After finishing your PhD, your math skills will reduce to Excel functions, so don't worry....

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