The Best Advice for Mathematics Students (from a mathematics graduate)
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- Опубліковано 1 жов 2024
- The advice I wish I'd received before going to study mathematics at university!
Study Tips: • University Mathematics...
Revision Tips: • Revising Maths? How I ...
To recap:
1. Don’t be scared!
2. Embrace the variety of mathematics on offer
3. Review lecture material after the lecture
4. Make recipe cards, practice questions and figure out how you complete example sheets best
5. It’s okay if if gets hard at times
6. Enjoy!!
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For those of you that are new here, hi there 🌞 my name is Ellie and I'm a Part III Mathematics Graduate from the University of Cambridge! This channel is where I nerd out about maths, physics, space and coding so if that sounds like something you're interested in, click the subscribe button to follow along ☺️
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To recap:
1. Don’t be scared!
2. Embrace the variety of mathematics on offer
3. Review lecture material after the lecture
4. Make recipe cards, practice questions and figure out how you complete example sheets best
5. It’s okay if if gets hard at times
6. Enjoy!!
Any questions, just comment below! 😌
I love you deeply! 😍
My question: Do you love me?
How to be really good at Topology and real Analysis. Kindly Make videos on it
How to be really good at Topology and real Analysis. Kindly Make some videos on it
My advice: Don't think you're the only one who doesn't understand a certain problem or concept. You're not.
Why didn't you go for a PhD? Will you do one in the future?
List of math books you studied plz - abhihiro
The BEST MATH UA-cam CHANNEL.
I’m a first year studying mathematics. I took the advance version of math courses that everyone is required to take for their math degree. It’s a little hard and I’m so nervous about midterms and exams because most of the times I can’t solve the assignments completely on my own and it makes me nervous about exams. Would be great if you can give an advice about this situation :’) by the way I love your videos and I always watch them :)
Something I'd add from my studies of mathematics at Cambridge, if you're not from a private school, is don't be intimidated by seemingly confident/cocky privately educated posh sounding students around you asking or pointing out clever sounding things in mathematics lectures (some are lovely, some are not..), if you follow Ellie's advice you'll likely do way better than them - most did crap in their exams compared to us non-privately educated students at Cambridge mathematics certainly in my year cohort, despite the tens of thousands that had been spent on them prepping for and giving them a leg up into university :)
I don’t think all private students are cocky and overconfident like that.
@@Kristianres Correct, not all are; several friends both from the Cambridge mathematics degree and my professional colleagues (and some of my relatives) went to private school and like I said were/are lovely - but that said a fair proportion on the Cambridge mathematics degree and noticeably a bigger proportion on other degrees were cocky/quite arrogant, yet didn't do so well in their exams (I suspect their abilities had 'peaked' just to get in having had the extra benefit of private school which as an aside makes the whole "what school did you go to?" thing a total nonsense - not a criticism of their ability, the Cambridge mathematics degree is hard even for smart people). This shouldn't put anyone off doing the maths degree or Cambridge in general, I was also pleasantly surprised by how many down to earth and lovely people both private and state school background there were.
Just because all cocky students are privately educated doesn't mean all privately educated students are cocky.
Why are you looking at a maths channel if you don't understand basic set theory?
@@theartisticactuary In both my original comment and my subsequent reply to someone who commented, I stated that some privately educated students were lovely. Furthermore I literally stated that I did mathematics at Cambridge, which is why the channel is interesting to me.
@@electrocademyofficial893Wasn't aimed at you, mate. It's Kristianres who doesn't seem to understand set theory.
im so happy that im early!! :)
Could you please make a whole video on your journey?
A dream PROFESSION☺
Math PhD here. Nice video!
Long post ahead.. :)
I like that you bring up the fear most, if not all math students feel. When I started I assumed everyone else would be some much more clever and better at math than me.
And I constantly thought that the next course or exam would be way beyond my capabilities and I would eventually make a fool of myself.
Nothing of this was true. But the constant struggle against your fears and impostor syndrome was very real.
What you eventually realize though, is that you are not alone. Almost everyone feels and thinks the same way to some extent.
You are not supposed to be perfect. You are there to learn, to question, not to give an impression to be some perfect all knowing student.
I would like to add what is my most important point if I could go back in time and start over:
* Try to really understand what the intuitive meaning behind everything you learn is and why and when what you learn is important. Especially how it is connected to other stuff you already know, and also how it is new and different. Don't skip examples and applications.
The professors/teachers will be very happy if you ask them about such things and you can benefit a lot from their experience.
When I started studying I did not care about applications at all. I had read that one should see math as some kind of art where the beauty of the subject itself should be enough.
I did not question or reflect much about what I learned and why the contents of the definitions and theorems where chosen as they were.
This was a mistake. You should do the opposite as much as possible. Never rely on some authority argument that what you learn is good for you. You need to internalize it for yourself.
When you see a new definition, think about all parts of it and try to figure out why the definition is as it is. Why is it useful? Can you find examples satisfying it, examples which do not?
What would happen if you skipped or added some part of the definition, would it be meaningful? How does the definition connect to your previous knowledge? What new stuff does it bring?
Do not just read and think "Ok, I understand what it says, but it seems pretty random and strange to me." Then you don't really understand it.
The same goes with reading and understanding proofs. You can read a proof, understand every symbol and every logical step from start to finish, but still totally miss the intuition and deeper understanding of why the proof works. It would be comparable to reading a chapter of a book word for word, understanding every word but not paying attention to the story told.
Almost all proofs have deeper meaning which you typically miss at a first reading. Understanding and uncovering those deeper insights is an important aspect of really learning math and also gives it much more meaning. Otherwise everything will just feel like facts on top of each other without structure.
Did you ever do any self studying? I'm currently a 2nd year at a Russel group university in the UK studying maths but I often find the course having a smaller scope and having a much slower pace covering less content. I want to Study part 3 at Cambridge for pure maths; do you have an advice on trying to bridge the gap? (currently going through Dexter's lecture notes at cambridge).
I'm MSc maths like you, and your advice is spot on. I do hobby research, and are working on two papers at the moment with new stuff. The best advice I will give on top of yours is, that that is possible with a math degree. You can do new math. Build up contexts where you use tools from the uni-toolbox, and prove properties of objects in the context. Evening after evening with hard problems and where the outcome is unknown. The great satisfaction it gives when you succeed, and can type the whole thing up in Latex. In the projects I've used number theory, group theory, vector spaces, metric spaces, measure theoy, topology and real analysis. Without my master degree, the whole thing would be impossible!
I’ve just started my computer science degree, and I’m already diving into some of the math-heavy content. One of my first modules is on set theory, which is discrete math, which I’ve learned is a whole branch of mathematics. It hasn’t been too difficult yet, but the lecturers say the pace will pick up gradually. I’m looking forward to the challenge as the content becomes more advanced. Thanks for the advice.
Great advice, Ellie. Couldn't agree more. 👍
I'd only add that there is now a great wealth of help on-line, with videos of worked examples and lectures here on UA-cam, and elsewhere -- which wasn't the case when I did my degree, but is the case now.
hello, i need advice on proofs, how to mature mathematically and write better proofs?
Do you recommend a double major in both math and CS?
this is a very broad question that the depends on your specific life circumstances
NICE
Taught math>won't use it for anything useful in the world>get a degree in math>teach it to others who won't use it for anything useful>they get degrees and then teach it to others who won't use it for anything useful
math is a way of thinking which helps us to make good decisions and it is not just a subject, it is the first thing to use it for living, after food. Math is the ground that we built the other science on.
😊😊😊😊🧠🧠🚀🚀you are a precious!!!
You are good girl.
Wth
log off bro
Ok man.
My best advice for math students is always try to find applications for your math study and apply more step by step , otherwise math science will be just for nonsense ....
❤
You are looking gorgeous 😊
My advice, which is not a really serious one but sort of important one is, learn LaTeX asap