Everything I've learnt in my THIRD YEAR as an OXFORD MATHEMATICS student... but make it a tier list
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- čas přidán 24. 07. 2024
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Tier-ranking my first-year courses video: • Everything I've learnt...
Tier-ranking my second-year courses video: • Everything I've learnt...
Hello everybody!!! ❤️ I'm Ioana - a Fourth-Year Mathematics student at the University of Oxford and in this video I am sharing all my thoughts about the courses that I took in my Third Year of university by tier ranking them!! Hope you find this useful and enjoyable, even though it's a very Mathsy video! 👩🏫
If you're interested in university-related content, studying, or Maths-related content - join me on my journey! ✨
My socials:
Instagram: @ioanaroman27
TikTok: @portlibrimo
LinkedIn: / ioana-roman27
Hope you have a lovely day!! xx
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Miss Ioana or Miss Math...I highly call you to study the proofs of Islam
believe me , if you study it with the same logic you use in mathematics ,open minded .. without biased mentality , you will find the truth in It shining like the sun or even brighter
Hello Ioana. I took Mathematics with Physics at Cambridge University 1962 to 1965.
Looking back on my life, I would say that it is hard to predict which modules in my course would be most useful in later life.
Linear Algebra has definitely been a very useful core topic with broad application, and the same is true for differential and integral calculus (especially differential equations).
The greatest value for me, however, was that my courses gave me a deep love of mathematics.
The Physics courses also gave me a greater understanding of how the world works, and how to model it.
However, during my 40-year career of research in AI, it has been my extra-curricular studies, learning about topics just because they looked interesting, that have been most fruitful.
Often, I explored a topic out of curiosity, and many years later that turned out to be important for my research..
I came to the conclusion that expertise comes from the depth of your knowledge, but creativity comes from your BREADTH of knowledge.
You can often see analogies between two areas, and pull across ideas from one area to another.
The best structure for your knowledge is thus T-shaped.
I was a university professor for a while and I encouraged my PhD students to indulge their curiosity and broaden their knowledge, and not just dive deep into one area
One more thing:
I have been interested in machine learning ever since I was a teenager in the 1950s.
However, when I was doing research in AI, there was a lot of peer pressure NOT to work on learning, but to hand-craft systems based on logic or probability theory.
When neural networks became respectable, I felt that useful as they were, they were not adequately modelling human capabilities.
For example, we may learn motor skills through many repetitions and hill-climbing, but we learn a great deal through one-shot learning: “That was HOT, don’t touch it again!”
So, I started trying to learn about the neuroanatomy and neurophysiology of the cerebral cortex.
I concluded the cortex is best described as a prediction machine, and it sits on top of the older, simpler “reptilian” part of our brain, from which it learns, and which it over-rides according to its predictions.
Now that I am retired I am watching with great interest developments in neuroscience and brain modelling on one hand, and the amazing performance of Large Language Models on the other.
(LLMs are built by learning to predict the text of the conversation.)
So, I wish you well in your career, and I would encourage you to follow your interests and your intuitions.
People have the idea that mathematics is purely logical and proceeds step by step.
That is not entirely true.
Proofs may be presented in a logical and step by step form, but FINDING proofs is a process full of intuition, guesswork, analogy, filling in gaps, trial end error. Again, the more you know, the easier that can be.
Very best wishes.
Damn you’re smart; I’ve always wanted to meet someone like you.
I have a question - basically, I’m in my Mid-20’s and I really want to go university and study. I’m just not sure what to do - maths, physics or computer science? My goal is to do a degree + PhD and hopefully make some discoveries. If you were my age, what would you do? And how would you decide what to study if you find all 3 subjects interesting. Currently,
I’m working in IT but I want to start doing a degree.
you make some wise points there.
Wow! Such an inspiring comment Dr. Harry Barrow. A quick look at your CV reveals that you've had an interesting career. I've met very few college instructors who are curious and who can create excitement in learning and understanding how things work, the way you do.
All the best to you sir.
I'm in the first year of a math degree, and these videos give me a good idea of what I can look forward to in later courses. Really enjoy your content, keep it up!
Brings back good memories of my time at Oxford.
Super interesant! Felicitări, Ioana!❤❤❤
Mulțumesc frumos!! ❤️❤️❤️
@ioanaroman2947 Thanks can yiu PLEASE share do you have plenty of free time to.travel.and have fun and is studying 8.hours a day 5 days a week.mostly enough? Thanks for your time.
@ioanaroman2947 Do you have a lot of chances to travel and a lot of vacation time? Hope to hear from you!
Statistical learning is so fun!
Wow. The best video of all. I'm studing undergraduation in Statistics at USP, Brazil and I like this conteud.
IME or ICMC? i’m also at USP hahaha
@@ellevasc IME.
ahhh one of my favourite tiktokers on math :))) thanks for sharing i agree with your ranking of subject
Did they teach you polar code in information theory?
Was there an option to get into the kind of logic philosophy stuff that Bertrand Russell and Ludwig Wittgenstein got up to?
I recognize some of that, but lady, you're well above and beyond where I left off! I will say to everyone who says, "I'll never use match," I've found that even over 60 I am constantly using math to solve real-world issues. My entire career was based in math!
An impressive academic/mathematical resume' IR - At my (significantly) inferior math-acumen, I think absorption of the content referenced would take me 3-5 years to attain any degree of competency. I can grasp the landscape of what you comprehensively expressed, & am envious of your diligent pursuit, so my respects to your academic acheivements here. Only thing I didn't hear (directly) was much tensor calculus - I'm sure it was in there somewhere (perhaps too much of a physics lean, to provoke your interest). Think I'll watch this video a number of times to help me improve my own slow/late maths journey. Regards. 🐄
In 1994 without distraction of these day internet and social media, with have only one choice: make as possible exercise, extract some theory and good result from these exercises, and we do too much Hamiltonian Mechanics that not include in, and also Mechanic of Continuous Medium, .
Hard to explain, but very proud of you.
Easily digested calculus, linear algebra and differentials, but taking longer in stochastic study. Please share your knowledge/materials/resources with me😅?
ioanaroman2947 Do you think some people have a higher aptitude for pure mathematics than statistics (and vice versa)?
Spatii Banach se faceau la Electronica si tc. din Bucuresti acum 40+ ani, in primul an.
What is your tuition cost?
Can this by any chance be an applied math program? I find it very surprising that you didn't have any (abstract) algebra courses. The math program at Stockholm University is completely different, it's more focused on pure math.
I agree. it misses out number theory, topology, algebraic geometry, group theory, differential geometry and lots more. It seems to have parts of an economics course embedded into it.
@@Andrew-rc3vh Differential Geometry is more of a graduate class, no?
I'm an auto-didact that naively thought "why go to college for a math degree? Just get some textbooks." I HATE pure math -- except for abstract algebra: that is FASCINATING.
@@jessejordache1869 I see differential geometry like many subjects in maths where there is a point where you learn the basics and as you go on in your mathematical studies you learn a bit more on each subject, so they track each other.
I was listening to a mathematician who was saying he wish he had learnt category theory & type theory long before he did because he realised how it was such a powerful tool which explains large areas of maths.
@@Andrew-rc3vh That makes a lot of sense. The books I have on differential geometry are all pitched at postgrads, but the reason, for me, it's a hard subject is that it requires you to be really fluent with calculus. I don't have that fluency -- it's one of the downsides of learning everything out of books: there's no mechanism to drill things that require a bunch of different techniques until you don't have to keep looking them up. Well, I could be disciplined when I'm first learning them, but what's the fun in that? 😀
Another downside is that most books begin with the same introduction to ZFC set theory, and it's just like, "come ON already."
Since I'm a programmer, I've been exploring category theory and combinatorial logic and so forth on my own, since neither are down-the-middle parts of a math degree. It helps to make slippery concepts... not so slippery.
@@jessejordache1869 I come from a physics background so one gets familiar with being able to visualise geometries.
I'm also into programming and I'm trying to develop my own programming language, so I have an interest in computation theory. I had a look at this ZFC set theory and notice this was an area von Neumann was working in. Scott Aaronson is an interesting person to listen to regarding complexity theory in computation and how one can build quantum computation systems.
Time fly fast. Back when I come across your channel, I was a highschool graduated, and u were in first year making video on what u learned in first year. I knew this app call “goodnotes” from you. Now I’m in second year and you’re in third year lol.
That's lovely to hear!! Thanks for sticking around! ☺️
hi ioana!! your videos are so inspiring and i was wondering what college in oxford are you in? i love all your videos
Thank you so much!! I’m at St. Anne’s College! 🥰
can you share your note? ❤
I might not have arranged the courses in that way, but you explain the reasons for your choices very well, so it's coherent haha x)
Oh and did you had Christl Donely by any chance?
PS: Congrats 🥳 and carry on !
Thank you!! 🙏 Yes, I did have her in first year, great lecturer!! ☺️
Very nice! I haven't seen your other videos, but have you taken algebraic geometry? There's a very interesting monograph by Sumio Watanabe called "Algebraic Geometry and Statistical Learning". I think you will personally find it enlightening.
Thanks for the recommendation, will definitely check it out!! 😊
Great Video. Where did you intern?
Thank you!! ☺️ Cisco (Data Science/ML) after second year, Finbourne Technologies (Quant Developer) after third year
I was trying to choose between buying ARM stock or a few others and CZcams algorithm says I should invest in you.
I’m thinking of taking topology, any feedback from this course from other students? Thanks 👍
Definitely crucial if you want to go further into pure Maths! It's quite exciting and you learn a lot of cool stuff, especially if you enjoy the proofs and ideas developed in Metric Spaces!
Hi Ioana. I was wondering whether Oxford has a course in projective geometry. Apparently, the Nobel winner Paul Dirac once did a course in Projective Geometry and used it to derive one of his equations.
It is in algebraic curves course.
Hi, which book did you use for probability measure and martingales?
And for applied probability? :)
Felicitări, Ioana!❤
Mulțumesc frumos!! ❤️
Heyy Ioana!Can you do a video trying a gcse higher maths paper please
Hey, can definitely try, that sounds like an exciting video! ☺️
What career do you want?
Ideally quantitative research 😇
Can you get a work visa for the UK?@@ioanaroman2947
I can get the "right to work" without needing a visa, as I am a European Union citizen 😅
Even though the UK has left the EU? That is amazing!@@ioanaroman2947
What kind of internships have you done?
Data Science after second year at Cisco; Quant Development after third year at Finbourne Technologies ☺️
Do you already know what you want to work in the future?
For now I wanna go into quantitative research/development, and will start working as a quant dev this autumn! I will see if this is actually the right career path for me or not 😅
Second question: did you have good grades?
I’d say so, but at uni level they’re definitely not the ones making the difference for your future career!! 😅
@@ioanaroman2947 you really don't think so? I'd say they're important when applying for research projects / internships...
How old are you (in this video)?
22 😇
@@ioanaroman2947 WOW! You are too mature to be only 22!
Can you share your lecture notes? Thx
I'm too low IQ to relate to this video, I guess the youtube algo malfunctioned. Anyway, it's cool to see someone speak so passionately about something most people dislike. You're so lucky to not only enjoy Maths but be so superior to billions of people on Earth at it. I wish you all the best.
Thank you so much, I appreciate it!! 🙏☺️
No Category Theory? :'(
At university a million years ago, functional analysis was taught very very dry. sin and cos as infinite dimensional bases for continuous functions is a cool thing to encounter ... but it wasn't until I did Probability Theory -> Measure Theory that I realised there were the same ideas as in FA, but this time they were interesting and more relatable.
Imagine that a pre-established harmoney where female begin to waken and re-member that math is the madness that bubbles from the mind.
When ladies sat and thought alot of stories about time,
Then the word was started to ASK the men to listen,
And feel that long lost feeling that you get from Irish kissin
Uh, where were girls like this when I was in university!?
Dang were you John von Neumann in your last life?
I wish I was half as intelligent as you. You should be proud of all that you have accomplished
Really appreciate it!! 🥹 don’t downplay yourself though, everyone’s great at their own thing!! 🙏
@@ioanaroman2947How old are you?
Hi Ioana ... Mathematics is definitely an interesting science for many females but for the rare special females so I expect math will shape you to more reasonable and logical but I hope not to be more in depth with materialism after all ...
I can easily understand you as a non English origin by accent so where are you originally from please ?
@@scottychen2397What the hell are you talking about ???... What ( heart-ed ) comment ?!... Who is asking for ( heart-ed ) comment ?!... and who is discussing her gender anyway ???... Are you under medication or something ?!..
If only talent-lack hadn't unjustly kept me out of Oxford...
If you're interested in financial markets read and listen to everything by Nassim Nicholas Taleb.
Thanks for the recommendation, will definitely check out his books!! 😊
I will never requite the European logic of expressing _math_ as _maths._ If a fourth-year Oxford mathematics (*) student has not yet acknowledged the mapping of non-partitionable mathematical fields to a unitary domain as being formally consistent, then Europeans will have to abide by other semi-insane conventions, like switch the comma and the period in numerical nomenclature. _Horrors!_
Every revolution must start with one person saying, I will not be a slave anymore!
(*) _Aha!_ you say, “maths“ is an abbreviation of “mathematics“, so _quod erat demonstrandum;_ however, “mathematics _student_ (my italics)“ in this context is _correctly_ expressed as “student _of_ mathematics“, as the word is an adjective, and not (formally) a noun: which would make it a circular definition. _Aha yourself!_ *:-)*
I am surprised about the low level of the courses that you mention for a 4th year student. In Spain for example such "Functional Analysis course" is a 2nd year course. On the other hand it is well known that universities in the UK have lowered a lot their standards because they are at the mercy of the rich students from abroad paying huge tuition fees. And they don't want to fail and pay again. For example, there was an exchange program between the Math students of Complutense University in Madrid and those of Liverpool University, and the third year students of the latter had to be assigned to 2nd year courses at Complutense because their level was too low.
Non-scammy endorsement alert!
the British universities lead the world in youtuber production
For the love of god, can we please go back to calling math "math" or "mathematics" rather than the infinitely grating, awkward and annoying "maths"?
We say maths in Britain and Ireland. Deal with it.
@draoi99 When a person studies medicine, it is implied they are studying all branches of medicine, at least to some degree. There is no need to say they are studying "medicines". In addition, an "s" sound is awkward directly following a "th" sound. Try it. "Maths" is irritating, "mathematics" rolls off the tongue.
Has anyone told you that you have Lea Seydoux vibes? You look like her, talk like her, and simply just give off her energy...She was James Bond's wife in the recent films...go check her out if you don't know...She was also in "Midnight in Paris" at the end.
where is the algebraic geometry, Galois theory, or mathematical logic? least based courseload.
considering how theres many courses she cud have taken, its hard to know which ones which are better when really its all subjective and you shud just take what youre interested in
@@Skryzeeful if you didn't take at least two abstract algebra based courses, you didn't major in math. All these "degree tracks" are commodified spinoffs of the original oxford math curriculum that did not include any of this financial math.
@@balls4644 I disagree. math is broad and who are you to say if anyone didnt major in math or not. what a obsurd and arrogant take. Oxford is the best of the best so clearly they know what they are doing
@@Skryzeeful No you really haven't majored in math if you haven't taken abstract algebra. I mean come on, seriously, judging from the courses she took it looks like an applied math program, not math program. I still can't wrap my head around the fact that she didn't take abstract algebra at the very least, maybe it wasn't offered.
It depends on the system and definitions. If your system typically has a 'general degree' and maths is the major, then you're probably right. In other systems, maths is the degree and the major is the flavour. In that case, what you are referring to would be would be a maths degree, with a Pure Mathematics major.