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This is what a Mathematics Exam Looks Like on the World's Hardest Degree
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- Опубликовано: 28 окт 2023
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So you want to know what an exam paper looks like from one of the world's hardest mathematics degrees? Well, wait no further! In today's video, I dive into an exam from Part III of the Mathematical Tripos at the University of Cambridge or what is more formally known as once of the hardest and most intensive courses in the world!
My full solutions (as seen in this video): payhip.com/b/tWNTB
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Important note: I deliberately selected a course, paper and question that would be easy to follow without having any prerequisite material. This video covers one of the easiest questions ever set on the Tripos and is in no way representative of every exam. Please take that into consideration.
![Why you didn't learn tetration in school[Tetration]](http://i.ytimg.com/vi/Ea1_1aVfwl4/mqdefault.jpg)
Hey everyone! Some updates:
My full solutions (as seen in this video): payhip.com/b/tWNTB
Also, I’ve noticed a lot of people commenting about this being very astrophysics related and here’s why! Part III has Astrophysics courses within the Mathematical tripos that are more mathematical than the physics courses :) so these courses have a nice portion of astrophysics but with large emphasis on mathematics and they were awesome!
This question I did in this video (as mentioned in the description) is the easiest question ever set on the Dynamics of Astrophysical Discs course (a course within Part III Applied Maths). I chose it because I have a lot of subscribers who don’t have advanced mathematical background and wanted to show a question that was easier to follow but, I realise now, this did not show a true representation of Part III 😂 so I’ll be releasing a second video where I tackle another exam paper from Part III with very hard questions! Subscribe to stay updated!
brilliant.org/EllieSleightholm - Try everything Brilliant has to offer for FREE for a full 30 days! The first 200 of you that click on the link will get 20% off Brilliant's Annual Premium subscription 👀
Sorry princess but the hardest degree to do in the world is aerospace engineering.
And the math says it is.
I'm Australian but went to college in America ay U. of Illinois. On basic credits (we called them hours) which mostly equated to lecture hours (and why they were called hours) we had to do at least 134. I think it was Nuclear engineering in second place at 132. All of the generic arts and science degrees were 120 and that included Maths degrees.
Other than the almost insane math we have to learn we also have to apply it to the real world and do the equivalent of 9 semesters in 8, including all those infuriating arts type classes to make us "well rounded." The math doesn't lie on that.
Sure the classes for a Maths degree get damn hard.
I won't deny you that.
I know because in aerospace we had to do an extra 2 pure maths classes over normal engineers. 1 of those was reasonably easy in matrices but the other was in advanced differential calculus and was required BEFORE doing things like aerodynamics.
The hardest class I did was actually in space craft dynamics and it still gives me nightmares 36 years later.
Could you pass the HKALE Pure Maths(in history now) easily??
@@viscourtroy I had never heard of the HKALE so I had a quick look. Anyone who's done the advanced maths classes in Mech, Elec, Aerospace, Nuclear or Chem engineering should be able to pass it.
The thing is - unless you are doing that sort of math stuff on a regular basis you lose the practice you used to pass those classes.
I did aerospace and I know I am capable of passing that level of stuff *BUT* if I tried right now I'd struggle and most likely fail. *BUT THEN* if I had time to practice for a few weeks I'd probably pass.
a blond girl talking about mathmatics, girls are not known for their brain, especially blond ones. am I wrong?
You should probably pin this
Ive done a fair share of maths, and took a few relativity courses in college. This was a nice refresher, albeit way harder that what my exams used to look like.
Her explanations were so clear i felt like i understood how to do everything.
Low key wanna do physics now.
As a physicist, i found this content to be very interesting and enjoyable! Great video!
Thank you so much!!
@EllieSleightholm Can you share how you don't get bored and frustrated and fed up with math and how to make research contributions? I could never admit I'm not a math genius. Thanks for sharing and hope you can respond whenever you can!
I didn't understand a single thing she said.
Skill issue
@@JustMe-zt3fsbruhh i opened this comment to reply this 😂😂, you have already did 😂
Us bro
I understood nothing neither.
I'm only left wondering: Why recommend this video to me? Is RUclips trying to kill simple-minded folks these days?
Anyways, I watched the video to the and enjoyed the beautiful girl's presentation.
And, dare I say, nerdiness aside, you are an angel inside @Elliesleightholm 😊
Is that you DJT?
❗️NOTE❗️
I deliberately selected a course, paper and question that would be easy to follow without having any prerequisite material as not all my followers have a strong math background. This video covers one of the easiest questions ever set on the Tripos and is in no way representative of every exam. It is also from the Astrophysics section of Part III Maths, if you’d like to see a more mathematical exam, let me know!!
Yes, please. This video was great to watch and your explanations were fab...
Takes me back. Did Part III 1987-88. I’ll certainly check out your other videos on this topic.
My full solutions (as seen in this video): payhip.com/b/tWNTB
Note: I have set the price to optional - if you want to support my channel then consider inputting what you thought my video was worth :) thank you so much for any contributions you send; it allows me to continue making content!
This was significantly beyond the difficulty of what I was asked in my undergrad of my astrophysics degree, however still easier than the content in my PhD level courses. This difficulty of questions would certainly not have been asked in my PhD exams however, so I find it interesting these were exam questions at undergrad level.
I got an astro degree from a UC (California). This is just above what we studied. However, with some work, I think I have the tools to solve the problems.
@@speedspeed121 I felt the dynamics questions were easy, and the rest was somewhat hard although I always hated MHD and disk stuff. It’s probably pretty straightforward if you re-read the relevant textbook sections. If you wanted to solve these problems I’d recommend Binney and Tremaine for the dynamics and Frank King and Raine for the MHD accretion physics.
Also it looks like this is a graduate course, hence why it is above the level of undergrad material where I studied and more on par with PhD level courses
@@chrisallen9509 As a third year student who was just trying to figure out mechanics, I took a galaxy class that studied discs. It's not easy, but it was fun.
@@chrisallen9509 Part 2 Maths at Cambridge is normally the final year of the undergraduate maths degree at Cambridge, however if you intend to go on and do further study, eg PhD then you would normally take the extra undergraduate year doing Part 3 as shown here to prepare. So it is an undergraduate course, though not done by everyone.
@@mattc3581 Wouldn't an integrated masters still be "graduate level" in the US? In Europe, most PhD programs require you to be at the level of masters students in the US already given the relevant coursework
Even though I´m only a highschooler barely finishing a precalculus course I find your videos very interesting to watch. Thanks
Looks like a very interesting topic/exam... I branched off from the mathematical physics type stuff after second year (doing more pure maths and probability/mathematical statistics stuff in Part III ) but I'd have probably enjoyed that one!
I honestly thought it was an amazing course! I'd love to see some notes from the mathematical statistics stuff though!
@@EllieSleightholm I still have a fair amount of them dotted about; in future when they're to hand and I have a spare window of time, I'll dig some out for you :)
@electrocademyofficial893 that’s very kind of you, thank you!
@@EllieSleightholm ah totally welcome Ellie :-)
Very nice breakdown Ellie. The maths are procedural indeed, though the concepts require astro background.
Thanks!! Just don't delete this at any point, I will see this before my exams.
It would be nice if you showed the answers to the other two questions. Would you also be explaining the past papers for the other modules you took as well? I think it would nake for a very interesting and educating series. Thanks for the video
I might go live on RUclips and show the solutions to the other two questions :) that sounds like a good idea for a series! Thank you, I'll consider it! 🤩
@@EllieSleightholm Please do.
As a grade12 learner at south Africa I really love this topic compared to thermodynamics mechanics in n-dimensional vertalisationality
Hy
It does remind me so much of my Oxford maths finals 25 years ago. I wish I knew maths at that level now!
Awesome video, I really enjoyed this, thank you for posting.
I understood nothing, but I am motivated to learn math. thank you
I only know formula for g=GM/r²😅
Hi Ellie, thanks for an inspiring video, even though im just on the Astrophysics unit at A level, I still found this motivational. Ill try Brilliant. Can I ask how you learnt how to present like this on your i pad as I have one and would like to do the same. Thanks for sharing your time :)
Thank you so much! I just screen-record on my ipad and sync it to my video recording but I think you can do it a bit more sophisticatedly on OBS or something similar! ☺️
Many thanks for the update and all the best with the new job.@@EllieSleightholm
I love how your channel is just college’s I can never get into / tests I’d never be able to take / pass.
I’m a mathematician at heart - but standardized tests, I advocate against.
I’m happy that you build a strong community of mathematicians though. That’s cool.
zed and beeta. I thoroughly enjoyed this. Thank you!
Nice!! Keep up the good work girl !!
I sat the putnam maths paper in 2021.
I got just 5 marks out of 120. I got a call back on my new idea when cominb across an equation that i saw as curvature in space in 4th dimension
I thought i was good
😐😑
This is a very interesting video! Love it
Great video! Hope to see more.
شكرا جزيلا على المجهودات، أنا مشترك لمتابعة دروسك رغم أني لا أفهم الانجليزية
This is a great video! Would love to see the full review of the exam paper
Thank you so much! I'll work on getting the full review out on my channel 😎
This is a great video and you are very great scientist.
This video is very interesting. Can you recommend a textbook for further self-study? Thank you.
You are too smart for for and USA our engineers should wear high heels .
You should make video on jee advanced mathematics.will happy to hear your views on it
I was able to work out it was a two hour exam . . . . . then nothing 😮
How does RUclips know to recommend me stuff like this when I took Cambridge Maths Part III in 1986, and passed probably only because I played an absolute blinder on the two hour, two unit exam on Newtonian And Relativistic Accretion?
remember when math used to have numbers and not letters
other than maths what are your interesting topics?
She’s brilliant
Have you tried the subjects of the competition of the ENS ?
(École normale supérieure )
What is this actually used for?
It's not a math exam but an exam of calcul...
I hate showering; and I have to take a shower. I hate math. Very torn on what to do. I chose listening to this math explanation. Thank you for showing me that I hate showering more than I hate math. (My biggest accomplishment in college was getting an A- in Statistics and Organic Chemistry) 25 years later and it still matters. 😂
I have 3 time 0 out of 70 In maths and that is true and before that I have cut off in jee both is really true
Please make a vid on math books recomendations with difficult Ranking
Well... Not Lev Landau's theoretical minimum, but still pretty tough : thumbs up
Hello, can u take a look over Math D - ens Ulm. It is an exam I am taking in April . it is a 6 hours exam and pretty interesting actually
Watching this video, that's why I dig ditches for a living😂
I'm surprised you took this paper as well since I did in astrophysics part 3
I am an Indian doing masters in Artificial intelligence and machine learning at IIIT ,but enjoying this video...
I love fluid dynamics. 🙂
I am from India ❤ nice video sister
How about the Prépa questions, the admission exam for the prestigious French grandes écoles?
I am a student of IIT Bombay.....
Thanks for this useful video ❤
thats a good video sister!!
RUclips recommend me this for no reason
But i love the video, even not understand any of them :)
Sounds a lot like the mathematics program at MIT.
I have GAD and the only wat to escape it is to delve into a wealth of subjects, last time I did algebra was in middle school, whereas at high school I completely neglected those stuff, as I was doing classical studies and here in Italy you have 12 subjects in total by the end of the fifth year, which is mental. I was wondering where to start with maths to exercise my problem-solving skills in my spare time. Any books preferably in English for beginners? Also, what do you think about the following?
Yesterday I was wondering about the validity of mathematical axioms which carry on certain attributes such as aprioristic self-validation with no need to further prove any validity. The same attributes usually describe divinities and the Whole as the metaphysical trascendent holistic unity (see Parmenide). Considering that math is based on axioms and it is computed by using the deductive methods, is it possible to assume that math is a logical model that doesn't carry any ontological truth? As the truth of its fundamental component must be believed to be true without any further questioning?
Have you see the entrance exams paper for Indian Statistical Institute (ISI)? It is extremely tough as well.
I would have failed from the beginning since the test expects one to be able to count to two .
we need the full paper!!
Why do they ass an s on word that's already plural without the s
Physics major from California! I’m surprised that I was able to kinda follow. :)
Suddenly my BSEE, emphasizing CPU design, looks like child's play.
Do you ever get asked about spherical cows in a vacuum?
i understand everything she said but when I combined it I have no idea, this just tells uoft math is not even hard compare to this paper
I bailed the moment I heard "dynamics of astrophysical discs"
Hey ellie good job ❤❤❤😊
Can you make a vid abt the formulas?
In my next life, I wish God would give me a brain to put all of this together. Math & I makes 2 in this life. I fully understand the concepts, but when it comes to the math involved, I just cannot understand why it all gets put together.
My dream was to go into physics. I could barely pass algebra & trigonometry. I memorized formulas in calculus like one memorizes poetry & learned to apply the correct one that was most likely to apply to the problem. I passed calculus with a top grade without ever understanding why that particular formula was the correct one. Long story short, I went into medicine, am a full professor in a renowned university, have my name as editor of major textbooks. Medicine makes sense to me! I can think of different ways to solve problems and am known for being a pioneer in my area, because I can think of different approaches to saving the lives of patients when a clear diagnosis is not evident and have always been able to do so. It comes naturally to me. Math in the other hand makes absolutely no sense.I guess that area of my brain has not developed. I love to solve clinical problems using in a totally different manner, and people ask me “how did you come up with that”? Calculus and advanced math are the only areas I was and will never understand. At age 70, I am still working as a physician, because I love what I do. Now for a straight question for one of you geniuses out there can opine.I did at one time in my life, in the 1970’s when a colleague of mine working at Rockwell gave me access to a reverse engineering project they were working on.I do not have an NDE but he did, nevertheless here goes. Supra-luminal is possible. Take this at face value for all it is worth. From reverse engineering; these crafts manage to do so by “hiding M” fro E= MC^2. My physics friends tell me that “its impossible”! By looking at the arrangement of the craft, this was what I came up with.
This turned out to be true at the end. The math wizards finally came up with a solution, approaching it in a way, that they had not thought possible. They were looking from concentrating on gravity waves. How they did it I don’t know, but it turned out my approach was much simpler. What is the biggest impediment to achieving faster than light travel? Mass becomes infinite . The easiest one to me was hiding “M” being the biggest problem. That took them in another direction, and I don’t know how, but this was how the problem was solved. I don’t know how, but this is how it was done in the early 1970’s. Creating some kind of field, I suspect, allows to do so, not affecting the sub-atomic nor the physical properties of the matter including living people contained within the “hidden space”.
Plz Upload Calculus illustration videos .
This is really useful - thank you so much!
If I switch from applied physics major to mathematics it’s Ellie’s fault.
Is it tougher than Putnam problems
I did this blindfold, with both hands tied behind my back, whilst buried beneath 10 meters of concrete. A cakewalk! 😇
From Kolkata West Bengal India
Thankyou so much ma'am 🥺🥺🥺😭😭😭😭
#kolkata
Do you have to have these formulas memorized?? Thanks.
Can you try iit jee it would be great if you gave some tips on them
@hyperbot1127 yes! I’ve filmed a JEE advanced paper and it’ll be up on my channel soon 👀
@@EllieSleightholm than you have got a new sub my mam
@@EllieSleightholm I was really struggling with jee maths and after seeing this you made my day ...thanks
Wow this is harder than jee adv maths 😅
bruh I cant even do 428+728 without a calculator.
We all start somewhere in math I guess haha
Mathematics isn't a subject it's a language we need to explore science . Physics uses it the most followed by the distant "second boy" chemistry.
proof that maths need astrophysics and astrophysics needs math
What happens if answer all three?
What is the world hardest degree ?
Humans are amazing.
Where I can download it,sis ?
Which programme do you use on your iPad to take notes? :)
So what's the actual degree?
Review Indian statistical Institute's b. stat subjective paper 2023
CAMBRIDGE UNIVERSITY is my favorite dream UNIVERSITY ever)
hey there watching you from india just wanted you to make a video on a video for an indian or may be foreienger that how to apply for cambridge
What a shame you're not asked to frequently appear on network TV as a role model for younger people to aspire to rather than therelentless sport or pop star aspiration narrative.
what happens if you do answer all three?
i think they take your two best answers but some lecturers might only mark the first two. in these exams its very unlikely that you'd have enough time to answer all three!
What is your answer to 6÷2(1+2)? Is it 1 or 9
Bro...
i'd imagine it's the same as your IQ.
Very interesting RUclips CHANNEL 😊
would love to see your reaction to some other countries hardest test for exemple in France we have Maths Ulm D and the Agregation of mathematics being hardest maths exam respectively for Sophomore students and post Master students
Ooooo I’ll take a look and make a video on it!! Thank you!
Nice! If you need any help for translation don't hesitate to ask. Good luck with your channel🫶@@EllieSleightholm
Especially Maths Ulm D from the 1966 exam, there is a funny story about it and how hard it was.
On sent que les videos de @axel_arnot on fait le tour du ytb francais 😁
@@EllieSleightholmIt's the toughest exam in mathematics in the world since Paris Saclay is the best University in Mathematics
Awesome handwriting, ahh Ipad pen writing…🙃
thank you :) do you not like ipad pen writing?😂
@@EllieSleightholm Ahh, I miss the old world charm and noise and smell and aesthetics of a real pen screeching against paper🙃
It’s a lot harder to make videos with paper otherwise I would :)
@@EllieSleightholm It’s alright , studying Math at Cambridge is so hard and demanding , it’s an achievment in itself that you find the time and energy to shoot and edit videos
@@EllieSleightholm You’re so charming, intelligent and dare I say, beautiful that if I could, I would’ve went on a date with you although I know it’s way beyond my means /dreams. Thanks for all your videos though, I binge watch all of them, and specially your interesting turn of career from pure mathematics to astronomical data science is quite unique. The great thing in the UK or the West is the vast plethora of opportunities available for people who dare to take the risk.
I’m not supposed to be here I don’t even belong here I need to finish school first XD
can we get more videos like this ; )
Is this an undergraduate course?
Try to give "JEE ADVANCED" paper. It is considered one of the toughest exams in the world. High schoolers of grade 12 have to take this exam to get into IITs, an Indian equivalent to MIT. It has Physics, Chem, and Math questions which have to be attempted in a 3-hour frame................ You will really like attempting it try attempting "Jee advanced 2022 ". In math, the syllabus is calculus, coordinate geometry and algebra.
@--uz7tp already filmed a video on the JEE advanced mathematics exam from 2016🫡 keep an eye on my channel for the video going live 👀