This is what a Mathematics Exam Looks Like on the World's Hardest Degree

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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!
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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.

[@EllieSleightholm]

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 👀

[@tonywilson4713]

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.

[@viscourtroy]

Could you pass the HKALE Pure Maths(in history now) easily??

[@tonywilson4713]

@@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.

[@seanLee-sk2mi]

a blond girl talking about mathmatics, girls are not known for their brain, especially blond ones. am I wrong?

[@YRO.]

You should probably pin this

[@ih8tusernam3s]

I didn't understand a single thing she said.

[@JustMe-zt3fs]

Skill issue

[@Dream2503XD]

​​@@JustMe-zt3fsbruhh i opened this comment to reply this 😂😂, you have already did 😂

[@aiseop31415]

Us bro

[@victorkimani4613]

I understood nothing neither. I'm only left wondering: Why recommend this video to me? Is KZbin 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 😊

[@berniepragle948]

Is that you DJT?

[@diniaadil6154]

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.

[@EllieSleightholm]

❗️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!!

[@ankit13]

Yes, please. This video was great to watch and your explanations were fab...

[@EllieSleightholm]

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!

[@faznaz7455]

As a physicist, i found this content to be very interesting and enjoyable! Great video!

[@EllieSleightholm]

Thank you so much!!

[@leif1075]

​@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!

[@EVA.nefilim]

Even though I´m only a highschooler barely finishing a precalculus course I find your videos very interesting to watch. Thanks

[@AliciaMazeki]

As a grade12 learner at south Africa I really love this topic compared to thermodynamics mechanics in n-dimensional vertalisationality

[@AliciaMazeki]

Hy

[@koifishes]

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

[@EllieSleightholm]

I might go live on KZbin and show the solutions to the other two questions :) that sounds like a good idea for a series! Thank you, I'll consider it! 🤩

[@gadxxxx]

@@EllieSleightholm Please do.

[@trumpeterjones6638]

It does remind me so much of my Oxford maths finals 25 years ago. I wish I knew maths at that level now!

[@joe_hoeller_chicago]

Awesome video, I really enjoyed this, thank you for posting.

[@kunal_kumar-]

You should make video on jee advanced mathematics.will happy to hear your views on it

[@davidhill8163]

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 :)

[@EllieSleightholm]

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! ☺️

[@davidhill8163]

Many thanks for the update and all the best with the new job.@@EllieSleightholm

[@user-abdAllah.benomar]

شكرا جزيلا على المجهودات، أنا مشترك لمتابعة دروسك رغم أني لا أفهم الانجليزية

[@epikherolol8189]

I only know formula for g=GM/r²😅

[@williamnangauta1759]

Nice!! Keep up the good work girl !!

[@athomefootcaresatx9008]

zed and beeta. I thoroughly enjoyed this. Thank you!

[@aurelias1919]

This is a great video! Would love to see the full review of the exam paper

[@EllieSleightholm]

Thank you so much! I'll work on getting the full review out on my channel 😎

[@theartisticactuary]

How does KZbin 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?

[@kingk2405]

Have you tried the subjects of the competition of the ENS ? (École normale supérieure )

[@jonahbresler4317]

I'm surprised you took this paper as well since I did in astrophysics part 3

[@vjaykodvara6356]

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

[@electrowizard2658]

thats a good video sister!!

[@keungsophia6475]

How about the Prépa questions, the admission exam for the prestigious French grandes écoles?

[@rakeshdudekula]

other than maths what are your interesting topics?

[@sganguly01]

Have you see the entrance exams paper for Indian Statistical Institute (ISI)? It is extremely tough as well.

[@mariec544]

Which programme do you use on your iPad to take notes? :)

[@thk2005]

KZbin recommend me this for no reason But i love the video, even not understand any of them :)

[@pinkpanther0001]

Hey ellie good job ❤❤❤😊

[@NextGeneration_]

bruh I cant even do 428+728 without a calculator.

[@majin007]

proof that maths need astrophysics and astrophysics needs math

[@sonicbluster3360]

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

[@chevyDboyMike]

Why do they ass an s on word that's already plural without the s

[@shayandutta9284]

Is it tougher than Putnam problems

[@billyoung8118]

Suddenly my BSEE, emphasizing CPU design, looks like child's play.

[@iiSxmz]

Can you make a vid abt the formulas?

[@meshackgaolathe6492]

What happens if answer all three?

[@aelinwhitehorn3526]

what happens if you do answer all three?

[@EllieSleightholm]

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!

[@Avishek.Actuary]

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.

[@armanavagyan1876]

Very interesting KZbin CHANNEL 😊

[@mrdraco3787]

can we get more videos like this ; )

[@MarkHopewell]

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.

[@seventhunder777]

Is this an undergraduate course?

[@---uz7tp]

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.

[@EllieSleightholm]

@--uz7tp already filmed a video on the JEE advanced mathematics exam from 2016🫡 keep an eye on my channel for the video going live 👀

[@JeffPellegrin_7]

I love math but Iam not good at it

[@MnJiman]

Love the Video. Hate the ad I was shown. A&W sucks.

[@Use-ry-w6b]

What is the world hardest degree ?

[@hayday7899]

I’m not supposed to be here I don’t even belong here I need to finish school first XD

[@samarthbagwe1736]

Try solving JEE advanced maths paper especially try the 2016 Jee advanced math paper This paper is attempted by high school students aged 17 This is an entry level paper for admission in india's prestigious IIT universities

[@luvgoswami7082]

​@@EllieSleightholmalso try the jee advanced 2022 exam it is known for its mathematics

[@Keltaras]

@@luvgoswami7082 The one thing that irks me strongly about the jee is that it's basically a memory test - only on subjects a high school graduate cannot have any grasp about. Understanding math should be the key not becoming a bad immitation of wolfram alpha in human form. They are basically testing in a way that guarantees the final graduates being drones and not being able to apply their skills in solving problems in their respective fields.

[@artophile7777]

It's just highschool math, nothing interesting really.

[@luvgoswami7082]

@@artophile7777 for someone who is just 16-17 years of age that paper gives me goosebumps with the perspective of a high schooler it is a top tier exam, it will be easy for someone who is practicing higher mathematics

[@artophile7777]

@@luvgoswami7082 That's why this is not a good place to recommend it.

[@Viper24ful]

Yeahhh......the algorithm just brought me here and I watched the whole video without understanding a single thing :D real cool though

[@ssaalktbi2970]

Hello , at first before you start studying math did you really thought that you can solve this kind of problems?

[@Pradeepsingh-lz5zs]

From mathematical perspective you need learn to solve partial differential equations, mathematical methods, linear algebra and calculus of variations (and considering you know all undergraduate level mathematics(both applied and pure)). But from just mathematical perspective it isn't that toughest (in the sense rigor)

[@garvitporwal9855]

try JEE advanced maths section..

[@financialanalyst1111]

Thats easy but but TRICKY graduation students will easily answer.

[@PhrontDoor]

I just hate multi-part multi-part questions. It's like : here is question 1. Here is part A of question 1.. Here are the 5 section problems of part A of 1. Here are the next 3 section problems of part A of 1. grrr. For people writing a MATH exam, they seem rather obtuse about the math of the situation.

[@Aaron_1112]

How tf im gonna use this in real life

[@americanexploring7440]

Math is broken. Kurt Gödel put an end to it in 1931.

[@miladirani4313]

I don't understand your comment? What did Godel exactly?

[@americanexploring7440]

@@miladirani4313 kzbin.info/www/bejne/opKZc35rjZd_f5o

[@viscourtroy]

I give up at first 😅

[@joeoleary1961]

when it is actually rocket science :/

[@armanavagyan1876]

Too hard to watch☹️

[@kashmir.zindabad]

Competitive exam students like here ❤

[@IamCaptainDeadpo0l]

The only math i like is meth we are not the same.

[@michaelfuxeklint4909]

I've just paseed a video with (-1)(-1), 😅😂🤣🤔🤣

[@davidc4408]

Many Quant traders taking this degree?

[@EllieSleightholm]

yes, quite a few :)

[@davidc4408]

@@EllieSleightholm those guys will be in the $30 to $100 million club within 5 to 15 years. Stay in touch with them 🤔😉

[@davidc4408]

@@EllieSleightholm I know a lot of the top quant shops love Cambridge maths grads (of course top performing Russell group grads) but I have seen quite a few LinkedIn profiles with traders with this degree. Just did not know if taking a MSc in financial mathematics would be better prep. However, they prop just prefer the raw academic ability that someone can survive and do well on that Part 3 Masters , then teach them the basics of quant trading .

[@michaelnaretto3409]

If I saw that in front of me, I would raise a white flag then get up and leave.

[@brissance]

you people seek fun in this , its sick really.

[@NegativeAccelerate]

Her explanations were so clear i felt like i understood how to do everything. Low key wanna do physics now.

[@wildcat9905]

remember when math used to have numbers and not letters

[@chrisallen9509]

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.

[@speedspeed121]

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.

[@chrisallen9509]

@@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

[@speedspeed121]

@@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.

[@mattc3581]

@@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.

[@chrisallen9509]

@@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

[@gavintillman1884]

Takes me back. Did Part III 1987-88. I’ll certainly check out your other videos on this topic.

[@AnalystPioneer1723]

I understood nothing, but I am motivated to learn math. thank you

[@drankursinha]

Wow this is harder than jee adv maths 😅

[@paulduncan3214]

I was able to work out it was a two hour exam . . . . . then nothing 😮

[@69erthx1138]

Very nice breakdown Ellie. The maths are procedural indeed, though the concepts require astro background.

[@baruchba7503]

This video is very interesting. Can you recommend a textbook for further self-study? Thank you.

[@tonytor5346]

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”.

[@Coding_MC]

Thanks!! Just don't delete this at any point, I will see this before my exams.

[@zaffarmohammed2984]

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

[@viscourtroy]

😐😑

[@ramprasadprajapat2004]

I am from India ❤ nice video sister

[@stephenasare5787]

If I switch from applied physics major to mathematics it’s Ellie’s fault.

[@catherinesmith4264]

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. 😂

[@pablolarrieu1436]

It's not a math exam but an exam of calcul...

[@ibuprofenPill]

Sounds a lot like the mathematics program at MIT.

[@Ghost-soul-pirate]

From Kolkata West Bengal India Thankyou so much ma'am 🥺🥺🥺😭😭😭😭 #kolkata

[@AM-zk7pj]

What is this actually used for?

[@AbhikNandi-ui4gu]

Review Indian statistical Institute's b. stat subjective paper 2023

[@Somnath_Banerjee.]

I am a student of IIT Bombay..... Thanks for this useful video ❤

[@JamesJoyce12]

Do you ever get asked about spherical cows in a vacuum?

[@tronghai55]

You are too smart for for and USA our engineers should wear high heels .

[@SunriseLAW]

I do better on multiple choice exams that don't involve math. :)

[@kanishk7267]

Humans are amazing.

[@ragz37]

She’s brilliant

[@jj-uo9ti]

ahh haa haa easy question picking haa haa

[@thaquietk1d]

Just use pythagoras

[@hyperbot1127]

Can you try iit jee it would be great if you gave some tips on them

[@EllieSleightholm]

@hyperbot1127 yes! I’ve filmed a JEE advanced paper and it’ll be up on my channel soon 👀

[@hyperbot1127]

@@EllieSleightholm than you have got a new sub my mam

[@hyperbot1127]

@@EllieSleightholm I was really struggling with jee maths and after seeing this you made my day ...thanks

[@kheersagarpatel3195]

I am an Indian doing masters in Artificial intelligence and machine learning at IIIT ,but enjoying this video...

[@Thoth608]

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

[@fidgetykoala]

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?

[@halfbakedproductions7887]

Habibti, I studied Computer Science at a Top 10 university and get treated like the cow pat on your Wellingtons. it's the year 2023, and we are still in a position where only Oxbridge graduates count for anything, or are allowed to amount to anything. We get it. I have no future. At least my crayons taste nice, which I suppose brings modest consolation.

[@armanavagyan1876]

CAMBRIDGE UNIVERSITY is my favorite dream UNIVERSITY ever)

[@BadAss_691]

Awesome handwriting, ahh Ipad pen writing…🙃

[@EllieSleightholm]

thank you :) do you not like ipad pen writing?😂

[@BadAss_691]

@@EllieSleightholm Ahh, I miss the old world charm and noise and smell and aesthetics of a real pen screeching against paper🙃

[@EllieSleightholm]

It’s a lot harder to make videos with paper otherwise I would :)

[@BadAss_691]

@@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

[@BadAss_691]

@@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.

[@bazsnell3178]

Far too much waffle, waffle, waffle in the first 3 minutes! Just needs 30 seconds, then dive right in girl!