Why is Undergrad Math Harder in Other(non US) Countries?

It seems that math is harder in other countries(non US). It seems it's much harder from my experience. Why? Do you agree/disagree?

Please leave any comments or questions in the comment section below. Thank you:)

[steliostoulis]

In Germany we learn calculus I in Highschool. And when you go to uni you start with real analysis.

[bebarshossny]

Im an international student in germany and we're already doing real analysis in the 2nd month of the first semester man

[jeorgealonso]

Have you considered that you are comparing students that are in their originary country (the US) and students that have gone to the US from other countries? Probably in some cases (if not most of the cases you've seen) the access to those US universities was granted due to their merit and excellence in the first place. Of course it could also be (and probably is to some degree) because of cultural and educational differences, but I think that this reason should also be taken into account.

[teteucontagemmg]

By the way, one thing I learned from my mathematical journey is that SOLVING PROBLEMS is one of the most important ways to learn. I could only learn Analysis and Abstract Algebra by solving many, many exercises. It was not enough to read the book, change books, increase the number of hours studied, etc. I'm saying this because when I was studying Analysis, your solved exercises (here on your channel) helped me a lot. I do not agree with that old idea of ​​having only the answers of odd exercises, typical in mathematics books. Keep up the good work. Greetings from Brazil.

[anirudhd]

Probably because students in other countries have a head start. In India, we do a lot of calculus in high school (11th and 12th grade). You need to take entrance exams to get into an engineering college for undergrad, which focuses a lot on calculus (for math). Same is true for physics (mechanics, thermodynamics, fluids, basic electrical) and chem (physical and organic). This helps with math you do in undergrad.

Should also add, I went to grad school in the US and yes, like you mention, it evens out at grad school.

[willilow]

That is true! I am from Chile and I studied in a well known private US University and it was so easy for me. Here in Chile professors compete themselve to make the hardest excercise, you won't find it in any text book. But, but, US university still win because you put a lot of money in research. We don't

[mouadrimwind]

I am from Montreal Canada, in here we have an institution called Cegep which is the link between uni and highschool . Once you go to cegep depending on what you have chosen to study either in buisness or science you'll have to take Calculus 1 and 2, and linear Algeabra. Once you get to uni depending on your program you start dealing with more complex stuff. From my side I remember Calculus as the good old days when you study hard and get A. Once I started uni and went into Computer Science, I had to deal with Discrete Math then I realized that Calculus is not necessarily the best indicator of any solid ability in math because of its straightforward nature, In my mind someone who is truly good at math is capable of abstract thinking, in order to solve different problems that are only solvable if you get the big picture at large. That is what Discrete Math made me realize. Hopefully I could get into the end of my degree.

[aLEJUO]

It makes me remember of my chinese friend, he was very young like 19-21 years old and he was one of the best students of the faculty (Chemistry). He had A+ everywhere. I don't know what kind of education he got in China but I notice he had a very good memory and he memorise things very easy. He was so good and he went directly from the bachelor degree to the PhD. Now he is doing his phD in organic materials (polymers) and he is possible the smartest guy I have ever seen in my life

[ahmadahmadi]

Two reasons come to my mind, first we (I am from Iran) have a very highly competitive system to enter the universities. You have to compete with a million guys to study in a field that you like. We have no choice but to study very hard. I didn't pass the test, therefore I traveled to U.S. to study Electrical Engineering at University of Illinois @ Chicago Circle. Passing those pressure in Iran, U of I was like a heaven for me. Second reason the material that was arranged for us was huge. In tenth grade we studied Solid Geometry, Trigonometry, Analytic Geometry, Set & logic. In eleventh Statistics, Calculus, art of proof . In twelfth Discrete math (Number Theory, Combinatorics, Graph Theory & Probability), Linear Algebra & Analysis. One thing that I have to say is about the quality of American students. Most of them are excellent & fine plus creative & hard working, but their high school math textbooks are not that great. I suggest you look at India, Iran England & U.S. Math textbooks and compare it yourself.(all of them are available online). I think India's are the best, even their math videos & math video lectures are very fine. I know I am an engineer and should not mess with mathematicians. Wish the best.

[WojciechowskaAnna]

I think its an illusion. I studied in Poland, and usually in secondary school and at university there were around 2 ppl out of 30, and at university maybe 10 out of 180 who were genuine thinkers. Those ppl usually came from intelligent homes, had extra lessons early in life, usually tutored by someone from the family, sent to special classes, taking part in competitions called "olympics". And only those ppl would make it to the US and any other foreign country as part of their "career". And looking then at their life stories... well... except for very few cases they do regular jobs. People CLAIM they do calculus (since when it so hard, prooving cocepts is hard) but they hardly undustand it. Math to some degree can be taught like a mind puzzle. And that gives illusion of a higher level. Skilled repetition does not make one a real mathematician, but might be needed.

[peterbehnke]

I'm from Canada and studying math at the University of Waterloo. Most of our schools are pretty similar to yours in America, but the University of Waterloo kind of takes things to extreme. We have 25% international students from Asia (the absolute maximum the government will allow) and the programs are ridiculously competitive because you have kids who have been doing calculus since grade 9. I also think your math might be easier because it is mandatory in high school (from what I've heard) whereas in Canada you choose what math you want to take (although you have to take at least 3 in your 4 years).

[FunctionalIntegral]

The following program you learn in Germany at undergraduate level in mathematics:

Linear Algebra and Analytical Geometry I and II
Analysis I to IV
Applied mathematics, mostly numerical mathematics and a computer course, often also stochastics and linear optimization.

[NexuSound]

I'm from the Netherlands and what I noticed in the US it is hard to get IN a (good) university, here it is relatively easy to get in but quite difficult to STAY, as the programs can be quite rigorous.

[Sipnayan]

Students who go to the US for undergrad/grad school particularly those on scholarships are probably at the top 20% since studies under a scholarship are very competitive. For instance, from our country, those who go abroad to study are mostly from the top universities.

[thomasstokes]

In the UK we go to university a year later than in America. Also in the British education system you specialise a lot quicker than in the American education system. For example in England by the time you are 16 you are only doing three or four subjects. This allows individual subjects to be taught in much more detail. Like in most other European countries, first year Maths students in the UK do Real Analysis, Group theory and multivariable calculus.

[paulhmason]

When I was in high school in South Africa (admittedly, a long time ago) algebra and differential calculus, as well as introductory integral calculus were part of the high school (last 2 years) mathematics curriculum. First year university mathematics was pretty brutal compared to what is covered in most US universities (from what I can see) - very proof heavy.

[shelbyhuffman]

When I was in high school (I am from Oklahoma) we were really only required to learn basic algebra and trig, but we had the option to take Calculus with approval. I had an internship and one of my mentors was from India and he was telling me how when he was in high school that during his last year or so that he had the option to choose a focus "computer science" which could be a reason why students have more skills in other countries.

[gustavofring]

Here in Italy we have 5 years of HS. The last year we do Calculus(Integrals, improper integrals, Riemann Integral, numerical integration), Newton's method and bisection method to determine the zeros of a funcion and lastly we have been doing functions in 2 variables(Lagrange systems, functions with constraints...)

[goumiyagi]

Warning: Long comment, I am currently a third year undergrad student in Amsterdam and I’ll go by what was taught to me per semester.

Semester 1:

Introduction to mathematics:
In this course we covered the basics such as: formal proof methods, equivalence relations, elementary number theory, cardinalities of sets, construction of number systems etc. Basically the basics to follow any other math course.

Real analysis: In this course we covered sequences, epsilon delta proofs, bolzano weierstrass, sub sequences, continuity, differentiability, mean value theorem, intermediate value theorem, integrability of functions, equivalence of riemann summs compared to Darboux summs etc.

Linear algebra: matrices and properties, determinants, vectorspaces, linear maps, isomorphism theorems, quotient spaces, dual spaces, eigenvalues and eigenvector, jordan normal form and generalized eigenvectors.

Stochastics 1:

We started off with a “rigorous” treatment of probability spaces, sigma algebras etc. Covered random variables, discrete and continuous, as well as multivariate discreet and continuous random variables, moments and moment generating function and some limit theorems such as law of large numbers, weak law of large numbers.

Then a computational math course, here we learned programming in python, the basics.

Second semester:

Multivariable analysis:
We covered some point set topology in this course, partial derivatives, total derivatives and went up until Taylor polynomials of functions from R^n to R^m, inverse function theorem, implicit function theorem and lagrange multipliers.

Group theory:
Definition examples of groups, subgroups, cyclic groups, cosets, normal subgroups, quotient groups, isomorphism theorems, group actions, burnside lemma, automorphisms and semidirect products, classification of groups, Jordan holder and Sylow theorems.

Introduction to graph theory:
Just the basics, definition of graphs, Euler and hamiltonian graphs, some algorithms, colourability max/min flow algorithms etc.

Introduction to logic:
Just propositional logic and up until completeness and soundness with a small introduction to predicate logic.

Numerical mathematics:
Here we learned some algorithms to find fixpoints of functions linear maps, singular value docomposition, polar value decomposition and dyadic number systems.

And this was just the first year, it was hard but fun!

[teteucontagemmg]

I loved your video. I thought that only I had realized this, I was already paranoid.

Just get a Russian "Calculus" book, for example, from the MIR publisher, and get a typical American Calculus book (Stewart, Thomas, Anton, etc.). I'm not downplaying American books (I even think it's best to start with them, you strengthen your mathematical foundations), but it is a fact that when they tell the joke that in Russia you learn Differential Equations in High School, there is a real background to this.