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I don't think the majority high school students in any country would think that's an easy problem. However, there are differences between the U.S. and a number of other countries that do go some way towards explaining why something like that might be on a university entrance exam in other countries: Some countries have separate "elite" streams for the ...
listen. Don't feel bad you couldn't complete one problem. This is not a problem that tests knowledge but rather skill. I have a lot of passion for mathematics and spend my free time reading about it. For this particular problem, try to see why it works. First, put all a=b=c. Then you can get an idea of when the equality conditions holds. Then try proving ...
You know actually you'll probably be fine. Solving exercises is a skill you develop over time. But when you get to graduate school in math you'll discover that there are very very few other Americans in the program. And some other countries put very little emphasis on solving exercises. For example, in Italy they are obsessed with having you remember ...
To some extent, a high subject GRE score will serve as a substitute. Prospective schools will also look at other data, such as your grades in math and cs courses as an undergrad (they better be close to perfect), your letters of rec (this could be an issue for you), and your personal statement. My suggestion is to list explicitly which books you studied on ...
Just take the standard courses going forward: -college (or AP) chemistry: You don't technically need this, but it is good background to some aspects of physics, especially the baby P-chem that forms most of the course. -calc 3 (multivariable calculus) -differential equations ("calc 4", needed for college level E&M and really key course to not freak ...
What made me to choice my field of studies? Passion and amusement.
The following courses make up the preparation program for a PhD in financial mathematics at my university; it might help you get an idea on how to prepare: Advanced Calculus and Integration Financial Derivatives Financial Management Stochastic Calculus for Finance Financial Economics Probability Theory
I have created some autocorrected online exercises in Mathematics that you could use as supplemental material. I have also started an online index to the fourth edition of James Stewart’s Calculus textbook, as a subset of “Mike’s Ready Reference”. My online index is much more detailed than that of the textbook itself.
Well, it depends on the book. The statement of this theorem seems like it's assuming some other types of analysis/ general topology (esp. since many of these theorems are generalized in topology.) However, that's the trouble with specific math courses, they tend to actually assume some mathematical maturity from other courses you have studied. So, check out ...
I would recommend Cori and Lascar's Mathematical Logic: A Course with Exercises. It has a lot of examples from algebra, so is appropriate for a math major who has taken abstract algebra.
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