<p>I finished high school and will enroll in a college with a top math program this fall. About my mathematical tastes: I love number theory, and also like combinatorics and algebra(linear and abstract included). I did a good amount of math in my country: I'm nearly IMO-level at number theory, and good at algebra and combinatorics. I had a precocious aptitude for math, participated in national and international contests and sometimes had really original insights during them(found remarkable formulas on my own).</p>
<p>However, I don't like calculus. I had 2 years of calculus in HS, and find little pleasure in studying it. It doesn't arouse my curiosity, I often find calculus proofs quite artificial, and can't understand how some people can solve difficult analysis problems(not talking about homework here). I did enjoy learning a few theoretical things, like Taylor series, but I don't think I ever solved an analysis problem for pure fun.</p>
<p>So, I'd like to become a mathematician, but use very little analysis. Is this even possible? Of course, I know that I have to take real&complex analysis and differential equations as an undergrad, but afterwards, how much analysis would I have to take in graduate school(in a great PhD program in the US)? </p>
<p>Every school has their own requirements for admission to the PHD program, so I suggest you start visiting the school website and look at their PHD admission pages.
On the other hand, every Math major to my knowledge has to take all the Calculus series form 1 to 3, plus linear algebra, and other higher math classes. Then again that depends on the undergraduate school you are attending.
So, whatever undergraduate institution you are going to attend has planned for math major, that is what you have to take to graduate.
In addition, visit the web page of the graduate schools that you are interested in, and see their graduation requirements for Maths majors;
Example:
<a href=“Graduate”>http://math.mit.edu/academics/grad/</a>
or
<a href=“Ph.D. Programs - Mathematical Sciences - Mellon College of Science - Carnegie Mellon University”>http://math.cmu.edu/graduate/PhDprogram.html</a></p>
<p>Fun fact: mathematical disciplines blend at the graduate level. If you want to be a number theorist, you’ll be exposed to a fair bit of analysis. Better start getting used to it. </p>
<p>Every graduate program in the country will either test you or require coursework on measure theory and functional analysis. If you want to avoid all analysis beyond that, you’d have to hide in specialties dealing with very finite and discrete objects, like combinatorics. (Though there are analytical tools used in combinatorics as well…)</p>