I dislike calculus/analysis. Can I still get to do research in math?

College Majors Math/Computer Science Majors
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<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'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)? </p>

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<p>Number theory is so much more fun than analysis! That said, have you tried taking a more theoretical approach to calculus? Take a look at the following two (freshman level) courses at MIT:

  1. 18.014 Calculus with Theory - <a href=“Calculus with Theory | Mathematics | MIT OpenCourseWare”>http://ocw.mit.edu/courses/mathematics/18-014-calculus-with-theory-fall-2010/&lt;/a&gt;
  2. 18.024 Multivariable Calculus with Theory - <a href=“Multivariable Calculus with Theory | Mathematics | MIT OpenCourseWare”>http://ocw.mit.edu/courses/mathematics/18-024-multivariable-calculus-with-theory-spring-2011/&lt;/a&gt;&lt;/p&gt;

<p>While this doesn’t directly answer your question, it might help analysis seem a little more bearable.</p>

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<p>Haha I also came across Calculus with Theory today(though I first heard about ocw some time ago). Indeed, I think I’d prefer a rigorous, theory-oriented rather than problem-oriented approach to calculus, but maybe not as arid as, say, baby Rudin. I’ll check that course and see whether it works for me. Glad to see you also prefer NT to analysis, that’s quite rare, I think(though frankly, I sometimes wish I were the other way around).</p>

<p>Analysis would surely seem more bearable if I knew for sure when I could stop studying it. I know that in order to qualify for a PhD, you typically have to pass an algebra/analysis(and topology, maybe) exam, but after that would I still be required to take analysis courses? Can a math PhD clarify this for me?</p>

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<p>It does not look like math PhD programs tend to have much in the way of specific graduate level math course requirements, although they do assume knowledge of various topics that an undergraduate math major should know, including real and complex analysis (tested in preliminary or qualifying examinations).</p>

<p><a href=“Coursework”>http://math.mit.edu/academics/grad/timeline/coursework.html&lt;/a&gt;
<a href=“PhD Program | Department of Mathematics at University of California Berkeley”>PhD Program | Department of Mathematics at University of California Berkeley;
<a href=“Program Requirements | Math”>https://www.math.princeton.edu/graduate/requirements&lt;/a&gt;
<a href=“Harvard Mathematics Department Graduate Information”>Harvard Mathematics Department Graduate Information;

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<p>Analysis is one of the pillars of Math, and I think any mathematician should know it. You can be a researcher in another area, although because Mathematics have great inter-connectivity between each area, you would be kind of incomplete without it and you wouldn’t have a great scope to do research (in my opinion).</p>

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<p>Yes, there are many areas in Math for research that is not “analysis/real analysis-based”…BUT…there is just about NO chance you will avoid Analysis. Even the B.A.-version of Math degrees may give you an option to take Abstract Algebra and maybe an option of 2nd-semester Analysis but YOU HAVE to take at least one semester of Analysis. Even many graduate Applied Math program will make you take minimum one semester of graduate analysis.</p>

<p>My B.S. degree is in Computational Mathematics (a hybrid Math/CS degree) and I still had to take Advanced Calculus (which was my school’s “lighter-version of Real Analysis”).</p>

<p>Cannot escape it.</p>