How important is it that I study Probability if I like Analysis/Algebra much more?

Question

Is it crucial to a student's undergraduate studies in Math that he/she takes a course in Probability and/or Statistics? I am much more interested in Analysis/ Algebra and I was wondering if it would be seriously harmful if I chose not to take these courses.

Answer 1

I have waited to reply because my field is probability and statistics, so I was afraid you'd consider my views biased. Now I would like to agree with the Comments, but with a little more detail. For several reasons, based on my own experience and the paths of many students I have advised over the years, I believe it is too early for you to limit your options.

It is possible, but by no means certain, that you really know at this point what your main interests are going to be when you get into your graduate study. Charismatic faculty and student friends can go a long way towards influencing your current preferences. Also, the advanced versions of some topics may be more or less interesting to you than the relatively introductory versions you have seen so far.

Eventually, you will need to think what your career will be like after you finish graduate work. Maybe you will remain in an academic setting and maybe you won't. Either way, a field of mathematics that is tremendously exciting during a few years as a student may seem less interesting when you think of your long-term career path. Some very interesting research in the mathematical sciences is done in universities, but other types of deep and important mathematical research are done at government agencies and research campuses of major corporations. (I believe it is fair to say that some entire sub-fields of mathematics are either secret or proprietary.)

Fields of mathematics have a way of blending together in advanced research. My own PhD thesis was technically in abstract probability theory but about half of it was metric topology. A few additional examples: Group theory has also provided important insights in probability theory and modeling. Computer graphics and simulation have become valuable assets for visualization in certain areas of geometry, topology, and group theory. Parts of cryptography and number theory are now essentially indistinguishable. Parts of meteorology and partial differential equations are inseparable. CERN is full of mathematicians and statisticians. Big data analysis is in its irreverent and exploratory 'teenage' years, and it is not yet clear what parts of mathematics (presumably in addition to statistics) will eventually be useful. Brain science is becoming more mathematical by the day, and in surprising ways.

Once again: much too early to limit your options.

Answer 2

You're an undergraduate. You don't know that you like analysis or algebra yet. Give it time.

Everything at higher levels blends together anyway. You like analysis? In functional analysis, you will deal with measure theory. Measure theory is probability.