Advice for classes?

[kate25]

Hey guys,

I'm planning to start a PhD program in statistics next fall, and I'm trying to choose two of the four following classes to take next semester. Which do you think would prepare me better?

Automata, Computability, and Complexity: Circuits and decision trees, finite automata, Turing machines and computability, efficient algorithms and reducibility, the P versus NP problem, NP-completeness, the power of randomness, cryptography and one-way functions, computational learning theory, and quantum computing. Examines the classes of problems that can and cannot be solved in various computational models.

Number Theory: Primes, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions, partitions.

Introductory Topology: Topological spaces and continuous functions, connectedness, compactness, separation axioms, and selected further topics such as function spaces, embedding theorems, dimension theory, or covering spaces and the fundamental group.

Optimization Methods: Linear programming, network optimization, integer programming, and decision trees. Applications to logistics, manufacturing, transportation, marketing, project management, and finance.

Thanks in advance.

Edited December 27, 2011 by kate25

[cyberwulf]

Meh, none of these are likely to be helpful in your usual graduate-level statistics courses. The reason for taking AC&C or OM would be to learn a bit more about computational techniques and theory, which can be useful background for a stats grad student. The reason for taking NT or IT would be to get exposure to more advanced mathematical ideas, which is never a bad thing.

My advice: take what seems interesting and is likely to be well taught!

[Matt W]

I can't comment on the Automata, etc. course.

Elementary number theory courses, like the one you described, are usually intended for weaker students. If you've taken abstract algebra then this course would be a waste of time and won't improve your application. If not, then you may want to take it for further breadth.

Depending on what you've seen before and which area of stats you want to go into, the topology course may prove useful. Metric spaces (an important type of topological space) will be useful if you're going for a more theoretical route. Metric spaces with Borel probability measures are an important class of probability spaces. If you haven't had much exposure to metric spaces before, then I would recommend that you take this course. Otherwise, this course would still look good for demonstrating mathematical ability.

The optimization course could be useful if you end up working in industry.