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Hello forum, I will be an undergrad senior majoring in mathematics. Instead of taking the ordinary 5-course workload, I am thinking of doing 3 courses per semester and postpone graduation by an year. But I am wondering if by doing so my graduate application is going to be affected negatively. I...
2. ### Getting involved with research without graduate degree?

Hello, I am studying mathematics and biology as an undergrad. I have always want to do a PhD, but due to having a B- average, I need to set up a realistic plan, (i.e, not going to grad school and try to find a job) although I have not given up hope entirely. I am seriously interested in aging...
3. ### Prove that alpha = aleph_alpha where

Define alpha_0 = 0, alpha_n+1 = aleph_alpha_n. Let alpha = sup{alpha_n : n is a natural number). Prove that alpha = aleph_alpha. My attempt: As alpha <= aleph_alpha is obvious, I've been trying to prove the other direction of inequality, so that being both <= and >= implies =, but now I'm not...
4. ### Well-orderings are rigid proof

Hi I've been trying to understand this proof, but there is one step that I don't get at all. Proof: Suppose f is an automorphism of (E,<=). Consider a set D, a set of non-fixed points under f. If D is empty, f is an identity mapping. Suppose, toward a contradiction, that D is nonempty. Then D...
5. ### Non-Academic career for Molecular Biology PhD?

Hello everyone, I will be entering my third year of university majoring in applied math and biology. I am currently looking for graduate school opportunities. My interest leans slightly towards the biology side but I am terribly worried about not getting a decent job after graduation if I do...
6. ### Courses suggestions for a finance-wannabe?

Hello all, I am an applied math/physics major who wishes to land on a finance-related jobs (including insurance) with a bachelor's degree. The coursework includes ODEs, PDEs, Calculus of Variations, Numerical Analysis, etc., with three faculty elective courses. Here is a list of courses that I...
7. ### A sub-field of relatively employable applied/experimental physics

Hello, I am a rising sophomore at university majoring in physics. Since high school and through university lectures and labs, I have discovered that applied/experimental physics is my cup of tea and I wish to pursue a doctorate degree. But also, I do not wish to be drowning with debts after I...
8. ### Programs CS courses for a Physics major

Hello PF :) I am a physics-major-wannabe who wishes to increase his employability by supplementing my degree with computer science courses. I have already taken Python and C and will most likely take C++ with Unix next semester. I have a room for two more elective courses, but as a non-CS...