Such as..
Yale?
Harvard?
Stanford?
Washington and Lee?
I really dont want links to the University pages, and i dont need specifics,
but estimated tuition would be great!

If I apply to Harvard for admission, other than marks in SAT and/or ACT, what to they take into account for admission?
I wanna apply for a UG degree, with English as my main subject.

Can anyone tell me please how good/competitive is Master’s Degree from Harvard’s university? And what is the tuition rate? What is the objective opinion on Harvard’s extention school programs?

please answer this?

I am a second year mathematics/philosophy undergraduate student at a fourth tier university. I don’t want to sound conceited or anything of that sort, but I suppose that I’m what you might call a "gifted" student; that is, I maintain a high GPA, participate in a good deal of academic and extra-curricular activities (e.g. community activism, Putnam competitor, debate, mathematics tutor, 6th grade math teaching assistant, presented papers at academic conferences, etc.).

Unfortunately, I don’t find myself well served (at all) at my current institution, Wayne State University. My departmental (mathematics) adviser is a nightmare, who essentially told me not to try and get into a top PhD program in maths. The facilities are somewhat sub-par, and the administration is a generally clunky, bureaucratic nightmare.

Therefore (I am getting to the "question" part soon enough!), I am hoping to transfer, either to the University of Michigan, Ann Arbor (Go blue!), Michigan State U’s honors college, UNC–Chapel Hill, or Vanderbilt. Due to this, there will be a lapse in my mathematics education for a while. Despite having a deep familiarity with high-level mathematics, up to the level of algebraic topology/homology theory (I am researching the general Grothendieck cohomology right now), I will not have as much de facto experience to show for it.

My dream is a PhD program in pure maths or in logic (via applied maths) at Harvard, Columbia, MIT, Berkeley, or UCLA. However, I think that I would benefit from a year-or-so of advanced mathematics courses, beyond the basic undergraduate level. I wish to do something similar to the Tripos III program (Cambridge) PRIOR to taking the math subject GRE, in order to see if I have the wherewithal to commit to a graduate course in mathematics.

I was wondering if I should simply apply, upon graduation, to non-degree/"special student status" programs at Harvard, Princeton, Yale, and other "reach" schools, as these are often easier to get into and provide greater flexibility, while bolstering the strength of one’s curriculum vitae. Should I just take the subject GRE and apply directly to PhD programs? Should I take the GRE and apply to both? What would you suggest?

Thank you!