I asked precisely this same question before, but I was far too longwinded and it likely won't be answered any time soon, so here is a more palatable, short version. My stats, and the schools to which I'm applying, and my plea to the community to tell me whether or not I have a chance in hell.
A lot of this is hypothetical. It is the 'ideal situation' from where I'm at to when I graduate
School: Bad fourthtier, known for faculty's research in algebraic topology, hosts large regional seminar
Majors: Math/physics/honors
GPA: I will likely graduate with around a 3.7 with a 3.85 in the major.
Courses, grades: * denotes 500level course **denotes 600/700level course
() denotes hypothetical, but I have the background in each case to make the assumption
calc I  C+
calc II  A
calc III  F , repeated for A
Linear algebra  withdraw/failing , retook for B
Ordinary diff eq's  A
*Numerical analysis  A
*Number theory  A
*Algebra I&II  A,(A)
*Advanced calculus  A
*Analysis I&II  (A),(A)
*logical systems  withdraw/passing
**complex analysis  (A)
**Graduate algebra I&II  (A),(A)
**Graduate real analysis  (A),(A)
**Graduate topology I&II  (A),(A)
**Algebraic topology I&II  (A),(A)
**Commutative algebra  (A)
**Algebraic geometry  (A)
GRE:>860
Research interests: higher functorial structures in Algebraic Geometry, Representation Theory, and Mathematical Physics; motivic cohomology, cohomological determinants, topoi, stacks, the Beilinson conjectures, Hodge theory and the conjecture.
Pros: presented talks at conferences (5+), undergrad research, honors thesis, publications, good recommendations.
Cons: started off very poorly, failed calc III first time around, go to a noname institution, took additional year and a half to complete my degree after changing majors.
Schools to which I'm applying:
UOregon, UMassAmherst, UConn, LSU, Dartmouth, Utah, Stony Brook, Chicago (reach), Rutgers (reach), Michigan State, CUNY, USC, UWO, UGA, Miami, Notre Dame, UIUC, Buffalo, Arizona, Boston College (new PhD program), Northeastern, Riverside, Kansas State (safety, want to go for D. Yetter, as I'm interested in higher algebras & quantum representation theory)
Admissions chaces? A concise version of my former post...

 Posts: 5
 Joined: Mon May 17, 2010 3:24 am
Re: Admissions chaces? A concise version of my former post...
i would say impressive.
Re: Admissions chaces? A concise version of my former post...
I think you need to step back and look at your profile.
So, you phucked up Freshman year...given the rest of your profile it makes you look human.
The classes you have taken, it appears that your "Bad fourthtier" school has an active research community.
Assuming that is true, then don't worry about the schools generally reputation, as the Math department reputation will count.
However, endowments are hit pretty bad. So, your large list might make sense. Unless you want to wait a year or two.
So, you phucked up Freshman year...given the rest of your profile it makes you look human.
The classes you have taken, it appears that your "Bad fourthtier" school has an active research community.
Assuming that is true, then don't worry about the schools generally reputation, as the Math department reputation will count.
However, endowments are hit pretty bad. So, your large list might make sense. Unless you want to wait a year or two.