problems in mathematics

Question

Where can i find long and interesting problems related to analysis (or to mathematics in general) in order to prepare for the Phd qualifying exams (outside of usa) i don't want research problems, but enough difficult for self training and that can be solved in some hours.

In my university, the final exam for M.Sc. in mathematics and to continue for PhD requires deep knowledge in undergraduate stuff, but basic and advanced. — Timbuc, Feb 01 '15 at 13:50

score 3 · Answer 1 · answered Aug 21 '15 at 14:40

I know I'm late, but in case somebody else, like me, gets here looking for the same answer as you:

Problems and Solutions in Mathematics looks quite advanced and meets your topic requirements. The cambridge tripos archives, should also meet your needs... You Also have Problems and Theorems in Analysis I & II.

At Slightly lower level (regarding required knowledge, not difficulty), you have "Berkeley Problems in Mathematics". Also, as you speak French "Agrégation Externe de Mathématiques" could be a good warm-up.

I'll start training on those alongside my job, for the same reason as you. Hope it'll help some people.

score 1 · Answer 2 · answered Feb 01 '15 at 15:13

1

Do you speak French? Polytechnique, Centrale (look for Mathematiques 1 & 2)

answered Feb 01 '15 at 15:13

Clement C.

67,323

1

Yes, i speak french, but these "concours" are somewhat very basic, i need problems that involve advanced maths like measure theory, functional analysis, pde's, differential geometry, (algebraic) topology and harmonic analysis. – mahamath Feb 03 '15 at 10:22

score 1 · Answer 3 · answered Aug 21 '15 at 14:45

1

Most universities have their PhD qualifying exams posted on their websites. For example:

University of Florida http://gma.math.ufl.edu/past-exams/first-year-analysis/

UCLA https://www.math.ucla.edu/grad/handbook/quals

Stanford http://mathematics.stanford.edu/academics/graduate/phd-program/phd-qualifying-exams/

To name a few. I googled "phd qualifying exams math." It appears the page at the University of Florida also has qualifiers for Measure Theory, Complex Analysis, and Functional Analysis.

answered Aug 21 '15 at 14:45

Joel

16,256

1

UIUC also has their old comp exams online: http://www.math.illinois.edu/GraduateProgram/Study/study.html – Gregory J. Puleo Aug 21 '15 at 14:47
@GregoryJ.Puleo that's good to know. I like to collect these sorts of problems myself. – Joel Aug 21 '15 at 14:47

score 0 · Answer 4 · edited Feb 01 '15 at 13:34

0

I'm not sure what exactly you seek, but do you know the Berkeley problems in Mathematics?

edited Feb 01 '15 at 13:34

Travis Willse

99,363

answered Feb 01 '15 at 13:25

Quickbeam2k1

2,139

Actually, i am looking for problems involving deep and advanced math concepts (advanced undergrad. level) – mahamath Feb 03 '15 at 10:23

problems in mathematics

4 Answers4