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  Math Graduate Study in the USA:

The first step is to prepare for the TOEFL and GRE and to search good universities. For detail information about the university, visit both Graduate School website and the Departmental website. The second step is to find graduate schools well matched to your talents and interests.
Documents required for Graduate Admission and Graduate Assistantship:
Signed and dated application forms (you can download these forms from the graduate school website).
Graduate Assistantship application forms (download these forms from the departmental website).
Official College Transcripts (Include B.Sc./B.A. , M.Sc./M.A. transcripts).
Three Recommendation letters (at least two academic). Ask your professors for recommendation letters.
Resume(describe your Education, Work and Professional experiences and publications, if any). 
Test Scores 
Some department recommened GRE. High GRE Score - High chances of earning financial support. Send official test scores, if possible. Otherwise you may send photocopy or scanned copy of test score. 
Statement of Purpose/Personel Essay   
This essay is very important. Include your academic background, reasons for choosing mathematics as a major, your academic interests, your future plans, reasons for choosing USA for graduate studies and your plans after pursuing graduate studies.
Application fee
First write an email asking for waiving the fee or deferring fee until your admission. If they waive or defer the application fee, you are lucky. Otherwise you need to pay the application fee.
Send the completed application package to the departmental address. Department will forward your application to the Graduate School.
Almost all US mathematics graduate programs admit students with full support in the form of teaching assistantship or research assistantship. The quality and quantity of teaching assignments varies from institution to institution.
Graduate Record Exam (GRE) resources:

GRE Companion (provides free GRE tutorial and unlimited practice tests).

GRE Online (provides GRE Test preparation practice exercises).

Kaplan GRE Home

WordHacker Free  Barron's and Taisha GRE Word Lists

Guru's GRE Wordlist Homepage

Vocabulary Software download

GRE BigBook Wordlist

GRE FlashCards Wordlists


Applying to US for Graduate Studies??? Here are useful sites:

USA Math Sites (provides links to the mathematics department of all US Universities)

The Princeton Review (provides information about test preparation, college admission and scholarships)

US News(provides ranking and comparison of US graduate schools)

Notes On the PHD Degree

PhDs Org (provides advice and data about graduate programs in mathematics)

AMS undergraduate mathematics major page

English with Jennifer (A site for language learner)

Rachel's English (YouTube channel for language learner)

Learn American English Online (YouTube channel for language learner)

English Pronunciation (A free online taking dictionary pronunciation)

American English Sounds (Watch the video to learn how to pronounce different English sounds)

English Pronunciation Podcast (Free English pronunciation and accent reduction lessions)