CV for a PhD application in applied mathematics
Firstly, the Career Objective section is a thing of past and should not be present in a CV or resume. Not only it is old-fashioned, it actually makes one change their CV or resume every time one applies to different organization and position. It is much better to place relevant position-focused information in a cover letter, which should be adjusted to a particular position anyway.
Secondly, do not put personal details, like mailing and physical address, on CV or resume. An e-mail address and, maybe, a phone number is more than enough. You don't expect potential employers to send you postal mail, do you? Plus, the physical address would jeopardize the security of one's identity.
Thirdly, the section Research Interests should be higher in the list - I would say, even prior to the section Education (or, at least, right after it).
Fourthly, I suggest you to create two versions of your CV (the following is not applicable to resume) - one with references, for organizations that require them as part of initial application, and another without ones, for those that require them later or using different communication channel (say, Interfolio).
Fifthly, go ahead and search Internet for examples of academic cover letters (there are plenty of them - stick with the ones from reputable universities). Hope this helps. Good luck!


P.S. I would reword section titles, as follows: Conference Presentations => Talks &amp; Presentations; Research Interest => Research Interests; Co-curricular Activities => not sure it makes sense to extract them in a separate section - why not list them below relevant educational info; Extra-curricular Activities => Extracurricular Activities.