Management & Interpersonal skills

I have a hard time differentiating those two set of skills.

i.e. PMBOK considers the following skills as management one: "presentation, negotiating, writing, and public speaking skills" (p264)

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Interpersonal skills is your ability to deal and influence the people

Management is about effective application of management skills, for sake of PMP, you can consider this as application of 9 Knowledge areas. In addition presentation, negotiation, written communication, Public speaking are soft skills required to be good manager.

 Thanks for you feedback

You said:"In addition presentation, negotiation, written communication, Public speaking are soft skills required to be good manager." 

It seems that those skills are both management skills and soft/interpersonal skills, but we consider them as management skills if a question ask for the category of those skills ...