As far as I know, putting up advertisement in a newspaper looking for US Citizens for the job only applies if the employer is sponsoring you for a Green Card. I believe the law says that if you cannot find US Citizen with a skill set that's needed for the job, an employer might hire an non US Citizen individual who meets those skill set and sponsor their GC. I think that doesn't apply for H1-B's but I could be wrong. You might want to double check that. I don't believe USCIS favors any certain field of study while granting visas. As for the convincing part, I am not really good at that so I will let other Sajha users give their expertise in this case.