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<p>First of all, I don’t recommend auditing classes. If you are going to pay to attend classes, I would take them for credit. I would also only take classes that are upper level ME classes and that are taught by active researchers at the school. I would then work very hard, attend office hours, talk to the professors, and see if you can get into a research lab with one of them (or at least get to know one well enough for a reference to a graduate school or to know your name when you submit an application to that college). </p>
<p>I also would not seek full-time employment. It would look really bad if you quit after just a year. Rather, look for an internship through your school’s career services department. There are some companies that will hire you for a year as an intern or co-op. Another option is to seek full-time employment then consider working on an MS in ME at night. You can usually find an employer that will pay for the MS, and many ME departments will accept Math majors with some leveling courses.</p>