Math Publications for an undergraduate?

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11thHeaven
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I've just started an undergrad maths course in the UK and I'm interested in trying out some maths publications/journals. I've always enjoyed reading science magazines in general (ie. New Scientist, Scientific American) and now that I'm at University I feel now could be a good time to move onto some more dedicated, serious material (particularly as I'm considering a career in mathematical/scientific research).

I've had a look at some things like this http://imammb.oxfordjournals.org/content/29/3/263.full.pdf+html - it looks interesting but very heavy going. Does one need a PhD in maths to be able to get anything out of these journals? Are there any that might be suitable for someone like me?

I'm grateful for any suggestions!