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I know only about Resonance published by Indian Academy of Sciences and I've read most of the content from it's math portion of all the issues.

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    See here: http://mathoverflow.net/questions/36850/journals-for-undergraduates – 2017-01-22

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AMS's journal is better. John Baez's stuff is quite interesting site, and I recommend Qiaochu Yuan's, too.

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While it is not a journal or magazine, Introduction To Modern Mathematics by Helena Rasiowa is a great book. It covers introductory set theory, logic, and a bit of abstract algebra at the end.

It works through the proofs in detail so it is a very friendly read.