My daughter is Muslim and considering marrying a man who is not Muslim. Is she permitted to do so?
If you are just considering Muslim by name, then we dont have much to say. It's all upto you... But, If you are a true belevier and believes that, 1)Allah is the creator and he has the right on us to set the law on how to live in earth, 2)muhammed pbum is his messenger, 3) Quran is there words of God then the below versa, that explains about the same would be good enough to understand the islamic view of the question.
Allah SWT says:
وَلَا تَنْكِحُوا الْمُشْرِكٰتِ حَتّٰى يُؤْمِنَّ ۚ وَلَأَمَةٌ مُّؤْمِنَةٌ خَيْرٌ مِّنْ مُّشْرِكَةٍ وَلَوْ أَعْجَبَتْكُمْ ۗ وَلَا تُنْكِحُوا الْمُشْرِكِينَ حَتّٰى يُؤْمِنُوا ۚ وَلَعَبْدٌ مُّؤْمِنٌ خَيْرٌ مِّنْ مُّشْرِكٍ وَلَوْ أَعْجَبَكُمْ ۗ أُولٰٓئِكَ يَدْعُونَ إِلَى النَّارِ ۖ وَاللَّهُ يَدْعُوٓا إِلَى الْجَنَّةِ وَالْمَغْفِرَةِ بِإِذْنِهِۦ ۖ وَيُبَيِّنُ ءَايٰتِهِۦ لِلنَّاسِ لَعَلَّهُمْ يَتَذَكَّرُونَ "And do not marry polytheistic women until they believe. And a believing slave woman is better than a polytheist, even though she might please you. And do not marry polytheistic men [to your women] until they believe. And a believing slave is better than a polytheist, even though he might please you. Those invite [you] to the Fire, but Allah invites to Paradise and to forgiveness, by His permission. And He makes clear His verses to the people that perhaps they may remember." (QS. Al-Baqara: Verse 221)