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I am in a predicament when deciding on classes for my graduating year of my undergrad next year.

In first year I thought I wanted to be in physics so I didn't take proofs in second year, so it delayed me getting abstract algebra courses. This means I have to take Abstract Algebra I next year.

I talked to the professor teaching Algebraic Number Theory next year and asked how under-prepared I would be for the course if I was taking Abstract Algebra 1 along side it.

He said it would be pretty difficult but he would be willing to waive the requirement as he is one of my directed studies supervisors.

I am wondering how important it is for me to take Algebraic Number Theory in my undergrad or if it is something I can take the Masters level equivalent of in my first year of grad school?

I am hoping to get into a Cryptography program for my masters if that affects the answer.

If I don't have to do it in my undergrad it would give me more time to focus on my directed studies and hopefully get honours.

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  • $\begingroup$ Yes in particular for crytography you need Galois theory. $\endgroup$ – reuns Mar 11 at 21:36
  • $\begingroup$ I know plenty of math PhD's (including myself) who know little to no algebraic number theory, so no, I don't think it's required. I doubt the grad programs you apply to will expect everyone to know it. However, it may help. If it's a math dpeartment, they will likely at least expect you to have a decent handle on abstract algebra. $\endgroup$ – Jair Taylor Mar 12 at 1:29
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My short answer is that if you feel you need that subject for your application to the graduate program, then do it. But if you think you need it for future studies at the graduate level, then for now it might not be very urgent.

The biggest problem that I faced when starting my Master's in maths is not any particular area of knowledge, but the level of mathematical maturity that the Master program requires. This includes things like self-discipline, and the ability to look at a problem and see different angles from which you can tackle it. Virtually all my current subjects challenge me on those skills, and I feel like getting better at them has helped me a lot with fill in the gaps in my knowledge. If you can apply yourself and have 2-3 months between your graduation and the start of your Master's program, I think you still have time to catch up by then.

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I am a first year grad student, and am currently taking my first algebraic number theory course.

You’ll be fine without taking it in undergrad.

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