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So first let me introduce myself. I am planning to apply for masters in mathematics in this year. I am student of bsc. 3rd year of Mathematics. Although my initial interest was to study about algebraic number theory, to know about algebraic number theory deeply, i think one should know about commutative algebra also. So I started a readership on commutative algebra under a professor. But as the time passed I also stared to grow liking for commutative algebra. And now I want to explore more commutative algebra before diving deep into algebric number theory, so here comes the problem.

In the Sop while applying to foreign is it okay to write about having multiple subject of interest as one is prerequisite of other. Or should I specify one of them. I really want to study algaebric number theory but I also want to know more about commutative algebra. Any help will be appreciated. Thanks in advance.

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The Statement of Purpose should reflect your interest in your mathematics and give an impression of both you as a scholar and why the department you are applying to should think that you will be successful. As such, you have great freedom in explaining what you find exciting and interesting, and if that includes your desire to look into multiple areas, then that seems like a fine approach to writing a SoP.

In other words, I would not overthink this: Write why you want to go to grad school and why anyone should think that you will succeed there!

(As a comment on the side: I would suggest you spend more time proof reading what you write. There is a typo in the title of your question, and multiple language and grammar mistakes in the question itself. I don't know whether English is your first language, but at the very least typos are completely avoidable; not proofreading what you write just makes you look sloppy and unprofessional.)

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A statement of purpose offers the selection committee an insight into who you are beyond your grades and credentials. Telling them you like more than one topic is absolutely fine.

More generally, it is important that you emphasize your recent, refutable, achievements. Recent, as in not “I started loving mathematics since I got an A in first grade math”, but rather your achievements in university (especially if you did anything extraordinary like research, teach, participate in math olympiads etc). Talk about lecturers you particularly liked and how they inspired you, etc. if you make a claim about yourself it has to be refutable. “I am passionate about commutative algebra” is an empty statement; “I am passionate about commutative algebra, and am studying it with professor X” is not. If you say you’re hard-working, you need to provide evidence that this is the case.

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