The three core graduate mathematics courses normally taken in the first semester are:

• 640:501 Theory of Functions of a Real Variable I.
  Text: Real Analysis: Modern Techniques and Their Applications (2nd Edition), Gerald B. Folland
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• 640:551 Abstract Algebra I.
  Text: Nathan Jacobson, Basic Algebra, Volumes 1 and 2, second edition.
  Important Note These volumes seem to be out of print. Copies are available from various used book websites (e.g. addall.com. Please look for the book well before the semester begins. If you have trouble finding the books, please send an email addressed to BOTH grad-sec@math.rutgers.edu and Professor Weibel (weibel@math.rutgers.edu).
• 640:503 Theory of Functions of a Complex Variable I.
  Text: Function Theory of One Complex Variable: Third Edition (Graduate Studies in Mathematics), Robert E. Greene and Steven G. Krantz