Hi! I plan on taking the algebra and analysis exams relatively early into graduate school. To people who have taken your qualifying exams (or anybody with a good sense of resources), what are some texts you would recommend in algebra and analysis to sharpen my skills before the exam? Thanks!

The Quals at my home institution follow closely with

Dummit and Foote, Abstract Algebra

Gerald Follad, Real Analysis

Dummit and Foote, Abstract Algebra

Gerald Follad, Real Analysis

It probably would be better to consult with your grad department and focus on the material they use.

Here's what I found from UNC's Graduate Handbook:

There are five qualifying exams:

Algebra: Math 676 and 677

Analysis: Math 653 and 656

Geometry-Topology: Math 680 and 681

Methods of Applied Mathematics: Math 668 and 669

Scientific Computation: Math 661 and 662

Looking through previous courses, it's safe to say the Algebra Qual follows Dummit and Foote, the Analysis Qual follows Ahlfors and Baby Rudin, and the rest follow their own texts.

Most schools use Dummit and Foote for their Algebra Qual, the top schools use Lang, and for some reason, my school uses Aluffi, Serre's Rep Thy, and A-M. There was a question on derived functors and another on integral closures on my Algebra Qual.

There are five qualifying exams:

Algebra: Math 676 and 677

Analysis: Math 653 and 656

Geometry-Topology: Math 680 and 681

Methods of Applied Mathematics: Math 668 and 669

Scientific Computation: Math 661 and 662

Looking through previous courses, it's safe to say the Algebra Qual follows Dummit and Foote, the Analysis Qual follows Ahlfors and Baby Rudin, and the rest follow their own texts.

Most schools use Dummit and Foote for their Algebra Qual, the top schools use Lang, and for some reason, my school uses Aluffi, Serre's Rep Thy, and A-M. There was a question on derived functors and another on integral closures on my Algebra Qual.

Find out what your department uses for the corresponding courses. You can probably find this by looking for course webpages from this year. At my department, the qualifying exams offered in the fall (the ones you can take upon entry if you are just starting) are written by the same professor who taught the course the previous year. Of course, this may be different at your department.

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