UCSB Math Qualifying Exams

Created on June 7, 2017

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Graduate Program Handbook

Previous qualifying exams (log-in with your UCSB Gmail account)

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Analysis

Here are my (very rough) solutions of old analysis qual problems (use your UCSB connect account to log in). Use them as a guide as you would need to provide full details in the actual exam.

• Common examples and couterexamples

• Commonly used theorems

• Analysis Qual Book, courtesy of Alumni Jon T. Lo Kim Lin.

Texts

• A good reference text for Real Analysis is Rudin’s Principles of Mathematical Analysis (chapters 1-7).

• And for Complex Analysis: Basic Complex Analysis by Marsden and Hoffman.

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Algebra

Added May 6, 2019

• Fall16 solution

• Groups

• Rings

• Some useful formulas

• Algebra Qual Book

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Geometry

Added April 27, 2019

• Solutions to some commom problems

• Elementary Differential Geometry Cookbook

• Sp17Full, Sp16, Sp15, F16, F15

• Condensed notes from Pressley

• Some useful formulas

• Notes on isometries

• Geometry Qual Book

Texts

• Elementary Differential Geometry by A. Pressley (Springer Undergraduate Mathematics Series 2010) (chapters 1-10, 13) [SpringerLink]

• Differential Geometry of Curves and Surfaces by M. P. do Carmo (2nd edition, Dover 2016) (chapters 1-4)

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Other Resources

• Nice qual study guides by Jim Hateley.

• Berkeley Problems in Mathematics by de Souza and Silva [Springer 2004]. (This book is also really good for learning how to write clear and consise proofs from.)

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Good luck and have fun preparing!