Notes & Exams

Preliminary & Qualifying Exam Study Materials

Below you can find a number of study materials compiled by various Ph.D. students as they prepared for their preliminary and qualifying exams. When using these guides, always fully attempt the problem first before looking at any solution. The absolute worst way to prepare for the preliminary or qualifying exams would be to read through these guides like a book. The onus is on you, as a Ph.D. student, to use these responsibly. These guides may contain errors; however, they come as is. Even when correct, these guides may not represent the best possible argument or may contain other issues. You have been warned! Note in the case of the Analysis and Complex Quals, students will often intermix their materials because the exams are linked. Therefore, if you are looking for materials for one or the other, be sure to check all the links in both for materials! We thank all the initialed contributors for their amazing contributions to these guides! To contribute to these study materials, email the MGO Webmaster (find their email here).

Analysis & Algebra Prelims

Algebra Prelims

Analysis Prelims

Statistics Prelims

Currently not available.

Algebra Qual

Analysis Qual

Complex Qual

Topology Qual

Course Notes

Below you can a number of lecture notes from various graduate mathematics courses at Syracuse University. You should these notes to supplement your learning. They are not intended to replace your course notes nor do they necessarily have to be exactly representative of what you will cover. Moreover, these notes do not excuse failing to attend the course! These notes may contain errors; however, all notes come as is. We thank all the initialed contributors for their amazing contributions to these course notes! To contribute to these notes, email the MGO Webmaster (find their email here).