Carnegie Mellon University

Mathematical Sciences

Mellon College of Science

Mellon College of Science › Mathematical Sciences › Graduate › Ph.D. Programs › Previous and Sample Basic Exams

Previous and Sample Basic Examinations

1. General Topology

general_topology_basic_exam_sample_I [pdf]
general_topology_basic_exam_sample_II [pdf]
general_topology_2013-2 [pdf]
general_topology_2015-1 [pdf]
general_topology_2015-2 [pdf]
general_topology_2016-1 [pdf]
general_topology_2016-2 [pdf]
general_topology_2017-1 [pdf]
general_topology_2017-2 [pdf]
general_topology_2018-1 [pdf]
general_topology_2018-2 [pdf]
general_topology_2019-1 [pdf]
general_topology_2019-2 [pdf]
general_topology_2020-1 [pdf]
general_topology_2020-2 [pdf]
general_topology_2021-1 [pdf]
general_topology_2021-2 [pdf]
general_topology_2022-1 [pdf]
general_topology_2022-2 [pdf]
general_topology_2023-1 [pdf]
general_topology_2023-2 [pdf]

2. Functional Analysis

functional_analysis_basic_exam_sample [pdf]
functional_analysis_2014-2 [pdf]
functional_analysis_2015-1 [pdf]
functional_analysis_2015-2 [pdf]
functional_analysis_2016-2 [pdf]
functional_analysis_2017-2 [pdf]
functional_analysis_2018-2 [pdf]
functional_analysis_2019-2 [pdf]
functional_analysis_2020-1 [pdf]
functional_analysis_2020-2 [pdf]
functional_analysis_2021-1 [pdf]
functional_analysis_2021-2 [pdf]
functional_analysis_2022-1 [pdf]
functional_analysis_2022-2 [pdf]
functional_analysis_2023-2 [pdf]

3. Measure and Integration

4. Probability

5. Set Theory

6. Algebra

7. Model Theory

model_theory_basic_exam (to appear)

8. Discrete Mathematics

DMPC_basic_exam_sample [pdf] (Old format Discrete Mathematics and Probabilistic Combinatorics exam)
DM_2019-1 [pdf]
DM_2020-1 [pdf]
DM_2023-1 [pdf]

9. Probabilistic Combinatorics

DMPC_basic_exam_sample [pdf] (Old format Discrete Mathematics and Probabilistic Combinatorics exam)
PC_basic_exam_sample [pdf]
probabilistic_combinatorics_2023-1 [pdf]
probabilistic_combinatorics_2023-2 [pdf]

10. Differential Equations