## Comprehensive Written Master’s Exam

The Department’s written comprehensive Master’s Exam is given in three subjects: the MS Algebra exam, the MS Analysis exam, and the MS Statistics exam. Master’s students who choose to take the MS Exams to satisfy the capstone requirement (alternatives for the capstone requirement are a thesis or project, see the graduate bulletin for detail) must pass any combination of two of these exams except those who choose the statistics option. Master’s students who choose the MS Statistics option must pass the MS Statistics exam and either the MS Algebra exam or the MS Analysis exam. Students can pass the exams one at a time; and there is no limitation on the number of times a student can take each exam. Each of the exams lasts three hours and is offered three times a year in one week in January, May/June, and August. The January and August MS exams are offered in the week preceding the first week of instruction, and the May/June MS exams are offered in the second week after the spring semester ends.

Students must sign up for the exams at least one week ahead of the scheduled exam dates. Approximately a month before the next scheduled exam week, the Department will send an email to inform the students about the coming MS exam and ask the students to sign up. If no students sign up for a particular subject exam, this subject exam will be cancelled. In the past, most students have taken the MS Algebra and the MS Analysis exams. Copies of past MS exams can be obtained from the Departmental main office.

### MS Algebra Exam

The MS Algebra exam is based on the course sequence Math 631 – 632 and it covers these topics: linear algebra, group theory, rings and modules.

**References:**

Algebra, M. Artin (2nd Ed): Chapters 1-4, Sections 6.7 – 6.11, 7.1 – 7.7, 7.9, 7.10, Chapter 8, Sections 11.1 – 11.8, Chapter 12, Sections 14.1, 14.2, 14.5, and 14.7;

or

Abstract Algebra, Dummit & Foote (3rd ed): Chapters 1-5, 7-8, 9.1-9.4, 10.1-10.2, 11.1-11.4, and Chapter 12.

### MS Analysis Exam

The MS Analysis exam is based on the course sequence Math 621-622 and it covers these topics: sequences, continuity, differentiation, integration, series and functions of several variables.

**References:
**Principles of Mathematical Analysis, Walter Rudin: Chapter 3-7 and Chapter 9;

or

A Friendly Introduction to Analysis, Witold A. J. Kosmala: Chapter 2-8 and Chapter 10-11.

MS Analysis Exam Example (PDF)

### MS Statistics Exam

The MS Statistics exam is based on the course sequence MthStat 761–762 and it covers these topics: axiomatics of probability, random variables and vectors, distributions, transformations, expected value and moments, asymptotics, point estimation, confidence intervals and hypothesis testing. References:

Statistical Inference, G. Casella and R.L. Berger (2002, second edition);

or

Modern Mathematical Statistics, E.J. Dudewicz and S.N. Mishra (1988).