**Department of Mathematics & Computer Science**

The Department of Mathematics and Computer Science have outlined specific comprehensive examination guidelines for each discpline:

**Mathematics Comprehensive Examination Guidelines****Computer Science Comprehensive Examination Guidelines**

#### Mathematics Comprehensive Examination Guidelines

The comprehensive examination in the Ph.D. degree program majoring in Theoretical and Computational Science with a concentration in Applied Mathematics or Pure Mathematics consists of two separate 3-hour written comprehensive examinations from the following two areas: Analysis and Algebra. In addition, there is an oral component to the comprehensive examination which will take place after a student has passed the written component.

To guide the committee’s evaluation of the written portion of the comprehensive exams, the Department Graduate Education Committee Chair or Graduate Coordinator in Mathematics and Computer Science directs that each examination be graded by an expert in the appropriate area. If a student obtains at least 60% in each area, the student shall pass the written component. If a student has an average score of less than 50%, the student shall fail and shall be required to rewrite both exams (if this is the first attempt). In the case of any other outcome, the comprehensive examination committee will meet, review the exams, and make a decision as to whether the student has passed or needs to rewrite one or both exams.

The written portion of the graduate comprehensive examination for students with a concentration in Applied Mathematics or Pure Mathematics will test material that might normally be taught in the following two areas: Analysis 5505/7505 and Algebra 5405/7405 (combined with material taught in our undergraduate offerings). The precise topics and references can be obtained from the Chair of the Department Graduate Education Committee in Mathematics and Computer Science. A list of approximately 100 problems in Analysis and a list of approximately 100 problems in Algebra will be provided to the students. Problems on the comprehensive examinations will be substantively similar to problems on these lists. The lists, together with examples of problems that are “substantively similar,” can also be obtained from the Chair of the Department Graduate Education Committee.

Normally, a student should complete the written portion of the comprehensive exam within 9 months of entering the Ph.D. program. This portion of the exam must be satisfactorily completed with 12 months of entering the program. The oral component of the comprehensive examination will be on the student’s research topic for their thesis. It will consist of a 30-minute presentation by the student, followed by questions from the committee. The maximum length of the oral exam is two hours, not including the presentation. The student’s comprehensive exam committee will decide upon the material to be covered in the presentation and the questions, and will provide this information to the student. This material could include chapters from a textbook or articles relevant to the proposed research project. The oral component of the comprehensive exam must be completed within 16 months of entering the program.

A maximum of two attempts on each written comprehensive examination is allowed. The student has two attempts to pass the oral exam. Please review the Comprehensive Examination Policy in the Graduate Studies Calendar and Course Catalogue for additional details.

The above deadlines may be waived by the Department Graduate Education Committee in exceptional circumstances.

## Computer Science Comprehensive Examination Guidelines

This proposal specifies the policies regarding the written component of the PhD comprehensive examination in the following major and concentration: Theoretical and Computational Science major with a concentration in Computer Science. For the oral component, the general policies as specified by the School of Graduate Studies Doctor of Philosophy Policies and Procedures will be followed.

All PhD students majoring in the above listed major and related concentration will be required to declare their research areas three months before the comprehensive examination as one of Algorithms, Systems, or Computational Intelligence. As part of the written comprehensive exam, each PhD student will be required to write an exam in the other two areas outside of his/her declared research area. The part of the written exam in the research area, as well as the oral component of the comprehensive exam, will be set by the Comprehensive Examination Committee.

A reading list, sample questions, and the exams for the written comprehensive exam in each of the three areas will be determined every two years by a committee of computer science faculty members in the area. A common exam in each area will be offered to PhD students majoring in the above listed major and related concentration twice a year, with opportunities to rewrite the exam, if necessary. A maximum of two attempts on each written comprehensive examination is allowed. The reading list will be given to the student at the beginning of his/her program. The length of the exam and criteria for passing the exam in each area will be determined by the committee and communicated to the students in advance. Each committee will be responsible for grading the exams in that area.

The student can take the oral component of the comprehensive exam only after he/she has passed the written exams. A maximum of two attempts on the oral component is allowed. Please review the Comprehensive Examination Policy in the Graduate Studies Calendar and Course Catalogue for additional details.