# Comprehensive Examination

Each graduate student will take a comprehensive examination upon completion of the 12 hour math/stat core coursework.

### Content

Below are the key concepts that students should expect on the comprehensive examination. A few notes: These lists are only subsets of the course material that students will be responsible for as part of the course grade, i.e., faculty expectations in each course will include but not be limited to mastery of these concepts. Also, a particular seating for the comprehensive examination might not include every topic listed below.

- MAT 5230: Linear Algebra.

- Mastery of computational skills from undergraduate linear algebra
- Understanding of theoretical concepts related to real and complex vector spaces and linear transformations
- Understanding of spectral theory and diagonalization
- Understanding of inner product spaces and orthogonality

- MAT 5330: Mathematical Modeling.

- Knowledge of the cycle and process of modeling
- Ability to create a mathematical formulation of a problem
- Ability to produce, interpret, analyze, and critique a formulation or solution
- Understanding of the roles sensitivity and uncertainty play in the modeling process

- MAT 5610: Analysis I.

- Understanding of continuity and uniform continuity
- Mastery of limit definitions for differentiation and integration
- Understanding of convergence and divergence of sequences and series
- Understanding of point-wise and uniform convergence and applications to integration

- STT 5811: Statistical Concepts and Applications I.

- Appropriate use of technology
- Appropriate presentation of graphics and descriptive statistics
- Understanding of probability and sampling distributions
- Understanding of statistical inference, including using correct procedures, and drawing proper conclusions

### Timing and Administration

The exam will be offered each April, November, and July at approximately mid-month, and students are expected to take the exam as soon as they have completed the core courses.

The exam will consist of a seated, timed component and a take-home component. The take-home component is designed to be completed in 6-8 hours; however, in order to accommodate studentsâ€™ class and teaching schedules, they will be given 5 days to finish the take-home component.

### Grading

Students will be graded based upon the following standards.

- Strong Pass: The student has demonstrated deep understanding of core concepts in each area through thoughtful, clear, and professional writing.
- Pass: The student has demonstrated at least basic understanding of core concepts in each area.
- Indeterminate: The student has demonstrated strong or basic understanding of core concepts in some but not all of the areas. These students may be required to answer some additional questions successfully to earn a passing grade.
- Fail: The student has not demonstrated at least basic understanding of core concepts in several areas. These students will be given one opportunity to retake the examination; while the standard timeline will be to take the examination again at the next regular offering, students taking the exam for the first time during their last term of enrollment may be granted permission to complete a retake after waiting two weeks.

## Contact

Program Directors

Ross Gosky and Holly Hirst

828.262.3050

gradmath@appstate.edu

or individually:

GoskyRM@appstate.edu

HirstHP@appstate.edu