Prefix, Number and Name of Course: MAT 491 Capstone Research in Mathematics

 

Credit Hours: 3                  

In Class Instructional Hours: 3                Labs:  0          Field Work: 0

 

Catalog Description:

Prerequisites: MAT301, MAT417, and senior status; or instructor permission.

Independent research under the direction of the instructor. Composition of a research paper and presentation of results at a seminar for faculty and students.

 

Reasons for Addition:

To provide a framework in which students can work on a comprehensive project and foster independent learning and discovery in mathematics. This capstone course will more fully develop our studentsŐ research, writing and presentation skills before they begin their careers. Students will engage in the exploration and communication of mathematical ideas not covered in their prior mathematics courses. MAT 491 will be the culmination of a mathematics major's experience in our department.

 

 

Student Learning Outcomes

Students will:

Content

References

Assessment

 

1. Integrate mathematical knowledge learned in other mathematics courses.

II; IV

1. Oral presentations, written exams and term research projects.

2. Demonstrate, at an advanced level, command of the methods and techniques of modern mathematics.

II; III

2. Results of preliminary investigations, oral presentations and research projects.

3. Apply mathematical laws and theories in the conduct of research in mathematics.

II; III

3. Oral presentations, written exams and term research projects.

4. Demonstrate ability to communicate mathematical ideas with clarity and precision by means of written reports and oral presentations.

II; IV; V

4. Quality of class presentations, research papers, presentations.

5. Locate, read, and interpret mathematical literature. Compose an annotated bibliography and abstract.

II; III; IV

5. Outcomes obtained and reported on preliminary investigations; research papers; presentations.

 

Text Box: Course Content: I. OVERVIEW OF CORE MATHEMATICS: LINEAR ALGEBRA, ABSTRACT ALGEBRA AND REAL ANALYSIS A. Review of vector spaces; linear dependence, basis and dimension; matrices and determinants; linear systems; linear transformations B. Review of group theory C. Review of sequences, continuous functions, limits of functions, differentiation, mean-value theorem, the Riemann integral II. ADVANCED TOPICS IN LINEAR ALGEBRA, ABSTRACT ALGEBRA AND REAL ANALYSIS A. Topics in Linear Algebra: Characteristic polynomials, upper triangular and Jordan canonical forms, inner product spaces, linear functionals, duality B. Topics in abstract algebra: Rings, fields, Integral domains, field extensions, Galois theory C. Topics in real analysis: Topology, compact sets, metric spaces, the Lebesgue integral III. RESARCH EXPERIENCE IN MATHEMATICS A. Research topics and problems selected by each student B. Instructor works with each student on his/her topic or problem C. Students present preliminary results to the class and instructor IV. WRITING RESEARCH IN MATHEMATICS A. Instructor regularly reviews drafts and addresses any shortcomings B. Classmates critique research drafts and presentations C. Final completion of all research papers V. CAPSTONE PRESENTATION A. Students present their research papers to the class, to the mathematics department and at the annual Student Research and Creativity Celebration.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Resources:

 

Classic Scholarship in the Field:

 

Gallian, J., How to Give a Good Talk, Math Horizons, MAA, Vol. 5, Apr 1998.

 

Gillman, L., Writing Mathematics Well: A Manual for Authors, MAA, Washington, D.C., 1987.

Krantz, S. G., A Primer of Mathematical Writing, AMS, 1997, 223 pp.

 

Current Scholarship in the Field:

 

CUPM Curriculum Guide 2004, a publication of the Mathematical Association of America on undergraduate programs and courses in the mathematical sciences.

 

Bolinger, K. D.; Engle, R. A.; Gendler, S. I.; McConnell, M. J., Ten Years of Change: The Evolution of a Senior Seminar, Primus, Vol. 11, No. 4, pgs. 347-58, Dec 2001.

 

Hathaway, D. K.; Atkinson, D., The Senior Seminar: Preparation for Life After College, Primus, Vol. 11, No. 4, pgs. 326-36, Dec 2001.

 

Mastrangeli, J., Practice Makes Almost Perfect: A Seminar Experience, Primus, Vol. 11, No. 4, pgs. 337-46, Dec 2001.

 

Periodicals:

 

American Mathematical Monthly, a publication of the Mathematical Association of America, http://www.maa.org/pubs/monthly.html

 

Pi Mu Epsilon, an undergraduate mathematics journal, http://www.pme-math.org

 

Primus, A quarterly journal devoted to all aspects of teaching undergraduate mathematics, http://www.dean.usma.edu/math/pubs/primus/

 

The College Mathematics Journal, a publication of the Mathematical Association of America, http://www.maa.org/pubs/cmj.html

 

The Pentagon, an undergraduate journal published by Kappa Mu Epsilon, http://www.kme.eku.edu/pentagon.html

 

The Rose-Hulman Institute of Technology Undergraduate Mathematics Journal, http://www.rosehulman.edu/mathjournal/navbar/nav.htm

 

Electronic and/or Audiovisual Resources:

 

http://www.maa.org/cupm/ Committee on the Undergraduate Program in Mathematics

 

http://www.maa.org/saum/ Supporting Assessment in Undergraduate Mathematics

 

http://web.mit.edu/jrickert/www/mathadvice.html Writing a Research Paper in Mathematics by Ashley Reiter

 

http://www.jcu.edu/math/constum/gallian.pdf How to Give a Good Talk ; The MAA suggests that students preparing to give a talk read Joseph Gallian's article in the April 1998, Math Horizons