Department of Mathematics
Course Proposal
I. Number and title of course
Mathematics 270 - Discrete Mathematics III. Reasons for modification of present curricula
A. To provide a greater emphasis on proof and proof techniques
B. To eliminate the section on graph theory, which is taught in MAT 370III. Major objectives of the course
A. The student will be introduced to the non?continuous side of mathematics.
B. The student will gain skills, using the tools and vocabulary of mathematical rigor, in writing original proofs.IV. Topical outline
A. The language of mathematics.
1. The role of proof, conjecture, theorem, and counter?example.
2. The language of sets.B. Logic.
1. Sentential logic.
2. Quantificational logic.C. Introduction to proof.
1. Proofs in mathematics.
2. Analysis of the logical form of a mathematical statement.
3. Proof strategies.D. Induction.
1. The Principle of Mathematical Induction.
2. Inductive definitions.
3. Solving recurrence relations (optional).E. Set Theory.
1. Set operations and relationships.
2. Proofs about set operations and relationships.
3. Indexed families of sets.F. Functions and relations.
1. Properties of relations.
2. Equivalence relations.
3. Definition of a function.
4. Properties of functions (one?to?one, onto, composition, inverse).G. Counting Methods.
1. Sum and product rules.
2. Permutations and combinations.
3. Binomial theorem.
4. Pigeon-hole principle.
5. Inclusion-exclusion principle.
Barnier & Feldman, Introduction to Advanced Mathematics, Prentice Hall, NJ, 1990.
Baxter, N., Dubinsky, E. & Levin, G., Learning Discrete Mathematics with ISETL, Springer?Verlag, New York, 1989.
Dymacek, W. & Sharp, H. Jr., Introduction to Discrete Mathematics, McGraw?Hill, Boston, MA, 1998.
Epp, Susanna, Discrete Mathematics with Applications, PWS, Albany, NY, 1995.
Fletcher, Peter & Patty, C. Wayne, Foundations of Higher Mathematics. 2nd Edition, PWS?Kent, Boston, 1992.
Goodaire, E. & Parmenter, M., Discrete Mathematics with Graph Theory, Prentice Hall, Upper Saddle River, NJ, 1998.
Grimaldi, Ralph, Discrete and Combinatorial Mathematics, Addison?Wesley, Reading, MA, 1994.
Johnsonbaugh, Richard, Discrete Mathematics, Prentice Hall, Upper Saddle River, NJ, 1997.
Saddle River, NJ, 1996.
Maurer, Stephen & Ralston, Anthony, Discrete Algorithmic Mathematics, AddisonWesley, Reading, MA, 1991.
Kenney, Margaret, ea., Discrete Mathematics across the Curriculum. K?12, 1991 Yearbook, National Council of Teachers of Mathematics, Reston, VA, 1991.
Rosen, Kenneth, Discrete Mathematics and Its Applications, McGraw?Hill, New York, NY, 1995.
Ross, K. & Wright, C., Discrete Mathematics, Prentice Hall, Englewood Cliffs, NJ, 1992
Rotman, Joseph, Journey into Mathematics, Prentice Hall, NJ, 1998.
Schumacher, Carol, Fundamental Notations of Abstract Mathematics, Addison?Wesley, NY, 1996.
Solow, Daniel, How to Read and Do Proofs, Second Edition, John Wiley & Sons, New York, 1990.
Velleman, Daniel, How to Prove It, Cambridge University Press, NY, 1994.VI. Presentation and Evaluation:
Presentation through lectures, class discussions, and computer demonstrations. Evaluation through projects, assigned problems, and written examinations.VII. Prerequisites
MAT 126 or MAT 161.
VIII. Credit
3 semester hours.
IX. Departmental Approval
This course proposal was examined in accordance with recommended procedures and was approved by the faculty of the Mathematics Department on______________________(Date) ________________________Department ChairX. Catalog Description
MAT 270 - DISCRETE MATHEMATICS I.This course is an introduction to the non-continuous side of mathematics. The student will gain skills in proof, logic, sets, relations,functions, and counting methods.XI. Statement of Qualifications:
A. A masters' degree in mathematics is the minimum formal education required.
B . Several members of the Mathematics Department meet this requirement, including the following: Dr. Daniel Cunningham, Dr. Joaquin Carbonara, Dr. Robin Sanders, Dr. Eileen SchoaffXII. Support Services Required:
Current classroom facilities are adequate.