MATH 451
MATHEMATICAL LOGIC

  1. Catalog Entry

MATH 451. Mathematical Logic
Three hours lecture (3).

Prerequisites: MATH 403 or MATH 423 or MATH 430

An introduction to mathematical logic, including the completeness theorem for predicate calculus.

  1. Detailed Description of Content of Course

This course will cover the following topics:

1. Well-Formed Formulas
2. Rules of Inference
3. Propositional Calculus
4. Theorems and Proofs
5. First Order Theories with or without Equality
6. Deduction Theorem
7. Models and Satisfiability
8. Consistency
9. Lindenbaum's Lemma
10. Henkin's Proof of the Completeness Theorem for Predicate Calculus
11. Skolem-Lowenheim Theorem
12. Compactness Theorem
13. Categoricity of Theories
14. Decidability

  1. Detailed Description of Conduct of Course

This is a lecture based course. Presentations by students may also be required by the instructor. Students will develop an understanding of the material by working exercises.

  1. Goals and Objectives of the Course

This course is primarily for mathematics majors and includes as it goals:

1. to develop an understanding of the foundations of mathematics,
2. to develop a strong understanding of mathematical methods, including proofs and axiomatic systems.
3. to develop an understanding of the consistency and satisfiability of axiomatic systems.

  1. Assessment Measures

Assessment measures include a final examination and may include any of the following: in-class tests, quizzes, exercises, in-class presentations and research papers.

  1. Other Course Information

The instructor may require that the students use a computer in exercises designed to enhance the understanding of theoretical material.

  1. Review and Approval

DATE ACTION APPROVED BY
Sept. 2001 Review Stephen Corwin, Chair