Corequisite or Prerequisite 64311 Unified Calculus I

Description

This course is designed to introduce students to the techniques of understanding and writing mathematical proof. Emphasis is on technical writing and on the language skills necessary for clear and concise communication in mathematics. Problems from a variety of mathematical areas are considered. Topics include set notation and operations, propositional and predicate calculus, elementary proof techniques, and induction.

Statement of Course Need

Honors courses in mathematics have been developed to provide mathematically talented students the opportunity to obtain a level of rigor not currently available in existing courses. The concept of mathematical proof is fundamental to all areas of mathematics, but is not stressed in any of the currently offered-courses. The ability to understand the underlying logic in proof requires effective mathematical communication. This course will introduce the student to both the language and the logic used by mathematicians to work through problems that can not be solved by simply plugging numbers into a template.

Place of Course in College Curriculum

1. Satisfies general education requirements in mathematics and science.
2. Serves as one-credit of a mathematics elective for all programs.
3. Serves as one-credit of an honors elective in mathematics.

1. Work with complex mathematical statements, including definitions, conjectures, and theorems.
2. Understand the logical relationship between similar-looking mathematical definitions and theorems.
3. Comprehend and write proofs from different areas of mathematics.
4. Demonstrate skill in thinking precisely and communicating one's thoughts effectively in the terminology and style used by professional mathematicians.

1. Sets and Numbers
   1. Numbers and problem solving
   2. Set definition
   3. Operations
   4. Axioms
2. Language and Proofs
   1. Quantifiers and logical statements
      1. negation
      2. word order
      3. terminology and notation
      4. order of quantifiers
      5. negation of quantifiers
   2. Compound statements and sets
      1. logical connectives
      2. logical equivalences
   3. Elementary Proof Techniques
      1. Direct
      2. contrapositive
      3. contradiction
3. Induction
   1. Principle of induction
   2. Applications
   3. Strong induction

Methods for student Evaluation
Will vary according to the instructional style of the teaching faculty.
Lab Fees--None; Date: Jan, 1997, Sponsoring Dept: Mathematics