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Preface Preface

This text is intended for a first course in proof-writing. The course builds fluency with proof techniques through examples from discrete math, number theory, and set theory. It emphasizes learning mathematical structure from logic and applying the strucure in a variety of contexts.
The material was developed for an Introduction to Proofs course at Linfield University. The course is currently taught as an intensive one month “January Term” course. The course is generally taken by math majors in their first year or two or by math minors who wish to improve their proof-writing ability.
There are no specific prerequisites besides some familariy with mathematical statements. The text assumes a familiarity with calculus, but only in that it references examples of statements from calculus. A background in calculus is not required for the content of the course.

Course Goals.

  • To introduce basic mathematical terminology such as sets, functions, relations, and cardinality.
  • To introduce proof techniques such as direct proof, proof by contrapositive, proof by contradiction, and mathematical induction.
  • To develop proficiency in both reading and writing mathematical proofs.
  • To develop an understanding of logical structure.
  • To increase confidence in working through mathematical challenges.
  • To foster an appreciation and use of abstract reasoning.
  • To improve problem-solving abilities.