Up to an including the college-level calculus series (generally 2 years of study), students generally focus on the calculational side of mathematics. Advanced courses tend to focus more on concepts and students are expected to produce “proofs” of mathematical statements.

Martin Day from Virginia Tech was finding it difficult to find a textbook that helped students bridge the switch in focus. He wanted to help students “start thinking in terms of properties of mathematical objects and logical deduction, and to get them used to writing in the customary language of mathematics.” He explains that too many textbooks view proofs as a meaningless ritual (I remember those and saw them much the same way). His goal is to encourage students to begin thinking like mathematicians.

This text may not be entirely beneficial for self-study. Day feels providing solutions to students offers a temptation most cannot resist. He implores instructors to not make them available in electronic format and emphatically states that he will not make them available to students who request them. He suggests students seek help from an experienced mathematician.

## Chapter Titles of *An Introduction to Proofs and the Mathematical Vernacular* Textbook

- Some Specimen Proofs
- Mathematical Language and Some Basic Proof Structures
- Sets and Functions
- The Integers
- Determinants and Linea Algebra in R
^{n}.

*An Introduction to Proofs and the Mathematical Vernacular* also includes an appendices entitled Mathematical Words and The Greek Alphabet and Other Notation.

View this Free Online Material at the source:

An Introduction to Proofs and the Mathematical Vernacular