An Introduction to Proofs and the Mathematical Vernacular 1st Edition by Martin V Day

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Author: Martin V. Day

An Introduction to Proofs and the Mathematical Vernacular by Martin V. Day is designed for undergraduate students beginning their transition from computational mathematics to theoretical mathematics. The book introduces students to the language and structure of mathematical proofs and helps build the foundational skills necessary for more advanced courses in mathematics.

This text emphasizes clarity in writing and logical reasoning, guiding students through key concepts such as set theory, logic, functions, relations, and induction. What sets this book apart is its focus on the “mathematical vernacular”—the precise language and style used in mathematical writing. Through examples, exercises, and carefully structured explanations, students are trained to read and write proofs in a way that aligns with how mathematicians communicate.

Whether used in a “bridge” course or for self-study, this book supports learners in becoming confident and competent in proof-based mathematics.

Table of contents:

Preface: To the Student
1 Some Specimen Proofs
2 Mathematical Language and Some Basic Proof Structures
3 Sets and Functions
4 The Integers
5 Polynomials
6 Determinants and Linear Algebra in R
Appendix: Mathematical Words
Appendix: The Greek Alphabet and Other Notation
Bibliography
Index

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Tags: Martin V Day, An Introduction, to Proofs and the, Mathematical Vernacular