A Transition to Proof An Introduction to Advanced Mathematics Textbooks in Mathematics Series
Auteur : Nicholson Neil R.
A Transition to Proof: An Introduction to Advanced Mathematics describes writing proofs as a creative process. There is a lot that goes into creating a mathematical proof before writing it. Ample discussion of how to figure out the "nuts and bolts'" of the proof takes place: thought processes, scratch work and ways to attack problems. Readers will learn not just how to write mathematics but also how to do mathematics. They will then learn to communicate mathematics effectively.
The text emphasizes the creativity, intuition, and correct mathematical exposition as it prepares students for courses beyond the calculus sequence. The author urges readers to work to define their mathematical voices. This is done with style tips and strict "mathematical do?s and don?ts", which are presented in eye-catching "text-boxes" throughout the text. The end result enables readers to fully understand the fundamentals of proof.
Features:
- The text is aimed at transition courses preparing students to take analysis
- Promotes creativity, intuition, and accuracy in exposition
- The language of proof is established in the first two chapters, which cover logic and set theory
- Includes chapters on cardinality and introductory topology
Symbolic Logic
Sets
Introduction to Proofs
Mathematical Induction
Relations
Functions
Cardinality
Introduction to Topology
Properties of the Real Number System
Proof Writing Tips
Selected Solutions and Hints
Dr. Neil R. Nicholson is Associate Professor of Mathematics at North Central College. He holds a Ph.D. in Mathematics from The University of Iowa, specializing in knot theory. His research interests have consistently been topics accessible to undergraduates; collaborating with them on original research is a fundamental goal of his professional development. In 2015, he earned the Clarence F. Dissinger Award for Junior Faculty Teaching at North Central College. He serves as the Faculty Athletic Representative to the NCAA for North Central College.
Date de parution : 01-2023
15.6x23.4 cm
Date de parution : 03-2019
15.6x23.4 cm
Thèmes d’A Transition to Proof :
Mots-clés :
Water Park; Transition to advanced mathematics; Vice Versa; Proof theory; Real Number Line; Logic; Subspace Topology; Set theory; Topological Space; Mathematical induction; Standard Topology; Functions; Truth Table; logical reasoning; Discrete Topology; inductive reasoning; Open Intervals; mathematical voice; Point Set Topology; symbolic logic; Logically Equivalent; mathematical do's and don'ts; Partitioning Sets; Pigeonhole Principle; Mathematical Expression; Logical Connectives; General Continuous Function; Open Set; Product Topology; Prove Corollary; Logical Deduction; Countable Sets; Modus Ponens; Finite Sets; Conditional Statement; Infinite Sets