About this title Focusing on the formal development of mathematics, this book shows readers how to read, understand, write, and construct mathematical proofs.
The mathematical content for this text is drawn primarily from elementary number theory, including congruence arithmetic; elementary set theory; functions, including injections, surjections, and the inverse of a function; relations and equivalence relations; further topics in number theory such as greatest common divisors and prime factorizations; and cardinality of sets, including countable and uncountable sets.
See Sections 1. Another important goal of this text is to provide students with material that will be needed for their further study of mathematics. Instruction in the Process of Constructing Proofs One of the primary goals of this book is to develop students' abilities to construct mathematical proofs.
Instruction on how to write proofs begins in Section 1. Following are some of the important ways this text will help with this transition. This type of course has now become a standard part of the mathematics major at many colleges and universities.Chapter 7 introduces the concepts of relations and equivalence relations. This is in contrast to many upper-level mathematics courses, where the emphasis is on the formal development of abstract mathematical ideas, and the expectations are that students will be able to read and understand proofs and be able to construct and write coherent, understandable mathematical proofs. All rights reserved. Emphasis on Writing in Mathematics The issue of writing mathematical exposition is addressed throughout the book. The primary goals of the text are as To help students learn how to read and understand mathematical definitions and proofs; To help students learn how to construct mathematical proofs; To help students learn how to write mathematical proofs according to accepted guidelines so that their work and reasoning can be understood by others; and To provide students with some mathematical material that will be needed for their further study of mathematics. Emphasis is placed on writing correct and useful negations of statements, especially those involving quantifiers. Includes ";Activities"; throughout that relate to the material contained in each section. A native of rural southern Virginia, he studied painting at Rhode Island School of Design before an interest in computer graphics and visualization led him to mathematics. In Chapter 4, we take a break from introducing new proof techniques. Chapter content covers an introduction to writing in mathematics, logical reasoning, constructing proofs, set theory, mathematical induction, functions, equivalence relations, topics in number theory, and topics in set theory. Share This: Book Description Mathematical Reasoning: Writing and Proof is a text for the first college mathematics course that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics. This is needed today because the principal goals of most calculus courses are developing students' understanding of the concepts of calculus and improving their problem-solving skills. Since this is a text that deals with constructing and writing mathematical proofs, the logic that, is presented in Chapter 2 is intended to aid in the construction of proofs. Chapter 8 continues the study of number theory. These guidelines are introduced as needed and begin in Chapter 1.
This type of course is becoming a standard part of the mathematics major at most colleges and universities.