Introduction to Mathematical Proofs: A Transition to Advanced Mathematics: 26 (Textbooks in Mathematics)
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Introduction to Mathematical Proofs: A Transition to Advanced Mathe...
Book Details
• Author: Roberts, Charles
• Brand: CRC Press
• Edition: 2
• Binding: Hardcover
• Number Of Pages: 416
• Release Date: 17-12-2014
• ISBN-13: 9781482246872
• Languages: English
Details:
Introduction to Mathematical Proofs helps students develop the necessary skills to write clear, correct, and concise proofs. Unlike similar textbooks, this one begins with logic since it is the underlying language of mathematics and the basis of reasoned arguments. The text then discusses:
• Deductive mathematical systems
• Systems of natural numbers, integers, rational numbers, and real numbers
• Elementary topics in set theory
• Properties of relations and functions
• Theorems proved using induction
The final chapters introduce:
• Cardinalities of sets
• Concepts and proofs in real analysis and group theory
The book includes more than 125 new exercises titled More Challenging Exercises, numerous examples illustrating how to write proofs and solve problems, and biographical sketches and historical comments to enrich the text. Written in a conversational style with mathematical rigor, it prepares students for advanced mathematics courses such as abstract algebra and analysis.
