An Introduction to Writing Mathematical Proofs: Shifting Gears from Calculus to Advanced Mathematics

Name: An Introduction to Writing Mathematical Proofs: Shifting Gears from Calculus to Advanced Mathematics
Brand: Academic Press
SKU: 9780443439247
Price: 5763.0 INR
Availability: InStock

by Thomas Bieske

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ISBN13: 9780443439247
Binding: Paperback
Subject: N/A
Publisher: Academic Press
Publisher Imprint: Academic Press
Publication Date: January 13, 2026
Pages: 122
Original Price: USD 100.0
Language: English
Edition: N/A
Item Weight: 450 grams
BISAC Subject(s): General

About The Book

An Introduction to Writing Mathematical Proofs: Shifting Gears from Calculus to Advanced Mathematics addresses a critical gap in mathematics education, particularly for students transitioning from calculus to more advanced coursework. It provides a structured and supportive approach, guiding students through the intricacies of writing proofs while building a solid foundation in essential mathematical concepts. Sections introduce elementary proof methods, beginning with fundamental topics such as sets and mathematical logic, systematically develop the properties of real numbers and geometry from a proof-writing perspective, and delve into advanced proof methods, introducing quantifiers and techniques such as proof by induction, counterexamples, contraposition, and contradiction.

Finally, the book applies these techniques to a variety of mathematical topics, including functions, equivalence relations, countability, and a variety of algebraic activities, allowing students to synthesize their learning in meaningful ways. It not only equips students with essential proof-writing skills but also fosters a deeper understanding of mathematical reasoning. Each chapter features clearly defined objectives, fully worked examples, and a diverse array of exercises designed to encourage exploration and independent learning. Supplemented by an Instructors' Resources guide hosted online, this text is an invaluable companion for undergraduate students eager to master the art of writing mathematical proofs.

About The Author

Bieske, Thomas: -

Professor Thomas Bieske earned his PhD from the University of Pittsburgh, United States, in 1999. His research concerns partial differential equations and analysis in metric spaces, with a focus on sub-Riemannian spaces. Professor Bieske is currently serving as the Department of Mathematics and Statistics Chair of the Undergraduate Committee-Upper Level, focusing on the performance of mathematics and statistics majors in upper-level courses, at the University of South Florida, Tampa, United States.

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