Applied Nonstandard Analysis: Coloring Book

Book Details:

• Publisher: Dover

• Author: Martin Davis

• Language: English

• Binding: Paperback

• Edition: 1st Edition

• ISBN: 9780486442297

• Number of Pages: 208

• Dimensions: 8.5 x 5.5 x 0.8 inches

• Release Date: 26-07-2005

About The Book:

"The Logic of Nonstandard Analysis" by Martin Davis is a comprehensive introduction to the applications of nonstandard analysis, designed for upper-level undergraduates and graduate students. The book explores the key techniques of nonstandard analysis without requiring any prior knowledge of mathematical logic.

The text begins with a powerful construction and builds from there, providing a nonstandard approach to the real number system. Students are guided through nonstandard treatments of basic topics in elementary real analysis, topological spaces, and Hilbert space. This approach allows students to see the concepts of analysis from a new perspective, offering insight into the flexibility and applicability of nonstandard methods.

The book focuses on presenting the material in a clear and accessible manner, making it suitable for students who are not yet familiar with the complexities of mathematical logic but are interested in exploring the applications of nonstandard analysis in various mathematical fields.

Key Features:

• Approach to Nonstandard Analysis: Focuses on the practical applications of nonstandard analysis with a powerful construction as the foundation.

• No Assumed Knowledge of Mathematical Logic: Suitable for students with no prior exposure to mathematical logic, making it accessible to a broader audience.

• Comprehensive Treatment: Covers essential topics such as the real number system, elementary real analysis, topological spaces, and Hilbert space, all from a nonstandard analysis perspective.

• Clear and Accessible Style: Written in an accessible style, ensuring that students can grasp complex concepts without prior background in logic.

Ideal for:

• Upper-level Undergraduates and Graduate Students: Especially those studying advanced mathematics and analysis, looking to explore nonstandard approaches.

• Educators: A useful resource for teaching nonstandard analysis to students with basic knowledge of real analysis and topology.

• Researchers: A valuable introduction to nonstandard methods for those looking to apply them in research areas such as analysis and topology.

Conclusion:

"The Logic of Nonstandard Analysis" provides a clear and approachable introduction to nonstandard analysis, making it an ideal textbook for students and researchers interested in this specialized area of mathematics. Through a nonstandard treatment of essential topics, it opens up new perspectives on familiar concepts in real analysis and topology, making it a valuable resource for learning and exploration.