This groundbreaking book makes the fascinating world of topology accessible to undergraduate students and mathematics enthusiasts. Through intuitive explanations, historical context, and carefully chosen examples, Prof. Lewandowski guides readers from basic topological concepts to advanced ideas.
Topology for Beginners offers a fresh approach to what is often considered one of the most challenging subjects in undergraduate mathematics. Rather than beginning with abstract definitions, Prof. Lewandowski introduces topological concepts through familiar examples and intuitive explanations, gradually building to more formal treatments.
The book begins with an exploration of continuity and connectedness in familiar settings before introducing topological spaces. Concepts such as compactness, separation axioms, and metric spaces are presented with numerous examples that highlight their relevance and applications. Throughout, the author emphasizes the geometric intuition behind topological ideas, using diagrams and metaphors that make abstract concepts tangible.
A distinguishing feature of this textbook is its accessibility. Each chapter opens with motivating questions and real-world applications, making the material relevant to students from various backgrounds. Historical notes are interspersed throughout, providing context about the mathematicians who developed topological concepts and the problems they were trying to solve.
The exercises range from computational practice to theoretical explorations, with many focused on developing intuition rather than technical mastery. Complete solutions to odd-numbered exercises are provided at the end of the book, while additional practice problems and interactive demonstrations are available on the companion website.
The final chapters introduce more advanced topics such as algebraic topology and manifolds, providing a glimpse into the rich landscape of modern topology while remaining accessible to beginners. These sections serve as a bridge to more specialized courses for students who wish to pursue the subject further.
| Language | English |
|---|---|
| Paperback | 482 pages |
| Publisher | Kraków Mathematical Press |
| Edition | 2nd Edition (2023) |
| ISBN | 978-83-2145-974-1 |
| Dimensions | 17 × 24 cm |
After struggling with several other topology textbooks, this one finally made the subject click for me. Lewandowski's approach of starting with intuitive examples before introducing formal definitions is brilliant. The historical notes provide context that helped me understand why topological concepts were developed. I particularly appreciated the applications to data science, which showed the relevance of the subject to my field of study.
I've adopted this book for my undergraduate topology course, and the results have been remarkable. Students who previously feared the subject are now engaged and enthusiastic. The carefully structured progression from concrete to abstract concepts helps build confidence, and the diverse exercises accommodate different learning styles. The applications chapters have been especially valuable for motivating students from applied mathematics and computer science backgrounds.
This is an outstanding introduction to topology that balances intuition with rigor. The author's writing style is engaging and clear, making difficult concepts accessible without sacrificing mathematical precision. My only suggestion would be to include more challenging exercises for students who want to push themselves further. That said, the companion website does provide additional problems, which partially addresses this issue.
