This groundbreaking textbook makes the complex subject of algebraic geometry accessible to undergraduate students and beginning graduate students. Written by renowned Polish mathematician Prof. Jan Kowalski, it bridges the gap between abstract theory and concrete applications.
Foundations of Algebraic Geometry provides a fresh approach to this fundamental area of mathematics, making it accessible to a wider audience without sacrificing mathematical rigor. Starting with concrete examples and geometric intuition, Prof. Kowalski gradually introduces the abstract machinery that makes modern algebraic geometry such a powerful tool.
The book begins with classical algebraic varieties, using them to motivate the more abstract notion of schemes. This approach allows students to develop intuition before encountering the technical difficulties of scheme theory. Throughout the text, examples from projective geometry illuminate theoretical concepts, and historical notes provide context for the development of key ideas.
A distinguishing feature of this textbook is its emphasis on applications. Separate chapters are devoted to exploring how algebraic geometry is used in cryptography, coding theory, robotics, and computer vision. These sections provide concrete motivation for the abstract theory and demonstrate its relevance to modern technology.
The exercises range from routine calculations to challenging problems that develop deeper understanding. Complete solutions to selected exercises are provided at the end of the book, while additional problems and computational explorations are available on the companion website.
This new edition includes expanded coverage of tropical geometry and an introduction to derived categories, reflecting recent developments in the field that have found important applications.
| Language | English |
|---|---|
| Hardcover | 684 pages |
| Publisher | Warsaw Mathematical Press |
| Edition | 2nd Edition (2023) |
| ISBN | 978-83-7641-925-3 |
| Dimensions | 19 × 25 cm |
As someone working in computer vision research, I've found this book invaluable. Kowalski's ability to connect abstract algebraic concepts with practical applications is remarkable. The chapters on multiple view geometry have directly informed my research, and the exercises helped solidify my understanding. This is the text I wish I had during my graduate studies.
The book contains excellent material and the applications sections are fascinating. However, despite claiming to be accessible to undergraduates, I found some sections required more background than stated. The progression from varieties to schemes felt rushed, and additional examples would have been helpful. Still a valuable resource, but be prepared to supplement with other materials if you're new to the subject.
I've used this book for an advanced undergraduate/beginning graduate course for the past two years. The historical context and motivation Kowalski provides help students understand why algebraic geometry developed as it did. The applications chapters are particularly effective for engaging students from different backgrounds. My only suggestion would be to include more fully worked examples in the scheme theory sections.
