Linear Algebra by ExamplePainos 1

This book offers a modular, concept-driven introduction to linear algebra designed for undergraduate students across mathematics, engineering, computer science, and the sciences. Emphasizing core ideas such as symmetry, transformation, and structure, it supports flexible pacing and multiple instructional pathways while remaining accessible to students with diverse mathematical backgrounds.

What sets this text apart is its intentional structure and student-centered design. Each chapter begins with a visual flowchart that makes dependencies explicit, allowing instructors to customize coverage. Proofs are introduced gradually through examples and activities rather than formal presentation, helping students develop mathematical reasoning with confidence.

Key features include:

• Modular chapter design with dependency flowcharts
• Scaffolded examples and classroom-tested activities
• Integrated SageMath and Python exploration
• Built-in AI prompts for responsible, productive use
• Applications ranging from classic topics to ray tracing, molecular symmetry, and structural engineering

This book is intended for first undergraduate courses in linear algebra, including service courses and active-learning classrooms, and is suitable for both instruction and self-study.