# Why do we learn algebra

## Learning from sample solutions for analysis and linear algebra

The mastery of the basic course in mathematics is largely determined by successfully solving the given exercises. However, this requires a professionalism that students have to slowly grow into. This book aims to support you in this process. It creates role models in the form of detailed sample solutions for typical tasks from analysis and linear algebra. In addition, it provides instructions for understanding, practicing and reflecting on essential strategies and techniques. The book aims to present the complete solution paths including the generation of ideas and possible alternatives. In the exercise part, switching back and forth between compressed and detailed sample solutions is trained.

Basics of learning theory - phase model - sample solutions from Analysis 1- sample solutions from Analysis 2 - sample solutions from linear algebra 1 - sample solutions from linear algebra 2 - writing detailed sample solutions - writing compressed sample solutions - proposed solutions to the comprehension questions and to the exercises

First-year students in mathematics

Lecturers for mathematics and didactics of mathematics

Dr. Christoph Ableitinger received his doctorate in mathematics didactics and is currently working on the "Understanding Mathematics Better" project at the University of Duisburg-Essen.

Angela Herrmann studied mathematics and chemistry for high school teaching and is currently also working on the “Understanding Mathematics Better” project at the University of Duisburg-Essen.

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