Grundwissen Mathematikstudium – Analysis und Lineare Algebra mit Querverbindungen

This four-color textbook is aimed at students of mathematics in bachelor's and teaching degree programs. It provides a vivid picture of the mathematical content typically covered in the first year of study (and much more) in a single volume. Mathematics students will find important terms, theorems, and proofs explained in detail with many examples, and will be introduced to fundamental concepts and methods. The focus is on understanding mathematical relationships and the structure of theory, as well as the structures and ideas behind important theorems and proofs. It not only presents a coherent theoretical framework but also illustrates how it is developed and what the content will be used for later.

Outstanding features include:

• Consistently four-color layout with over 600 illustrations
• Concisely formulated key ideas serve as section headings
• Self-tests at short intervals allow for learning checks while reading
• Colored highlight boxes emphasize the most important points
• "Under-the-Microscope" boxes zoom into proofs, motivate, and explain details
• "Background-and-Outlook" boxes establish connections to other areas and advanced topics
• Summaries for each chapter as well as overview boxes
• More than 400 comprehension questions, calculation tasks, and proof problems
• German-English symbol and term glossary

The content focus is on the topics of the lectures Analysis 1 and 2, as well as Linear Algebra 1 and 2. Additionally, it covers content and methodological competencies that are often taught in the first year of mathematics education. Hints, solution paths, and results for all tasks in the book are available as PDF files on the publisher's website. The book will be a reliable companion for all mathematics students from the beginning of their studies through to higher semesters. The second edition has been thoroughly revised.