This course teaches the essentials from real analysis, which are relevant to informatics. Whenever possible, applications of theoretical concepts are highlighted. After finishing this course, students possess the mathematical skills required for solving basic problems in a formal and structured way and they will have developed a good understanding of differential and integral calculus.
This course consists of five chapters. After revisiting basic facts about natural numbers, integers, and rational numbers, the first milestone is to understand the concept of real numbers and their properties. We then study sequences and series of real numbers and learn about the idea of convergence. The third chapter introduces real functions in one variable and focuses on the property of continuity and its consequences. Differentiation and integration are covered in the last two chapters.
The topics are presented in the form of lectures and tutorials. Weekly homework assignments are handed out, graded, and discussed.
The course grade is determined by the results of the homework assignments (30%), the written midterm exam (30%), and the written final exam (40%).
- Kenneth A. Ross. Elementary Analysis: The Theory of Calculus. Undergraduate Texts in Mathematics. Second Edition. Springer, 2012
- Additional material will be provided through the course homepage.