Are all cardinality groups ten isomorphic

Getting started with math right

Would you like to study mathematics, but you don't yet know what to expect?

In the first year of mathematics studies, the high degree of rigor and abstraction often represents a major hurdle - despite the significant content overlap with school mathematics. Often this is due to a shift in emphasis away from “arithmetic” towards understanding and developing mathematics. This book introduces readers to the scientific-mathematical way of thinking at universities without repeating school mathematics. Computer science students also receive a basis for understanding the concepts of their own subject and algorithmic access to mathematics, which is often only understood as a tool. The text is intended in particular for self-study, with many programming examples in Python and numerous exercises including all associated solutions and program codes.

The book is divided into two parts. The first part introduces the basics of logical work: Mathematics has to do with logic, but how exactly and what is logic? What is the basis for mathematical thinking, when are mathematical trains of thought precise and how do you express them and write them down? The second part deals with the question of what numbers actually are and where they come from. From the natural through the whole and rational numbers, the path leads to the real numbers, which can usually no longer be written down exactly as a decimal number, but can only be approximated as precisely as required. It is better to use a computer to carry out such calculation processes, so programming with Python is also introduced in parallel to mathematics.
All algorithms developed, starting with the definition of an addition by simple counting up to the arbitrarily precise approximation of the circle number π, are realized with it. In addition to a solid introduction to the basics of mathematics, the reader also receives the necessary tools for programming applications.

the authors

Prof. Dr. Peter Knabner has held the Chair of Applied Mathematics 1 at FAU Erlangen-Nürnberg for 25 years.

Balthasar Reuter works as a research assistant at FAU with numerics and parallel computing.

Dr. Raphael Schulz has been at FAU Erlangen-Nürnberg since 2012 and teaches in the fields of analysis and numerics.


Keywords

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Authors and affiliations

  • Peter Knabner
  • Balthasar Reuter
  • Raphael Schulz
  1. 1. Department of Mathematics, Chair of Applied Mathematics 1 University of Erlangen-NürnbergErlangenGermany
  2. 2nd Department of Mathematics, Chair of Applied Mathematics 1 University of Erlangen-NürnbergErlangenGermany
  3. 3. Department of Mathematics, Chair of Applied Mathematics 1University Erlangen-Nürnberg ErlangenGermany

About the authors

Prof. Dr. Peter Knabner obtained his doctorate in mathematics from the University of Augsburg and has been the owner for over 20 years
of the Chair of Applied Mathematics 1 at the FAU Erlangen-Nürnberg. In addition to his research in the
In the area of ​​analysis, modeling and numerics, teaching is very important to him. So is a series of textbooks
and exercise volumes were created, some of which are also available in English.

Balthasar Reuter studied Computational Engineering and Scientific Computing at the FAU Erlangen-Nürnberg and
of the KTH Stockholm. He has been working as a research assistant and doctoral candidate at FAU since 2013 and employs
deal with numerical methods for ocean modeling and parallel computing.

Dr. Raphael Schulz studied mathematics and physics at the TU Darmstadt and received his doctorate there in 2012. He is currently
research assistant and habilitation candidate at the FAU Erlangen-Nürnberg and teaches in the fields of analysis and
Numerics. His research work deals, among other things, with partial differential equations in
Relation to fluid dynamics and variable porous media.

Bibliographic information

  • Book TitleStart math right
  • Book Subtitle An introduction with an integrated application of the Python programming language
  • AuthorsPeter Knabner
    Balthasar Reuter
    Raphael Schulz
  • DOIhttps: //doi.org/10.1007/978-3-662-59230-4
  • Copyright InformationSpringer-Verlag GmbH Germany, part of Springer Nature2019
  • Publisher NameSpringer Spektrum, Berlin, Heidelberg
  • eBook Packages Life Science and Basic Disciplines (German Language)
  • Softcover ISBN978-3-662-59229-8
  • eBook ISBN978-3-662-59230-4
  • Edition Number1
  • Number of PagesXII, 475
  • Number of Illustrations26 b / w illustrations, 13 illustrations in color
  • TopicsMathematics, general
  • Buy this book on publisher's site