id: 06549346
dt: b
an: 2016d.00494
au: Lepetic, Vladimir
ti: Principles of mathematics. A primer.
so: Hoboken, NJ: John Wiley \& Sons (ISBN 978-1-119-13164-9/hbk;
978-1-119-13169-4/ebook). xiii, 654~p. (2016).
py: 2016
pu: Hoboken, NJ: John Wiley \& Sons
la: EN
cc: E35 E45 H65 H45 I25 H35 E65
ut: introductory mathematics; linear algebra; group theory; logic; functions;
sets
ci:
li:
ab: The first four chapters of the book cover a general introduction into
mathematics. The chapters are: Set theory, Logic, Proofs and Functions.
The themes are treated rather deeply. For instance the chapter on sets
also covers the integers, the rational numbers and the reals and even
transfinite numbers. The first chapter comes quickly into a discussion
of set theoretic problems and the GĂ¶del theorems. Chapter 5 is on
group theory. It covers the first steps into group theory as normal
subgroups and the isomorphism theorems. An introduction into linear
algebra is given in Chapter 6 consisting of nearly 200 pages. Standard
material is covered here such as basis, linear transformations, the
general linear group, systems of linear equations, determinants and
eigenvalues. The book has many examples and exercises to help the
reader. There are no prerequisites necessary in order to start reading.
Nevertheless some parts are quite abstract to read.
rv: Stephan Rosebrock (Karlsruhe)