The Math Problems Notebook

Problems.- Number Theory.- Algebra and Combinatorics.- Geometry.- Analysis.- Solutions and Comments to the Problems.- Number Theory Solutions.- Algebra and Combinatorics Solutions.- Geometry Solutions.- Analysis Solutions.

Aus den Rezensionen:“Der vorliegende Band wendet sich an alle jene Personen, welche einerseits Freude am Lösen von Aufgaben aus unterschiedlichen mathematischen Bereichen haben und die andererseits das betreffende mathematische Umfeld kennenlernen möchten ... Im Anhang finden sich viele einschlägige Formeln und Aussagen. Dieses Buch ist auch deshalb sowohl Studierenden als auch Vortragenden sehr zu empfehlen, weil die unterschiedlichen Lösungsansätze nicht nur isoliert dargestellt, sondern untereinander verzahnt werden, sodass insgesamt ein Lehrbuch zu Problemlösungstechniken auf hohem Niveau vorliegt.“ (P. Paukowitsch, in: IMN Internationale Mathematische Nachrichten, April/2010, Issue 213, S. 43)

The Math Problems Notebook is a collection of nontrivial, unconventional problems requiring deep insight and imagination reminiscent of those discussed at Sunday Math Circles. These circles have become a place for disseminating beautiful mathematics at an elementary level for college students who have a common passion for mathematics.
The problems cover many topics, including number theory, algebra, combinatorics, geometry and analysis, of varying levels of difficulty. The presentation of each topic begins with simple exercises and follows with more difficult problems, challenging enough even for the experienced problem solver. The easier problems focus on basic methods and tools, while the more advanced problems develop problem-solving techniques, intuition and promote further research.
Undergraduates and teachers of advanced mathematics, as well as the casual mathematician will mutually enjoy The Math Problems Notebook.

Provides students with practice problems for topics such as number theory, algebra and combinatorics, geometry and analysis Includes solutions for each problem. Open-ended problems are followed by comments and recommended reading to promote further research Contains a glossary of mathematical terms and the more obscure definitions and identities