Discovering mathematics: a problem-solving approach to mathematical analysis

The book contains chapters of structured approach to problem solving in mathematical analysis on an intermediate level. It follows the ideas of G.Polya andothers, distinguishing between exercises and problem solving in mathematics. Interrelated concepts are connected by hyperlinks, pointing toward easier or more difficult problems so as to show paths of mathematical reasoning. Basic definitions and theorems can also be found by hyperlinks from relevant places. Problems are open to alternative formulations, generalizations, simplifications, and verification of hypotheses by the reader; this is shown to be helpful insolving problems. The book presents how advanced mathematical software can aid all stages of mathematical reasoning while the mathematical content remains in foreground. The authors show how software can contribute to deeper understanding and to enlarging the scope of teaching for students and teachers of mathematics." - May be applied to a wide range of disciplines - Contains a net of hyperlinked problems, hints, plans of solutions, definitions and theorems withsolutions provided separately, thus enabling the reader to choose preferred level of difficulty - Problems m INDICE: Part I Concepts: Mappings, composite and inverse functions.- Infinite sequences.- Periodicity.- Part II Tools: Finite Sums.- Inequalities.- Collocation and least squares methods.- Part III Applications: Maximal and minimalvalues.- Arcs and curves.- Center of mass and moments.- Miscellaneous.- Part IV Appendix.

• ISBN: 978-0-85729-054-0
• Editorial: Springer
• Encuadernacion: Rústica
• Páginas: 268
• Fecha Publicación: 29/11/2010
• Nº Volúmenes: 1
• Idioma: Inglés