Discovering Mathematics

The book contains chapters of structured approach to problem solving in mathematical analysis on an intermediate level. It follows the ideas of G.Polya and others, 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 in solving 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 with solutions provided separately, thus enabling the reader to choose preferred level of difficulty Problems mostly assume the use of advanced mathematical software, avoiding routine calculations wherever possible and enabling quick hypotheses checks when necessary Includes supplementary material: sn.pub/extras

Klappentext

Discovering Mathematics: A Problem-Solving Approach to Analysis with Mathematica and Maple provides a constructive approach to mathematical discovery through innovative use of software technology. Interactive Mathematica and Maple notebooks are integral to this books' utility as a practical tool for learning. Interrelated concepts, definitions and theorems are connected through hyperlinks, guiding the reader to a variety of structured problems and highlighting multiple avenues of mathematical reasoning.

Interactivity is further enhanced through the delivery of online content (available at extras.springer.com), demonstrating the use of software and in turn increasing the scope of learning for both students and teachers and contributing to a deeper mathematical understanding.

This book will appeal to both final year undergraduate and post-graduate students wishing to supplement a mathematics course or module in mathematical problem-solving and analysis. It will also be of use as complementary reading for students of engineering or science, and those in self-study.

Inhalt
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 minimal values.- Arcs and curves.- Center of mass and moments.- Miscellaneous.- Part IV Appendix.