Mathematical bridges
著者
書誌事項
Mathematical bridges
Birkhäuser , Springer, c2017
- hbk
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注記
Bibliography: p. 309
内容説明・目次
内容説明
Building bridges between classical results and contemporary nonstandard problems, this highly relevant work embraces important topics in analysis and algebra from a problem-solving perspective. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics. Instructors and motivated mathematics students from high school juniors to college seniors will find the work a useful resource in calculus, linear and abstract algebra, analysis and differential equations. Students with an interest in mathematics competitions must have this book in their personal libraries.
目次
Mathematical (and Other) Bridges.- Cardinality.- Polynomial Functions Involving Determinants.- Some Applications of the Hamilton-Cayley Theorem.- A Decomposition Theorem Related to the Rank of a Matrix.- Equivalence Relations on Groups and Factor Groups.- Density.- The Nested Intervals Theorem.- The Splitting Method and Double Sequences.- The Number e.- The Intermediate Value Theorem.- The Extreme Value Theorem.- Uniform Continuity.- Derivatives and Functions' Variation.- Riemann and Darboux Sums.- Antiderivatives.
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