This concisely written book gives an elementary introduction to a classical area of mathematics—approximation theory—in a way that naturally leads to the modern field of wavelets. The exposition, driven by ideas rather than technical details and proofs, demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications. Key features and topics: * Description of wavelets in words rather than mathematical symbols * Elementary introduction to approximation using polynomials (Weierstrass’ and Taylor’s theorems) * Introduction to infinite series, with emphasis on approximation-theoretic aspects * Introduction to Fourier analysis * Numerous classical, illustrative examples and constructions * Discussion of the role of wavelets in digital signal processing and data compression, such as the FBI’s use of wavelets to store fingerprints * Minimal prerequisites: elementary calculus * Exercises that may be used in undergraduate and graduate courses on infinite series and Fourier series Approximation Theory: From Taylor Polynomials to Wavelets will be an excellent textbook or self-study reference for students and instructors in pure and applied mathematics, mathematical physics, and engineering. Readers will find motivation and background material pointing toward advanced literature and research topics in pure and applied harmonic analysis and related areas.

When the first European missionaries arrived on other continents, it was decided that the indigenous languages would be used as the means of christianization. There emerged the need to produce grammars and dictionaries of those languages. The study of this linguistic material has so far not received sufficient attention in the field of linguistic historiography. This volume is the first published collection of papers on missionary linguistics world-wide; it represents the insights of recent research, containing an introduction and papers on methodology, meta-historiography, the historical and cultural background. The book contains studies about early-modern linguistic works written in Spanish, Portuguese, English and French, describing among others indigenous languages from North America and Australia, Maya, Quechua, Xhosa, Japanese, Kapampangan, and Visaya. Topics dealt with include: innovations of individual missionaries in lexicography, grammatical analysis, phonology, morphology, or syntax; creativity in descriptive techniques; differences and/or similarities of works from different continents, and different religious backgrounds (Catholic or Protestant).