Focusing on an approach of solving rigorous problems and learning how to prove, this volume is concentrated on two specific content themes, elementary number theory and algebraic polynomials. The benefit to readers who are moving from calculus to more abstract mathematics is to acquire the ability to understand proofs through use of the book and the multitude of proofs and problems that will be covered throughout. This book is meant to be a transitional precursor to more complex topics in analysis, advanced number theory, and abstract algebra. To achieve the goal of conceptual understanding, a large number of problems and examples will be interspersed through every chapter. The problems are always presented in a multi-step and often very challenging, requiring the reader to think about proofs, counter-examples, and conjectures. Beyond the undergraduate mathematics student audience, the text can also offer a rigorous treatment of mathematics content (numbers and algebra) for high-achieving high school students. Furthermore, prospective teachers will add to the breadth of the audience as math education majors, will understand more thoroughly methods of proof, and will add to the depth of their mathematical knowledge. In the past, PNA has been taught in a "problem solving in middle school” course (twice), to a quite advanced high school students course (three semesters), and three times as a secondary resource for a course for future high school teachers. PNA is suitable for secondary math teachers who look for material to encourage and motivate more high achieving students.
Principles of Electron Optic: Volume Three: Wave Optics, discusses this essential topic in microscopy to help readers understand the propagation of electrons from the source to the specimen, and through the latter (and from it) to the image plane of the instrument. In addition, it also explains interference phenomena, notably holography, and informal coherence theory. This third volume accompanies volumes one and two that cover new content on holography and interference, improved and new modes of image formation, aberration corrected imaging, simulation, and measurement, 3D-reconstruction, and more. The study of such beams forms the subject of electron optics, which divides naturally into geometrical optics where effects due to wavelength are neglected, with wave optics considered. Includes authoritative coverage of the fundamental theory behind electron beams Describes the interaction of electrons with solids and the information that can be obtained from electron-beam techniques Addresses recent, relevant research topics, including new content on holography and interference, new modes of image formation, 3D reconstruction and aberration corrected imaging, simulation and measurement
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