This exposition is primarily a survey of the elementary yet subtle innovations of several mathematicians between 1929 and 1934 that led to partial and then complete solutions to Hilbert’s Seventh Problem (from the International Congress of Mathematicians in Paris, 1900). This volume is suitable for both mathematics students, wishing to experience how different mathematical ideas can come toge…
This book explains how mathematical tools can be used to solve problems in signal processing. Assuming an advanced undergraduate- or graduate-level understanding of mathematics, this second edition contains new chapters on convolution and the vector DFT, plane-wave propagation, and the BLUE and Kalman filters. It expands the material on Fourier analysis to three new chapters to provide addition…
Mathematics Education; Mathematics Learning; Mathematics Teaching; Mathematics Teachers; ICME-13; 13th Congress on Mathematical Education; Empirical Studies in Mathematics Education; Theoretical Reflections on Mathematics Education; Tertiary Mathematics Education; Secondary Mathematics Education; Primary Mathematics Education; Society of Didactics of Mathematics; Mathematics Educators; Improvem…
This open access book covers aspects of unsupervised machine learning used for knowledge discovery in data science and introduces a data-driven approach to cluster analysis, the Databionic swarm (DBS). DBS consists of the 3D landscape visualization and clustering of data. The 3D landscape enables 3D printing of high-dimensional data structures. The clustering and number of clusters or an absenc…
Degree students of mathematics are often daunted by the mass of definitions and theorems with which they must familiarize themselves. In the fields algebra and analysis this burden will now be reduced because in A Handbook of Terms they will find sufficient explanations of the terms and the symbolism that they are likely to come across in their university courses. Rather than being like an alph…
This book is concerned with the well-established mathematical technique known as Fourier analysis (or alternatively as harmonic or spectral analysis). It is a handbook comprising a collection of the most important theorems in Fourier analysis, presented without proof in a form that is accurate but also accessible to a reader who is not a specialist mathematician. The technique of Fourier analys…
This book constitutes the refereed proceedings of the 8th International Conference on Artificial General Intelligence, AGI 2015, held in Berlin, Germany in July 2015. The 41 papers were carefully reviewed and selected from 72 submissions. The AGI conference series has played and continues to play, a significant role in this resurgence of research on artificial intelligence in the deeper, origin…
This guide book to mathematics contains in handbook form the fundamental working knowledge of mathematics which is needed as an everyday guide for working scientists and engineers, as well as for students. Easy to understand, and convenient to use, this guide book gives concisely the information necessary to evaluate most problems which occur in concrete applications. In the newer editions emph…
This open access Topical Survey offers a brief overview of the current state of research on and activities for mathematically gifted students around the world. This is of interest to a broad readership, including educational researchers, research mathematicians, mathematics teachers, teacher educators, curriculum designers, doctoral students, and other stakeholders. It first discusses research …
With the ninth edition of the four-yearly review of mathematics education research in Australasia, the Mathematics Education Research Group of Australasia (MERGA) discusses the Australasian research in mathematics education in the four years from 2012-2015. This review aims to critically promote quality research and focus on the building of research capacity in Australasia.