Course Description: An important branch of mathematical logic is model theory, the study of first-order theories and the classes of models defined by such theories. This course will include numerous applications of model theory to algebra, especially ordered fields and differential fields. All of the necessary background in mathematical logic and algebra will be presented in detail. Among the h...

Despite mathematicians valuing the ability to visualize a problem and psychologists finding positive correlations of visual-spatial ability with success in mathematics, many educationists remain unconvinced about the benefits of visualization for mathematical understanding. This paper describes research that compared a ‘visual’ to a ‘verbal’ teaching approach through teaching a range of early s...

The goal of Howitt’s positive mathematical programming procedure is to calibrate a mathematical programming model so that it will reproduce a set of base data for the primal variables. This article develops an analogous procedure allowing one to specify the levels of both primal and dual variables. This article also sheds light on a potential ambiguity of Howitt’s procedure (with attendant poli...

mathematical visualization algorithms applications and numerics What to say and what to do when mostly your friends love reading? Are you the one that don't have such hobby? So, it's important for you to start having that hobby. You know, reading is not the force. We're sure that reading will lead you to join in better concept of life. Reading will be a positive activity to do every time. And d...

We present an approach to mathematical information retrieval (MIR) that exploits a special kind of technical terminology, referred to as a mathematical type. In this paper, we present and evaluate a type detection mechanism and show its positive effect on the retrieval of research-level mathematics. Our best model, which performs query expansion with a type-aware embedding space, strongly outpe...

Index-sets are an integral and fundamental part of every mathematical modeling language. They assist the modeler in grouping various objects and entities. Indexsets are also used extensively in the mathematical notation in order to write an expression in a concise way. An example is the sigma notation for formulating the summation of an unknown positive number n of terms. In this paper, the con...

This series of lecture notes were taken for the topic class on mathematical General Relativity given by Professor Rick Schoen in the spring quarter of 2012 at Tsinghua University. These lectures start from basic introduction of General Relativity, and then move on to several fundamental mathematical subjects in this field. Particularly, the notes cover the conformal method of solving the vacuum...

where φp(s) is a p-Laplacian operator, that is, φp(s)= |s|p−2s, p > 1, η ∈ (0,1) is a given constant, α > 0, γ > 0, β ≥ 0, δ ≥ 0, g : [0,1]→ [0,∞) has countable many singularities on (0,1/2). In recent years, because of the wide mathematical and physical backgrounds [7, 8], the existence of positive solutions for nonlinear boundary value problems with p-Laplacian received wide attention. Especi...

Epilepsy is one of the most prevalent chronic disorders of childhood which can threaten child development and mental health. Among cognitive disorders, dyscalculia is one of the most important. In this study, 39 children and adolescents with idiopathic epilepsy underwent clinical and neuropsychological assessment to determine the intellectual level, math skills, reading and writing performance ...