{"title":"Connecting Humans to Equations","authors":"Ole Ravn, O. Skovsmose","doi":"10.1007/978-3-030-01337-0","DOIUrl":"https://doi.org/10.1007/978-3-030-01337-0","url":null,"abstract":"","PeriodicalId":388748,"journal":{"name":"History of Mathematics Education","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125883595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Modern Mathematics","authors":"G. Choquet","doi":"10.2307/3614084","DOIUrl":"https://doi.org/10.2307/3614084","url":null,"abstract":"The introduction The aim of this course is to teach the probabilistic techniques and concepts from the theory of stochastic processes required to understand the widely used financial models. In particular concepts such as martingales, stochastic integration/calculus, which are essential in computing the prices of derivative contracts, will be discussed. The specific topics include: Brownian motion (Gaussian distributions and processes, equivalent definitions of Brownian motion, invariance principle and Monte Carlo, scaling and time inversion, properties of paths, Markov property and reflection principle, applications to pricing, hedging and risk management, Brownian martingales), martingales in continuous time, stochastic integration (including It^{o}'s formula), stochastic differential equations (including Feynman-Kac interested in learning from data. Students with other backgrounds such as life sciences are also welcome, provided they have maturity in mathematics. The mathematical content in this course will be linear algebra, multilinear algebra, dynamical systems, and information theory. This content is required to understand some common algorithms in data science. I will start with a very basic introduction to data representation as vectors, matrices, and tensors. Then I will teach geometric methods for dimension reduction, also known as manifold learning (e.g. diffusion maps, t-distributed stochastic neighbor embedding (t-SNE), etc.), and topological data reduction (introduction to computational homology groups, etc.). I will bring an application-based approach to spectral graph theory, addressing the combinatorial meaning of eigenvalues and eigenvectors of their associated graph matrices and extensions to hypergraphs via tensors. I will also provide an introduction to the application of dynamical systems theory to data including dynamic mode decomposition and the Koopman operator. Real data examples will be given where possible and I will work with you write code implementing these algorithms to solve these problems. The methods discussed in this class are shown primarily for biological data, but are useful in handling data across many fields. A course features several guest lectures from industry and government. This course introduces the measure theory and other topics of real analysis for advanced math master’s students, and AIM and non-math graduate students. The main focus will be on Lebesgue measure theory and integration theory. Tentative topics included: Lebesgue measure, measurable functions, Lebesgue integral, convergence theorems, metric spaces, topological spaces, Hilbert and Banach spaces. This course has some overlaps with MATH 597, but covers about 1/2 of the content and proceeds at a slower pace. bifurcations transcritical, subcritical, supercritical, Hopf), unstable dissipative attractors, logistic period-doubling, renormalization, Lyapunov fractals, Hausdorff Lorenz nonlinear oscillations, quasiperiodicity, Hamiltonian sy","PeriodicalId":388748,"journal":{"name":"History of Mathematics Education","volume":"112 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1963-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128007985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Toward Mathematics for All","authors":"N. Ellerton, M. A. Clements","doi":"10.1007/978-3-030-85724-0","DOIUrl":"https://doi.org/10.1007/978-3-030-85724-0","url":null,"abstract":"","PeriodicalId":388748,"journal":{"name":"History of Mathematics Education","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116999048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Oral History and Mathematics Education","authors":"","doi":"10.1007/978-3-030-16311-2","DOIUrl":"https://doi.org/10.1007/978-3-030-16311-2","url":null,"abstract":"","PeriodicalId":388748,"journal":{"name":"History of Mathematics Education","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130593624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}