Curriculum Guidelines for Undergraduate Programs in Data Science

The Park City Math Institute (PCMI) 2016 Summer Undergraduate Faculty Program met for the purpose of composing guidelines for undergraduate programs in Data Science. The group consisted of 25 undergraduate faculty from a variety of institutions in the U.S., primarily from the disciplines of mathematics, statistics and computer science. These guidelines are meant to provide some structure for institutions planning for or revising a major in Data Science

Algorithmic and Statistical Perspectives on Large-Scale Data Analysis

In recent years, ideas from statistics and scientific computing have begun to interact in increasingly sophisticated and fruitful ways with ideas from computer science and the theory of algorithms to aid in the development of improved worst-case algorithms that are useful for large-scale scientific and Internet data analysis problems. In this chapter, I will describe two recent examples---one having to do with selecting good columns or features from a (DNA Single Nucleotide Polymorphism) data matrix, and the other having to do with selecting good clusters or communities from a data graph (representing a social or information network)---that drew on ideas from both areas and that may serve as a model for exploiting complementary algorithmic and statistical perspectives in order to solve applied large-scale data analysis problems.Comment: 33 pages. To appear in Uwe Naumann and Olaf Schenk, editors, "Combinatorial Scientific Computing," Chapman and Hall/CRC Press, 201

What Do Paraconsistent, Undecidable, Random, Computable and Incomplete mean? A Review of Godel's Way: Exploits into an undecidable world by Gregory Chaitin, Francisco A Doria, Newton C.A. da Costa 160p (2012) (review revised 2019)

In ‘Godel’s Way’ three eminent scientists discuss issues such as undecidability, incompleteness, randomness, computability and paraconsistency. I approach these issues from the Wittgensteinian viewpoint that there are two basic issues which have completely different solutions. There are the scientific or empirical issues, which are facts about the world that need to be investigated observationally and philosophical issues as to how language can be used intelligibly (which include certain questions in mathematics and logic), which need to be decided by looking at how we actually use words in particular contexts. When we get clear about which language game we are playing, these topics are seen to be ordinary scientific and mathematical questions like any others. Wittgenstein’s insights have seldom been equaled and never surpassed and are as pertinent today as they were 80 years ago when he dictated the Blue and Brown Books. In spite of its failings—really a series of notes rather than a finished book—this is a unique source of the work of these three famous scholars who have been working at the bleeding edges of physics, math and philosophy for over half a century. Da Costa and Doria are cited by Wolpert (see below or my articles on Wolpert and my review of Yanofsky’s ‘The Outer Limits of Reason’) since they wrote on universal computation, and among his many accomplishments, Da Costa is a pioneer in paraconsistency. Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019

CoCalc as a Learning Tool for Neural Network Simulation in the Special Course "Foundations of Mathematic Informatics"

The role of neural network modeling in the learning content of the special course "Foundations of Mathematical Informatics" was discussed. The course was developed for the students of technical universities - future IT-specialists and directed to breaking the gap between theoretic computer science and it's applied applications: software, system and computing engineering. CoCalc was justified as a learning tool of mathematical informatics in general and neural network modeling in particular. The elements of technique of using CoCalc at studying topic "Neural network and pattern recognition" of the special course "Foundations of Mathematic Informatics" are shown. The program code was presented in a CoffeeScript language, which implements the basic components of artificial neural network: neurons, synaptic connections, functions of activations (tangential, sigmoid, stepped) and their derivatives, methods of calculating the network's weights, etc. The features of the Kolmogorov-Arnold representation theorem application were discussed for determination the architecture of multilayer neural networks. The implementation of the disjunctive logical element and approximation of an arbitrary function using a three-layer neural network were given as an examples. According to the simulation results, a conclusion was made as for the limits of the use of constructed networks, in which they retain their adequacy. The framework topics of individual research of the artificial neural networks is proposed.Comment: 16 pages, 3 figures, Proceedings of the 13th International Conference on ICT in Education, Research and Industrial Applications. Integration, Harmonization and Knowledge Transfer (ICTERI, 2018