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Articles 1381 - 1410 of 27203
Full-Text Articles in Entire DC Network
Gurevich's Quizani Dialogs As An Example Of Explainable Mathematics, And How This Is Related To Quantum Space-Time Ideas That Can Speed Up Computations, Olga Kosheleva, Vladik Kreinovich
Gurevich's Quizani Dialogs As An Example Of Explainable Mathematics, And How This Is Related To Quantum Space-Time Ideas That Can Speed Up Computations, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Everyone talks about the need for Explainable AI -- when, to supplement a long difficult-to-understand sequence of computational steps leading to AI's decision, we are looking for a shorter and understandable more-informal explanation for this decision. In this paper, we argue that this need is a particular case of what we call Explainable Mathematics -- when we want to supplement a long sequence of arguments and/or computations with a shorter and understandable more-informal explanation. Important instances of Explainable Mathematics are Yuri Gurevich's Quizani dialogs that help explain complex results from theoretical computer science and physicists' more-informal explanations of complex physical …
Unfortunately, The Universal Predictor Cannot Be Made Constructive, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich
Unfortunately, The Universal Predictor Cannot Be Made Constructive, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
A recent article in the Notices of the American Mathematical Society reminded the mathematics community that, under the Axiom of Choice, it is possible to have a universal predictor: if we input, into this predictor, the values of a function for all moments t < to for some to, then, for almost all to, this predictor correctly predicts the next values of this function on some interval [to, to + ε). This predictor cannot be used for actual predictions: it is based on the Axiom of Choice and is, therefore, not constructive. A natural question is: maybe it is possible to have another universal predictor, which is constructive? In this paper we show that, unfortunately, it is not possible to have a constructive universal predictor. In other words, the above universal predictor result cannot be used for actual predictions.
Discrete Math For Computer Science - Chapter 8: Union And Intersection And Complement: Set Identities, Houman Kamran Habibkhani
Discrete Math For Computer Science - Chapter 8: Union And Intersection And Complement: Set Identities, Houman Kamran Habibkhani
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Discrete Math For Computer Science - Chapter 15: Mathematical Induction, Houman Kamran Habibkhani
Discrete Math For Computer Science - Chapter 15: Mathematical Induction, Houman Kamran Habibkhani
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Discrete Math For Computer Science - Chapter 13: Sequences: Recurrence Relations, Houman Kamran Habibkhani
Discrete Math For Computer Science - Chapter 13: Sequences: Recurrence Relations, Houman Kamran Habibkhani
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Discrete Math For Computer Science - Chapter 26: Introduction To Graphs: Graph Representations, Houman Kamran Habibkhani
Discrete Math For Computer Science - Chapter 26: Introduction To Graphs: Graph Representations, Houman Kamran Habibkhani
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Discrete Math For Computer Science - Chapter 2: Logical Equivalence: Laws Of Propositional Logic, Houman Kamran Habibkhani
Discrete Math For Computer Science - Chapter 2: Logical Equivalence: Laws Of Propositional Logic, Houman Kamran Habibkhani
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Discrete Math For Computer Science - Chapter 11: Inverse Of A Function: Composition Of Functions, Houman Kamran Habibkhani
Discrete Math For Computer Science - Chapter 11: Inverse Of A Function: Composition Of Functions, Houman Kamran Habibkhani
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Discrete Math For Computer Science - Chapter 16: Recursive Definitions: Recursive Algorithms, Houman Kamran Habibkhani
Discrete Math For Computer Science - Chapter 16: Recursive Definitions: Recursive Algorithms, Houman Kamran Habibkhani
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Discrete Math For Computer Science, Houman Kamran Habibkhani
Discrete Math For Computer Science, Houman Kamran Habibkhani
Pacific Open Texts
Discrete Mathematics and its Applications is a focused introduction to the primary themes in a discrete mathematics course, as introduced through extensive applications, expansive discussion, and detailed exercise sets. These themes include mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, and enhanced problem-solving skills through modeling. Its intent is to demonstrate the relevance and practicality of discrete mathematics to all students.
Discrete Math For Computer Science - Chapter 4: Logical Reasoning: Rules Of Inference, Houman Kamran Habibkhani
Discrete Math For Computer Science - Chapter 4: Logical Reasoning: Rules Of Inference, Houman Kamran Habibkhani
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The Mathematical Experience Museum: Breathing Life Into Theorems And Formulas, Jin Akiyama, Jude Buot, Mark Anthony C. Tolentino
The Mathematical Experience Museum: Breathing Life Into Theorems And Formulas, Jin Akiyama, Jude Buot, Mark Anthony C. Tolentino
Mathematics Faculty Publications
No abstract provided.
Discrete Math For Computer Science - Chapter 14: Summations, Houman Kamran Habibkhani
Discrete Math For Computer Science - Chapter 14: Summations, Houman Kamran Habibkhani
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Discrete Math For Computer Science - Chapter 19: Number Representation, Houman Kamran Habibkhani
Discrete Math For Computer Science - Chapter 19: Number Representation, Houman Kamran Habibkhani
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Discrete Math For Computer Science - Chapter 27: Paths And Cycles: Graph Connectivity, Houman Kamran Habibkhani
Discrete Math For Computer Science - Chapter 27: Paths And Cycles: Graph Connectivity, Houman Kamran Habibkhani
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Discrete Math For Computer Science - Chapter 28: Introduction To Trees: Properties Of Trees, Houman Kamran Habibkhani
Discrete Math For Computer Science - Chapter 28: Introduction To Trees: Properties Of Trees, Houman Kamran Habibkhani
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Discrete Math For Computer Science - Chapter 29: Tree Traversals: Spanning Trees, Houman Kamran Habibkhani
Discrete Math For Computer Science - Chapter 29: Tree Traversals: Spanning Trees, Houman Kamran Habibkhani
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(Si14-12) Some Novel Fractional Discrete Inequalities Of Gronwall-Bellman Type And Their Applications To Fractional Difference Equations, Subhash Kendre, Nagesh Kale, Dimplekumar Chalishajar
(Si14-12) Some Novel Fractional Discrete Inequalities Of Gronwall-Bellman Type And Their Applications To Fractional Difference Equations, Subhash Kendre, Nagesh Kale, Dimplekumar Chalishajar
Applications and Applied Mathematics: An International Journal (AAM)
In this study, we develop multiple power nonlinear generalizations of Gronwall-Bellman type fractional discrete inequalities and fractional sum inequalities through combining functions with powered unknown functions.We have employed technique of reducing power non-linearity into linearity to furnish these refinements. These novel findings present a broader framework for dealing with wider range of nonlinear fractional difference equations and fractional sum-difference equations. The utilization of these inequalities enables to study certain crucial classes of fractional difference equations that arise in the realm of fractional difference calculus, both quantitatively and qualitatively. Several illustrations are provided to examine the boundedness of initial value problems …
Best Strategies For Bilingual Education: How Can We Explain Their Success?, Claudia Cabrera, Olga Kosheleva, Christian Servin, Vladik Kreinovich
Best Strategies For Bilingual Education: How Can We Explain Their Success?, Claudia Cabrera, Olga Kosheleva, Christian Servin, Vladik Kreinovich
Departmental Technical Reports (CS)
When designing AI-based tools for education, it is important to take into account the experience of human teachers. In this, it is necessary to distinguish between the education features that are justified by the general features of the corresponding education task -- these features should be taken into account in AI-based learning as well -- and features which are specific for traditional non-AI teaching. In this paper, on the important example of bilingual education, we show that several empirically successful teaching strategies can be explained in the general context -- and thus, should be implemented in AI-based teaching as well.
Discrete Math For Computer Science - Chapter 3: Predicates And Quantifiers: Quantified Statements, Houman Kamran Habibkhani
Discrete Math For Computer Science - Chapter 3: Predicates And Quantifiers: Quantified Statements, Houman Kamran Habibkhani
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Discrete Math For Computer Science - Chapter 1: Proposition, Logical Operations, And Conditional Statements, Houman Kamran Habibkhani
Discrete Math For Computer Science - Chapter 1: Proposition, Logical Operations, And Conditional Statements, Houman Kamran Habibkhani
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Discrete Math For Computer Science - Chapter 22: Counting By Complement: Permutations With Repetitions: Inclusion/Exclusion Principle, Houman Kamran Habibkhani
Discrete Math For Computer Science - Chapter 22: Counting By Complement: Permutations With Repetitions: Inclusion/Exclusion Principle, Houman Kamran Habibkhani
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Discrete Math For Computer Science - Chapter 20: Sum And Product Rules, Houman Kamran Habibkhani
Discrete Math For Computer Science - Chapter 20: Sum And Product Rules, Houman Kamran Habibkhani
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Discrete Math For Computer Science - Chapter 25: Conditional Probability And Independence, Houman Kamran Habibkhani
Discrete Math For Computer Science - Chapter 25: Conditional Probability And Independence, Houman Kamran Habibkhani
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Discrete Math For Computer Science - Chapter 24: Unions And Complements Of Events, Houman Kamran Habibkhani
Discrete Math For Computer Science - Chapter 24: Unions And Complements Of Events, Houman Kamran Habibkhani
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Discrete Math For Computer Science - Chapter 17: The Division Algorithm: Modular Arithmetic, Houman Kamran Habibkhani
Discrete Math For Computer Science - Chapter 17: The Division Algorithm: Modular Arithmetic, Houman Kamran Habibkhani
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Discrete Math For Computer Science - Chapter 23: Probability Of An Event, Houman Kamran Habibkhani
Discrete Math For Computer Science - Chapter 23: Probability Of An Event, Houman Kamran Habibkhani
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Discrete Math For Computer Science - Chapter 12: Introduction To Binary Relations, Houman Kamran Habibkhani
Discrete Math For Computer Science - Chapter 12: Introduction To Binary Relations, Houman Kamran Habibkhani
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Discrete Math For Computer Science - Chapter 21: Counting Permutations And Subsets, Houman Kamran Habibkhani
Discrete Math For Computer Science - Chapter 21: Counting Permutations And Subsets, Houman Kamran Habibkhani
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Discrete Math For Computer Science - Chapter 18: Prime Factorization: Gcd And Euclid’S Algorithm, Houman Kamran Habibkhani
Discrete Math For Computer Science - Chapter 18: Prime Factorization: Gcd And Euclid’S Algorithm, Houman Kamran Habibkhani
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