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PPT - UBC Department of CPSC Undergraduates
PPT - UBC Department of CPSC Undergraduates

... Every logical equivalence that we’ve learned applies to predicate logic statements. For example, to prove ~x  D, P(x), you can prove x  D, ~P(x) and then convert it back with generalized De Morgan’s. To prove x  D, P(x)  Q(x), you can prove x  D, ~Q(x)  ~P(x) and convert it back using the ...
Document
Document

... Able to tell what an algorithm is and have some understanding why we study algorithms ...
STUDY ON ELLIPTIC AND HYPERELLIPTIC CURVE METHODS
STUDY ON ELLIPTIC AND HYPERELLIPTIC CURVE METHODS

... • 2nd Step largely increases the probability that factors are found with a small increase in running time. Second, we investigated factoring using hyperelliptic curves through experiments. Using hyperelliptic curves for factoring is analyzed by Lenstra, Pila and Pomerance [8] from theoretical intere ...
"On Best Rational Approximations Using Large Integers", Ashley
"On Best Rational Approximations Using Large Integers", Ashley

CS 372: Computational Geometry Lecture 14 Geometric
CS 372: Computational Geometry Lecture 14 Geometric

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Chapter 8

Constructing university timetable using constraint
Constructing university timetable using constraint

Recent Progress on the Complexity of Solving Markov Decision
Recent Progress on the Complexity of Solving Markov Decision

... algorithm, we have Tφk+1 vφk = T vφk ≥ vφk , which by induction implies that Tφnk+1 vφk ≥ T vφk for every n ∈ N. Letting n → ∞, this means vφk+1 ≥ T vφk on each iteration k; by induction, this implies that the k th policy produced by the algorithm satisfies vφk ≥ T k vφ0 , where φ0 is the initial po ...
PRIMALITY TESTING A Journey from Fermat to AKS
PRIMALITY TESTING A Journey from Fermat to AKS

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Multiplicative Inverse

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Research Statement - Singapore Management University

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GigaTensor: Scaling Tensor Analysis Up By 100 Times

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Lecture 1 - DePaul University

... major deals heavily with this ...
GigaTensor: Scaling Tensor Analysis Up By 100 Times
GigaTensor: Scaling Tensor Analysis Up By 100 Times

... tensors (having attracted best paper awards, e.g. see [20]). However, the toolboxes have critical restrictions: 1) they operate strictly on data that can fit in the main memory, and 2) their scalability is limited by the scalability of Matlab. In [4, 20], efficient ways of computing tensor decomposi ...
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Chapter 5

There are 526915620 nonisomorphic one-factorizations of K12
There are 526915620 nonisomorphic one-factorizations of K12

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Variations of Diffie

On the Classification and Algorithmic Analysis of Carmichael Numbers
On the Classification and Algorithmic Analysis of Carmichael Numbers

... The results pertaining to the classification of Carmichael numbers with a proportion of Fermat witnesses of less than 50% are detailed in Section 3.1. This classification provides a lower bound for the smallest prime factor of certain Carmichael numbers with a proportion of Fermat witnesses of less ...
4 slides/page
4 slides/page

... ◦ To find a 100-digit prime; ∗ Keep choosing odd numbers at random ∗ Check if they are prime (using fast randomized primality test) ∗ Keep trying until you find one ∗ Roughly 100 attempts should do it ...
1 slide/page
1 slide/page

Objectives - University of Kentucky
Objectives - University of Kentucky

Clustering Methods
Clustering Methods

Addition and Subtraction
Addition and Subtraction

... In order to be able to do addition more quickly, mathematicians create an algorithm – a process to follow that will produce a guaranteed result. Many of you already know some algorithms, but we will introduce a few different algorithms. When you encounter a problem, having more than one set of tools ...
Artificial intelligence 1: informed search
Artificial intelligence 1: informed search

Artificial intelligence 1: informed search
Artificial intelligence 1: informed search

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Algorithm



In mathematics and computer science, an algorithm (/ˈælɡərɪðəm/ AL-gə-ri-dhəm) is a self-contained step-by-step set of operations to be performed. Algorithms exist that perform calculation, data processing, and automated reasoning.An algorithm is an effective method that can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing ""output"" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.The concept of algorithm has existed for centuries, however a partial formalization of what would become the modern algorithm began with attempts to solve the Entscheidungsproblem (the ""decision problem"") posed by David Hilbert in 1928. Subsequent formalizations were framed as attempts to define ""effective calculability"" or ""effective method""; those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's ""Formulation 1"" of 1936, and Alan Turing's Turing machines of 1936–7 and 1939. Giving a formal definition of algorithms, corresponding to the intuitive notion, remains a challenging problem.
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