Algorithmic Mathematics - QMUL Maths
(Algorithms do not necessarily represent functions The instruction: ‘Toss a coin; if the outcome is head, add 1 to x, otherwise, do nothing’ is legitimate and unambiguous, but not deterministic The output of an algorithm containing such instruction is not a function of the input alone Algorithms of this kind are called probabilistic ) 1
Mathematical Fundamentals and Analysis of Algorithms
of algorithms “n” is the size of the input • T(n) = O(f(n)) if there are constants c and n 0 such that T(n) < c f(n) for all n > n 0 › 10000n + 10 n log 2 n = O(n log n) › 00001 n2 ≠O(n log n) • Order notation ignores constant factors and low order terms
Discrete Mathematics, Chapter 3: Algorithms
Algorithms (Abu Ja ’far Mohammed Ibin Musa Al-Khowarizmi, 780-850) Definition An algorithm is a finite set of precise instructions for performing a computation or for solving a problem Example: Describe an algorithm for finding the maximum value in a finite sequence of integers Description of algorithms in pseudocode:
An Active Introduction to Discrete Mathematics and Algorithms
•An Active Introduction to Discrete Mathematics and Algorithms, 2014, Charles A Cusack This is a significant revision of the 2013 version (thus the slight change in title) •An Introduction to Discrete Mathematics and Algorithms, 2013, Charles A Cusack This document draws some content from each of the following
Position 1: Teaching traditional algorithms or procedures
algorithms begin to have problems as early as Algebra I (Budd, Carson, Garelick, Klein, Milgram, Raimi, Schwartz, Stotsky, Williams, & Wilson, 2005) The lack of understanding is behind the problems students experience in Algebra I Algorithms force children to give up their own thinking and remember the next steps (Kamii & Dominick, 1997)
Lecture 18 Solving Shortest Path Problem: Dijkstra’s Algorithm
Algorithms Solving the Problem • Dijkstra’s algorithm • Solves only the problems with nonnegative costs, i e , c ij ≥ 0 for all (i,j) ∈ E • Bellman-Ford algorithm • Applicable to problems with arbitrary costs • Floyd-Warshall algorithm • Applicable to problems with arbitrary costs • Solves a more general all-to-all shortest
Introduction to Decision Mathematics
Why Decision Maths? Decision mathematics has become popular in recent decades because of its applications to computer science Many of the problems involve Optimisation – finding an efficient solution – and hence methods are applicable to many real world situations
Mathematical induction & Recursion
3 CS 441 Discrete mathematics for CS M Hauskrecht Correctness of the mathematical induction Suppose P(1) is true and P(n) P(n+1) is true for all positive integers n Want to show x P(x)
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