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The Algorithm Design Manual

Discrete Mathematics & Theoretical Computer Science

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Lecture Catalan numbers. Pre-tutorial 2 questions Pre-tutorial 2 solutions Tutorial 2 questions Tutorial 2 solutions Extra problems 2 Extra problems 2 solutions. Pre-tutorial 3 questions Pre-tutorial 3 solutions Tutorial 3 questions Tutorial 3 solutions Extra problems 3 Extra problems 3 solutions. Assignment 1 - questions. Pre-tutorial 4 questions Pre-tutorial 4 solutions Tutorial 4 questions Tutorial 4 solutions Extra problems 4 Extra problems 4 solutions.

Discrete Mathematics | The Great Courses

Assignment 1 Due pm, 29 August. Pre-tutorial 5 questions Pre-tutorial 5 solutions Tutorial 5 questions Tutorial 5 solutions Extra problems 5 Extra problems 5 solutions. Assignment 1 - solutions Quiz 1 - sample Quiz 1 - sample solutions. Extra problems 6 Extra problems 6 solutions.

Karnaugh maps. Pre-tutorial 7 questions Pre-tutorial 7 solutions Tutorial 7 questions Tutorial 7 solutions Extra problems 7 Extra problems 7 solutions.

Discrete Mathematics Tutorial Index

Pre-tutorial 8 questions Pre-tutorial 8 solutions Tutorial 8 questions Tutorial 8 solutions Extra problems 8 Extra problems 8 solutions. Pre-tutorial 9 questions Pre-tutorial 9 solutions Tutorial 9 questions Tutorial 9 solutions Extra problems 9 Extra problems 9 solutions. The software determines the probability of a given train trip being completed on time in the UK uses Markov chains.

Archaeology uses discrete math to construct 3D images from scans of archaeological sites.

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Discrete Mathematics Tutorial

Determining voting districts, a process known as redistricting , is rife with problems and influenced by politics. Many researchers in various fields work on methods for fair redistricting, and some use lots of discrete math. Network flows, a part of discrete math, can be used to help protect endangered species from the threat of global warming see the abstract for this paper.

Power grids : Graph theory is used in finding the most vulnerable aspects of an electric grid.

Discrete Mathematics

Graph theory and linear algebra are used in power grid simulations. Robot arms are a type of linkage , the study of which is part of discrete geometry. Modeling possible fingertip movements and forces uses linear algebra. Graph theory is involved in routing concrete trucks.

Voting theory see earlier on this page can be used to decide how to prioritize among biodiversity conservation sites see the abstract for this paper. Graph theory is used in kidney donor matching bonus: the speaker on the podcast has given Daily Gathers at MathILy. Determining how best to add streets to congested areas of cities uses graph theory and in fact an area of graph theory taught in one of the MathILy branch classes!

Matching medical-school graduates to hospital residencies is solved using an algorithm that is provably optimal. Here are two articles that describe the discrete mathematics involved and what happens when this is extended to the problem of matching middle-school students to high schools. Measuring the evolutionary distance between genomes can be done using permutations, as described here. Graph theory is involved in searching for terrorist groups sending covert messages on public fora. Data compression , reduction of noise in data , and automated recommendations of movies all use the same tool from linear algebra.

The spread of infectious disease is affected by personal contacts and by behaviors influenced by information. One model of epidemics uses graph theory by encoding personal contacts and behaviors as layers in a large network. We can model a crystal structure based on a set of electron microscope images using discrete tomography. Linear programming can be used in discrete tomography. Discrete tomography can also be used in medical imaging , to reconstruct an image of an organ from just a few x-ray images.

Graph theory and linear algebra can be used in speeding up Facebook performance.

Truth Table Tutorial - Discrete Mathematics Logic

Assessing risk in heart-attack patients , categorizing species using few characteristics , and data mining analytics all use the same discrete math. Chemistry : Balancing chemical equations uses linear algebra, and understanding molecular structure uses graph theory. We can straighten an image taken by a misaligned camera using linear algebra. Many ways of producing rankings use both linear algebra and graph theory. Specific examples include ranking relevance of search results using Google , ranking teams for tournaments or chicken pecking orders , and ranking sports team performances or restaurant preferences that include apparent paradoxen.

Changing patterns in lizard skin are described by discrete cellular automata. Graph theory is used in DNA sequencing.