My Links .ATasteOfTWiki view a short introductory presentation on TWiki for beginners .WelcomeGuest starting points on TWiki .TWikiUsersGuide ...

15. Algebraic Structures: Groups, Rings, and Fields In this chapter, we are going to study the abstract properties of binary operations. Algebraic structures known ...

Alternatives to LaTeX Here are some tips for those of you that don't like LaTeX Microsoft Word 2007 Overview The Microsoft Equation Editor has improved by leaps ...

My Links .ATasteOfTWiki view a short introductory presentation on TWiki for beginners .WelcomeGuest starting points on TWiki .TWikiUsersGuide ...

My Links ATasteOfTWiki view a short introductory presentation on TWiki for beginners WelcomeGuest starting points on TWiki TWikiUsersGuide complete ...

Customise this topic; samples and ideas available at TWiki:TWiki.WebLeftBarCookbook. My links: My home page Groups etc My activities edit

Basic Unix Commands Some common UNIX gotchas.. If you want to run a program that's in your current directory, you need to preface it with ./ , e.g. ./tetris ...

On Time Versus Input Size Introduction Computer scientists seek not only to find correct solutions to a particular problem, but also to efficiently solve a problem ...

The Dating Game Imagine that you are a matchmaker, with 100 female clients and 100 male clients. Each of the women gives you a complete list of the 100 men, ordered ...

My Links .ATasteOfTWiki view a short introductory presentation on TWiki for beginners .WelcomeGuest starting points on TWiki .TWikiUsersGuide ...

My Links .ATasteOfTWiki view a short introductory presentation on TWiki for beginners .WelcomeGuest starting points on TWiki .TWikiUsersGuide ...

My Links ATasteOfTWiki view a short introductory presentation on TWiki for beginners WelcomeGuest starting points on TWiki TWikiUsersGuide complete ...

My Links ATasteOfTWiki view a short introductory presentation on TWiki for beginners WelcomeGuest starting points on TWiki TWikiUsersGuide complete ...

Cantor's Legacy: Infinity and Diagonalization Georg Cantor (1845 1918) The Ideal Computer The ideal computer has infinite memory. There are two ways to look at this ...

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Basic Information on Circuits You should already be familiar with logical functions like OR and AND. A gate is just a visual representation of these functions. For ...

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Combinatorial Games Combinatorial games are two person games with perfect information and no chance moves, and with a win or lose outcome. Such a game is determined ...

Combinatorial Games Combinatorial games are two person games with perfect information and no chance moves, and with a win or lose outcome. Such a game is determined ...

Correspondences and Choice Trees Gamblers and other people playing card or dice games depend on more than luck to succeed. They need to know the odds #8212;how likely ...

Pascal's Triangle, Polynomials, and Vector Programs The formula %\ (1 x)^n {n\choose 0}1 {n\choose 1}x {n \choose 2}x^2 . . . {n \choose k}x^k . . . ...

Recurring Problems and Correspondences Counting problems are an important part of theoretical computer science. For many such problems, there is no specific theory ...

Course Syllabus (PDF version) Welcome to 15 251! This course will take a philosophical and historical perspective on the development of theoretical computer science ...

My Links .ATasteOfTWiki view a short introductory presentation on TWiki for beginners .WelcomeGuest starting points on TWiki .TWikiUsersGuide ...

My Links .ATasteOfTWiki view a short introductory presentation on TWiki for beginners .WelcomeGuest starting points on TWiki .TWikiUsersGuide ...

My Links .ATasteOfTWiki view a short introductory presentation on TWiki for beginners .WelcomeGuest starting points on TWiki .TWikiUsersGuide ...

My Links .ATasteOfTWiki view a short introductory presentation on TWiki for beginners .WelcomeGuest starting points on TWiki .TWikiUsersGuide ...

Wiki Editing Information Thanks for helping improve the wiki! This is just a quick README to get you started. First, a quick request. Please don't mess up the wiki ...

Extra Stuff Cool articles about various things will appear here :). Ropes of 251. A guide on how to succeed on the homework assignments (Brendan Meeder) ...

The Golden Ratio, Fibonacci Numbers, and Other Recurrences Fibonacci numbers have links to many different kinds of mathematics. They can be defined recursively as ...

One Minute to Learn Programming: Finite Automata Today, we're gonna talk about an incredibly simple programming system that has a ton of real world applications: Finite ...

Thales and Gödel's Legacy: What is Proof? Thales #8217; Legacy: What Is A Proof? Thales Of Miletus (600 BC) Insisted on Proofs! #8220;first mathematician #8221; ...

Trees A tree is a connected acyclic graph. The number of edges it has is one less than the number of nodes, every two nodes are connected by exactly one path and if ...

Induction: One Step at a Time The most useful proof technique in computer science is mathematical induction. It is the primary way in which we: (A) Prove theorems ...

My Links .ATasteOfTWiki view a short introductory presentation on TWiki for beginners .WelcomeGuest starting points on TWiki .TWikiUsersGuide ...

LaTeX is a system of typesetting mathematical notation. You enter LaTeX markup language in a plain text file, and then typeset it using the program pdflatex . You ...

Lecture Notes Many of these lecture notes were based on a draft version of an upcoming textbook developed from 15 251. Please do not distribute them outside of CMU ...

My Links .ATasteOfTWiki view a short introductory presentation on TWiki for beginners .WelcomeGuest starting points on TWiki .TWikiUsersGuide ...

My Links .ATasteOfTWiki view a short introductory presentation on TWiki for beginners .WelcomeGuest starting points on TWiki .TWikiUsersGuide ...

My Links .ATasteOfTWiki view a short introductory presentation on TWiki for beginners .WelcomeGuest starting points on TWiki .TWikiUsersGuide ...

Nobody Group Member list: Set GROUP Persons/group who can change the list: Set ALLOWTOPICCHANGE TWikiAdminGroup Used to prevent dangerous ...

14. Modular Arithmetic and the RSA Cryptosystem Conventional modern day cryptography typically requires a key #151;a string of numbers #151;shared by both sender and ...

Pancakes with a Problem The cook at the Sunrise Cafe is sloppy: when she prepares pancakes, they come out all different sizes. The waiter, however, is tidy. Before ...

Converting Between File Types If you are using LaTeX to typeset your solutions, you can get PDF files by using pdflatex (if you want to get postscript, you can run ...

16. Polynomials, Secret Sharing, and Error Correcting Codes intro Polynomials Examples of polynomials in one variable over the reals: :`P(x) 3x^2 7x #8211 ...

Primes, Euclid #8217;s GCD, and Continued Fractions Determining the greatest common divisor is an example of finding an integer relation between two numbers. Dating ...

Counting in Terms of Proportions Distributions For any random event, like flipping a coin, each outcome has a value and a probability. A probability distribution ...

Random Walks on Graphs At any node, go to one of the neighbors of the node with equal probability. Let #8217;s start simple #8230;We #8217;ll just walk in a straight ...

Random Variables and Great Expectations Some problems involving probability can seem really messy. For example, if we randomly put 100 letters into 100 addressed envelopes ...

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My links: http://bestgaminglaptops.blogspot.com My activities edit

On Raising a Number to a Power The Egyptians, as well as other people in both ancient and modern times, spent a lot of time trying to figure out how to do calculations ...

Your Guide to 15 251 Homeworks This section is about how to succeed on the homework. The point of the homework exercises is to give you experience using the techniques ...

Solving Problems, Writing Proofs, and Enjoying the Pain: How to Succeed in This Class While humans are capable of rudimentary abstraction, our brains did not evolve ...

24. Grade School Revisited: How to Multiply Two Numbers Computers worldwide perform enormous numbers of multiplications each day. In most computers, each such operation ...

Using SFTP to Transfer Files on Windows SFTP is set up so you can connect to a remote server simply by entering the name of the server, or its Internet address in ...

Using SSH to Connect Remotely on Windows Computing Services supports the use of the SSH.com Secure Shell client on Windows. Its graphic interface follows most of the ...

nop StudentGroup Member list (comma separated list): Set GROUP LuisVonAhn Persons/group who can change the list: Set ALLOWTOPICCHANGE ...

TWiki Administrator Group Member list (comma separated list): Set GROUP AnupamGupta, LuisVonAhn, DanKilgallin, BradleyYoo, YoninaCooper, DannySleator ...

TWiki Administrator User The TWikiAdminUser has been added to TWiki 4.2.0 to make it possible to login without needing to create a TWiki User, or to temporarily login ...

TWiki Contributor Not an actual user of this site, but a person devoting some of his/her time to contribute to the Open Source TWiki project. TWikiContributor lists ...

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TWiki Groups These groups can be used to define fine grained .TWikiAccessControl in nop TWiki: New Group: Note: A group topic name must be a .WikiWord ...

The nop TWikiGuest User A guest of this TWiki web, not unlike yourself. You can leave your trace behind you, just add your name in .TWikiRegistration and create your ...

" }% FINALPREFERENCES locks site level preferences that are not allowed to be overridden by or user preferences: Set FINALPREFERENCES ATTACHFILESIZELIMIT ...

The nop TWikiRegistrationAgent User This is a TWiki User used by TWiki when it registers new users. This user has special access to write to , and does not need an ...

List of nop TWiki users Below is a list of users with accounts. If you want to edit topics or see protected areas of the site then you can get added to the list by ...

Technical Support Essentials Converting files to PDF Submitting Homework Accessing the 15 251 bulletin board Andrew Basic UNIX commands ...

Drawing Automata LaTeX Within LaTeX, the and http://www.lsv.ens cachan.fr/~gastin/gastex/gastex.html GasTeX packages may be useful to draw automata. The former ...

FTP/SFTP FTP is a transfer protocol used to move files from one machine to another. In this class, you will probably use FTP to transfer your homework to the handin ...

Homework Submission The rules for submitting written homework are as follows: You must hand in a single file in pdf format . See the Converting Between File ...

Java: Reading from Standard In Here is a bit of starter code, just as a quick aid to help java programmers that have never dealt with file input/output before. The ...

Telnet (SSH) Due to security restrictions, you must use SSH to connect to andrew machines. Windows The officially supported SSH client is SSH Secure Shell: it supports ...

Turing's Legacy: The Limits Of Computation Alan Turing (1912 1954) Grading Scripts and the HELLO Assignment Suppose we give you the following assignment: write a ...

Ancient Wisdom: Unary and Binary One of the key insights in problem solving is that we don't have to stick with the representation in which we encounter a problem ...

The nop UnknownUser User UnknownUser is a reserved name in TWiki. If the UnknownUser appears, it is probably because author information for a topic could not be recovered ...

User Form Note: This is a maintenance topic, used by the TWiki administrator. This form defines the form of the home pages of registered TWiki users listed in ...

Header of User Homepages Note: This is a maintenance topic, used by the TWiki administrator. The part between the horizontal rules gets included at the top of ...

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User List showing all photographs " size "large" title " $topic "}% If TWiki:Plugins.ImageGalleryPlugin is installed this page will show photos and names of all ...

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You can post to the class bulletin board, academic.cs.15 251, by emailing your post to the following address: post academic.cs.15 251 #64;andrew.cmu.edu Here ...

My Links .ATasteOfTWiki view a short introductory presentation on TWiki for beginners .WelcomeGuest starting points on TWiki .TWikiUsersGuide ...

TWiki's nop Main web The web for users, groups and offices. TWiki is an Enterprise Collaboration Platform.

Welcome to the 15 251 Wiki If you want to contribute to the wiki, please read Information for Editors Lecture Notes Course Syllabus Contains grading ...

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nop Main Web Preferences The following settings are web preferences of the Main web. These preferences overwrite the site level preferences in . and ...

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