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  • What is this "Change to Display" of math equations and why does it change the equation style in Word 2010?

    - by ysap
    I am writing an equation with the "new" Equation Editor in MS Word 2010 (Insert - Equation). When using one of the "large operators", for example the Sigma, with lower and upper limits, there are two styles for displaying the limits - below and above the Sigma, or to the right as super/subscripts. I am choosing the first style - limits above and below to get the standard notation, but Word formats the equation the other way. Now, the object has a bounding box with a context menu on its right. In this menu, I can select Change to Display and the equation is moved to a new line, w/o adjacent text - but, now the sigma limits appear as requested! Then, selecting Change to Inline reverts to the previous form. So, I want to know if there is away to force the requested form with an "inline" attribute? I know that I can use a MS Equation 3.0 object, but I want to remain with the new, "native" editor.

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  • O&rsquo;Reilly E-Book of the Day 15/Aug/2014 - Advanced Quantitative Finance with C++

    - by TATWORTH
    Originally posted on: http://geekswithblogs.net/TATWORTH/archive/2014/08/15/orsquoreilly-e-book-of-the-day-15aug2014---advanced-quantitative-finance.aspxToday’s half-price book of the Day offer from O’Reilly at http://shop.oreilly.com/product/9781782167228.do?code=MSDEAL is Advanced Quantitative Finance with C++. “This book will introduce you to the key mathematical models used to price financial derivatives, as well as the implementation of main numerical models used to solve them. In particular, equity, currency, interest rates, and credit derivatives are discussed. In the first part of the book, the main mathematical models used in the world of financial derivatives are discussed. Next, the numerical methods used to solve the mathematical models are presented. Finally, both the mathematical models and the numerical methods are used to solve some concrete problems in equity, forex, interest rate, and credit derivatives.”

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  • What Precalculus knowledge is required before learning Discrete Math Computer Science topics?

    - by Ein Doofus
    Below I've listed the chapters from a Precalculus book as well as the author recommended Computer Science chapters from a Discrete Mathematics book. Although these chapters are from two specific books on these subjects I believe the topics are generally the same between any Precalc or Discrete Math book. What Precalculus topics should one know before starting these Discrete Math Computer Science topics?: Discrete Mathematics CS Chapters 1.1 Propositional Logic 1.2 Propositional Equivalences 1.3 Predicates and Quantifiers 1.4 Nested Quantifiers 1.5 Rules of Inference 1.6 Introduction to Proofs 1.7 Proof Methods and Strategy 2.1 Sets 2.2 Set Operations 2.3 Functions 2.4 Sequences and Summations 3.1 Algorithms 3.2 The Growths of Functions 3.3 Complexity of Algorithms 3.4 The Integers and Division 3.5 Primes and Greatest Common Divisors 3.6 Integers and Algorithms 3.8 Matrices 4.1 Mathematical Induction 4.2 Strong Induction and Well-Ordering 4.3 Recursive Definitions and Structural Induction 4.4 Recursive Algorithms 4.5 Program Correctness 5.1 The Basics of Counting 5.2 The Pigeonhole Principle 5.3 Permutations and Combinations 5.6 Generating Permutations and Combinations 6.1 An Introduction to Discrete Probability 6.4 Expected Value and Variance 7.1 Recurrence Relations 7.3 Divide-and-Conquer Algorithms and Recurrence Relations 7.5 Inclusion-Exclusion 8.1 Relations and Their Properties 8.2 n-ary Relations and Their Applications 8.3 Representing Relations 8.5 Equivalence Relations 9.1 Graphs and Graph Models 9.2 Graph Terminology and Special Types of Graphs 9.3 Representing Graphs and Graph Isomorphism 9.4 Connectivity 9.5 Euler and Hamilton Ptahs 10.1 Introduction to Trees 10.2 Application of Trees 10.3 Tree Traversal 11.1 Boolean Functions 11.2 Representing Boolean Functions 11.3 Logic Gates 11.4 Minimization of Circuits 12.1 Language and Grammars 12.2 Finite-State Machines with Output 12.3 Finite-State Machines with No Output 12.4 Language Recognition 12.5 Turing Machines Precalculus Chapters R.1 The Real-Number System R.2 Integer Exponents, Scientific Notation, and Order of Operations R.3 Addition, Subtraction, and Multiplication of Polynomials R.4 Factoring R.5 Rational Expressions R.6 Radical Notation and Rational Exponents R.7 The Basics of Equation Solving 1.1 Functions, Graphs, Graphers 1.2 Linear Functions, Slope, and Applications 1.3 Modeling: Data Analysis, Curve Fitting, and Linear Regression 1.4 More on Functions 1.5 Symmetry and Transformations 1.6 Variation and Applications 1.7 Distance, Midpoints, and Circles 2.1 Zeros of Linear Functions and Models 2.2 The Complex Numbers 2.3 Zeros of Quadratic Functions and Models 2.4 Analyzing Graphs of Quadratic Functions 2.5 Modeling: Data Analysis, Curve Fitting, and Quadratic Regression 2.6 Zeros and More Equation Solving 2.7 Solving Inequalities 3.1 Polynomial Functions and Modeling 3.2 Polynomial Division; The Remainder and Factor Theorems 3.3 Theorems about Zeros of Polynomial Functions 3.4 Rational Functions 3.5 Polynomial and Rational Inequalities 4.1 Composite and Inverse Functions 4.2 Exponential Functions and Graphs 4.3 Logarithmic Functions and Graphs 4.4 Properties of Logarithmic Functions 4.5 Solving Exponential and Logarithmic Equations 4.6 Applications and Models: Growth and Decay 5.1 Systems of Equations in Two Variables 5.2 System of Equations in Three Variables 5.3 Matrices and Systems of Equations 5.4 Matrix Operations 5.5 Inverses of Matrices 5.6 System of Inequalities and Linear Programming 5.7 Partial Fractions 6.1 The Parabola 6.2 The Circle and Ellipse 6.3 The Hyperbola 6.4 Nonlinear Systems of Equations

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  • Disable MathML output of eLyXer

    - by Gryllida
    eLyXer is a standalone LyX to HTML converter. In the resulting file, equations are formatted as MathML, and the file itself starts with an XML tag. This causes two problems: LibreOffice does not read the XML file (it can read HTML files, but not XHTML). I am unable to copy and paste the equations into a document editor such as LibreOffice with the goal of subsequent conversion into .doc, because .doc files do not support MathML. The eLyXer help page mentions an option to only use simple math, but there is no option to set math equations to output as images. And I already set Document Settings Output Math equations Format: images in LyX, which presumably is saved in the lyx document somewhere. A web search did not come up with any solutions.

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  • Add Excel column without breaking equation

    - by CRAIG
    I have completed a very complex Excel spreadsheet with a lot of equations, except ... I forgot to include September I have Jan through Dec, all the months, except the calculations for September. Of course all the equations are currently perfect for the data that's here. How do I add a whole new column without ruining the previous equations? PS: tomorrow is my holidays and I have to go to work to finish this table, so bad

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  • How to replace all images in Libreoffice with their description

    - by user30131
    I have a very long document containing lots of svg images created using the extension TexMaths. This extension uses the latex installation to create svg image of the inputted equation (or set of equations). The latex code for each equation (or set of equations) is embedded in the image as part of its Description. Such a Description can be accessed by right clicking the svg image and choosing the option Description. I want to replace all the svg images using a suitable macro, by the embedded descriptions. e.g. from The Einstein's famous equation, [svg embedded equation : E = mc 2], tells us that mass can be converted to energy and vice-versa. To The Einstein's famous equation, E = mc^2, tells us that mass can be converted to energy and vice-versa. This will allow me to convert by hand the odt file containing numerous TexMaths equations to LaTeX.

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  • Discrete Math and Computing Course

    - by ShrimpCrackers
    I was recently admitted into a Computing and Software Systems program (basically software engineering) and one of the first courses I'll be taking is called Mathematical Principles of Computing. The course description: "Integrating mathematical principles with detailed instruction in computer programming. Explores mathematical reasoning and discrete structures through object-oriented programming. Includes algorithm analysis, basic abstract data types, and data structures." I'm not a fan of math, but I've been doing well in all my math classes mostly A's and B's ever since I started two years ago, and I've been doing math every quarter - never took a quarter without math - so I've been doing it all in sequence without gaps. However, I'm worried about this class. I've read briefly on what discrete math is and from what my advisor told me, its connection with computer science is that it has alot to do with proving algorithms. One thing that my instructors briefly touched on and never went into detail was proving algorithms, and when I tried, I just wasn't very good at mathematical induction. It's one of the things that I ignored every time it showed up in a homework problem (usually in Calculus III which I'm finishing up right now). Questions: 1. What can I expect from this class? 2. How can I prepare myself for this class? 3. Other tips? Thank you.

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  • Greasemonkey script for inserting math in gmail

    - by Elazar Leibovich
    I wish an easy way to communicate mathematical equations with gmail. There's a javascript script called AsciiMath, which should translate Tex-like equations into standard mathML. I thought that it would be nice to use this script with GM. I thought that before sending the email, this script would convert all the TeX-like equations in your email to MathML. Thus the reader which is using FF (or IE with MathPlayer installed) would be able to easily read those equations. Ideally, I wish to somehow keep the original TeX-like equations in a plain-text message, so that it would be readable by plain text email clients, such as mutt. Obviously the weakest link here is the client software, which most likely doesn't support MathML. Still if my correspondent is using Firefox and some kind of webmail (which is pretty reasonable) - it should work. My question is, is it possible? Did anyone do that? Do you see any technical problems with this approach (gmail filtering the MathML, client not parsing it correctly etc.)? Any smarter ideas?

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  • Logic error for Gauss elimination

    - by iwanttoprogram
    Logic error problem with the Gaussian Elimination code...This code was from my Numerical Methods text in 1990's. The code is typed in from the book- not producing correct output... Sample Run: SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS USING GAUSSIAN ELIMINATION This program uses Gaussian Elimination to solve the system Ax = B, where A is the matrix of known coefficients, B is the vector of known constants and x is the column matrix of the unknowns. Number of equations: 3 Enter elements of matrix [A] A(1,1) = 0 A(1,2) = -6 A(1,3) = 9 A(2,1) = 7 A(2,2) = 0 A(2,3) = -5 A(3,1) = 5 A(3,2) = -8 A(3,3) = 6 Enter elements of [b] vector B(1) = -3 B(2) = 3 B(3) = -4 SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS The solution is x(1) = 0.000000 x(2) = -1.#IND00 x(3) = -1.#IND00 Determinant = -1.#IND00 Press any key to continue . . . The code as copied from the text... //Modified Code from C Numerical Methods Text- June 2009 #include <stdio.h> #include <math.h> #define MAXSIZE 20 //function prototype int gauss (double a[][MAXSIZE], double b[], int n, double *det); int main(void) { double a[MAXSIZE][MAXSIZE], b[MAXSIZE], det; int i, j, n, retval; printf("\n \t SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS"); printf("\n \t USING GAUSSIAN ELIMINATION \n"); printf("\n This program uses Gaussian Elimination to solve the"); printf("\n system Ax = B, where A is the matrix of known"); printf("\n coefficients, B is the vector of known constants"); printf("\n and x is the column matrix of the unknowns."); //get number of equations n = 0; while(n <= 0 || n > MAXSIZE) { printf("\n Number of equations: "); scanf ("%d", &n); } //read matrix A printf("\n Enter elements of matrix [A]\n"); for (i = 0; i < n; i++) for (j = 0; j < n; j++) { printf(" A(%d,%d) = ", i + 1, j + 1); scanf("%lf", &a[i][j]); } //read {B} vector printf("\n Enter elements of [b] vector\n"); for (i = 0; i < n; i++) { printf(" B(%d) = ", i + 1); scanf("%lf", &b[i]); } //call Gauss elimination function retval = gauss(a, b, n, &det); //print results if (retval == 0) { printf("\n\t SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS\n"); printf("\n\t The solution is"); for (i = 0; i < n; i++) printf("\n \t x(%d) = %lf", i + 1, b[i]); printf("\n \t Determinant = %lf \n", det); } else printf("\n \t SINGULAR MATRIX \n"); return 0; } /* Solves the system of equations [A]{x} = {B} using */ /* the Gaussian elimination method with partial pivoting. */ /* Parameters: */ /* n - number of equations */ /* a[n][n] - coefficient matrix */ /* b[n] - right-hand side vector */ /* *det - determinant of [A] */ int gauss (double a[][MAXSIZE], double b[], int n, double *det) { double tol, temp, mult; int npivot, i, j, l, k, flag; //initialization *det = 1.0; tol = 1e-30; //initial tolerance value npivot = 0; //mult = 0; //forward elimination for (k = 0; k < n; k++) { //search for max coefficient in pivot row- a[k][k] pivot element for (i = k + 1; i < n; i++) { if (fabs(a[i][k]) > fabs(a[k][k])) { //interchange row with maxium element with pivot row npivot++; for (l = 0; l < n; l++) { temp = a[i][l]; a[i][l] = a[k][l]; a[k][l] = temp; } temp = b[i]; b[i] = b[k]; b[k] = temp; } } //test for singularity if (fabs(a[k][k]) < tol) { //matrix is singular- terminate flag = 1; return flag; } //compute determinant- the product of the pivot elements *det = *det * a[k][k]; //eliminate the coefficients of X(I) for (i = k; i < n; i++) { mult = a[i][k] / a[k][k]; b[i] = b[i] - b[k] * mult; //compute constants for (j = k; j < n; j++) //compute coefficients a[i][j] = a[i][j] - a[k][j] * mult; } } //adjust the sign of the determinant if(npivot % 2 == 1) *det = *det * (-1.0); //backsubstitution b[n] = b[n] / a[n][n]; for(i = n - 1; i > 1; i--) { for(j = n; j > i + 1; j--) b[i] = b[i] - a[i][j] * b[j]; b[i] = b[i] / a[i - 1][i]; } flag = 0; return flag; } The solution should be: 1.058824, 1.823529, 0.882353 with det as -102.000000 Any insight is appreciated...

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  • Generic applet style system for publishing mathematics demonstrations?

    - by Alex
    Anyone who's tried to study mathematics using online resources will have come across these Java applets that demonstrate a particular mathematical idea. Examples: http://www.math.ucla.edu/~tao/java/Mobius.html http://www.mathcs.org/java/programs/FFT/index.html I love the idea of this interactive approach because I believe it is very helpful in conveying mathematical principles. I'd like to create a system for visually designing and publishing these 'mathlets' such that they can be created by teachers with little programming experience. So in order to create this app, i'll need a GUI and a 'math engine'. I'll probably be working with .NET because thats what I know best and i'd like to start experimenting with F#. Silverlight appeals to me as a presentation framework for this project (im not worried about interoperability right now). So my questions are: does anything like this exist already in full form? are there any GUI frameworks for displaying mathematical objects such as graphs & equations? are there decent open source libraries that exposes a mathematical framework (Math.NET looks good, just wondering if there is anything else out there) is there any existing work on taking mathematical models/demos built with maple/matlab/octave/mathematica etc and publishing them to the web?

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  • VirtualBox - split partitioned VDI into separate VDIs

    - by mathematical.coffee
    I'm very new to VirtualBox. I set up an Arch Linux VM and a Ubuntu VM (Ubuntu host), both sharing the same .vdi like so (I had in my mind a dual-boot situation): VDI file (25GB) |- /dev/sda1: 5GB (Arch Linux) |- /dev/sda2: [Ubuntu] |- /dev/sda5 (swap, 1GB) |- /dev/sda6 Ubuntu /, 9GB |- /dev/sda7 Ubuntu /home, 10GB I've now realised that I don't want a dual-boot-type setup, I'd rather boot each machine independently (my initial thought was to share /home between Ubunto and Arch). So, my question: Can I split /dev/sda1 and /dev/sda2 each to their own .vdi files so I can use them as completely separate machines? I'd rather not have to re-install either Arch (because it took me ages to work it out!) or Ubuntu (because I've already done a few GB of updates and don't want to redo them). I haven't been able to find anything about this - most questions I see are about converting a .vdi to a partition on the host, or splitting a .vdi into multiple smaller files (that are not independent), or converting a partition on the host to a .vdi file. cheers.

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  • excel 2010 format and input issue

    - by Craig Gunn
    I have completed a very complex Excel spreadsheet with a lot of equations, except ... I forgot to include September I have Jan through Dec, all the months, except the calculations for September. Of course all the equations are currently perfect for the data that's here. How do I add a whole new column without ruining the previous equations? PS: tomorrow is my holidays and I have to go to work to finish this table, so bad. would really appreciate some kind expertise :) cheers craig.

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  • Ada and 'The Book'

    - by Phil Factor
    The long friendship between Charles Babbage and Ada Lovelace created one of the most exciting and mysterious of collaborations ever to have resulted in a technological breakthrough. The fireworks that created by the collision of two prodigious mathematical and creative talents resulted in an invention, the Analytical Engine, which went on to change society fundamentally. However, beyond that, we just don't know what the bulk of their collaborative work was about:;  it was done in strictest secrecy. Even the known outcome of their friendship, the first programmable computer, was shrouded in mystery. At the time, nobody, except close friends and family, had any idea of Ada Byron's contribution to the invention of the ‘Engine’, and how to program it. Her great insight was published in August 1843, under the initials AAL, standing for Ada Augusta Lovelace, her title then being the Countess of Lovelace. It was contained in a lengthy ‘note’ to her translation of a publication that remains the best description of Babbage's amazing Analytical Engine. The secret identity of the person behind those enigmatic initials was finally revealed by Prince de Polignac who, seventy years later, wrote to Ada's daughter to seek confirmation that her mother had, indeed, been the author of the brilliant sentences that described so accurately how Babbage's mechanical computer could be programmed with punch-cards. L.F. Menabrea's paper on the Analytical Engine first appeared in the 'Bibliotheque Universelle de Geneve' in October 1842, and Ada translated it anonymously for Taylor's 'Scientific Memoirs'. Charles Babbage was surprised that she had not written an original paper as she already knew a surprising amount about the way the machine worked. He persuaded her to at least write some explanatory notes. These notes ended up extending to four times the length of the original article and represented the first published account of how a machine could be programmed to perform any calculation. Her example of programming the Bernoulli sequence would have worked on the Analytical engine had the device’s construction been completed, and gave Ada an unassailable claim to have invented the art of programming. What was the reason for Ada's secrecy? She was the only legitimate child of Lord Byron, who was probably the best known celebrity of the age, so she was already famous. She was a senior aristocrat, with titles, a fortune in money and vast estates in the Midlands. She had political influence, and was the cousin of Lord Melbourne, who was the Prime Minister at that time. She was friendly with the young Queen Victoria. Her mathematical activities were a pastime, and not one that would be considered by others to be in keeping with her roles and responsibilities. You wouldn't dare to dream up a fictional heroine like Ada. She was dazzlingly beautiful and talented. She could speak several languages fluently, and play some musical instruments with professional skill. Contemporary accounts refer to her being 'accomplished in science, art and literature'. On top of that, she was a brilliant mathematician, a talent inherited from her mother, Annabella Milbanke. In her mother's circle of literary and scientific friends was Charles Babbage, and Ada's friendship with him dates from her teenage zest for Mathematics. She was one of the first people he'd ever met who understood what he had attempted to achieve with the 'Difference Engine', and with whom he could converse as intellectual equals. He arranged for her to have an education from the most talented academics in the country. Ada melted the heart of the cantankerous genius to the point that he became a faithful and loyal father-figure to her. She was one of the very few who could grasp the principles of the later, and very different, ‘Analytical Engine’ which was designed from the start to tackle a variety of tasks. Sadly, Ada Byron's life ended less than a decade after completing the work that assured her long-term fame, in November 1852. She was dying of cancer, her gambling habits had caused her to run up huge debts, she'd had more than one affairs, and she was being blackmailed. Her brilliant but unempathic mother was nursing her in her final illness, destroying her personal letters and records, and repaying her debts. Her husband was distraught but helpless. Charles Babbage, however, maintained his steadfast paternalistic friendship to the end. She appointed her loyal friend to be her executor. For years, she and Babbage had been working together on a secret project, known only as 'The Book'. We have a clue to what it was in a letter written by her nine years earlier, on 11th August 1843. It was a joint project by herself and Lord Lovelace, her husband, and was intended to involve Babbage's 'undivided energies'. It involved 'consulting your Engine' (it required Babbage’s computer). The letter gives no hint about the project except for the high-minded nature of its purpose, and its highly mathematical nature.  From then on, the surviving correspondence between the two gives only veiled references to 'The Book'. There isn't much, since Babbage later destroyed any letters that could have damaged her reputation within the Establishment. 'I cannot spare the book today, which I am very sorry for. At the moment I want it for constant reference, but I think you can have it tomorrow' (Oct 1844)  And 'I will send you the book directly, and you can say, when you receive it, how long you will want to keep it'. (Nov 1844)  The two of them were obviously intent on the work: She writes, four years later, 'I have an engagement for Wednesday which will prevent me from attending to your wishes about the book' (Dec 1848). This was something that they both needed to work on, but could not do in parallel: 'I will send the book on Tuesday, and it can be left with you till Friday' (11 Feb 1849). After six years work, it had been so well-handled that it was beginning to fall apart: 'Don't forget the new cover you promised for the book. The poor book is very shabby and wants one' (20 Sept 1849). So what was going on? The word 'book' was not a code-word: it was a real book, probably a 'printer's blank', plain paper, but properly bound so printers and publishers could show off how the published work might look. The hints from the correspondence are of advanced mathematics. It is obvious that the book was travelling between them, back and forth, each one working on it for less than a week before passing it back. Ada and her husband were certainly involved in gambling large sums of money on the horses, and so most biographers have concluded that the three of them were trying to calculate the mathematical odds on the horses. This theory has three large problems. Firstly, Ada's original letter proposing the project refers to its high-minded nature. Babbage was temperamentally opposed to gambling and would scarcely have given so much time to the project, even though he was devoted to Ada. Secondly, Babbage would have very soon have realized the hopelessness of trying to beat the bookies. This sort of betting never attracts his type of intellectual background. The third problem is that any work on calculating the odds on horses would not need a well-thumbed book to pass back and forth between them; they would have not had to work in series. The original project was instigated by Ada, along with her husband, William King-Noel, 1st Earl of Lovelace. Charles Babbage was invited to join the project after the couple had come up with the idea. What could William have contributed? One might assume that William was a Bertie Wooster character, addicted only to the joys of the turf, but this was far from the truth. He was a scientist, a Cambridge graduate who was later elected to be a Fellow of the Royal Society. After Eton, he went to Trinity College, Cambridge. On graduation, he entered the diplomatic service and acted as secretary under Lord Nugent, who was Lord Commissioner of the Ionian Islands. William was very friendly with Babbage too, able to discuss scientific matters on equal terms. He was a capable engineer who invented a process for bending large timbers by the application of steam heat. He delivered a paper to the Institution of Civil Engineers in 1849, and received praise from the great engineer, Isambard Kingdom Brunel. As well as being Lord Lieutenant of the County of Surrey for most of Victoria's reign, he had time for a string of scientific and engineering achievements. Whatever the project was, it is unlikely that William was a junior partner. After Ada's death, the project disappeared. Then, two years later, Babbage, through one of his occasional outbursts of temper, demonstrated that he was able to decrypt one of the most powerful of secret codes, Vigenère's autokey cipher.  All contemporary diplomatic and military messages used a variant of this cipher. Babbage had made three important discoveries, namely, the mathematical law of this cipher, the principle of the key periodicity, and the technique of the symmetry of position. The technique is now known as the Kasiski examination, also called the Kasiski test, but Babbage got there first. At one time, he listed amongst his future projects, the writing of a book 'The Philosophy of Decyphering', but it never came to anything. This discovery was going to change the course of history, since it was used to decipher the Russians’ military dispatches in the Crimean war. Babbage himself played a role during the Crimean War as a cryptographical adviser to his friend, Rear-Admiral Sir Francis Beaufort of the Admiralty. This is as much as we can be certain about in trying to make sense of the bulk of the time that Charles Babbage and Ada Lovelace worked together. Nine years of intensive work, involving the 'Engine' and a great deal of mathematics and research seems to have been lost: or has it? I've argued in the past http://www.simple-talk.com/community/blogs/philfactor/archive/2008/06/13/59614.aspx that the cracking of the Vigenère autokey cipher, was a fundamental motive behind the British Government's support and funding of the 'Difference Engine'. The Duke of Wellington, whose understanding of the military significance of being able to read enemy dispatches, was the most steadfast advocate of the project. If the three friends were actually doing the work of cracking codes by mathematical techniques that used the techniques of key periodicity, and symmetry of position (the use of a book being passed quickly to and fro is very suggestive), intending to then use the 'Engine' to do the routine cracking of each dispatch, then this is a rather different story. The project was Ada and William's idea. (William had served in the diplomatic service and would be familiar with the use of codes). This makes Ada Lovelace the initiator of a project which, by giving both Britain, and probably the USA, a diplomatic and military advantage in the second part of the Nineteenth century, changed world history. Ada would never have wanted any credit for cracking the cipher, and developing the method that rendered all contemporary military and diplomatic ciphering techniques nugatory; quite the reverse. And it is clear from the gaps in the record of the letters between the collaborators that the evidence was destroyed, probably on her request by her irascible but intensely honorable executor, Charles Babbage. Charles Babbage toyed with the idea of going public, but the Crimean war put an end to that. The British Government had a valuable secret, and intended to keep it that way. Ada and Charles had quite often discussed possible moneymaking projects that would fund the development of the Analytic Engine, the first programmable computer, but their secret work was never in the running as a potential cash cow. I suspect that the British Government was, even then, working on the concealment of a discovery whose value to the nation depended on it remaining so. The success of code-breaking in the Crimean war, and the American Civil war, led to the British and Americans  subsequently giving much more weight and funding to the science of decryption. Paradoxically, this makes Ada's contribution even closer to the creation of Colossus, the first digital computer, at Bletchley Park, specifically to crack the Nazi’s secret codes.

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  • Pandoc: Output two sumation signs in equal height in Word 2010

    - by Andy
    I need to output some complex equations in Word 2010 (docx). To do so I write most of the equations in tex and use pandoc to translate them as Word formulas. However I have a problem with the following tex equation: \sum_{m=1}^\infty\sum_{n=1}^\infty In Word the resulting two summation signs are not of the same size but the latter is smaler than the first one. Is there any workaround to solve this? I would deeply appreciate any help. Thank you Andy

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  • Mapping A Sphere To A Cube

    - by petrocket
    There is a special way of mapping a cube to a sphere described here: http://mathproofs.blogspot.com/2005/07/mapping-cube-to-sphere.html It is not your basic "normalize the point and your done" approach and gives a much more evenly spaced mapping. I've tried to do the inverse of the mapping going from sphere coords to cube coords and have been unable to come up the working equations. It's a rather complex system of equations with lots of square roots. Any math geniuses want to take a crack at it? Here's the equations in c++ code: sx = x * sqrtf(1.0f - y * y * 0.5f - z * z * 0.5f + y * y * z * z / 3.0f); sy = y * sqrtf(1.0f - z * z * 0.5f - x * x * 0.5f + z * z * x * x / 3.0f); sz = z * sqrtf(1.0f - x * x * 0.5f - y * y * 0.5f + x * x * y * y / 3.0f); sx,sy,sz are the sphere coords and x,y,z are the cube coords.

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  • Come up with a real-world problem in which only the best solution will do (a problem from Introduction to algorithms) [closed]

    - by Mike
    EDITED (I realized that the question certainly needs a context) The problem 1.1-5 in the book of Thomas Cormen et al Introduction to algorithms is: "Come up with a real-world problem in which only the best solution will do. Then come up with one in which a solution that is “approximately” the best is good enough." I'm interested in its first statement. And (from my understanding) it is asked to name a real-world problem where only the exact solution will work as opposed to a real-world problem where good-enough solution will be ok. So what is the difference between the exact and good enough solution. Consider some physics problem for example the simulation of the fulid flow in the permeable medium. To make this simulation happen some simplyfing assumptions have to be made when deriving a mathematical model. Otherwise the model becomes at least complex and unsolvable. Virtually any particle in the universe has its influence on the fluid flow. But not all particles are equal. Those that form the permeable medium are much more influental than the ones located light years away. Then when the mathematical model needs to be solved an exact solution can rarely be found unless the mathematical model is simple enough (wich probably means the model isn't close to reality). We take an approximate numerical method and after hours of coding and days of verification come up with the program or algorithm which is a solution. And if the model and an algorithm give results close to a real problem by some degree that is good enough soultion. Its worth noting the difference between exact solution algorithm and exact computation result. When considering real-world problems and real-world computation machines I believe all physical problems solutions where any calculations are taken can not be exact because universal physical constants are represented approximately in the computer. Any numbers are represented with the limited precision, at least limited by amount of memory available to computing machine. I can imagine plenty of problems where good-enough, good to some degree solution will work, like train scheduling, automated trading, satellite orbit calculation, health care expert systems. In that cases exact solutions can't be derived due to constraints on computation time, limitations in computer memory or due to the nature of problems. I googled this question and like what this guy suggests: there're kinds of mathematical problems that need exact solutions (little note here: because the question is taken from the book "Introduction to algorithms" the term "solution" means an algorithm or a program, which in this case gives exact answer on each input). But that's probably more of theoretical interest. So I would like to narrow down the question to: What are the real-world practical problems where only the best (exact) solution algorithm or program will do (but not the good-enough solution)? There are problems like breaking of cryptographic ciphers where only exact solution matters in practice and again in practice the process of deciphering without knowing a secret should take reasonable amount of time. Returning to the original question this is the problem where good-enough (fast-enough) solution will do there's no practical need in instant crack though it's desired. So the quality of "best" can be understood in any sense: exact, fastest, requiring least memory, having minimal possible network traffic etc. And still I want this question to be theoretical if possible. In a sense that there may be example of computer X that has limited resource R of amount Y where the best solution to problem P is the one that takes not more than available Y for inputs of size N*Y. But that's the problem of finding solution for P on computer X which is... well, good enough. My final thought that we live in a world where it is required from programming solutions to practical purposes to be good enough. In rare cases really very very good but still not the best ones. Isn't it? :) If it's not can you provide an example? Or can you name any such unsolved problem of practical interest?

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  • LibreOffice Math problem with greek letters

    - by Matheus de Araújo
    I've a problem with my LibreOffice. Using an old archive that I have (with the Maxwell's equations), the greek letters are like squares. I tried to change something in the alphabet but even the font don't have any greek letters (they appear like squares too), both Greek and iGreek letters package. Sounds like a packet that isn't installed or corrupted, but I still redownloaded and reinstalled the LO and I don't know whose I have to install. With the OO my equations worked well (I made the file with it). What am I supposed to do?

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  • Greek Letters rendered incorrectly in LibreOffice

    - by Matheus de Araújo
    Using an old archive that I have (with Maxwell's equations), the Greek letters display as squares. I tried to change something in the alphabet but even the fonts don't have any Greek letters (they appear like squares too), both Greek and iGreek letters packages. Sounds like a package that's not installed, or corrupted. I still re-downloaded and reinstalled LibreOffice. I don't know what I have to install. The equations look fine in OpenOffice.org (I made the file with it). What should I do?

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