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Programming for mathematicians (Universitext)/ (Record no. 179854)

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000 -LEADER
fixed length control field	00371nam a2200145Ia 4500
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number	354066422X
040 ## - CATALOGING SOURCE
Transcribing agency	CUS
082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number	519.7
Item number	SER/P
100 ## - MAIN ENTRY--PERSONAL NAME
Personal name	Seroul, Raymond
245 #0 - TITLE STATEMENT
Title	Programming for mathematicians (Universitext)/
Statement of responsibility, etc.	Raymond Seroul
250 ## - EDITION STATEMENT
Edition statement	2000
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication, distribution, etc.	New York:
Name of publisher, distributor, etc.	Springer,
Date of publication, distribution, etc.	2000.
300 ## - PHYSICAL DESCRIPTION
Extent	432p.
505 ## - FORMATTED CONTENTS NOTE
Formatted contents note	<br/>1. Programming Proverbs 1<br/>1.1. Above all, no tricks! 1<br/>1.2. Do not chewing gum while climbing stairs 2<br/>1.3. Name that which you still don't know 2<br/>1.4. Tomorrow, things will be better; the day after, better still<br/>... 2<br/>1.5. Never execute an order before it is given 3<br/>1.6. Document today to avoid tears tomorrow 3<br/>1.7. Descartes' Discourse on the Method 3<br/>2. Review of Arithmetic 5<br/>2.1. Euclidean Division 5<br/>2.2. Numeration Systems 6<br/>2.3. Prime Numbers 7<br/>2.3.1. The number of primes smaller than a given real number . 8<br/>2.4. The Greatest Common Divisor 9<br/>2.4.1. The Bezout Theorem 10<br/>2.4.2. Gauss's Lemma 10<br/>2.5. Congruences 11<br/>2.6. The Chinese Remainder Theorem 12<br/>2.7. The Euler phi Function 14<br/>2.8. The Theorems of Fermat and Euler 15<br/>2.9. Wilson's Theorem 16<br/>2.10. Quadratic Residues 17<br/>2.11. Prime Number and Sum of Two Squares 18<br/>2.12. The Moebius Function 19<br/>2.13. The Fibonacci Numbers 21<br/>2.14. Reasoning by Induction 22<br/>2.15. Solutions of the Exercises 25<br/>3. An Algorithmic Description Language 29<br/>3.1. Identifiers 30<br/>3.2. Arithmetic Expressions 31<br/>3.2.1. Numbers 31<br/>3.2.2. Operations 31<br/>Table of Contents<br/>3.2.3. Arrays 32<br/>3.2.4. Function calls and parentheses 32<br/>3.3. Boolean Expressions 32<br/>3.4. Statements and their Syntax 33<br/>3.4.1. Assignments 34<br/>3.4.2. Conditionals 34<br/>3.4.3. For loops 35<br/>3.4.4. While loops 35<br/>3.4.5. Repeat loops 35<br/>3.4.6. Sequences of statements 36<br/>3.4.7. Blocks of statements 36<br/>3.4.8. Complex statements 37<br/>3.4.9. Layout on page and control<br/>of syntax 38<br/>3.4.10. To what does the else belong? 40<br/>3.4.11. Semicolons: some classical errors 40<br/>3.5. The Semantics of Statements 42<br/>3.5.1. Assignments 42<br/>3.5.2. Conditionals 42<br/>3.5.3. First translations 43<br/>3.5.4. The boustrophedon order 45<br/>3.5.5. The for loop 47<br/>3.5.6. The while loop 48<br/>3.5.7. The repeat loop 50<br/>3.5.8. Embedded loops 51<br/>3.6. Which Loop to Choose? 51<br/>3.6.1. Choosing a for loop 52<br/>3.6.2. Choosing a while loop 52<br/>3.6.3. Choosing a repeat loop 52<br/>3.6.4. Inspecting entrances and exits 52<br/>3.6.5. Loops with accidents 54<br/>3.6.6. Gaussian elimination 55<br/>3.6.7. How to grab data 56<br/>4. How to Create an Algorithm 59<br/>4.1. The Trace of an Algorithm 59<br/>4.2. First Method: Recycling Known Code 60<br/>4.2.1. Postage stamps 60<br/>4.2.2. How to determine whether a postage is realizable<br/>... 61<br/>4.2.3. Calculating the threshold value 62<br/>4.3. Second Method: Using Sequences 64<br/>4.3.1. Creation of a simple algorithm 66<br/>4.3.2. The exponential series 67<br/>4.3.3. Decomposition into prime factors 69<br/>4.3.4. The least divisor function 71<br/>4.3.5. Cardinality of an intersection 71<br/>Table of Contents xi<br/>4.3.6. The CORDIC Algorithm 74<br/>4.4. Third Method: Deferred Writing 78<br/>4.4.1. Calculating two bizarre functions 80<br/>4.4.2. Storage<br/>of the first N prime numbers 81<br/>4.4.3. Last recommendations 84<br/>4.5. How to Prove an Algorithm 85<br/>4.5.1. Crashes 85<br/>4.5.2. Infinite loops 85<br/>4.5.3. Calculating the CCD of two numbers 86<br/>4.5.4. A more complicated example 86<br/>4.5.5. The validity of a result furnished by a loop 87<br/>4.6. Solutions of the Exercises 88<br/>5. Algorithms and Classical Constructions 91<br/>5.1. Exchanging the Contents of Two Variables 91<br/>5.2. Diverse Sums 92<br/>5.2.1. A very important convention 92<br/>5.2.2. Double sums 93<br/>5.2.3. Sums with exceptions 94<br/>5.3. Searching for a Maximum 95<br/>5.4. Solving a Triangular Cramer System 96<br/>5.5. Rapid Calculation<br/>of Powers 97<br/>5.6. Calculation of the Fibonacci Numbers 98<br/>5.7. The Notion of a Stack 99<br/>5.8. Linear Traversal of a Finite Set 101<br/>5.9. The Lexicographic Order 102<br/>5.9.1. Words of fixed length 102<br/>5.9.2. Words<br/>of variable length 104<br/>5.10. Solutions to the Exercises 105<br/>6. The Pascal Language 109<br/>6.1. Storage of the Usual Objects 109<br/>6.2. Integer Arithmetic in Pascal 110<br/>6.2.1. Storage of integers in Pascal 110<br/>6.3. Arrays in Pascal 113<br/>6.4. Declaration<br/>of an Array 114<br/>6.5. Product Sets and Types 115<br/>6.5.1. Product of equal sets 115<br/>6.5.2. Product<br/>of unequal sets 116<br/>6.5.3. Composite types 116<br/>6.6. The Role of Constants 117<br/>6.7. Litter 119<br/>6.8. Procedures 119<br/>6.8.1. The declarative part of a procedure 120<br/>xii fable of Contents<br/>6.8.2. Procedure calls 121<br/>6.8.3. Communication of a procedure with the exterior ... 122<br/>6.9. Visibility of the Variables in a Procedure 124<br/>6.10. Context Effects 125<br/>6.10.1. Functions 127<br/>6.10.2. Procedure or function? 128<br/>6.11. Procedures: What the Program Seems To Do 129<br/>6.11.1. Using the model 133<br/>6.12. Solutions of the Exercises 134<br/>7. How to Write a Program 135<br/>7.1. Inverse of an Order 4 Matrix 135<br/>7.1.1. The problem 136<br/>7.1.2. Theoretical study 136<br/>7.1.3. Writing the program 138<br/>7.1.4. The function det 140<br/>7.1.5. How to type a program 143<br/>7.2. Characteristic Polynomial<br/>of a Matrix 144<br/>7.2.1. The program Leverrier 147<br/>7.3. How to Write a Program 152<br/>7.4. A Poorly Written Procedure 156<br/>8. The Integers 159<br/>8.1. The Euclidean Algorithm 159<br/>8.1.1. Complexity of the Euclidean algorithm 160<br/>8.2. The Blankinship Algorithm 161<br/>8.3. Perfect Numbers 163<br/>8.4. The Lowest Divisor Function 165<br/>8.5. The Moebius Function 167<br/>8.6. The Sieve of Eratosthenes 169<br/>8.6.1. Formulation of the algorithm 171<br/>8.6.2. Transforming the algorithm to a program 172<br/>8.7. The Function pi(x) 175<br/>8.7.1. Legendre's formula 175<br/>8.7.2. Implementation of Legendre's formula 178<br/>8.7.3. Meissel's formula 179<br/>8.8. Egyptian Fractions 181<br/>8.8.1. The program 183<br/>8.8.2. Numerical results 186<br/>8.9. Operations on Large Integers 187<br/>8.9.1. Addition 187<br/>8.9.2. Subtraction 188<br/>8.9.3. Multiplication 189<br/>8.9.4. Declarations 190<br/>Table of Contents xni<br/>8.9.5. The program 191<br/>8.10. Division in Base b 194<br/>8.10.1. Description of the division algorithm 194<br/>8.10.2. Justification of the division algorithm 196<br/>8.10.3. Effective estimates of integer parts 197<br/>8.10.4. A good division algorithm 200<br/>8.11. Sums of Fibonacci Numbers 200<br/>8.12. Odd Primes as a Sum of Two Squares 203<br/>8.13. Sums of Four Squares 207<br/>8.14. Highly Composite Numbers 208<br/>8.14.1. Several properties of highly composite numbers . . . 210<br/>8.14.2. Practical investigation of highly composite integers . 212<br/>8.15. Permutations: Johnson's'Algorithm 213<br/>8.15.1. The program Johnson 215<br/>8.16. The Count is Good 218<br/>8.16.1. Syntactic trees 219<br/>9. The Complex Numbers 225<br/>9.1. The Gaussian Integers 225<br/>9.1.1. Euclidean division 226<br/>9.1.2. Irreducibles 226<br/>9.1.3. The program 231<br/>9.2. Bases of Numeration in the Gaussian Integers 234<br/>9.2.1. The modulo beta map 234<br/>9.2.2. How to find an exact system of representatives .... 235<br/>9.2.3. Numeration system in base beta 236<br/>9.2.4. An algorithm for expression in base beta 237<br/>9.3. Machin Formulas 240<br/>9.3.1. Uniqueness of a Machin formula 242<br/>9.3.2. Proof of Proposition 9.3.1 243<br/>9.3.3. The Todd condition is necessary 244<br/>9.3.4. The Todd condition is sufficient 244<br/>9.3.5. Kern's algorithm 245<br/>9.3.6. How to get rid of the Arctangent function 249<br/>9.3.7. Examples 251<br/>10. Polynomials 253<br/>10.1. Definitions 253<br/>10.2. Degree of a Polynomial 254<br/>10.3. How to Store a Polynomial 254<br/>10.4. The Conventions we Adopt 256<br/>10.5. Euclidean Division 259<br/>10.6. Evaluation of Polynomials: Homer's Method 261<br/>10.7. Translation and Composition 262<br/>xiv Table of Contents<br/>10.7.1. Change of origin 262<br/>10.7.2. Composing polynomials 265<br/>10.8. Cyclotomic Polynomials 265<br/>10.8.1. First formula 266<br/>10.8.2. Second formula 268<br/>10.9. Lagrange Interpolation 269<br/>10.10. Basis Change 273<br/>10.11. Differentiation<br/>and Discrete Taylor Formulas 275<br/>10.11.1. Discrete differentiation 275<br/>10.12. Newton-Girard Formulas 278<br/>10.13. Stable Polynomials 280<br/>10.14. Factoring a Polynomial with Integral Coefficients 286<br/>10.14.1. Why integer (instead of rational) coefficients? . . . 286<br/>10.14.2. Kronecker's factorization algorithm 288<br/>10.14.3. Use of stable polynomials 290<br/>10.14.4.<br/>The program 291<br/>10.14.5. Last remarks 294<br/>11. Matrices 297<br/>11.1. Z-Linear Algebra 297<br/>11.1.1. The bordered matrix trick 300<br/>11.1.2. Generators of a subgroup 301<br/>11.1.3. The Blankinship algorithm 301<br/>11.1.4. Hermite matrices 303<br/>11.1.5. The program Hermite 305<br/>11.1.6. The incomplete basis theorem 312<br/>11.1.7. Finding a basis<br/>of a subgroup 316<br/>11.2. Linear Systems with Integral Coefficients 318<br/>11.2.1. Theoretical results 318<br/>11.2.2. The case of a matrix in column echelon form .... 318<br/>11.2.3. General case 320<br/>11.2.4. Case of a single equation 321<br/>11.3. Exponential of a Matrix: Putzer's Algorithm 323<br/>11.4. Jordan Reduction 326<br/>11.4.1. Review 326<br/>11.4.2. Reduction of a nilpotent endomorphism 327<br/>11.4.3. The Pittelkow-Runckel algorithm 329<br/>11.4.4. Justification<br/>of the Pittelkow-Runckel algorithm . . . 332<br/>11.4.5. A complete example 333<br/>11.4.6. Programming 336<br/>12. Recursion 337<br/>12.1. Presentation 337<br/>12.1.1. Two simple examples 337<br/>Table of Contents xv<br/>12.1.2. Mutual recursion 339<br/>12.1.3. Arborescence of recursive calls 340<br/>12.1.4. Induction and recursion 340<br/>12.2. The Ackermann function 343<br/>12.3. The Towers of Hanoi 345<br/>12.4. Baguenaudier 348<br/>12.5. The Hofstadter Function 351<br/>12.6. How to Write a Recursive Code 352<br/>12.6.1. Sorting by dichotomy 353<br/>13. Elements of compiler theory 359<br/>13.1. Pseudocode 359<br/>13.1.1. Description of pseudocode 360<br/>13.1.2. How to compile a pseudocode program by hand . . 365<br/>13.1.3. Translation of a conditional 366<br/>13.1.4. Translation of a loop 368<br/>13.1.5. Function calls 369<br/>13.1.6. A very efficient technique 372<br/>13.1.7. Procedure calls 374<br/>13.1.8. The factorial function 377<br/>13.1.9. The Fibonacci numbers 379<br/>13.1.10. The Hofstadter function 381<br/>13.1.11.<br/>The Towers of Hanoi 382<br/>13.2. A Pseudocode Interpreter 385<br/>13.3. How to Analyze an Arithmetic Expression 400<br/>13.3.1. Arithmetic expressions 401<br/>13.3.2. How to recognize an arithmetic expression 404<br/>13.4. How to Evaluate an Arithmetic Expression 410<br/>13.5. How to Compile an Arithmetic Expression 415<br/>13.5.1. Polish notation 415<br/>13.5.2. A Compiler for arithmetic expressions 420<br/>
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Koha item type	General Books

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Withdrawn status	Lost status	Damaged status	Not for loan	Home library	Current library	Shelving location	Date acquired	Full call number	Accession number	Date last seen	Koha item type
				Central Library, Sikkim University	Central Library, Sikkim University	General Book Section	29/08/2016	519.7 SER/P	P34865	29/08/2016	General Books