Single Digits: In Praise of Small Numbers

By Marc Chamberland

The numbers one via 9 have striking mathematical houses and features. for example, why do 8 excellent card shuffles depart a customary deck of playing cards unchanged? Are there relatively "six levels of separation" among all pairs of individuals? and the way can any map want merely 4 colours to make sure that no areas of an identical colour contact? In Single Digits, Marc Chamberland takes readers on a desirable exploration of small numbers, from one to 9, taking a look at their historical past, purposes, and connections to numerous components of arithmetic, together with quantity thought, geometry, chaos idea, numerical research, and mathematical physics.

Each bankruptcy makes a speciality of a unmarried digit, starting with effortless strategies that develop into extra complex because the bankruptcy progresses. Chamberland covers immense numerical territory, comparable to illustrating the ways in which the quantity 3 connects to chaos concept, an unsolved challenge regarding Egyptian fractions, the variety of guards had to safeguard an artwork gallery, and problematical election effects. He considers the position of the quantity seven in matrix multiplication, the Transylvania lottery, synchronizing indications, and listening to the form of a drum. all through, he introduces readers to an array of puzzles, corresponding to excellent squares, the 4 hats challenge, Strassen multiplication, Catalan's conjecture, and a lot more. The book's brief sections might be learn independently and digested in bite-sized chunks--especially stable for studying concerning the Ham Sandwich Theorem and the Pizza Theorem.

Appealing to highschool and school scholars, specialist mathematicians, and people mesmerized via styles, this e-book indicates that unmarried digits provide a plethora of probabilities that readers can count number on.

Show description

Read more

Elementary Methods in Number Theory (Graduate Texts in Mathematics, Vol. 195)

By Melvyn B. Nathanson

This simple advent to quantity concept is perfect for people with no prior wisdom of the topic. the most subject matters of divisibility, congruences, and the distribution of best numbers are coated. Of specific curiosity is the inclusion of an explanation for essentially the most recognized ends up in arithmetic, the major quantity theorem. With many examples and routines, and simply requiring wisdom of a bit calculus and algebra, this e-book will swimsuit people with mind's eye and curiosity in following a mathematical argument to its end.

Show description

Read more

A First Course in Probability (8th Edition)

By Sheldon M. Ross

A First direction in chance, 8th Edition, positive aspects transparent and intuitive reasons of the maths of likelihood conception, impressive challenge units, and a number of various examples and functions. This publication is perfect for an upper-level undergraduate or graduate point creation to chance for math, technology, engineering and company scholars. It assumes a history in simple calculus.

Show description

Read more

Infinite Dimensional Optimization and Control Theory (Encyclopedia of Mathematics and its Applications)

This booklet issues lifestyles and worthy stipulations, corresponding to Potryagin's greatest precept, for optimum keep watch over difficulties defined through usual and partial differential equations. the writer obtains those valuable stipulations from Kuhn-Tucker theorems for nonlinear programming difficulties in limitless dimensional areas. The optimum regulate difficulties comprise keep watch over constraints, nation constraints and aim stipulations. Fattorini reviews evolution partial differential equations utilizing semigroup thought, summary differential equations in linear areas, essential equations and interpolation thought. the writer establishes life of optimum controls for arbitrary regulate units through a common thought of cozy controls. purposes comprise nonlinear structures defined by way of partial differential equations of hyperbolic and parabolic style and effects on convergence of suboptimal controls.

Show description

Read more

Introduction to Graph Theory (Dover Books on Mathematics)

By Richard J. Trudeau

A stimulating day trip into natural arithmetic aimed toward "the mathematically traumatized," yet nice enjoyable for mathematical hobbyists and severe mathematicians in addition. Requiring simply highschool algebra as mathematical historical past, the publication leads the reader from basic graphs via planar graphs, Euler's formulation, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, and a dialogue of The Seven Bridges of Konigsberg. workouts are integrated on the finish of every bankruptcy. "The subject matters are so good inspired, the exposition so lucid and pleasant, that the book's attraction may be almost common . . . each library must have a number of copies" — Choice. 1976 edition.

Show description

Read more

Approximation Algorithms, Corrected Second Printing 2003

By Vijay V. Vazirani

Uploader's Note: Ripped from SpringerLink.

Covering the fundamental concepts utilized in the newest learn paintings, the writer consolidates growth made thus far, together with a few very fresh and promising effects, and conveys the wonder and pleasure of labor within the box. He supplies transparent, lucid factors of key effects and ideas, with intuitive proofs, and offers serious examples and diverse illustrations to assist elucidate the algorithms. a few of the effects offered were simplified and new insights supplied. Of curiosity to theoretical desktop scientists, operations researchers, and discrete mathematicians.

Show description

Read more

MATLAB Matrix Algebra (Matlab Solutions)

By Cesar Perez Lopez

MATLAB is a high-level language and atmosphere for numerical computation, visualization, and programming. utilizing MATLAB, you could learn facts, improve algorithms, and create versions and purposes. The language, instruments, and integrated math services aid you discover a number of ways and achieve an answer swifter than with spreadsheets or conventional programming languages, corresponding to C/C++ or Java.

MATLAB Matrix Algebra introduces you to the MATLAB language with functional hands-on directions and effects, permitting you to speedy in attaining your pursuits. beginning with a glance at symbolic and numeric variables, with an emphasis on vector and matrix variables, you are going to move directly to research services and operations that help vectors and matrices as arguments, together with these in line with analytic father or mother services. Computational equipment for locating eigenvalues and eigenvectors of matrices are special, resulting in a variety of matrix decompositions. purposes corresponding to switch of bases, the class of quadratic types and the way to unravel platforms of linear equations are defined, with quite a few examples. a piece is devoted to sparse matrices and different sorts of unique matrices. as well as its remedy of matrices, additionally, you will find out how MATLAB can be utilized to paintings with arrays, lists, tables, sequences and sets.

What you’ll learn

• the way to use MATLAB to paintings with numeric and symbolic variables, together with vector and matrix variables.

• How MATLAB helps capabilities with vectors and matrices as arguments.

• functions akin to swap of bases, category of quadratic varieties and options of platforms of linear equations.

• how to define a variety of matrix decompositions utilizing MATLAB.

• tips on how to paintings with sparse matrices and different distinct matrices.

• how one can manage arrays, lists, tables, sequences and sets.

• tips on how to use MATLAB to paintings with matrix algebra over the complicated field.

Who this booklet is for

This ebook is for somebody who desires to paintings on matrix algebra difficulties in a realistic, hands-on demeanour utilizing MATLAB. you are going to have already got a middle realizing of undergraduate point linear algebra, and feature entry to an put in model of MATLAB, yet no past event of MATLAB is thought.

Show description

Read more