Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This is an introduction to recent developments in algebraic combinatorics and an illustration of how research in mathematics actually progresses. The author recounts the story of the search for and discovery of a proof of a formula conjectured in the late 1970s: the number of n x n alternating sign matrices, objects that generalize permutation matrices. While apparent that the conjecture must be true, the proof was elusive. Researchers became drawn to this problem, making connections to aspects of invariant theory, to symmetric functions, to hypergeometric and basic hypergeometric series, and, finally, to the six-vertex model of statistical mechanics. All these threads are brought together in Zeilberger's 1996 proof of the original conjecture. The book is accessible to anyone with a knowledge of linear algebra. Students will learn what mathematicians actually do in an interesting and new area of mathematics, and even researchers in combinatorics will find something new here.

Algebra --- Combinatorial analysis. --- Matrices. --- Statistical mechanics.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Factorization (Mathematics) --- Numbers, Prime --- Factorisation --- Nombres premiers --- 511.1 --- #TELE:d.d. Prof. R. Govaerts --- Prime numbers --- Numbers, Natural --- Mathematics --- Elementary arithmetic --- 511.1 Elementary arithmetic

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

In the second edition of the MAA classic, exploration continues to be an essential component. More than 60 new exercises have been added, and the chapters on Infinite Summations, Differentiability and Continuity, and Convergence of Infinite Series have been reorganized to make it easier to identify the key ideas. A Radical Approach to Real Analysis is an introduction to real analysis, rooted in and informed by the historical issues that shaped its development. It can be used as a textbook, as a resource for the instructor who prefers to teach a traditional course, or as a resource for the student who has been through a traditional course yet still does not understand what real analysis is about and why it was created. The book begins with Fourier's introduction of trigonometric series and the problems they created for the mathematicians of the early 19th century. It follows Cauchy's attempts to establish a firm foundation for calculus, and considers his failures as well as his successes. It culminates with Dirichlet's proof of the validity of the Fourier series expansion and explores some of the counterintuitive results Riemann and Weierstrass were led to as a result of Dirichlet's proof.

Mathematical analysis --- Functions of real variables --- Mathematical analysis. --- Analyse mathématique --- Fonctions d'une variable réelle --- 517.1 --- 517.1 Introduction to analysis --- Introduction to analysis --- Real variables --- 517.1 Mathematical analysis --- 517.1. --- Functions of complex variables --- Analyse mathématique. --- Fonctions d'une variable réelle.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

How our understanding of calculus has evolved over more than three centuries, how this has shaped the way it is taught in the classroom, and why calculus pedagogy needs to changeCalculus Reordered takes readers on a remarkable journey through hundreds of years to tell the story of how calculus evolved into the subject we know today. David Bressoud explains why calculus is credited to seventeenth-century figures Isaac Newton and Gottfried Leibniz, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus represents a sounder way for students to learn this fascinating area of mathematics.Delving into calculus's birth in the Hellenistic Eastern Mediterranean-particularly in Syracuse, Sicily and Alexandria, Egypt-as well as India and the Islamic Middle East, Bressoud considers how calculus developed in response to essential questions emerging from engineering and astronomy. He looks at how Newton and Leibniz built their work on a flurry of activity that occurred throughout Europe, and how Italian philosophers such as Galileo Galilei played a particularly important role. In describing calculus's evolution, Bressoud reveals problems with the standard ordering of its curriculum: limits, differentiation, integration, and series. He contends that the historical order-integration as accumulation, then differentiation as ratios of change, series as sequences of partial sums, and finally limits as they arise from the algebra of inequalities-makes more sense in the classroom environment.Exploring the motivations behind calculus's discovery, Calculus Reordered highlights how this essential tool of mathematics came to be.

Calculus. --- Mathematics --- MATHEMATICS / Calculus. --- Math --- Science --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Mathematical analysis --- Functions --- Geometry, Infinitesimal --- History.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Integraalvergelijkingen --- Theorie van Lebesgue --- Integrals, Generalized