Grundlagen Der Analysis: With Complete German-English Vocabulary. Third Edition

Edmund Landau

Reference

Chelsea Pub. Co

This book is a gem. It fills the gap between the standard introductory material on PDEs that an undergraduate is likely to encounter after a good ODE course (separation of variables, the basics of the second-order equations from mathematical physics) and the advanced methods (such as Sobolev spaces and fixed point theorems) that one finds in modern books. Although this is not designed as a textbook for applied mathematics, the approach is strongly informed by applications. For instance, there are many existence and uniqueness results, but they are usually approached via very concrete techniques. 
The text contains the standard topics that one expects in an intermediate PDE course: the Dirichlet and Neumann problems, Cauchy's problem, characteristics, the fundamental solution, PDEs in the complex domain, plus a chapter on finite differences, on nonlinear fluid mechanics, and another on integral equations. It is an excellent text for advanced undergraduates or beginning graduate students in mathematics or neighboring fields, such as engineering and physics, where PDEs play a central role.

Partial Differential Equations

Science & Math

Garabedian, Paul R.

Mathematics

A clear, readable introductory treatment of Hilbert Space. The multiplicity theory of continuous spectra is treated, for the first time in English, in full generality.

Introduction to Hilbert Space: And the Theory of Spectral Multiplicity

Halmos, P.R.

Contains sections on Reductive groups, representations, Automorphic forms and representations.

Automorphic Forms, Representations, and L-Functions: Symposium in Pure Mathematics. Volume XXXIII Part 1

Borel, Armand

Casselman, W.

In addition to the standard topics, this volume contains many topics not often found in an algebra book, such as inequalities, and the elements of substitution theory. Especially extensive is Chrystal's treatment of the infinite series, infinite products, and (finite and infinite) continued fractions. The range of entries in the Subject Index is very wide. To mention a few out of many hundreds: Horner's method, multinomial theorem, mortality table, arithmetico-geometric series, Pellian equation, Bernoulli numbers, irrationality of e, Gudermanian, Euler numbers, continuant, Stirling's theorem, Riemann surface. This volume includes over 2,400 exercises with solutions.

Algebra: An Elementary Text-book for the Higher Classes of Secondary Schools and for Colleges

Chrystal, G.

From the Preface: "This textbook has evolved from a set of lecture notes ... In both the course and the book, I have in mind first- or second-year graduate students in Mathematics and related fields such as Physics ... It is necessary for the reader to have a foundation in advanced calculus which includes familiarity with: least upper bound (LUB) and greatest lower bound (GLB), the concept of function, $\epsilon$'s and their companion $\delta$'s, and basic properties of sequences of real and complex numbers (convergence, Cauchy's criterion, the Weierstrass-Bolzano theorem). It is not presupposed that the reader is acquainted with vector spaces ... , matrices ... , or determinants ... There are over four hundred exercises, most of them easy ... It is my hope that this book, aside from being an exposition of certain basic material on Hilbert space, may also serve as an introduction to other areas of functional analysis."

Introduction to Hilbert Space (2nd ed)

Sterling K. Berberian

In addition to the standard topics, this volume contains many topics not often found in an algebra book, such as inequalities, and the elements of substitution theory. Especially extensive is Chrystal's treatment of the infinite series, infinite products, and (finite and infinite) continued fractions. The range of entries in the Subject Index is very wide. To mention a few out of many hundreds: Horner's method, multinomial theorem, mortality table, arithmetico-geometric series, Pellian equation, Bernoulli numbers, irrationality of $e$, Gudermanian, Euler numbers, continuant, Stirling's theorem, Riemann surface. This volume includes over 2,400 exercises with solutions.

Algebra : An Elementary Text-Book (2 volume set)

Perhaps the first truly famous book devoted primarily to finite groups was Burnside's book. From the time of its second edition in 1911 until the appearance of Hall's book, there were few books of similar stature. Hall's book is still considered to be a classic source for fundamental results on the representation theory for finite groups, the Burnside problem, extensions and cohomology of groups, $p$-groups and much more. For the student who has already had an introduction to group theory, there is much treasure to be found in Hall's Theory of Groups. From the Preface to the Second Edition (1976): ``The present volume is intended to serve a dual purpose. The first ten chapters are meant to be the basis for a course in group theory, and exercises have been included at the end of each of these chapters. The last ten chapters are meant to be useful as optional material in a course or as reference material. When used as a text, the book is intended for students who have had an introductory course in modern algebra comparable to a course taught from Birkhoff and Mac Lane's A Survey of Modern Algebra. I have tried to make this book as self-contained as possible, but where background material is needed references have been given, chiefly to Birkhoff and Mac Lane.''

Theory of Groups

Hall, Marshall, Jr.

This is a translation of Landau's famous Elementare Zahlentheorie with added exercises by Paul T. Bateman and Eugene E. Kohlbecker. This three-volume classic work is reprinted here as a single volume

Elementary Number Theory

LANDAU, EDMUND

Ramanujan occupies a unique place in analytic number theory: his formulas, identities and calculations are still amazing mathematicians three-quarters of a century after his death. Many of his discoveries seem to have appeared as if from the ether. His mentor and primary collaborator was G.H. Hardy. Here, Hardy collects 12 of his own lectures on topics stemming from Ramanujan's life and work. The topics include: partitions, hypergeometric series, Ramanujan's tau-function and round numbers.

Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work

Hardy, G. H.

Biographies & Memoirs

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