Three diverting puzzles involve the proof of a basic law governing the world of numbers known to be correct in all tested cases—the problem is to prove that the law is always correct. The challenges concern van der Waerden’s theorem on arithmetic progressions, the Landau-Schnirelmann hypothesis and Mann’s theorem, and a solution to Waring’s problem. Proofs and explanations of the answers included.

The book may serve as a text for an undergraduate course in complex variables designed for scientists and engineers or for mathematics majors interested in further pursuing the general theory of complex analysis. The only prerequistite is a basic knowledge of advanced calculus. The presentation is also ideally suited for self-study.

The classic text in advanced microeconomic theory, revised and expanded.
‘Advanced Microeconomic Theory’ remains a rigorous, up-to-date standard in microeconomics, giving all the core mathematics and modern theory the advanced student must master.
Long known for careful development of complex theory, together with clear, patient explanation, this student-friendly text, with its efficient theorem-proof organization, and many examples and exercises, is uniquely effective in advanced courses.

The classic text in advanced microeconomic theory, revised and expanded.
‘Advanced Microeconomic Theory’ remains a rigorous, up-to-date standard in microeconomics, giving all the core mathematics and modern theory the advanced student must master.

Primarily meant for graduate level students of Mathematics of different universities across India, the book provides the reader with the thorough understanding of the topics included in the UGC syllabus—Leibnitz’s Theorem, Maclaurian and Taylor Series Expansion, Rolle and Mean Value Theorem, Euler’s Theorem, Jacobians, Variables, Asymptotes, Curve Tracing to name a few. The explanation of the subject matter is systematic and all fundamental concepts of the included topics are explained with a micro-analysis. Sufficient number of well-graded solved examples have been given to let the students understand the various skills necessary to solve the problems.

This intuitive yet rigourous introduction derives the core results of digital communication from first principles. Theory, rather than industry standards, motivates the engineering approaches, and key results are stated with all the required assumptions. The book emphasizes the geometric view, opening with the inner product, the matched filter for its computation, Parseval's theorem, the sampling theorem as an orthonormal expansion, the isometry between passband signals and their baseband representation, and the spectral-efficiency optimality of quadrature amplitude modulation (QAM). Subsequent chapters address noise, hypothesis testing, Gaussian stochastic processes, and the sufficiency of the matched filter outputs. Uniquely, there is a treatment of white noise without generalized functions, and of the power spectral density without artificial random jitters and random phases in the analysis of QAM. This systematic and insightful book, with over 300 exercises, is ideal for graduate courses in digital communication, and for anyone asking 'why' and not just 'how'.

This self-contained textbook gives a thorough exposition of multivariable calculus. It can be viewed as a sequel to the one-variable calculus text, A Course in Calculus and Real Analysis, published in the same series. The emphasis is on correlating general concepts and results of multivariable calculus with their counterparts in one-variable calculus. For example, when the general definition of the volume of a solid is given using triple integrals, the authors explain why the shell and washer methods of one-variable calculus for computing the volume of a solid of revolution must give the same answer. Further, the book includes genuine analogues of basic results in one-variable calculus, such as the mean value theorem and the fundamental theorem of calculus.

The updated new edition of the classic and comprehensive guide to the history of mathematics
For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind’s relationship with numbers, shapes, and patterns. This revised edition features up-to-date coverage of topics such as Fermat’s Last Theorem and the Poincare Conjecture, in addition to recent advances in areas such as finite group theory and computer-aided proofs.

The implicit function theorem is one of the most important theorems in analysis and its many variants are basic tools in partial differential equations and numerical analysis. This book treats the implicit function paradigm in the classical framework and beyond, focusing largely on properties of solution mappings of variational problems.

Specification and Verification of Multi-agent Systems presents a coherent treatment of the area of formal specification and verification of agent-based systems with a special focus on verification of multi-agent programs. This edited volume includes contributions from international leading researchers in the area, addressing logical formalisms and techniques, such as model checking, theorem proving, and axiomatisations for (semi) automatic verification of agent-based systems.

This is the second edition of Shubin's classical book. It provides an introduction to the theory of pseudodifferential operators and Fourier integral operators from the very basics. The applications discussed include complex powers of elliptic operators, Hormander asymptotics of the spectral function and eigenvalues, and method of approximate spectral projection. Exercises and problems are included to help the reader master the essential techniques. This book is written for a wide audience of mathematicians, be they interested students or researchers.

Intends to bring out some of the most important concepts associates with the theoretical aspects. This book can help the student to learn the methods of Calculus and theoretical aspects.

The book treats Legendre symbols and quadratic reciprocity, the Bertrand Postulate, the Riemann ?-function, the Prime Number Theorem, arithmetic functions, diophantine equations, and more.

Table of contents
Dimensional Analysis.-Perturbation Methods.- Kinetics.-Diffusion.-Traffic Flow.-Continuum Mechanics: One Spatial Dimension.-Elastic and Viscoelastic Materials.- Continuum Mechanics: Three Spatial Dimensions.- Fluids.- Taylor's Theorem.- Fourier Analysis.- Stochastic Differential Equations.- Identities.- Equations for a Newtonian Fluid.- References.- Index.

All videos from the Khan Academy website (www.khanacademy.com) on Calculus.
Updated till Nov. 2011.

001 Introduction to Limits (HD)
002 Introduction to Limits
003 Limit Examples (part 1)
004 Limit Examples (part 2)
005 Limit Examples (part3)
006 Limit Examples w_ brain malfunction on first prob (part 4)

This second edition of Elements of Operator Theory is a concept-driven textbook that includes a significant expansion of the problems and solutions used to illustrate the principles of operator theory. Written in a user-friendly, motivating style intended to avoid the formula-computational approach, fundamental topics are presented in a systematic fashion, i.e., set theory, algebraic structures, topological structures, Banach spaces, and Hilbert spaces, culminating with the Spectral Theorem.

Numerous clearly stated, completely worked out examples together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to make students comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses.

Calculus 3 is considered by most to be a very difficult course to master in the realm of Calculus. This is because you will learn about many different topics, and each topic builds on the previous. If you dont understand something early on, the chances of catching up are drastically reduced as time goes on.

The Elliott Wave Analysis course is designed for intermediate to advanced traders with an interest in expanding the way they observe, identify, and trade market patterns. Through our end-to-end explanation of principle theorem and application of this paramount pattern of all chart patterns, the learner will emerge a confident trader in all market sectors.Once thought of as a theory burdened by complex mathematics, our step-by-step Elliott Wave Course was designed for all in mind so that a trader can understand the importance and practicality of Elliott Wave theory.

Chapter 1- Line and Angle Relations
1.1 Sets, Statements and Reasoning
1.2 Informal Geometry and Measurement
1.3 Early Definitions and Postulates
1.4 Angles and Their Relationships
1.5 Introduction to Geometric Proof
1.6 Relationships: Perpendicular Lines
1.7 The Formal Proof of a Theorem