The Series in Metallurgy and Materials Science was initiated during the Diamond Jubilee of the Indian Institute of Metals (IIM). In the last decade the progress in the study and development of metallurgy and materials science has been rapid and extensive, giving us a whole new array of materials, with a wide range of applications, and a variety of techniques for both processing and characterising them. This book is the first textbook in the series.

Since the 1920s modern powder metallurgy has been used to produce a wide range of structural Powder Metallurgy (PM) components, self-lubricating bearings and cutting tools. The conventional method involves the production of metal powders, and manufacture of useful objects from such powders by die compaction and sintering. Wrought products are also produced by this route. Powder injection moulding permits the production of stronger, more uniform and more complex PM parts. A detailed discussion of PM materials and products is given in the book.

UNIQUE FEATURES

• Sintering has been elaborated in two chapters—Sintering theory and Sintering technology.
  
• Testing and Quality Control of PM Materials and Products, is not found in many PM books.
  
• Techno-economics of PM processing are also described in detail.
  
• Powder metallurgical aspects of both metallic and ceramic systems are treated equally.
  
• Materials handling at various stages of processing
  
• Pressureless powder shaping
  
• Functionally graded materials
  
• Powder Metallurgy material code
  
• New approach
  - Pyrophoricity and toxicity in Chapter 3
  - Nanostructured materials and the electronic theory of sintering in chapter 7
  
• For powder metallurgical engineers
  - Various kinds of actual testing and quality control methods in Chapter 11
  - ceramics materials in Chapter 12
  - Wide range of practically applied parts in Chapter 13

The book is based on the experience of teaching undergraduate and postgraduate engineering students over several years. It serves as a textbook (both for undergraduate and postgraduate courses in engineering) and also as a handy reference book for engineers in the PM industry. In order to aid and broaden the problem-solving capability of students, worked examples are included in each chapter. In the end of chapter exercises, a variety of questions and problems are included.

104 Number Theory Problems is a valuable resource for advanced high school students, undergraduates, instructors, and mathematics coaches preparing to participate in mathematical contests and those contemplating future research in number theory and its related areas.

Special features:

• Contains problems developed for various mathematical contests, including the International Mathematical Olympiad (IMO)
• Builds a bridge between ordinary high school examples and exercises in number theory and more sophisticated, intricate and abstract concepts and problems
• Begins by familiarising students with typical examples that illustrate central themes, followed by numerous carefully selected problems and extensive discussions of their solutions
• Combines unconventional and essaytype examples, exercises and problems, many presented in an original fashion
• Engages students in creative thinking and stimulates them to express their comprehension and mastery of the material beyond the classroom

At the heart of the text is a semi-historical journey through the early decades of the subject as it emerged in the revolutionary work of Euler, Lagrange, Gauss, and Galois. Avoiding excessive abstraction whenever possible, the text focuses on the central problem of studying the solutions of polynomial equations. Highlights include a proof of the Fundamental Theorem of Algebra, essentially due to Euler, and a proof of the constructability of the regular 17-gon, in the manner of Gauss. Another novel feature is the introduction of groups through a meditation on the meaning of congruence in the work of Euclid. Everywhere in the text, the goal is to make clear the links connecting abstract algebra to Euclidean geometry, high school algebra, and trigonometry. Another goal is to encourage students, insofar as possible in a textbook format, to build the course for themselves, with exercises integrally embedded in the text of each chapter.

Actuarial science is an interdisciplinary science comprising four subjects—mathematics, statistics, economics and finance. Statistics plays a key role in laying the foundation of actuarial calculations in the presence of uncertainty in the mortality pattern of society and under varying economical conditions. Actuarial calculations mainly involve determination of premium rates and computation of reserves. This book discusses the application of various basic concepts and statistical techniques in the determination of premiums and reserves for a variety of standard insurance and annuity products, under a variety of conditions. Topics dealt with include application of utility theory to establish the feasibility of the insurance business, short-term risk models, distribution theory related to the future life time random variable, construction of aggregate and select life table, important concepts of financial mathematics, annuities certain, terms, endowment and whole life insurance products, monthly, quarterly, semi-annual and annual life annuities.

This book is self-contained and starts with the creation of basic tools using the completeness axiom. The continuity, differentiability, integrability, and power series representation properties of functions of a single variable are established. The next few chapters describe the topological and metric properties of Euclidean space. These are the basis of a rigorous treatment of differential calculus (including the Implicit Function Theorem and Lagrange Multipliers) for mappings between Euclidean spaces and integration for functions of several real variables. Special attention has been paid to the motivation for proofs. Selected topics, such as the Picard Existence Theorem for differential equations, have been included in such a way that selections may be made while preserving a fluid presentation of the essential material. Supplemented with numerous exercises, Advanced Calculus is a perfect book for undergraduate students of analysis.

Advances in Stainless Steels is the fourth book in the IIM–Universities Press book series on Metallurgy and Materials Science. The book focusses on various facets—processing, component design, properties, fabrication and applications—of the wonder alloy: stainless steel. Stainless steels are a class of versatile alloys, which can be tailored to exhibit a wide range of engineering properties by alloy design and controlled thermomechanical treatments to meet demanding service conditions. Stainless steel production in India is presently about 1.8 million tonnes and accounts for nearly 7% of global tonnage produced. This is likely to show an enormous increase in the near future.

This book covers a broad spectrum of topics spanning the entire life cycle of stainless steel—from alloy design and characterization to engineering design, fabrication, mechanical properties, corrosion, quality assurance of components, in-service performance assessment, life prediction and failure analysis of materials and components. The contents provide useful feedback for further developments aimed at effective utilization of this class of materials. The book comprises articles that bring out contemporary developments in stainless steels and is thematically classified into the following sections.

• Component design, modelling and structural integrity
• Manufacturing technology
• Property evaluation
• Alloy development and applications
• Non-destructive evaluation methods
• Corrosion and surface modification

The articles are of high relevance and interest to manufacturers, fabricators, researchers, designers, suppliers and end users of stainless steel, and serve as a valuable source for everyday reference and also as a guide for providing solutions for challenges connected with alloy design, material selection, melting, processing, fabrication, metallurgy and applications.