S. Kumaresan

Environmental stress factors which influence fish immune (and likely many other physiological) functions can be divided into two broad, but not mutually exclusive, categories, namely those which occur naturally and those which are artificial. Natural environmental stress factors include season, temperature, salinity and photoperiod.

Based on the authors’ combined 35 years of experience in teaching, A Basic Course in Real Analysis introduces students to the aspects of real analysis in a friendly way. The authors offer insights into the way a typical mathematician works observing patterns, conducting experiments by means of looking at or creating examples, trying to understand the underlying principles, and coming up with guesses or conjectures and then proving them rigorously based on his or her explorations. With more than 100 pictures, the book creates interest in real analysis by encouraging students to think geometrically. Each difficult proof is prefaced by a strategy and explanation of how the strategy is translated into rigorous and precise proofs. The authors then explain the mystery and role of inequalities in analysis to train students to arrive at estimates that will be useful for proofs. They highlight the role of the least upper bound property of real numbers, which underlies all crucial results in real analysis. In addition, the book demonstrates analysis as a qualitative as well as quantitative study of functions, exposing students to arguments that fall under hard analysis.Although there are many books available on this subject, students often find it difficult to learn the essence of analysis on their own or after going through a course on real analysis. Written in a conversational tone, this book explains the hows and whys of real analysis and provides guidance that makes readers think at every stage.

This book, taking a holistic view of geometry, introduces the reader to axiomatic, algebraic, analytic and differential geometry. Starting with an informal introduction to non-Euclidean plane geometries, the book develops the theory to put them on a rigorous footing. It may be considered as an explication of the Kleinian view of geometry a la Erlangen Programme. The treatment in the book, however, goes beyond the Kleinian view of geometry.Some noteworthy topics presented include:various results about triangles (including results on areas of geodesic triangles) in Euclidean, hyperbolic, and spherical planesaffine and projective classification of conicstwopoint homogeneity of the three planes and the fact that the set of distance preserving maps (isometries) are essentially the same as the set of lengths preserving maps of these planes.Geometric intuition is emphasized throughout the book. Figures are included wherever needed. The book has several exercises varying from computational problems to investigative or explorative open questions.