-
Mathematical analysis 1.
Claudio Canuto, Anita Tabacco,The recent European Programme Specifications have forced a reassessment of the structure and syllabi of the entire system of Italian higher education, and an ensuing rethinking of the teaching material. Nowadays many lecture courses, especially rudimentary ones, demand that students master a large amount of theoretical and practical knowledge in a span of just few weeks, in order to gain a small number of credits. As a result, instructors face the dilemma of how to present the subject matter. They must make appropriate choices about lecture content, the comprehension level required from the recipients, and which kind of language to use. This textbook is meant to help students acquire the basics of Calculus in curricula where mathematical tools play a crucial part (so Engineering, Physics, Computer Science and the like). The fundamental concepts and methods of Differential and Integral Calculus for functions of one real variable are presented with the primary purpose of letting students assimilate their effective employment, but with critical awareness. The general philosophy inspiring our approach has been to simplify the system of notions available prior to the university reform; at the same time we wished to maintain the rigorous exposition and avoid the trap of compiling a mere formulary of ready-to-use prescriptions.
-
Mathematical Analysis II
Claudio Canuto Anita Tabacco,This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed.
-
ALGEBRA and NUMBER THEORY
MARTYN R. DIXON,Algebra and number theory are two powerful, established branches of modem mathematics at the forefront of current mathematical research which are playing an increasingly significant role in different branches of mathematics (for instance, in geometry, topology, differential equations, mathematical physics, and others) and in many relatively new applications of mathematics such as computing, communications, and cryptography. Algebra also plays a role in many applications of mathematics in diverse areas such as modem physics, crystallography, quantum mechanics, space sciences, and economic sciences.