A conversational introduction to abstract algebra from a modern, rings-first perspective, including a treatment of modules.

This text on mathematical problem solving provides a comprehensive outline of "problemsolving-ology," concentrating on strategy and tactics. It discusses a number of standard mathematical subjects such as combinatorics and calculus from a problem solver's perspective.

This introduction to functional analysis is intended for advanced undergraduate students, typically final year, who have some background in real analysis. The author's aim is not to cover the standard material in a standard way, but to present results of applications in contemporary mathematics and to show the relevance of functional analysis to other areas. Unusual topics covered include geometry of finite-dimensional spaces, invariant subspace, fixed-point theorem, and the Bishop-Phelps theorem. An outstanding set of exercises run from the elementary to the challenging.

New Syllabus Mathematics is a series of four books. These books follow the Mathematics Syllabus for Secondary Schools, implemented from 2007 by the Ministry of Education, Singapore. The whole series covers the complete syllabus for the Singapore-Cambridge GCE �O� Level Mathematics. The sixth edition of New Syllabus Mathematics retains the goals and objectives of the previous edition, but has been revised to meet the needs of the current users, to keep materials up-to-date as well as to give students a better understanding of the contents. All topics are comprehensively dealt with to provide students with a firm grounding in the subject. Explanations of concepts and principles are precise and written clearly and concisely with supportive illustrations and examples. Examples and exercises have been carefully graded to aid students in progressing within and beyond each level. Those exercises marked with a require either more thinking or involve more calculations. Numerous revision exercises are provided at appropriate intervals to enable students to recapitulate what they have learnt. Some interesting features of this series include the following: � an interesting introduction at the beginning of each chapter complete with photographs or graphics � brief specific instructional objectives for each chapter � Just For Fun arouses the students� interests in studying mathematics � Thinking Time encourages students to think creatively and go deeper into the topics � Exploration provides opportunities for students to learn actively and independently � For Your Information provides extra information on mathematicians, mathematical history and events etc. � Problem Solving Tips provides suggestions to help students in their thinking processes. We also introduce problem solving heuristics and strategies systemically throughout the series. � Your Attention alerts students to misconceptions.

MATH 221 FIRST Semester CalculusBy Sigurd Angenent

This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader's attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics.