Conjecture and Proof (Classroom Resource Materials)
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Author: Miklós Laczkovich

The Budapest semesters in mathematics were initiated with the aim of offering undergraduate courses that convey the tradition of Hungarian mathematics to Englishspeaking students. This book is an elaborate version of the course on 'Conjecture and Proof'. It gives miniature introductions to various areas of mathematics by presenting some interesting and important, but easily accessible results and methods. The text contains complete proofs of deep results such as the transcendence of e, the BanachTarski paradox and the existence of Borel sets of arbitrary (finite) class. One of the purposes is to demonstrate how far one can get from the first principles in just a couple of steps. Prerequisites are kept to a minimum, and any introductory calculus course provides the necessary background for understanding the book. Exercises are included for the benefit of students. However, this book should prove fascinating for any mathematically literate reader.
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Yet Another Introduction to Analysis
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Author: Victor Bryant
Brand: Brand: Cambridge University Press

Mathematics education in schools has seen a revolution in recent years. Students everywhere expect the subject to be wellmotivated, relevant and practical. When such students reach higher education, the traditional development of analysis, often divorced from the calculus they learned at school, seems highly inappropriate. Shouldn't every step in a first course in analysis arise naturally from the student's experience of functions and calculus in school? And shouldn't such a course take every opportunity to endorse and extend the student's basic knowledge of functions? In Yet Another Introduction to Analysis, the author steers a simple and wellmotivated path through the central ideas of real analysis. Each concept is introduced only after its need has become clear and after it has already been used informally. Wherever appropriate, new ideas are related to common topics in math curricula and are used to extend the reader's understanding of those topics. In this book the readers are led carefully through every step in such a way that they will soon be predicting the next step for themselves. In this way students will not only understand analysis, but also enjoy it.
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Topology via Logic (Cambridge Tracts in Theoretical Computer Science)
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Author: Steven Vickers
Brand: Brand: Cambridge University Press

This advanced textbook on topology has three unusual features. First, the introduction is from the locale viewpoint, motivated by the logic of finite observations: this provides a more direct approach than the traditional one based on abstracting properties of open sets in the real line. Second, the author freely exploits the methods of locale theory. Third, there is substantial discussion of some computer science applications. As computer scientists become more aware of the mathematical foundations of their discipline, it is appropriate that such topics are presented in a form of direct relevance and applicability. This book goes some way towards bridging the gap for computer scientists.
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Continuous Geometry
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Author: John von Neumann
Brand: Brand: Princeton University Press

In his work on rings of operators in Hilbert space, John von Neumann discovered a new mathematical structure that resembled the lattice system Ln. In characterizing its properties, von Neumann founded the field of continuous geometry. This book, based on von Neumann's lecture notes, begins with the development of the axioms of continuous geometry, dimension theory, andfor the irreducible casethe function D(a). The properties of regular rings are then discussed, and a variety of results are presented for lattices that are continuous geometries, for which irreducibility is not assumed. For students and researchers interested in ring theory or projective geometries, this book is required reading.
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Orbit and Constellation Design and Management (Space Technology Library, Vol. 13)  Renewed Edition
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Author: James R Wertz
Brand: Brand: Microcosm, Inc

Orbit and Constellation Design and Management (OCDM) provides greatly expanded detail on many topics first introduced in the 2 of the earlier Wertz works  Spacecraft Attitude Determination and Control (SADC) and Space Mission Analysis and Design (SMAD). If these two books got you started in mission engineering and you need more detail on the key area of Spacecraft Orbit and Attitude Systems (SOAS), then this book provides more detail in SOAS requirements definition, mission geometry, orbit and constellation design, relative motion of satellites, observation and measurement systems engineering, orbit control and management, and similar topics.
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Orderly Tangles: Cloverleafs, Gordian Knots and Regular Polylinks
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Author: Alan Holden

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More Mathematical Quilts: No Sewing Required!, Grades 612
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Author: Diana Venters
Brand: Brand: Key Curriculum Press

Designed to help students improve visualization skills and understanding of geometric relationships, and to help them succeed at geometrybased deductive reasoning
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Excursions in Calculus: An Interplay of the Continuous and the Discrete (Dolciani Mathematical Expositions)
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Author: Robert M. Young

The purpose of this book is to explore the rich and elegant interplay that exists between the two main currents of mathematics, the continuous and the discrete. Such fundamental notions in discrete mathematics as induction, recursion, combinatorics, number theory, discrete probability, and the algorithmic point of view as a unifying principle are continually explored as they interact with traditional calculus. The book is addressed primarily to welltrained calculus students and those who teach them, but it can also serve as a supplement in a traditional calculus course for anyone who wants to see more. The problems, taken for the most part from probability, analysis, and number theory, are an integral part of the text. There are over 400 problems presented in this book.
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The Classification of Knots and 3Dimensional Spaces (Oxford Science Publications)
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Author: Geoffrey Hemion

Knot theory has recently emerged as a productive field of study in both the physical and mathematical sciences. This book is concerned with the fundamental question of the classification of knots, and more generally the classification of arbitrary (compact) topological objects which can occur in the normal space of physical reality. The author explains his classification algorithmusing the method of normal surfacesin a simple and concise way. The reader is thus shown the relevance of such traditional mathematical objects as the Klein bottle or the hyperbolic plane to this basic classification theory. The Classification of Knots and 3Dimensional Spaces will be of interest to mathematicians, physicists, and other scientists who want to apply this algorithm to their research in knot theory.


Numbers and Functions: Steps to Analysis
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Author: R. P. Burn
Brand: Brand: Cambridge University Press

The transition from studying calculus in schools to studying mathematical analysis at university is notoriously difficult. In this book, Dr Burn follows a route that proved successful with A Pathway to Number Theory and Groups: A Path to Geometry. He invites the student reader to tackle each of the key concepts in turn, progressing from experience (using computers for graph drawing where appropriate) through a structured sequence of several hundred problems to concepts, definitions and proofs of classical real analysis. The sequence of problems, which all have solutions supplied, draws students into constructing definitions and theorems for themselves. This natural development is informed by historical insight and complemented by historical discussion. The sequence also takes into account recent research which has shown how intuitive ideas about numbers, limits, functions and infinity may be at odds with the standard definitions. The novel approach to rigorous analysis offered here is designed to enable students to grow in confidence and skill and thus overcome the traditional difficulties. Teachers in sixth forms will find that questions at the beginning of every chapter provide ways of preparing those at school for university mathematics. Lecturers in universities will be challenged to rethink their conventions about the best way to introduce the central ideas of analysis to undergraduates.
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