This book covers thirty years of the Leningrad Mathematical Olympiad, which was, ostensibly, the very first formally organized, open, official city-level mathematical contest in the world. Founded in 1934 by a group of dedicated Soviet mathematicians, it played an outstanding (and often underappreciated) role in creating the Leningrad (St. Petersburg) school of mathematics of the 20th century.The book begins with the extensive introduction containing two prefaces (one of them written specifically for this edition), a large historical survey of the Leningrad Mathematical Olympiad, a section describing the logistical side of the contest, and a small chapter dedicated to the very first Mathematical Olympiad held in 1934, whose problems were recently found in the Soviet-era library archives.The main text contains approximately 1,100 highly original questions for students of grades 5 through 10 (ages 11-12 through 17-18) offered at the two concluding rounds of the Leningrad City Mathematics Olympiads in the years of 1961-1991. Full solutions, hints and answers are provided for all questions with very rare exceptions.It also includes 120 additional questions, offered at the various mathematical contests held in Leningrad over the same thirty-year period — on average, their difficulty is somewhat higher than that of the regular Mathematical Olympiad problems.

Beginning with a review of formal languages and their syntax and semantics, Logic, Proof and Computation conducts a computer assisted course in formal reasoning and the relevance of logic to mathematical proof, information processing and philosophy. Topics covered include formal grammars, semantics of formal languages, sequent systems, truth-tables, propositional and first order logic, identity, proof heuristics, regimentation, set theory, databases, automated deduction, proof by induction, Turing machines, undecidability and a computer illustration of the reasoning underpinning Godel's incompleteness proof. LPC is designed as a multidisciplinary reader for students in computing, philosophy and mathematics.

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

The AMS Page a Day Calendar is a collection of 366 mathematical morsels. Each day features a fun math fact, a tidbit of math history, a piece of art made using mathematics, a mathematical puzzle or activity, or another mathematical delight. Topics range from the serious to the silly, from the abstract to the very real. The calendar features mathematics done by people from different races, genders, geographic locations, and time periods. Anyone interested in mathematics will learn something new and have their imagination sparked by something they find in the calendar. It will be a mathematical companion for your year.

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

Developed for the new International A Level specification, these new resources are specifically designed for international students, with a strong focus on progression, recognition and transferable skills, allowing learning in a local context to a global standard. Recognised by universities worldwide and fully comparable to UK reformed GCE A levels. Supports a modular approach, in line with the specification. Appropriate international content puts learning in a real-world context, to a global standard, making it engaging and relevant for all learners. Reviewed by a language specialist to ensure materials are written in a clear and accessible style. The embedded transferable skills, needed for progression to higher education and employment, are signposted so students understand what skills they are developing and therefore go on to use these skills more effectively in the future. Exam practice provides opportunities to assess understanding and progress, so students can make the best progress they can.

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

What link might connect two far worlds like quantum theory and music? There is something universal in the mathematical formalism of quantum theory that goes beyond the limits of its traditional physical applications. We are now beginning to understand how some mysterious quantum concepts, like superposition and entanglement, can be used as a semantic resource.

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

This book proves there are messages in the Beale Treasure Location Code and it gives the first genuine method for decoding them. See for yourself. It's obvious the keys to decode are embedded in the code numbers themselves. Just add the code number digits. The best bit is the letter from St Louis has been with us all the time. Turn the letters of St Louis into numbers, S=7 or 19. T=20 or 6. And so on.

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

This second book on Unity Root Matrix Theory extends its original three-dimensional formulation, as given in the first book, to an arbitrary number of higher dimensions. Unity Root Matrix Theory is formulated with strong adherence to concepts in mathematical physics and it is thought it may provide a discrete formulation of physical phenomena at the Planck level and upward. Consequently, it is essential that the theory incorporates the geometric dimensionality present in established physical theories. In particular, it must naturally embody the four-dimensional spacetime of Special Relativity, the five dimensions of Kaluza-Klein theory, and the eleven or more dimensions of Grand Unified Theories such as String Theory. Not only has an n-dimensional extension of Unity Root Matrix Theory successfully been achieved, whilst retaining all the three-dimensional mathematical and physical properties detailed in the first book, but a complete n-dimensional solution has been obtained which exhibits the geometric property of compactification, or dimensional reduction. This solution shows that dimensional shrinkage of higher dimensions may occur over long evolutionary timescales. The emergence of compactification and other physical phenomena gives further confidence that n-dimensional Unity Root Matrix Theory may, indeed, offer a discrete formulation of Physics starting at its most elemental level.

As the operations of the world become more and more dependent on highly interconnected, massively complex, networked systems of computational devices, the need to develop a mathematical understanding of their properties and behaviours is increasingly pressing. Our approach, described in this monograph, is to combine the compositionality of formal specification -- using techniques from algebra, computation theory, logic, and probability theory -- with the control of level of abstraction afforded by the classical mathematical modelling method.

Statistics and their analysis are key to making mathematical sense of the world around us. In this textbook the authors underscore the importance of statistical methods and calculation skills and explain clearly and simply the key concepts and principles of statistics, so that they are easy to understand. The main purpose of the book is to make students more confident about handling statistical data and enable them to understand the meaning of the results obtained.

Statistical methods cover the collection of data, descriptive methods and inferential methods of analysis. Calculation skills cover elementary calculations, percentages and ratios, equations, graphs and interest calculations. The elementary calculations include basic calculations, such as exponents, decimals, scientific notation, logarithms, rounding and VAT calculations. This book teaches students with no mathematics background how to do basic calculations before concentrating on the statistical applications. For some courses, calculations such as interest, future values of investments, graphs and ratios form part of the core module and are also covered in this book.