Amy Campbell Library > Mathematics


By Danny Calegari

This ebook is a entire creation to the idea of sturdy commutator size, a big subfield of quantitative topology, with vast connections to 2-manifolds, dynamics, geometric staff thought, bounded cohomology, symplectic topology, and plenty of different matters. We use positive equipment at any time when attainable, and concentrate on primary and particular examples. We supply a self-contained presentation of a number of foundational ends up in the idea, together with Bavard's Duality Theorem, the Spectral hole Theorem, the Rationality Theorem, and the crucial restrict Theorem. The contents will be obtainable to any mathematician attracted to those matters, and are awarded with a minimum variety of necessities, yet with a purpose to purposes in lots of parts of arithmetic.

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The Complete Book of Fun Maths: 250 Confidence-boosting Tricks, Tests and Puzzles

The belief of this ebook is to aid construct self assurance with maths through a chain of checks and puzzles.  After a steady 'warm-up' part, the puzzles and exams get an increasing number of demanding over the process the book.  there's a tricks part for readers who get caught, in addition to a whole set of solutions for each try behind the e-book.

After the 'warm-up' part, there are puzzles and exams on 'lateral thinking', 'fun with numbers',  'logic puzzles', 'geometrical puzzles' and 'difficult puzzles'. Readers will quickly get to grips and happy with various methods and assessments, from magic quantity squares to Fibonacci numbers.

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Geometries (Student Mathematical Library, Volume 64)

By A. B. Sossinsky

The publication is an cutting edge sleek exposition of geometry, or particularly, of geometries; it's the first textbook within which Felix Klein's Erlangen application (the motion of transformation teams) is systematically used because the foundation for outlining quite a few geometries. The process examine awarded is devoted to the proposition that each one geometries are created equal--although a few, in fact, stay extra equivalent than others. the writer concentrates on numerous of the extra special and lovely ones, which come with what he phrases "toy geometries", the geometries of Platonic our bodies, discrete geometries, and classical non-stop geometries. The textual content is predicated on first-year semester direction lectures introduced on the self sufficient college of Moscow in 2003 and 2006. it's in no way a proper algebraic or analytic remedy of geometric subject matters, yet fairly, a hugely visible exposition containing upwards of 2 hundred illustrations. The reader is anticipated to own a familiarity with straightforward Euclidean geometry, albeit these missing this data may possibly discuss with a compendium in bankruptcy zero. according to the author's predilection, the ebook includes little or no concerning the axiomatic method of geometry (save for a unmarried bankruptcy at the background of non-Euclidean geometry), yet Appendices offer an in depth remedy of Euclid's and Hilbert's axiomatics. probably an important element of this direction is the issues, which look on the finish of every bankruptcy and are supplemented with solutions on the end of the textual content. by way of reading and fixing those difficulties, the reader becomes in a position to considering and dealing geometrically, even more so than by means of easily studying the speculation. eventually, the writer makes the excellence among concrete mathematical items referred to as "geometries" and the singular "geometry", which he is familiar with as a fashion of pondering arithmetic. even if the ebook doesn't tackle branches of arithmetic and mathematical physics corresponding to Riemannian and Kähler manifolds or, say, differentiable manifolds and conformal box theories, the ideology of type language and transformation teams on which the booklet relies prepares the reader for the examine of, and finally, learn in those very important and speedily constructing components of latest arithmetic.

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Ramsey Theory: Yesterday, Today, and Tomorrow (Progress in Mathematics, Vol. 285)

By Alexander Soifer

This booklet explores the theory’s historical past, fresh advancements, and a few promising destiny instructions via invited surveys written by means of popular researchers within the box. the 1st 3 surveys offer historic history at the topic; the final 3 handle Euclidean Ramsey thought and comparable coloring difficulties. furthermore, open difficulties posed in the course of the quantity and within the concluding open challenge bankruptcy will entice graduate scholars and mathematicians alike.

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General Topology: Chapters 1-4

This is often the softcover reprint of the English translation of 1971 (available from Springer in view that 1989) of the 1st four chapters of Bourbaki's Topologie générale. It offers all of the fundamentals of the topic, ranging from definitions. very important sessions of topological areas are studied, uniform constructions are brought and utilized to topological teams. genuine numbers are developed and their homes demonstrated. half II, comprising the later chapters, Ch. 5-10, is additionally to be had in English in softcover.

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A New Look at Geometry (Dover Books on Mathematics)

By Irving Adler

This richly designated review surveys the evolution of geometrical principles and the advance of the options of contemporary geometry from precedent days to the current. issues comprise projective, Euclidean, and non-Euclidean geometry in addition to the function of geometry in Newtonian physics, calculus, and relativity. Over a hundred workouts with solutions. 1966 edition.

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An Invitation to Abstract Mathematics (Undergraduate Texts in Mathematics)

This undergraduate textbook is meant basically for a transition path into greater arithmetic, even though it is written with a broader viewers in mind.  the guts and soul of this ebook is challenge fixing, the place every one challenge is punctiliously selected to elucidate an idea, exhibit a strategy, or to enthuse.  The routines require fairly huge arguments, artistic ways, or either, hence supplying motivation for the reader.  With a unified method of a various number of subject matters, this article issues out connections, similarities, and changes between matters every time possible.  This publication indicates scholars that arithmetic is a colourful and dynamic human firm by means of together with ancient views and notes at the giants of arithmetic, via declaring present task within the mathematical neighborhood, and by way of discussing many well-known and no more recognized questions that stay open for destiny mathematicians.

Ideally, this article might be used for a semester direction, the place the 1st direction has no necessities and the second one is a more difficult direction for math majors; but, the versatile constitution of the ebook permits it for use in numerous settings, together with as a resource of assorted independent-study and learn projects.

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The Heart of Cohomology

By Goro Kato

When you have now not heard approximately cohomology, the guts of Cohomology could be fitted to you. The ebook offers basic notions in cohomology for examples, functors, representable functors, Yoneda embedding, derived functors, spectral sequences, derived different types are defined in simple model. purposes to sheaf cohomology. moreover, the publication examines cohomological points of D-modules and of the computation of zeta services of the Weierstrass kinfolk.

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PI in the Sky: Counting, Thinking, and Being

By John D. Barrow

John D. Barrow's Pi within the Sky is a profound -- and profoundly diverse -- exploration of the realm of arithmetic: the place it comes from, what it truly is, and the place it's going to take us if we persist with it to the restrict in our look for the last word which means of the universe. Barrow starts by means of investigating no matter if math is a in simple terms human invention encouraged via our functional wishes. Or is it anything inherent in nature ready to be discovered?

In answering those questions, Barrow offers a bridge among the customarily irreconcilable worlds of arithmetic and theology. alongside the best way, he treats us to a historical past of counting around the world, from Egyptian hieroglyphics to logical friction, from quantity mysticism to Marxist arithmetic. And he introduces us to a number of surprising people who have suggestion the various inner most and strangest innovations that human minds have ever proposal, from Lao-Tse to Robert Pirsig, Charles Darwin, and Umberto Eco. Barrow therefore presents the ancient framework and the highbrow instruments essential to an realizing of a few of today's weightiest mathematical thoughts.

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