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All the mathematics projects included in the book are classroom tested which focus on concept development through creativity.\nThe sete-by-step easy projects explained in this book help to remove the mathematics phobia commonly present in students and boost their self-confidence.\n\nSalient Features:\nSimple and lucid language\n Attractive illustrations\/diagrams\n Creative skill-building ideas\n Concept-building ad decision-making projects\n Easy availability of project materials\nIndividual and partner projects promoting cooperative learning and systematic reasoning\nProjects based on the latest CCE curriculum of the CBSE and other State Boards’ standards\nReinforcement of previous knowledge\nThe book is a ‘must read’ for all, particularly the school children in the age group of 10 to 14 years.\n #v\u0026amp;spublishers","brand":"V\u0026S Publishers","offers":[{"title":"Default Title","offer_id":51597318062359,"sku":"9789350573990","price":295.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/1000395.jpg?v=1763189493"},{"product_id":"theory-of-nilpotent-groups-9783319662138","title":"Theory of Nilpotent Groups","description":"\u003cp\u003eThis monograph presents both classical and recent results in the theory of nilpotent groups and provides a self-contained, comprehensive reference on the topic.  While the theorems and proofs included can be found throughout the existing literature, this is the first book to collect them in a single volume.  Details omitted from the original sources, along with additional computations and explanations, have been added to foster a stronger understanding of the theory of nilpotent groups and the techniques commonly used to study them.  Topics discussed include collection processes, normal forms and embeddings, isolators, extraction of roots, P-localization, dimension subgroups and Lie algebras, decision problems, and nilpotent groups of automorphisms.  Requiring only a strong undergraduate or beginning graduate background in algebra, graduate students and researchers in mathematics will find The Theory of Nilpotent Groups to be a valuable resource.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52911987949847,"sku":null,"price":14846.17,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783319662138.jpg?v=1781503069"},{"product_id":"homological-and-combinatorial-methods-in-algebra-9783319741956","title":"Homological and Combinatorial Methods in Algebra","description":"\u003cp\u003eBased on the 4th Seminar on Algebra and its Applications organized by the University of Mohaghegh Ardabili, this volume highlights recent developments and trends in algebra and its applications. Selected and peer reviewed, the contributions in this volume cover areas that have flourished in the last few decades, including homological algebra, combinatorial algebra, module theory and linear algebra over rings, multiplicative ideal theory, and integer-valued polynomials. Held biennially since 2010, SAA introduces Iranian faculty and graduate students to important ideas in the mainstream of algebra and opens channels of communication between Iranian mathematicians and algebraists from around the globe to facilitate collaborative research. Ideal for graduate students and researchers in the field, these proceedings present the best of the seminar’s research achievements and new contributions to the field.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52912080060695,"sku":null,"price":12080.49,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783319741956.jpg?v=1781504087"},{"product_id":"advances-in-geometry-and-lie-algebras-from-supergravity-9783319744919","title":"Advances in Geometry and Lie Algebras from Supergravity","description":"\u003cp\u003eThis book aims to provide an overview of several topics in advanced differential geometry and Lie group theory, all of them stemming from mathematical problems in supersymmetric physical theories. It presents a mathematical illustration of the main development in geometry and symmetry theory that occurred under the fertilizing influence of supersymmetry\/supergravity. The contents are mainly of mathematical nature, but each topic is introduced by historical information and enriched with motivations from high energy physics, which help the reader in getting a deeper comprehension of the subject.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52912082583831,"sku":null,"price":21528.92,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783319744919.jpg?v=1781504588"},{"product_id":"mathematics-and-statistics-9783030528119","title":"Mathematics and Statistics","description":"\u003cp\u003eThis textbook emphasizes the interplay between algebra and geometry to motivate the study of linear algebra. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. By focusing on this interface, the author offers a conceptual appreciation of the mathematics that is at the heart of further theory and applications. Those continuing to a second course in linear algebra will appreciate the companion volume Advanced Linear and Matrix Algebra. Starting with an introduction to vectors, matrices, and linear transformations, the book focuses on building a geometric intuition of what these tools represent. Linear systems offer a powerful application of the ideas seen so far, and lead onto the introduction of subspaces, linear independence, bases, and rank. Investigation then focuses on the algebraic properties of matrices that illuminate the geometry of the linear transformations that they represent. Determinants, eigenvalues, and eigenvectors all benefit from this geometric viewpoint. Throughout, Extra Topic sections augment the core content with a wide range of ideas and applications, from linear programming, to power iteration and linear recurrence relations. Exercises of all levels accompany each section, including many designed to be tackled using computer software.Introduction to Linear and Matrix Algebra is ideal for an introductory proof-based linear algebra course. The engaging color presentation and frequent marginal notes showcase the author s visual approach. Students are assumed to have completed one or two university-level mathematics courses, though calculus is not an explicit requirement. Instructors will appreciate the ample opportunities to choose topics that align with the needs of each classroom, and the online homework sets that are available through WeBWorK.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52912094707991,"sku":null,"price":7422.41,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783030528119.jpg?v=1781504762"},{"product_id":"springer-texts-in-statistics-9783319648675","title":"Springer Texts in Statistics","description":"\u003cp\u003eThis textbook for graduate and advanced undergraduate students presents the theory of matrix algebra for statistical applications, explores various types of matrices encountered in statistics, and covers numerical linear algebra. Matrix algebra is one of the most important areas of mathematics in data science and in statistical theory, and the second edition of this very popular textbook provides essential updates and comprehensive coverage on critical topics in mathematics in data science and in statistical theory. Part I offers a self-contained description of relevant aspects of the theory of matrix algebra for applications in statistics. It begins with fundamental concepts of vectors and vector spaces; covers basic algebraic properties of matrices and analytic properties of vectors and matrices in multivariate calculus; and concludes with a discussion on operations on matrices in solutions of linear systems and in eigenanalysis. Part II considers various types of matricesencountered in statistics, such as projection matrices and positive definite matrices, and describes special properties of those matrices; and describes various applications of matrix theory in statistics, including linear models, multivariate analysis, and stochastic processes. Part III covers numerical linear algebra-one of the most important subjects in the field of statistical computing. It begins with a discussion of the basics of numerical computations and goes on to describe accurate and efficient algorithms for factoring matrices, how to solve linear systems of equations, and the extraction of eigenvalues and eigenvectors.Although the book is not tied to any particular software system, it describes and gives examples of the use of modern computer software for numerical linear algebra. This part is essentially self-contained, although it assumes some ability to program in Fortran or C and\/or the ability to use R or Matlab.The first two parts of the text are ideal for a course in matrix algebra for statistics students or as a supplementary text for various courses in linear models or multivariate statistics. The third part is ideal for use as a text for a course in statistical computing or as a supplementary text for various courses that emphasize computations. New to this edition * 100 pages of additional material* 30 more exercises-186 exercises overall* Added discussion of vectors and matrices with complex elements* Additional material on statistical applications* Extensive and reader-friendly cross references and index\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52912100999447,"sku":null,"price":14780.04,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783319648675.jpg?v=1781504927"},{"product_id":"hadamard-states-from-light-like-hypersurfaces-9783319643434","title":"Hadamard States from Light-like Hypersurfaces","description":"\u003cp\u003eThis book provides a rather self-contained survey of the construction of Hadamard states for scalar field theories in a large class of notable spacetimes, possessing a (conformal) light-like boundary. The first two sections focus on explaining a few introductory aspects of this topic and on providing the relevant geometric background material. The notions of asymptotically flat spacetimes and of expanding universes with a cosmological horizon are analysed in detail, devoting special attention to the characterization of asymptotic symmetries. In the central part of the book,  the quantization of a real scalar field theory on such class of backgrounds is discussed within the framework of algebraic quantum field theory.  Subsequently it is explained how it is possible to encode the information of the observables of the theory in a second, ancillary counterpart, which is built directly on the conformal (null) boundary.  This procedure, dubbed bulk-to-boundary correspondence, has the net advantage of allowing the identification of a distinguished state for the theory on the boundary, which admits a counterpart in the bulk spacetime which is automatically of Hadamard form. In the last part of the book, some applications of these states are discussed, in particular the construction of the algebra of Wick polynomials. This book is aimed mainly, but not exclusively, at a readership with interest in the mathematical formulation of quantum field theory on curved backgrounds.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52912101327127,"sku":null,"price":6072.63,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783319643434.jpg?v=1781504937"},{"product_id":"alfonsos-rectifying-the-curved-9783319773032","title":"Alfonso's Rectifying the Curved","description":"\u003cp\u003eThis volume offers a new English translation, introduction, and detailed commentary on Sefer Meyasher ''Aqov, (The Rectifying of the Curved), a 14th-century Hebrew treatise on the foundation of geometry. The book is a mixture of two genres: philosophical discussion and formal, Euclidean-type geometrical writing. A central issue is the use of motion and superposition in geometry, which is analyzed in depth through dialog with earlier Arab mathematicians. The author, Alfonso, was identified by Gita Gluskina (the editor of the 1983 Russian edition) as Alfonso of Valladolid, the converted Jew Abner of Burgos. Alfonso lived in Castile, rather far from the leading cultural centers of his time, but nonetheless at the crossroad of three cultures. He was raised in the Jewish tradition and like many Sephardic Jewish intellectuals was versed in Greek-Arabic philosophy and science. He also had connections with some Christian nobles and towards the end of his life converted to Christianity. Driven by his ambition to solve the problem of the quadrature of the circle, as well as other open geometrical problems, Alfonso acquired surprisingly wide knowledge and became familiar with several episodes in Greek and Arabic geometry that historians usually consider not to have been known in the West in the fourteenth century. 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First coined by C.J. Mulvey in 1986, quantales have since developed into a significant topic at the crossroads of algebra and logic, of notable interest to theoretical computer science. This book recasts the subject within the powerful framework of categorical algebra, showcasing its versatility through applications to C*- and MV-algebras, fuzzy sets and automata. With exercises and historical remarks at the end of each chapter, this self-contained book provides readers with a valuable source of references and hints for future research. This book will appeal to researchers across mathematics and computer science with an interest in category theory, lattice theory, and many-valued logic.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52912120103191,"sku":null,"price":14846.17,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783319789484.jpg?v=1781506010"},{"product_id":"multiscale-forecasting-models-9783319949925","title":"Multiscale Forecasting Models","description":"\u003cp\u003eThis book presents two new decomposition methods to decompose a time series in intrinsic components of low and high frequencies. The methods are based on Singular Value Decomposition (SVD) of a Hankel matrix (HSVD). The proposed decomposition is used to improve the accuracy of linear and nonlinear auto-regressive models. Linear Auto-regressive models (AR, ARMA and ARIMA) and Auto-regressive Neural Networks (ANNs) have been found insufficient because of the highly complicated nature of some time series. Hybrid models are a recent solution to deal with non-stationary processes which combine pre-processing techniques with conventional forecasters, some pre-processing techniques broadly implemented are Singular Spectrum Analysis (SSA) and Stationary Wavelet Transform (SWT). Although the flexibility of SSA and SWT allows their usage in a wide range of forecast problems, there is a lack of standard methods to select their parameters. The proposed decomposition HSVD and Multilevel SVD are described in detail through time series coming from the transport and fishery sectors. 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Aimed toward advanced undergraduate students and graduate students who have taken a basic course in abstract algebra that includes polynomial rings and ideals, this book serves as a core text for a course in combinatorial commutative algebra or as preparation for more advanced courses in the area.  The text contains over 600 exercises to provide readers with a hands-on experience working with the material; the exercises include computations of specific examples and proofs of general results. Readers will receive a firsthand introduction to the computer algebra system Macaulay2 with tutorials and exercises for most sections of the text, preparing them for significant computational work in the area. Connections to non-monomial areas of abstract algebra, electrical engineering, combinatorics and other areas of mathematics are provided which give the reader a sense of how these ideas reach into other areas.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52914804556055,"sku":null,"price":5397.75,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783319968766.jpg?v=1781507242"},{"product_id":"geometry-algebra-number-theory-and-their-information-technology-applications-9783319973791","title":"Geometry, Algebra, Number Theory, and Their Information Technology Applications","description":"\u003cp\u003eThis volume contains proceedings of two conferences held in Toronto (Canada) and Kozhikode (India) in 2016 in honor of the 60th birthday of Professor Kumar Murty. The meetings were focused on several aspects of number theory: The theory of automorphic forms and their associated L-functions Arithmetic geometry, with special emphasis on algebraic cycles, Shimura varieties, and explicit methods in the theory of abelian varieties The emerging applications of number theory in information technology Kumar Murty has been a substantial influence in these topics, and the two conferences were aimed at honoring his many contributions to number theory, arithmetic geometry, and information technology.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52914806751511,"sku":null,"price":17479.59,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783319973791.jpg?v=1781507308"},{"product_id":"information-geometry-and-its-applications-9783319977980","title":"Information Geometry and Its Applications","description":"\u003cp\u003eThe book gathers contributions from the fourth conference on Information Geometry and its Applications, which was held on June 12–17, 2016, at Liblice Castle, Czech Republic on the occasion of Shun-ichi Amari’s 80th birthday and was organized by the Czech Academy of Sciences’ Institute of Information Theory and Automation.  The conference received valuable financial support from the Max Planck Institute for Mathematics in the Sciences (Information Theory of Cognitive Systems Group), Czech Academy of Sciences’ Institute of Information Theory and Automation, and Università degli Studi di Roma Tor Vergata.  The aim of the conference was to highlight recent advances in the field of information geometry and to identify new research directions. To this end, the event brought together leading experts in the field who, in invited talks and poster sessions, discussed both theoretical work and achievements in the many fields of application in which information geometry plays an essential role.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52914807767319,"sku":null,"price":17479.59,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783319977980.jpg?v=1781507335"},{"product_id":"journey-through-representation-theory-9783319982717","title":"Journey Through Representation Theory","description":"\u003cp\u003eThis text covers a variety of topics in representation theory and is intended for graduate students and more advanced researchers who are interested in the field.  The book begins with classical representation theory of finite groups over complex numbers and ends with results on representation theory of quivers. The text includes in particular infinite-dimensional unitary representations for abelian groups, Heisenberg groups and SL(2), and representation theory of finite-dimensional algebras.  The last chapter is devoted to some applications of quivers, including  Harish-Chandra modules for SL(2). Ample examples are provided and some are revisited with a different approach when new methods are introduced, leading to deeper results. Exercises are spread throughout each chapter. Prerequisites include an advanced course in linear algebra that covers Jordan normal forms and tensor products as well as basic results on groups and rings.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52914810618135,"sku":null,"price":6747.52,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783319982717.jpg?v=1781507426"},{"product_id":"lower-algebraic-k-theory-of-virtually-cyclic-subgroups-of-the-braid-groups-of-the-sphere-and-of-zb4s2-9783319994895","title":"Lower Algebraic K-Theory of Virtually Cyclic Subgroups of the Braid Groups of the Sphere and of ZB4(S2)","description":"\u003cp\u003eThis volume deals with the K-theoretical aspects of the group rings of braid groups of the 2-sphere. The lower algebraic K-theory of the finite subgroups of these groups up to eleven strings is computed using a wide variety of tools. Many of the techniques extend to the general case, and the results reveal new K-theoretical phenomena with respect to the previous study of other families of groups. The second part of the manuscript focusses on the case of the 4-string braid group of the 2-sphere, which is shown to be hyperbolic in the sense of Gromov. This permits the computation of the infinite maximal virtually cyclic subgroups of this group and their conjugacy classes, and applying the fact that this group satisfies the Fibred Isomorphism Conjecture of Farrell and Jones, leads to an explicit calculation of its lower K-theory. Researchers and graduate students working in K-theory and surface braid groups will constitute the primary audience of the manuscript, particularly those interested in the Fibred Isomorphism Conjecture, and the computation of Nil groups and the lower algebraic K-groups of group rings. The manuscript will also provide a useful resource to researchers who wish to learn the techniques needed to calculate lower algebraic K-groups, and the bibliography brings together a large number of references in this respect.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52914811470103,"sku":null,"price":6072.63,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783319994895.jpg?v=1781507451"},{"product_id":"abel-prize-2013-2017-9783319990286","title":"Abel Prize 2013-2017","description":"\u003cp\u003eThe book presents the winners of the Abel Prize in mathematics for the period 2013–17: Pierre Deligne (2013); Yakov G. Sinai (2014); John Nash Jr. and Louis Nirenberg (2015); Sir Andrew Wiles (2016); and Yves Meyer (2017). The profiles feature autobiographical information as well as a scholarly description of each mathematician’s work. In addition, each profile contains a Curriculum Vitae, a complete bibliography, and the full citation from the prize committee.   The book also includes photos for the period 2003–2017 showing many of the additional activities connected with the Abel Prize.As an added feature, video interviews with the Laureates as well as videos from the prize ceremony are provided at an accompanying website (http:\/\/extras.springer.com\/). This book follows on The Abel Prize: 2003-2007. The First Five Years (Springer, 2010) and The Abel Prize 2008-2012 (Springer 2014), which profile the work of the previous Abel Prize winners.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52914816844055,"sku":null,"price":18829.37,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783319990286.jpg?v=1781507544"},{"product_id":"real-spinorial-groups-9783030004040","title":"Real Spinorial Groups","description":"\u003cp\u003eThis book explores the Lipschitz spinorial groups (versor, pinor, spinor and rotor groups) of a real non-degenerate orthogonal geometry (or orthogonal geometry, for short) and how they relate to the group of isometries of that geometry. After a concise mathematical introduction, it offers an axiomatic presentation of the geometric algebra of an orthogonal geometry. Once it has established the language of geometric algebra (linear grading of the algebra; geometric, exterior and interior products; involutions), it defines the spinorial groups, demonstrates their relation to the isometry groups, and illustrates their suppleness (geometric covariance) with a variety of examples. Lastly, the book provides pointers to major applications, an extensive bibliography and an alphabetic index. 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A wealth of illustrative examples, together with corrections and remarks on the original work, make this translation a valuable resource for today’s students of and researchers in number theory.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52914837717271,"sku":null,"price":14780.04,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783030015121.jpg?v=1781507807"},{"product_id":"stochastic-processes-and-applications-9783030028251","title":"Stochastic Processes and Applications","description":"\u003cp\u003eThis book highlights the latest advances in stochastic processes, probability theory, mathematical statistics, engineering mathematics and algebraic structures, focusing on mathematical models, structures, concepts, problems and computational methods and algorithms important in modern technology, engineering and natural sciences applications. It comprises selected, high-quality, refereed contributions from various large research communities in modern stochastic processes, algebraic structures and their interplay and applications. The chapters cover both theory and applications, illustrated by numerous figures, schemes, algorithms, tables and research results to help readers understand the material and develop new mathematical methods, concepts and computing applications in the future.  Presenting new methods and results, reviews of cutting-edge research, and open problems and directions for future research, the book serves as a source of inspiration for a broadspectrum of researchers and research students in probability theory and mathematical statistics, applied algebraic structures, applied mathematics and other areas of mathematics and applications of mathematics. The book is based on selected contributions presented at the International Conference on “Stochastic Processes and Algebraic Structures – From Theory Towards Applications” (SPAS2017) to mark Professor Dmitrii Silvestrov’s 70th birthday and his 50 years of fruitful service to mathematics, education and international cooperation, which was held at Mälardalen University in Västerås and Stockholm University, Sweden, in October 2017.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52914842992919,"sku":null,"price":17479.59,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783030028251.jpg?v=1781508032"},{"product_id":"algebraic-techniques-and-their-use-in-describing-and-processing-uncertainty-9783030385651","title":"Algebraic Techniques and Their Use in Describing and Processing Uncertainty","description":"\u003cp\u003eThis book discusses heuristic methods – methods lacking a solid theoretical justification – which are ubiquitous in numerous application areas, and explains techniques that can make heuristic methods more reliable. 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By developing mathematical language to describe symmetry, this textbook equips readers to explore symmetries with precision, illuminating commonalities across art and science.Beginning with an exploration of intuitive notions of symmetry, the author introduces the algebraic structure of groups by examining rotations and reflections. Topics that follow include the classification of two-dimensional patterns, the Platonic solids, and a study of real and prime numbers. This second edition features numerous new examples and exercises, Elements of Mathematics sections that more closely examine mathematical tools, and optional content that offers opportunities for extension. Figures are woven into the presentation throughout, with many illustrations now offered in motion as integrated video content.Symmetry suits a wide audience, demanding no mathematical training past high school basics, yet stretching the imagination of math and non-math majors alike. 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Throughout, “Extra Topic” sections augment the core content with a wide range of ideas and applications, from the QR and Cholesky decompositions, to matrix-valued linear maps and semidefinite programming. Exercises of all levels accompany each section. Advanced Linear and Matrix Algebra offers students of mathematics, data analysis, and beyond the essential tools and concepts needed for further study. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. A first course in proof-based linear algebra is assumed. 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Most practical constructions of multiple operator integrals are included along with fundamental technical results and major applications to smoothness properties of operator functions (Lipschitz and Hölder continuity, differentiability), approximation of operator functions, spectral shift functions, spectral flow in the setting of noncommutative geometry, quantum differentiability, and differentiability of noncommutative L^p-norms. Main ideas are demonstrated in simpler cases, while more involved, technical proofs are outlined and supplemented with references. 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Replete with surprising connections, deep insights, and brilliantly curated invitations to try problems at just the right moment, this journey weaves a rich body of knowledge that is ideal for those going on to study or teach mathematics. A pool of 200 ‘Dialing In’ problems opens the book, providing fuel for active enquiry throughout a course. The following chapters develop theory to illuminate the observations and roadblocks encountered in the problems, situating them in the broader mathematical landscape. Topics cover polygons and modular arithmetic; the fundamental theorems of arithmetic and algebra; irrational, algebraic and transcendental numbers; and Fourier series and Gauss sums. A lively accompaniment of examples, exercises, historical anecdotes, and asides adds motivation and context to the theory. Return trips to the Dialing In problems are encouraged, offering opportunities to put theory into practice and make lasting connections along the way. 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The ability to combine the flexibility of the Bayesian probabilistic framework with efficient numerical methods has contributed to the popularity of Bayesian inversion, with the prior distribution being the counterpart of classical regularization.  However, the interplay between Bayesian inference and numerical analysis is much richer than providing an alternative way to regularize inverse problems, as demonstrated by the discussion of time dependent problems, iterative methods, and sparsity promoting priors in this book. 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