Recommended resources for Mathematics and Statistics

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- Discrete-Time Dynamics of Structured Populations and Homogeneous Order-Preserving Operators by Horst R. ThiemeCall Number: QH352 .T44 2024ISBN: 9781470474652Publication Date: 2024-06-30Addresses the mathematical question of population extinction or persistence. It explores structured population dynamics using discrete-time dynamical systems, emphasizing spatial structure.
- Iwasawa Theory and Its Perspective Vol.1 by Tadashi OchiaiCall Number: QA247 .C32 2023ISBN: 9781470456726Publication Date: 2023-03-01Delves into Iwasawa theory, which originated in the late 1950s with Kenkichi Iwasawa’s work on ideal class groups in cyclotomic number fields. The theory was later extended to include elliptic curves and modular forms.
- Regression Inside Out by Eric W. Schoon; David M. Melamed; Ronald L. BreigerCall Number: QA278.2 .S35 2024ISBN: 9781108841108Publication Date: 2024-02-22Explores regression modeling, emphasizing cases (people, organizations, and nations) as the focal point. By re-analyzing influential research, the authors offer nuanced interpretations, emphasizing intuition and reproducible examples. Bridges the gap between quantitative and qualitative research.
- Type-3 Fuzzy Logic in Time Series Prediction by Oscar Castillo; Patricia MelinCall Number: QA280 .C37 2024ISBN: 9783031597138Publication Date: 2024-05-14Focuses on applying type-3 fuzzy logic to solve complex prediction problems. By employing higher-order fuzzy logic, neural networks, and fractal theory, the book enhances prediction results and explores hybrid intelligent methods and tests them on various prediction scenarios, including COVID-19 and stock market predictions.

- C∞- Algebraic Geometry with Corners by Kelli Francis-Staite and Dominic D. JoyceCall Number: QA564 .F73 2024ISBN: 9781009400169Publication Date: 2024-01-04Discover the fascinating world of ‘C∞-schemes with corners’—singular spaces in differential geometry equipped with well-defined notions of boundary and corners. This groundbreaking work lays the foundation for theories of derived manifolds and derived orbifolds with corners, with applications spanning symplectic geometry and moduli spaces of J-holomorphic curves.
- Applications of Group Theory in Cryptography by Delaram Kahrobaei; Ramón Flores; Marialaura Noce; Maggie E. Habeeb; Christopher BattarbeeCall Number: QA174.2 .K34 2024ISBN: 9781470474690Publication Date: 2024-05-31The authors explore group-based cryptography, bridging the gap between mathematicians and computer scientists. Focusing on recent developments, the book delves into families of groups—such as polycyclic groups and graph groups—highlighting their algorithmic properties and cryptographic applications.
- Automorphic Forms Beyond GL2 by Wee Teck Gan; Aaron Pollack; Zhiwei Yun; Ellen Elizabeth Eischen; Hang Xue (Editor)Call Number: QA353.A9 A94 2024ISBN: 9781470474928Publication Date: 2024-05-31Explore the fascinating world of automorphic forms beyond the GL₂ case in this insightful volume. Based on lecture notes from the twenty-fifth Arizona Winter School, the book covers topics such as rationality questions on unitary groups, theta lifts, quaternionic modular forms, and automorphic forms over function fields.

- Analysis of Monge-Ampère Equations by Nam Q. LeCall Number: QA377 .L3876 2024ISBN: 9781470474201Publication Date: 2024-04-17This book presents an extensive survey of fundamental results, essential techniques, and phenomena in the solvability, geometry, and regularity of Monge-Ampere equations. The modern treatment of boundary behaviors of solutions is thoroughly discussed.
- Polytopes and Graphs by Guillermo Pineda VillavicencioCall Number: QA640.3 .V55 2024ISBN: 9781009257817Publication Date: 2024-03-31The book includes results not previously found in other books, such as: edge connectivity; characterization of the cycle space; Minkowski decomposition; Lei Xue's recent lower bound theorem on the number of faces of polytopes with a small number of vertices; and Gil Kalai's rigidity proof of the lower bound theorem.
- Tensor-Based Dynamical Systems by Can ChenCall Number: QA200 .C44 2024ISBN: 9783031545047Publication Date: 2024-03-05This book provides a comprehensive review on tensor algebra, including products, unfolding, eigenvalues, and decompositions. The author provides an overview of existing literature on the topic.
- Krasner Hyperring Theory by Bijan Davvaz and Violeta Leoreanu-FoteaCall Number: QA174.2 .D3785 2024ISBN: 9811285403Publication Date: 2024-03-01Krasner hyperrings are a generalization of hyperfields, introduced by Marc Krasner (1912-1985) in order to study complete valued fields. This book presents an elaborate study on hyperstructures in algebra.
- Geometry of Linear Matrix Inequalities by Tim Netzer; Daniel PlaumannCall Number: eBookISBN: 9783031264542Publication Date: 2023-06-08This textbook provides a thorough introduction to spectrahedra, which are the solution sets to linear matrix inequalities, emerging in convex and polynomial optimization, analysis, combinatorics, and algebraic geometry.
- Prescribing Scalar Curvature in Conformal Geometry by Andrea MalchiodiCall Number: QA609 .M35 2023ISBN: 3985470529Publication Date: 2023Andrea Malchiodi tackles the classical problem posed by Kazdan and Warner: prescribing a given function on a closed manifold as the scalar curvature of a metric within a conformal class. With a focus on understanding the matter, the book combines variational techniques, Liouville-type theorems, blow-up analysis, elliptic regularity theory, and topological arguments to address both existence and compactness issues.
- Data Analysis: A Gentle Introduction for Future Data Scientists by Graham Upton; Dan BrawnCall Number: QA276 .U68 2023ISBN: 9780192885784Publication Date: 2023-11-28This book introduces the central concepts of modern data science. The book demands no particular software familiarity, since the methods presented can be implemented in Python, R (used by the authors), or any other statistical software. Introduces the different types of data, the distinction between sample and population, and methods for sampling populations. Introduces summary statistics concerning the location and variability of a set of data. Additionally introduces commonly used summary diagrams.

- Elements of Discrete Mathematics by Volker Diekert; Manfred Kufleitner; Gerhard Rosenberger; Ulrich HertrampfCall Number: QA297.4 .D54 2023ISBN: 9783111060699Publication Date: 2023-12-31This book treats the elements of discrete mathematics that have important applications in computer science, thus providing the necessary tools for the reader to come to a competent mathematical judgement of modern developments in the age of information.
- Imperfect Perception and Stochastic Choice in Experiments by Pablo Brañas-Garza; John Alan SmithCall Number: QA279 .B73 2023ISBN: 9781009454414Publication Date: 2024-02-01Explores psychophysics, a branch of psychology that examines how physical objects are perceived by individuals, and highlights how psychophysics insights are relevant in economics, particularly in understanding risk aversion and decision-making under uncertainty and techniques for uncovering hidden patterns within noisy data.
- Markov Decision Processes and Stochastic Positional Games by Dmitrii Lozovanu; Stefan Wolfgang PicklCall Number: QA274.7 .L69 2024ISBN: 9783031401794Publication Date: 2024-01-13Presents recent findings and results concerning the solutions of finite state-space Markov decision problems and determining Nash equilibria for related stochastic games with average and total expected discounted reward payoffs. Covers applications in areas such as ecology, economics, engineering, telecommunication, and biology.
- On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities by Guy Barles; Emmanuel ChasseigneCall Number: eBookISBN: 9783031493706Publication Date: 2023-12-30Presents a unified viewpoint on the study of Hamilton-Jacobi equations and control problems with discontinuities. Covers both codimension-1 discontinuities and the stratified case, emphasizing connections with deterministic control problems and providing numerous examples and applications.
- Probability: An Introduction Through Theory and Exercises by Paolo BaldiCall Number: eBookISBN: 9783031384912Publication Date: 2024-01-10Comprehensive one-semester course in probability with measure theory, covering essential topics such as probability measures, random variables, and their laws, along with applications to statistics. The book includes over 150 exercises with full solutions, making it suitable for guided self-study.
- Spin/Pin-Structures and Real Enumerative Geometry by Aleksey Zinger; Xujia ChenCall Number: QA612.63 .C44 2024ISBN: 9789811278532Publication Date: 2023-10-01Shows the role of spin- and pin-structures in orientability considerations in symplectic topology, and explores their applications in enumerative geometry. Establishes the equivalence of Spin- and Pin-structures from different perspectives, details constructions of orientations on determinants of real Cauchy-Riemann operators and applies these results to the enumerative geometry of real curves.
- The Theory of Zeta-Functions of Root Systems by Yasushi Komori; Kohji Matsumoto; Hirofumi TsumuraCall Number: eBookISBN: 9789819909094Publication Date: 2023-05-14Presents a unified framework that generalizes Witten zeta-functions, Mordell-Tornheim multiple zeta-functions, and Euler-Zagier multiple zeta-functions. Covers topics such as meromorphic continuation, recursive analytic structure, special values at integer points, and functional relations. Notably, the authors connect these zeta-functions to Witten’s volume formula and demonstrate their relevance to multiple zeta values (MZVs) and Zagier’s conjecture.
- Conformal Vector Fields, Ricci Solitons and Related Topics by Ramesh Sharma; Sharief DeshmukhCall Number: eBookISBN: 9789819992577Publication Date: 2024-01-20Introduces manifolds, submanifolds, semi-Riemannian geometry, and their applications in geometry and physics. It explores conformal vector fields, their properties, and their interplay with Ricci solitons.
- Exploring Mathematical Analysis, Approximation Theory, and Optimization by Nicholas J. Daras (Editor); Michael Th. Rassias (Editor); Nikolaos B. Zographopoulos (Editor)Call Number: eBookISBN: 9783031464867Publication Date: 2024-01-05Compilation of research and surveys focuses on mathematical analysis, approximation theory, and optimization. The contributions are dedicated to branches of mathematics influenced by A.-M. Legendre. Topics covered include inequalities, dynamic contact problems, polynomial methods, and more.
- Künneth Geometry: Symplectic Manifolds and their Lagrangian Foliations by M. J. D. Hamilton; D. KotschickCall Number: eBookISBN: 9781108902977Publication Date: 2023-12-07Covers geometry and topology of symplectic manifolds equipped with pairs of complementary Lagrangian foliations. Notably, it systematically develops the foundations of Lagrangian foliations, and explores Künneth geometry from a basic differential topology.perspective
- Derived Algebraic Geometry by Renaud GauthierCall Number: QA564 .G38 2024ISBN: 9783111333663Publication Date: 2024-01-29Presents schemes, simplicial sets, higher categories, model categories, derived algebraic geometry, and spectral algebraic geometry in a self-contained manner. It discusses Motives, Goodwillie Calculus, Higher Galois, Supersymmetry, and topics in physical mathematics.
- Linear Models and the Relevant Distributions and Matrix Algebra Volume 2 by David A. HarvilleCall Number: eBookISBN: 9781032471235Publication Date: 2023-10-23Comprehensive work that delves into the mathematical foundations of linear models. It covers topics such as matrix algebra, statistical distributions, and their relevance in the context of linear modeling.
- Spectra and Normal Forms by Luís Barreira; Claudia VallsCall Number: eBookISBN: 9783031518966Publication Date: 2024-02-09Exposition of the construction of normal forms and smooth conjugacies for perturbations of tempered exponential dichotomies. These dichotomies exhibit nonzero Lyapunov exponents, and the book covers both difference and differential equations.
- Advances in Number Theory and Applied Analysis by Pradip Debnath; H. M. Srivastava; Kalyan Chakraborty; Poom KumamCall Number: eBookISBN: 9789811272592Publication Date: 2023-05-01Explores the applications of various techniques in number theory and mathematical analysis across diverse fields, including engineering, mathematics, physics, biology, and statistics. Features contributions from renowned scientists and mathematicians worldwide, presenting recent developments and original research.
- Enumerative Combinatorics: Volume 2 by Richard StanleyCall Number: eBookISBN: 9781009262491Publication Date: 2023-08-17Comprehensive exploration of enumeration techniques, covering topics such as recursion, generating functions, sieve methods, and inversion formulas. The book delves into counting problems related to sets, multisets, permutations, partitions, graphs, and trees. It’s an essential resource for anyone interested in discrete mathematics
- A Royal Road to Topology by Szymon DoleckiCall Number: QA611 .D655 2024ISBN: 9789811232107Publication Date: 2022-08-01Early topics cover set-theoretic topology from a filter convergence viewpoint, while later sections reveal these concepts as consequences of advanced convergence theory. The approach’s strength lies in its closure under natural operations, unlike topologies. Convergence theory complements topology similarly to how complex numbers complete the real numbers.
- Bertrands Paradox and the Principle of Indifference by Nicholas ShackelCall Number: eBookISBN: 9781032597935Publication Date: 2023-12-01This book casts a new light on Bertrand's Paradox, giving original analyses of the paradox, its possible solutions, the source of the paradox, the philosophical errors we make in attempting to solve it and what the paradox proves for the philosophy of probability.

- Discrete, Finite and Lie Groups by Pietro Giuseppe FréCall Number: QA183 .F74 2023ISBN: 9783111200750Publication Date: 2023-08-07r. First discrete and finite group theory, that includes the entire chemical-physical field of crystallography is developed self consistently, followed by the structural theory of Lie Algebras with a complete exposition of the roots and Dynkin diagrams lore. A primary on Fibre-Bundles, Connections and Gauge fields, Riemannian Geometry and the theory of Homogeneous Spaces G/H is also included and systematically developed.
- Cox Rings by Ivan Arzhantsev; Ulrich Derenthal; Jürgen Hausen; Antonio LafaceCall Number: eBookISBN: 9781139175852Publication Date: 2014-10-05Introduction to Cox rings, emphasizing concrete aspects of the theory. Key topics covered include finitely generated Cox rings, their relation to toric geometry, various classes of varieties with group actions, and applications in arithmetic problems (such as Manin’s conjecture).
- Analytic Information Theory by Michael Drmota; Wojciech SzpankowskiCall Number: eBookISBN: 9781108474443Publication Date: 2023-09-30Explores problems of communication, compression, and learning, emphasizing efficient algorithms for extracting information in its most compact form. Through information theory, it models and analyzes communication and compression problems, viewing learning as compression with side information. Delves into topics such as universal codes, minimax redundancy, and Markov sources.
- Analytic Pattern Matching by Philippe Jacquet; Wojciech SzpankowskiCall Number: TK7882.P3 J33 2015ISBN: 9780521876087Publication Date: 2015-06-30Highlights the probabilistic approach, which predicts the performance of pattern matching algorithms using analytic combinatorics and information theory. Part I compiles known results via analytic methods, while Part II focuses on applications to data structures like digital trees and string-based compression.

- Residuated Structures in Algebra and Logic by George Metcalfe; Constantine TsinakisCall Number: QA10 .M48 2023ISBN: 9781470469856Publication Date: 2023-12-31Explores both algebraic and algorithmic perspectives on residuated structures that serve as a bridge between algebra and logic, providing insights into their properties and relationships.
- Conductive Homogeneity of Compact Metric Spaces and Construction of p-Energy by Jun KigamiCall Number: QA611.28 .K54 2023ISBN: 9783985470563Publication Date: 2023Explores constructing p-energy on compact metric spaces. By considering a scaling limit of discrete p-energies on graphs approximating the original space, Kigami introduces the concept of conductive homogeneity, which allows for the construction of reasonable p-energy when p exceeds the Ahlfors regular conformal dimension of the space.
- The Limiting Absorption Principle for Massless Dirac Operators, Properties of Spectral Shift Functions, and an Application to the Witten Index of Non-Fredholm Operators by Alan CareyCall Number: QA329 .C37 2023ISBN: 9783985470495Publication Date: 2023Detailed investigation of the spectral properties of multi-dimensional, massless Dirac operators. The authors derive a limiting absorption principle for the free massless Dirac operator on any compact interval in ℝ(\setminus){0}. They also prove the absence of singular continuous spectrum for interacting massless Dirac operators.
- Self-Similar and Self-Affine Sets and Measures by Balázs Bárány; Károly Simon; Boris SolomyakCall Number: QA274.9 .B37 2023ISBN: 9781470470463Publication Date: 2023-12-30Focuses on self-similar and self-affine sets, specific types of fractals where this resemblance is precise and given by a contracting similitude or affine transformation. Topics include self-similar sets, measures with overlaps (including infinite Bernoulli convolutions), and the study of self-affine systems using ergodic theory and dynamical systems methods.
- 3D Printing in Mathematics by Maria Trnkova (Editor); Andrew Yarmola (Editor)Call Number: TA1560 .A18 2023ISBN: 9781470469160Publication Date: 2024-01-31Focused on the process and applications of 3D printing for mathematical education, research, and visualization, alongside a discussion of the challenges and open mathematical problems that arise in the design and algorithmic aspects of 3D printing.
- Euclidean Buildings: Geometry and Group Actions by Guy RousseauCall Number: QA174.2 .R68 2023ISBN: 9783985470396Publication Date: 2023Develops the general abstract theory of Euclidean buildings, which are structures with Euclidean affine spaces as apartments. The book emphasizes the metric aspects of these objects, viewing them as CAT(0) spaces similar to Riemannian symmetric spaces of non-compact type
- Hurwitz’s Lectures on the Number Theory of Quaternions by Nicola Oswalk and Jörn SteudingCall Number: QA196 .O89 2023ISBN: 9783985470112Publication Date: 2023English translation of Adolf Hurwitz’s 1919 textbook on quaternions, along with his famous 1-2-3-4 theorem on composition algebras. This comprehensive work sheds historical light on the development of quaternion number theory, including its connections to classical preparatory works and analogies to algebraic numbers.

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