Reviewables
Books in brackets have been offered to a reviewer and may no longer be available. Books marked with an asterisk are
ones I am particularly eager to get reviewed. Books marked with a question mark have been on the list for quite a while
without finding a reviewer, and so they are getting close to the “I give up” moment.
General Science, Math for the General Public, Recreational, Fiction, and
Generally Hard to Classify
*Mulcahy. Mathematical Card Magic: Fifty-Two New Effects (CRC)
Elementary Mathematics, Liberal Arts Mathematics, College Algebra,
Precalculus
Mathematics Education
*Page, ed. Applications of Mathematics in Economics (MAA Notes; “shows instructors what
mathematics is used at the undergraduate level in various parts of economics”)
*Ledder, Carpenter, Comar, eds. Undergraduate Mathematics for the Life Sciences: Models,
Processes, and Directions (MAA Notes; “for mathematics and biology faculty who want to
develop courses and programs in mathematics for life science students”)
History of Math, History of Science, Biography
?Maugin. Continuum Mechanics Through the Twentieth Century: A Concise Historical Perspective
(Springer Solid Mechanics and its Applications)
Philosophy of Math, Psychology of Math, Just-plain-Philosophy
Rescher. On Leibniz, Expanded Edition (Univ of Pittsburgh Press)
Logic, Set Theory, Theory of Computation, Category Theory
Pudlák. Logical Foundations of Mathematics and Computational Complexity (Springer
Monographs; a graduate textbook)
Proofs, Transition to Advanced Math, Problem Books, Discrete Mathematics,
Mathematical Modeling, Capstone Courses, “Mathematical Methods”, and
Surveys
*Ledder. Mathematics for the Life Sciences: Calculus, Modeling, Probability, and Dynamical
Systems (Springer Undergraduate Texts in Mathematics and Technology)
Beltrami. Mathematical Models for Society and Biology 2nd ed (Academic Press)
*Meerschaert. Mathematical Modeling 4th ed (Elsevier; undergraduate text)
Moore, Siegel. A Mathematics Course for Political and Social Research (Princeton; textbook for a
kind of “mathematical methods” course)
*Brown. Discrete Structures and their Interactions (CRC; undergraduate text)
?Blinder. Guide to Essential Math: A Review for Physics, Chemistry and Engineering Students 2nd
ed (Elsevier Insights; big book)
?Beckenbach, ed. Modern Mathematics for the Engineer 1st Series, 2nd Series (Dover; two volumes
collecting various introductions to mathematical topics useful in engineering)
?Louridas, Rassias. Problem-Solving and Selected Topics in Euclidean Geometry: In the Spirit of
the Mathematical Olympiads (Springer)
?Bin, Yee, eds. Mathematical Olympiad in China (2009–2010): Problems and Solutions (World
Scientific)
Algebra and Number Theory
Aigner. Markov’s Theorem and 100 Years of the Uniqueness Conjecture: A Mathematical Journey
from Irrational Numbers to Perfect Matching (Springer; mixes Diophantine approximation, trees,
modular groups, and words; looks very good)
Mullen, Panario. Handbook of Finite Fields (CRC; a massive book that attempts to record the state
of the art on finite fields)
Puntanen, Styan, Isotalo. Formulas Useful for Linear Regression Analysis and Related Matrix
Theory: It’s Only Formulas But We Like Them (Springer Briefs; the subtitle won me over)
Halter-Koch. Quadratic Irrationals: An Introduction to Classical Number Theory (CRC Pure and
Applied Math)
Grynkiewwicz. Structural Additive Theory (Springer Developments in Mathematics; on “additive
combinatorics” or “additive number theory”; high-level introduction)
van zur Gathen, Gerhard. Modern Computer Algebra, 3rd ed (Cambridge; on the algorithms
underlying mathematical software, especially in algebra and number theory)
?Rutherford. Substitutional Analysis (Dover; representation theory of the symmetric group)
?Passman. Infinite Crossed Products (Dover)
Analysis, Calculus
Vince. Calculus for Computer Graphics (Springer)
Willem. Functional Analysis: Fundamentals and Applications (Birkhäuser Cornerstones; graduate
textbook)
Kris, Pultr. Introduction to Mathematical Analysis (Birkhäuser; does real analysis in several
variables and complex analysis, with a bit of functional analysis at the end)
Cohn. Measure Theory 2nd ed (Birkhäuser Advanced Texts)
Makarov, Podkorytov. Real Analysis: Measures, Integrals and Applications (Springer UTX;
graduate textbook on measure and integration)
Garling. A Course in Mathematical Analysis, Volume I: Foundations and Elementary Real Analysis
(Cambridge)
*Penot. Calculus without Derivatives (Springer GTM; non-smooth analysis)
*Çinlar, Vanderbei. Real and Convex Analysis (Springer UTM; back cover describes it as a “first
course in analysis for scientists and engineers”)
Ovchinnikov. Measure, Integral, Derivative: A Course on Lebesgue’s Theory (Springer UTX)
*Lauritzen. Undergraduate Convexity: From Fourier and Motzkin to Kuhn and Tucker (World
Scientific)
Van Dijk. Distribution Theory: Convolution, Fourier Transform, and Laplace Transform (De
Gruyter Graduate Lectures; small book)
Bressan. Lecture Notes on Functional Analysis with Applications to Linear Partial Differential
Equations (AMS GSM)
?Clarke. Functional Analysis, Calculus of Variations, and Optimal Control (Springer GTM)
?Bosch, Swartz. Functional Calculi (World Scientific)
?Helffer. Spectral Theory and its Applications (Cambridge Studies in Advanced Mathematics)
Geometry and Topology
López. Constant Mean Curvature Surfaces with Boundary (Springer Monographs)
Bezdek. Lectures on Sphere Arrangements — The Discrete Geometric Side (Springer Fields
Institute Monographs)
Karpenkov. Geometry of Continued Fractions (Springer Algorithms and Computation for
Mathematics series; multidimensional generalizations of continued fractions with applications)
Farb et al, eds. Moduli Spaces of Riemann Surfaces (AMS/PCMI)
*McInerney. First Steps in Differential Geometry: Riemannian, Contact, Symplectic (Springer
UTM, so meant as an undergraduate text)
Sussman, Wisdom. Functional Differential Geometry (MIT Press; based on a course for physics
students, emphasizes clarity of notation and connects to functional programming)
*Singh. Elements of Topology (CRC; undergraduate text, point-set topology, fundamental groups,
covering spaces)
Levi-Civita. The Absolute Differential Calculus (Dover)
?Goubault-Larrecq. Non-Hausdorff Topology and Domain Theory: Selected Topics in Point-Set
Topology (Cambridge NMM; research monograph on new point-set topology, with applications to
such things as the semantics of computer languages)
?Naimpally, Peters. Topology with Applications: Topological Spaces via Near and Far (World
Scientific; introduction to general topology and applications, via proximity spaces)
?Hales. Dense Sphere Packings: A Blueprint for Formal Proofs (Cambridge LMS Lecture Notes;
an outline of his proof of the Kepler conjecture)
?Wright. Invariants of Quadratic Differential Forms (Dover)
Combinatorics, Graph Theory, Discrete Mathematics, Game Theory
Graham, Nešetřil, Butler, eds. The Mathematics of Paul Erdős I, II 2nd ed (Springer; articles about
Erdős and his mathematics)
*Beinecke, Wilson, eds. Topics in Structural Graph Theory (Cambridge Encyclopedia series)
?Bretto. Hypergraph Theory: An Introduction (Springer Mathematical Engineering series)
?Pach, ed. Thirty Essays on Geometric Graph Theory (Springer; “research and survey papers”)
Differential Equations, Calculus of Variations, Dynamical Systems, Ergodic
Theory, Control Theory
*Costanda. Differential Equations: A Primer for Scientists and Engineers (Springer Undergraduate
Texts in Math and Technology)
*Upadhyay, Iyengar. Introduction to Mathematical Modeling and Chaotic Dynamics (CRC; upperlevel undergraduate textbook)
Barrat, Barthélemy, Vespignani. Dynamical Processes on Complex Networks (Cambridge)
*Robinson. An Introduction to Dynamical Systems 2nd ed. (AMS Pure and Applied Textbooks; the
first edition was from Pearson; fat book)
Barreira, Pesin. Introduction to Smooth Ergodic Theory (AMS GSM)
?Barreira. Dimension Theory of Hyperbolic Flows (Springer Monographs)
?Nipp, Stoffer. Invariant Manifolds in Discrete and Continuous Dynamical Systems (EMS Tracts)
?Gros. Complex and Adaptive Dynamical Systems: A Primer 3rd ed (Springer Complexity)
?Banasiak. Mathematical Modelling in One Dimension: An Introduction via Difference and
Differential Equations (Cambridge AIMS Library)
?Salsa, Vegni, Zaretti, Zunino. A Primer on PDEs (Springer Unitext)
Probability
Klenke. Probability Theory: A Comprehensive Course (Springer UTX; graduate textbook)
Privault. Understanding Markov Chains (Springer SUMS; aimed at undergraduates)
Ibe. Markov Processes for Stochastic Modeling 2nd ed (Elsevier Insights; graduate text)
Kisielewicz. Stochastic Differential Inclusions and Applications (Springer Optimization and
Applications)
Spǎtaru. Analysis and Probability (Elsevier Insights; graduate text in probability)
Stepanov. Stochastic World (Springer Mathematical Engineering; an intro to stochastic processes
for physicists)
Borovkov. Probability Theory (Springer UTX; big graduate text translated from Russian)
Haigh. Probability Models 2nd ed (Springer UTX)
*Stroock. Mathematics of Probability (AMS GSM; graduate intro to probability and measure
theory)
Nelson. Foundations and Methods of Stochastic Simulation: A First Course (Springer)
*Çinlar. Introduction to Stochastic Processes (Dover)
*Gut. Probability: A Graduate Course 2nd ed (Springer)
?Paul, Baschnagel. Stochastic Processes: From Physics to Finance 2nd ed (Springer)
?Cohen, Istas. Fractional Fields and Applications (Springer Mathématiques et Applications; fancy
stochastic stuff)
?Beran, Feng, Ghosh, Kulik. Long Memory Processes: Probabilistic Properties and Statistical
Methods (Springer)
?Khinchin. Mathematical Methods for the Theory of Queuing (Dover)
?Révész. Random Walk in Random and Non-Random Environments (World Scientific)
Statistics
Chaudhuri, Christofides. Indirect Questioning in Sample Surveys (Springer)
*Holicky. Introduction to Probability and Statistics for Engineers (Springer; one more
undergraduate textbook, but a slim one: 181 pages for $70)
Haviv. Queues: A Course in Queueing Theory (Springer Series in OR and Management Science)
Westfall, Henning. Understanding Advanced Statistical Methods (CRC)
Abramovich, Ritov. Statistical Theory: A Concise Introduction (CRC)
Hilbe, Robinson. Methods of Statistical Model Estimation (CRC)
Willink. Measurement, Uncertainty and Probability (Cambridge; “promotes the correct
understanding of the classical statistical viewpoint” for scientists)
?Wang. Geometric Structure of High-Dimensional Data and Dimensionality Reduction (Springer)
?Farebrother. L1-Norm and L∞-Norm Estimation: An Introduction to the Least Absolute Residuals,
the Minimax Absolute Residual and Related Fitting Procedures (Springer Briefs)
?Mittelhammer. Mathematical Statistics for Economics and Business 2nd ed (Springer)
Numerical Analysis, Scientific Computation, Optimization, Inverse Problems,
Approximation Theory, etc.
Sergeyev, Strongin, Lera. Introduction to Global Optimization Exploiting Space-Filling Curves
(Springer Briefs)
Foucart, Rauhut. A Mathematical Introduction to Compressive Sensing (Birkhäuser Applied and
Numerical Harmonic Analysis series)
Bürgisser, Cucker. Condition: The Geometry of Numerical Algorithms (Springer Grundlehren)
Amidor. Mastering the Discrete Fourier Transform in One, Two or Several Dimensions: Pitfalls
and Artifacts (Springer Computational Imaging and Vision)
*Nassif, Fayyad. Introduction to Numerical Analysis and Scientific Computing (CRC)
*Lange. Optimization 2nd ed (Springer Texts in Statistics; graduate text aimed at nonmathematicians)
*Butt. Applied Linear Algebra and Optimization using MATLAB (Mercury Learning)
Mathematical Physics, Classical Mechanics, etc.
*Hall. Quantum Theory for Mathematicians (Springer GTM)
Shapiro, Berredo-Peixoto. Lecture Notes on Newtonian Mechanics: Lessons from Modern Concepts
(Springer Undergraduate Lecture Notes in Physics)
Faraoni. Special Relativity (Springer Lecture Notes in Physics)
*Batchelor. An Introduction to Fluid Dynamics (Cambridge; a BLL*** book)
*Meyer. Introduction to Mathematical Fluid Dynamics (Dover; a BLL book)
?Lannes. The Water Waves Problem: Mathematical Analysis and Asymptotics (AMS S&M)
?Ben-Artzi, Croisille, Fishelov. Navier-Stokes Equations in Planar Domains (Imperial College
Press)
?Sohr. The Navier-Stokes Equations: An Elementary Functional Analysis Approach (Birkhäuser
Modern Classics)
Applied Mathematics, non-physics
Cozzens, Miller. The Mathematics of Encryption: An Elementary Introduction (AMS Mathematical
World)
Chafaï, Guédon, Lecué, Pajor. Interactions Between Compressed Sensing, Random Matrices, and
High Dimensional Geometry (SMF Panoramas et Synthèses)
Joshi, Paterson. Introduction to Mathematical Portfolio Theory (Cambridge)
Smith, Keyfitz. Mathematical Demography: Selected Papers (Springer; a kind of sourcebook
covering the last century of work on demography)
Tangian. Mathematical Theory of Democracy (Springer; big book)
Albrecher, Binder, Lautscham, Mayer. Introduction to Quantitative Methods for Financial Markets
(Birkhäuser Compact Textbooks in Mathematics)
?Priour. A Finite Element Method for Netting: Application to Fish Cages and Fishing Gear
(Springer Briefs; seems interesting, but a very short notice is sufficient)
?Soomere, Quak, eds. Preventive Methods for Coastal Protection: Towards the Use of Ocean
Dynamics for Pollution Control (Springer; part of MPE2013; probably far too technical, but here in
case someone would like to take a look)
?Marsan, Bellomo, Tosin. Complex Systems and Society: Modeling and Simulation (Springer
Briefs)
?Zhao, ed. Mathematics in Image Processing (IAS/Park City Mathematics Series; emphasis on the
theoretical basis for methods)
?Rosini. Macroscopic Models for Vehicular Flows and Crowd Dynamics: Theory and Applications
(Springer Complexity)
?Raval, Ray. Introduction to Biological Networks (CRC)
?Lovejoy, Schertzer. The Weather and Climate: Emergent Laws and Multifractal Cascades
(Cambridge)