Mathematical Reasoning and Visualization -- Visualization in Logic and Mathematics -- From Symmetry Perception to Basic Geometry -- Naturalism, Pictures, and Platonic Intuitions -- Mathematical Activity -- Mathematical Explanation and Proof Styles -- Tertium Non Datur: On Reasoning Styles in Early Mathematics -- The Interplay Between Proof and Algorithm in 3rd Century China: The Operation as Pr…
Trigonometric Fundamentals -- Introductory Problems -- Advanced Problems -- Solutions to Introductory Problems -- Solutions to Advanced Problems.103 Trigonometry Problems contains highly-selected problems and solutions used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Though many problems may initially appear impenetrable to the novice, most can be solv…
Sturm’s 1836 Oscillation Results Evolution of the Theory -- Sturm Oscillation and Comparison Theorems -- Charles Sturm and the Development of Sturm-Liouville Theory in the Years 1900 to 1950 -- Spectral Theory of Sturm-Liouville Operators Approximation by Regular Problems -- Spectral Theory of Sturm-Liouville Operators on Infinite Intervals: A Review of Recent Developments -- Asymptotic Metho…
Modeling Text Databases -- An Overview of Probabilistic and Time Series Models in Finance -- Stereological Estimation of the Rose of Directions from the Rose of Intersections -- Approximations for Multiple Scan Statistics -- Krawtchouk Polynomials and Krawtchouk Matrices -- An Elementary Rigorous Introduction to Exact Sampling -- On the Different Extensions of the Ergodic Theorem of Information…
Operators on Sequences -- Basic Rank Selectors, Pulses and Impulses -- LULU-Smoothers, Signals and Ambiguity -- LULU-Intervals, Noise and Co-idempotence -- Smoothing and Approximation with Signals -- Variation Reduction and Shape Preservation -- Multiresolution Analysis of Sequences -- The Discrete Pulse Transform -- Fair Comparison with Linear Smoothers -- Interpretation and Future.This monogr…
Introduction: Basic Notions and Methods -- Heterogeneous Rod -- Heterogeneous Plate -- Finite Rod Structures -- Lattice Structures -- The Multi-Scale Domain Decomposition.Numerous applications of rod structures in civil engineering, aircraft and spacecraft confirm the importance of the topic. On the other hand the majority of books on structural mechanics use some simplifying hypotheses; these …
4d Formalism -- On Establishing Balance and Conservation Laws in Elastodynamics -- From Mathematical Physics to Engineering Science -- Evolving Interfaces -- The Unifying Nature of the Configurational Force Balance -- Generalized Stefan Models -- Explicit Kinetic Relation from “First Principles” -- Growth & Biomechanics -- Surface and Bulk Growth Unified -- Mechanical and Thermodynamical Mo…
Squares -- Numbers, Numbers Everywhere -- Fibonacci Numbers -- Prime Numbers -- Choice and Chance -- Geometrical Constructions -- The Algebra of Group.Mathematics Is Not a Spectator Sport challenges the reader to become an active mathematician. Beginning at a gentle pace, the author encourages the reader to get involved, with discussions of an exciting variety of topics, each placed in its hist…
Introduction: The Birth and Growth of a Community -- History or Heritage? An Important Distinction in Mathematics and for Mathematics Education -- Ptolemy’s Mathematical Models and their Meaning -- Mathematics, Instruments and Navigation, 1600–1800 -- Was Newton’s Calculus a Dead End? The Continental Influence of Maclaurin’s Treatise of Fluxions -- The Mathematics and Science of Leonhar…
Mathematics, Art and Architecture -- Mathematics, Art and Architecture -- From Tiling the Plane to Paving Town Square -- Mathematics in Contemporary Arts — Finite and Infinity -- De Insana Geometria -- Ovals in Borromini’s Geometry -- Fractals: A Resonance between Art and Nature -- Mathland — From Topology to Virtual Architecture -- Visual Mathematics and Computer Graphics -- Introduction…