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An Introduction to Mathematics of Financial Derivatives
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2. A Primer on Arbitrage Theorem
3. Calculus in Deterministic and Stochastic Environments
4. Pricing Derivatives: Models and Notation
5. Tools in Probability Theory
6. Martingales and Martingale Representations
7. Differentiation in Stochastic Environments
8. The Wiener Process and Rare Events in Financial Markets
9. Integration in Stochastic Environments: The Ito Integral
10. Ito...
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Intuitive Concepts in Elementary Topology
Intuitive Concepts in Elementary TopologyB.H. Arnold0. Statements and Proofs in Mathematics
1. What is Topology?
2. Networks and Maps
3. Topological Equivalence in Three-Dimensional Space
4. Maps on a Sphere with Handles
5. The Jordan Curve Theorem
6. Sets
7. Transformations
8. Spaces
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Elements of the Topology of Plane Sets of Points
Elements of the Topology of Plane Sets of PointsM.H.A. NewmanI. Sets
II. Closed sets and open sets in metric spaces
III. Homeomorphism and continuous mappings
IV. Connection
V. Separation theorems
VI. Simply- and multiply-connected plan domains
VII. Homotopy properties
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Topological Methods in Algebraic Geometry
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2. The cobordism ring
3. The Todd genus
4. The Riemann-Roch theorem for algebraic manifolds
Appendix 1 door R.L.E. Schwarzenberger
Appendix 2 door A. Borel
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Famous Problems of Elementary Geometry
Famous Problems of Elementary GeometryFelix KleinExpanded version of the famous 1894 Easter lectures at Göttingen University
The Duplication of the Cube
The Trisection of an Angle
The Quadrature of the Circle
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Metric Affine Geometry
Metric Affine GeometryErnst Snapper, Robert J. Troyer1. Affine Geometry
2. Metric Vector Spaces
3. Metric Affine Spaces
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The Non-Euclidean, Hyperbolic Plane
The Non-Euclidean, Hyperbolic PlanePaul Kelly, Gordon MatthewsI. Some Historical Background
II. Absolute Plane Geometry
III. Hyperbolic Plane Geometry
IV. A Euclidean Model of the Hyperbolic Plane
Appendix: Distance Geometries
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Graphs and their Uses
Graphs and their UsesOystein Ore1. What is a Graph?
2. Connected Graphs
3. Trees
4. Matchings
5. Directed Graphs
6. Questions Concerning Games and Puzzles
7. Relations
8. Planar Graphs
9. Map Coloring
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Algebraic Curves
Algebraic CurvesWilliam Fulton1. Affine Algebraic Sets
2. Affine Varieties
3. Local Properties of Plane Curves
4. Projective Varieties
5. Projective Plane Curves
6. Varieties, Morphisms, and Rational Maps
7. Resolution of Singularities
8. Riemann-Roch Theorem
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Algebra - Erster Teil
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1. Zahlen und Mengen
2. Gruppen
3. Ringe und Körper
4. Vektorräume und Tensorräume
5. Ganzrationale Funktionen
6. Körpertheorie
7. Fortsetzung der Gruppentheorie
8. Die Theorie von Galois
9. Ordnung und Wohlordnung von Mengen
10. Unendliche Körpererweiterungen
11. Reelle Körper
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Algebra - Zweiter Teil
Algebra - Zweiter TeilB.L. van der WaerdenUnter Benutzung von Vorlesungen von E. Artin und E. Noether
12. Lineare Algebra
13. Algebren
14. Darstellungstheorie der Gruppen und Algebren
15. Allgemeine Idealtheorie der kommutativen Ringe
16. Theorie der Polynomideale
17. Ganze algebraische Grössen
18. Bewertete Körper
19. Algebraische Funktionen einer Variablen
20. Topologische Algebra
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Fundamentals of Galois Theory
Fundamentals of Galois TheoryM.M. PostnikovPart I. The elements of Galois theory
1. Elements of field theory
2. Basic information from group theory
3. Galois theory
Part II. The soltuion of equations in radicals
1. Supplementary information form the general theory of groups
2. Equations which are solvable in radicals
3. Structure of equations which are not solvable in radicals
4. Non-solvability in radicals of the general equation of degree n >= 5
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Introduction to Analytic Number Theory
Introduction to Analytic Number TheoryTom M. ApostolHistorical Introduction
1. The Fundamental Theorem of Arithmetic
2. Arithmetical Functions and Dirichlet Multiplication
3. Averages of Arithmetical Functions
4. Some Elementary Theorems on the Distribution of Prime Numbers
5. Congruences
6. Finite Abelian Groups and Their Characters
7. Dirichlet’s Theorem on Primes in Arithmetical Progressions
8. Periodic Arithmetical Functions and Gauss Sums
9. Quadratic Residues and the Quadratic Reciprocit...
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The Theory of Numbers and Diophantine Analysis
The Theory of Numbers and Diophantine AnalysisRobert D. CarmichaelI. Elementary Properties of Integers
II. On the Indicator of an Integer
III. Elementary Properties of Congruences
IV. The Theorems of Fermat and Wilson
V. Primitive Roots Modulo m
VI. Other Topics
----
I. Introduction. Rational Triangles. Method of Infinite Descent
II. Problems Involving a Multiplicative Domain
III. Equations of the Third Degree
IV. Equations of the Fourth Degree
V. Equations of Degree Higher Than the Fourth. The ...
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Theory of Sets
Theory of SetsE. KamkeI. The Rudiments of Set Theory
II. Arbitrary Sets and Their Cardinal Numbers
III. Ordered Sets and Their Order Types
IV. Well-Ordered Sets and Their Ordinal Numbers
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Elementary Differential Equations and Boundary Value Problems
Elementary Differential Equations and Boundary Value ProblemsWilliam E. Boyce, Richard C. DiPrima1. Introduction
2. First Order Differential Equations
3. Second Order Linear Equations
4. Series Solutions of Second Order Linear Equations
5. Higher Order Linear Equations
6. The Laplace Transform
7. Systems of First Order Linear Equations
8. Numerical Methods
9. Nonlinear Differential Equations and Stability
10. Partial Differential Equations and Fourier Series
11. Boundary Value Problems and Sturm...
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Ordinary Differential Equations
Ordinary Differential EquationsA.I. Kiselev, M.L. Krasnov, G.I. Makarenko1. Basic concepts
2. The method of isoclines
3. Euler's method
4. Equations with separable variables
5. Homogeneous equations
6. Linear equations of the first order. Bernoulli equations
7. Total differential equations. Integrating factors
8. Differential equations of the first order not solved for the derivative
9. Formation of differential equations of families of curves. Problems on trajectories
10. Various problems
11. D...
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Lehrbuch der Differential-Gleichungen
Lehrbuch der Differential-GleichungenA.R. Forsyth1. Einleitung
2. Differentialgleichungen erster Ordnung
3. Die allgemeine lineare Differentialgleichung mit konstanten Koeffizienten
4. Verschiedenartige Integrationsmethoden
5. Integration durch Reihen
6. Hypergeometrische Reihen
7. Lösung durch bestimmte Integralen
8. Gewöhnliche Differentialgleichungen mit mehr als zwei Veränderlichen
9. Partielle Differentialgleichungen erster Ordnung
10. Partielle Differentialgleichungen zweiter und höher...
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Grundzüge der Differential- und Integralrechnung
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II. Grenzwerte
III. Die rationalen Rechnungsoperationen
IV. Funktionen einer Veränderlichen
V. Geometrische Interpretation der Zahlen und Funktionen
VI. Differentiation von Funktionen einer Veränderlichen
VII. Unendliche Reihen
VIII. Einige Anwendungen der Potenzreihen
IX. Maxima und Minima
X. Differentiation von Funktionen mehrerer Veränderlicher
XI. Maxima und Minima
XII. Umkehrung von...
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Linear Algebra and Differential Equations
Linear Algebra and Differential EquationsCharles G. Cullen1. First-Order Ordinary Differential Equations
2. Matrices and Systems of Linear Equations
3. Vector Spaces and Linear Transformations
4. Eigenvalues and Eigenvectors
5. Higher-Order Linear Differential Equations
6. Systems of Linear Differential Equations
7. Variable Coefficients and Solutions in Series Form
8. The Laplace Transform
9. Representation Theory for Linear Transformations
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Lectures on Tensor Calculus and Differential Geometry
Lectures on Tensor Calculus and Differential GeometryJ.C.H. Gerretsen1. Linear vector spaces
2. Metric vector spaces
3. Bilinear and quadratic forms
4. Tensors
5. Manifolds in a metric point space
6. Curves
7. Geodesic differentiation
8. Hypersurfaces
9. Theory of curvature of general manifolds
10. Theory of integrability
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Differentialgeometrie der Kurven und Flächen und Tensorrechnung
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I. Grundlehren über ebene und räumliche Kurven
Flächentheorie
II. Die erste Grundform und ihre Anwendungen
III. Die zweite Grundform und ihre Anwendungen
IV. Besondere Flächen
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Einführung in die Differentialtopologie
Einführung in die DifferentialtopologieTheodor Bröcker, Klaus Jänich1. Mannigfaltigkeiten und differenzierbare Strukturen
2. Der Tangentialraum
3. Vektorraumbündel
4. Lineare Algebra für Vektorraumbündel
5. Lokale und tangetielle Eigenschaften
6. Der Satz von Sard
7. Einbettung
8. Dynamische Systeme
9. Isotopien von Einbettungen
10. Die zusammenhängende Summe
11. Differentialgleichungen 2. Ordnung und Sprays
12. Exponentialabbildung und Tubenumgebungen
13. Berandete Mannigfaltigkeiten
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A Course of Modern Analysis
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An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions
I. Complex Numbers
II. The Theory of Convergence
III. Continuous Functions and Uniform Convergence
IV. The Theory of Riemann Integration
V. The fundamental properties of Analytic Functions; Taylor's, Laurent's, and Liouville's Theorema
VI. The Theory of Residues; applicati...
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Functional Analysis
Functional AnalysisFrigyes Riesz, Béla Sz.-NagyPart One. Modern Theories of Differentiation and Integration
1. Differentiation
2. The Lebesgue Integral
3. The Stieltjes Integral and Its Generalizations
Part Two. Integral Equations. Linear Transformations
4. Integral Equations
5. Hilbert and Banach Spaces
6. Completely Continuous Symmetric Transformations of Hilbert Space
7. Bounded Symmetric, Unitary, and Normal Transformations of Hilbert Space
8. Unbounded Linear Transformations of Hilbert Spa...
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Calculus vol. I
Calculus vol. ITom M. ApostolI. Introduction
Part 1. Historical Introduction
Part 2. Some Basic Concepts of the Theory of Sets
Part 3. A Set of Axioms for the Real Number System
Part 4. Mathematical Induction, Summation Notation, and RelatedTopics
1. The Concepts of the Integral Calculus
2. Some Applications of Differentiation
3. Continuous Functions
4. Differential Calculus
5. The Relation between Integration and Differentiation
6. The Logarithm, the Exponential, and the Inverse TrigonometricFu...
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Calculus vol. II
Calculus vol. IITom M. ApostolPart 1. Linear analysis
1. Linear spaces
2. Linear transformations and matrices
3. Determinants
4. Eigenvalues and eigenvectors
5. Eigenvalues of operators acting on Euclidean spaces
6. Linear differential equations
7. Systems of differential equations
Part 2. Nonlinear analysis
8. Differential calculus of scalar and vector fields
9. Applications of the differential calculus
10. Line integrals
11. Multiple integrals
12. Surface integrals
Part 3. Special topics
13....
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Functions of a Complex Variable
Functions of a Complex VariableE.G. PhillipsFunctions of a complex variable
Conformal representations
Some special transformations
The complex integral calculus
The calculus of residues
Miscellaneous examples
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Beknopt leerboek der rekenkunde
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Optelling
Aftrekking
Vermenigvuldiging
Gedurige producten
Deeling
Machtsverheffing
Worteltrekking
Deelbaarheid
Grootste gemeene deeler
Kleinste gemeene veelvoud
Kenmerken van deelbaarheid door optelling en aftrekking
Vraagstukken
Breuken
Verhoudingen
Evenredigheden
Maten, gewichten en munten
Aanhangsel
Antwoorden
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Geprogrammeerde Instructie Wiskunde
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2. Eigenschappen, breuken, exponenten
3. Cirkels van Euler
4. Wortels
5. Machten van tien en logaritmen
6. Vergelijkingen, merkwaardige producten
7. Permutaties, combinaties
8. Tabellen
9. Afrondingen
10. Rekenliniaal
11. Rekenliniaal
12. Rekenliniaal
13. Rekenliniaal
14. Overzicht rekenliniaal
15. Histogram en polygoon
16. Variabelen
17. Richtingscoëfficiënt
18. Functies
19. Inverse functies
20. Rijen
21. Sigma-teken
22. Limieten...
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Geprogrammeerde instructie - Matrix Algebra
Geprogrammeerde instructie - Matrix AlgebraW.F. van Raaij1. Vektoren
2. Afstand en richting
3. Projektie en orthogonale basis
4. Volumina en determinanten
5. Determinanten
6. Matrices
7. Matrixvermenigvuldiging
8. Soorten matrices
9. Matrix-inversie
10. Matrix-rotatie en orthogonaliteit
11. Matrix-transformatie
12. Rang van een matrix
13. Eigenvektoren en eigenwaarden
14. Matrix-rekening
15. Principale componenten
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A First Course in the Qualitative Theory of Differential Equations
A First Course in the Qualitative Theory of Differential EquationsJames Hetao Liu1. A Brief Description
2. Existence and Uniqueness
3. Linear Differential Equations
4. Autonomous Differential Equations in R2
5. Stability. Part I
6. Bifurcation
7. Chaos
8. Dynamical Systems
9. Stability. Part II
10. Bounded Solutions
11. Periodic Solutions
12. Some New Types of Equations
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A Book of Problems in Ordinary Differential Equations
A Book of Problems in Ordinary Differential EquationsM.L. Krasnov, A.I. Kiselyov, G.I. MakarenkoI. Differential Equations of the First Order
II. Differential Equations of Higher Orders
III. Systems of Differential Equations
IV. Stability Theory
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Introduction to Mathematical Probability
Introduction to Mathematical ProbabilityJ.V. UspenskyI. Computation of probability by direct enumeration of cases
II. Theorems of total and compound probability
III. Repeated trials
IV. Probabilities of hypotheses and Bayes' theorem
V. Use of difference equations in solving problems of probability
VI. Bernoulli's theorem
VII. Approximate evaluation of probabilities in Bernoullian case
VIII. Further considerations on games of chance
IX. Mathematical expectation
X. The law of large numbers
XI. App...
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A First Course in Probability
A First Course in ProbabilitySheldon Ross1. Combinatorial Analysis
2. Axioms of Probability
3. Conditional Probability and Independence
4. Random Variables
5. Continuous Random Variables
6. Jointly Distributed Random Variables
7. Properties of Expectation
8. Limit Theorems
9. Additional Topics in Probability
10. Simulation
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Probability and Statistics for Engineers
Probability and Statistics for EngineersRichard Johnson, John Freund, Irwin Miller1. Introduction
2. Organization and Description of Data
3. Probability
4. Probability Distributions
5. Probability Densities
6. Sampling Distributions
7. Inferences Concerning a Mean
8. Comparing Two Treatments
9. Inferences Concerning Variances
10. Inferences Concerning Proportions
11. Regression Analysis
12. Analysis of Variance
13. Factorial Experimentation
14. Nonparametric Tests
15. The Statistical Content of ...
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Population System Control
Population System ControlSong Jian, Yu Jingyuan 1. Introduction
2. Mathematical Models of Population Systems
3. Demographic Indices
4. Dynamic Analysis of a Population System
5. Stability Theory of Population Systems
6. Population Projections and Policies
7. Population Structure in an Ideal Society
8. Optimal Control of Population Processes
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The Basic Practice of Statistics
The Basic Practice of StatisticsDavid S. Moore1. Examining Distributions
2. Examining Relationships
3. Producing Data
4. Sampling Distributions and Probability
5. Introduction to Inference
6. Inference for Distributions
7. Inference for Proportions
8. Inference for Two-Way Tables
9. One-Way Analysis of Variance: Comparing Several Means
10. Inference for Regression
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Applied Multivariate Statistical Analysis
Applied Multivariate Statistical AnalysisRichard A. Johnson, Dean W. WichernCD-ROM included
1. Aspects of Multivariate Analysis
2. Matrix Algebra and Random Variables
3. Sample Geometry and Random Sampling
4. The Multivariate Normal Distribution
5. Inferences about a Mean Vector
6. Comparisons of Several Multivariate Means
7. Multivariate Linear Regression Models
8. Principal Components
9. Factor Analysis and Inference for Structured Covariance Matrices
10. Canonical Correlation Analysis
11. Di...
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Misuded Statistics - Straight Talk for Twisted Numbers
Misuded Statistics - Straight Talk for Twisted NumbersA.J. Jaffe, Herbert F. SpirerNumerous misuses of statistics are described and illustrated, and ways of recognizing and avoiding such misuse are discussed. The following five categories of statistical misuse are identified: a lack of knowledge of the subject matter, the quality of the basic data, the preparation of the study and the report, the statistical methodology, and a deliberate suppression of data. Topics addressed include non-statisti...
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