by Reitano
ISBN: 9780262333139  Copyright 2010
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Contents (pg. vii)  
List of Figures and Tables (pg. xix)  
Introduction (pg. xxi)  
1 Mathematical Logic (pg. 1)  
1.1 Introduction (pg. 1)  
1.2 Axiomatic Theory (pg. 4)  
1.3 Inferences (pg. 6)  
1.4 Paradoxes (pg. 7)  
1.5 Propositional Logic (pg. 10)  
1.6 Mathematical Logic (pg. 23)  
1.7 Applications to Finance (pg. 24)  
2 Number Systems and Functions (pg. 31)  
2.1 Numbers: Properties and Structures (pg. 31)  
2.2 Functions (pg. 49)  
2.3 Applications to Finance (pg. 51)  
3 Euclidean and Other Spaces (pg. 71)  
3.1 Euclidean Space (pg. 71)  
3.2 Metric Spaces (pg. 82)  
3.3 Applications to Finance (pg. 93)  
4 Set Theory and Topology (pg. 117)  
4.1 Set Theory (pg. 117)  
4.2 Open, Closed, and Other Sets (pg. 122)  
4.3 Applications to Finance (pg. 134)  
5 Sequences and Their Convergence (pg. 145)  
5.1 Numerical Sequences (pg. 145)  
5.2 Limits Superior and Inferior (pg. 152)  
5.3 General Metric Space Sequences (pg. 157)  
5.4 Cauchy Sequences (pg. 162)  
5.5 Applications to Finance (pg. 167)  
6 Series and Their Convergence (pg. 177)  
6.1 Numerical Series (pg. 177)  
6.2 The lpSpaces (pg. 196)  
6.3 Power Series (pg. 206)  
6.4 Applications to Finance (pg. 215)  
7 Discrete Probability Theory (pg. 231)  
7.1 The Notion of Randomness (pg. 231)  
7.2 Sample Spaces (pg. 233)  
7.3 Combinatorics (pg. 247)  
7.4 Random Variables (pg. 252)  
7.5 Expectations of Discrete Distributions (pg. 264)  
7.6 Discrete Probability Density Functions (pg. 287)  
7.7 Generating Random Samples (pg. 301)  
7.8 Applications to Finance (pg. 307)  
8 Fundamental Probability Theorems (pg. 347)  
8.1 Uniqueness of the m.g.f. and c.f. (pg. 347)  
8.2 Chebyshev’s Inequality (pg. 349)  
8.3 Weak Law of Large Numbers (pg. 352)  
8.4 Strong Law of Large Numbers (pg. 357)  
8.5 De Moivre–Laplace Theorem (pg. 368)  
8.6 The Normal Distribution (pg. 377)  
8.7 The Central Limit Theorem (pg. 381)  
8.8 Applications to Finance (pg. 386)  
9 Calculus I: Differentiation (pg. 417)  
9.1 Approximating Smooth Functions (pg. 417)  
9.2 Functions and Continuity (pg. 418)  
9.3 Derivatives and Taylor Series (pg. 450)  
9.4 Convergence of a Sequence of Derivatives (pg. 478)  
9.5 Critical Point Analysis (pg. 488)  
9.6 Concave and Convex Functions (pg. 494)  
9.7 Approximating Derivatives (pg. 504)  
9.8 Applications to Finance (pg. 505)  
10 Calculus II: Integration (pg. 559)  
10.1 Summing Smooth Functions (pg. 559)  
10.2 Riemann Integration of Functions (pg. 560)  
10.3 Examples of the Riemann Integral (pg. 574)  
10.4 Mean Value Theorem for Integrals (pg. 579)  
10.5 Integrals and Derivatives (pg. 581)  
10.6 Improper Integrals (pg. 587)  
10.7 Formulaic Integration Tricks (pg. 592)  
10.8 Taylor Series with Integral Remainder (pg. 598)  
10.9 Convergence of a Sequence of Integrals (pg. 602)  
10.10 Numerical Integration (pg. 609)  
10.11 Continuous Probability Theory (pg. 613)  
10.12 Applications to Finance (pg. 641)  
References (pg. 685)  
Index (pg. 689)  
Contents (pg. vii)  
List of Figures and Tables (pg. xix)  
Introduction (pg. xxi)  
1 Mathematical Logic (pg. 1)  
1.1 Introduction (pg. 1)  
1.2 Axiomatic Theory (pg. 4)  
1.3 Inferences (pg. 6)  
1.4 Paradoxes (pg. 7)  
1.5 Propositional Logic (pg. 10)  
1.6 Mathematical Logic (pg. 23)  
1.7 Applications to Finance (pg. 24)  
2 Number Systems and Functions (pg. 31)  
2.1 Numbers: Properties and Structures (pg. 31)  
2.2 Functions (pg. 49)  
2.3 Applications to Finance (pg. 51)  
3 Euclidean and Other Spaces (pg. 71)  
3.1 Euclidean Space (pg. 71)  
3.2 Metric Spaces (pg. 82)  
3.3 Applications to Finance (pg. 93)  
4 Set Theory and Topology (pg. 117)  
4.1 Set Theory (pg. 117)  
4.2 Open, Closed, and Other Sets (pg. 122)  
4.3 Applications to Finance (pg. 134)  
5 Sequences and Their Convergence (pg. 145)  
5.1 Numerical Sequences (pg. 145)  
5.2 Limits Superior and Inferior (pg. 152)  
5.3 General Metric Space Sequences (pg. 157)  
5.4 Cauchy Sequences (pg. 162)  
5.5 Applications to Finance (pg. 167)  
6 Series and Their Convergence (pg. 177)  
6.1 Numerical Series (pg. 177)  
6.2 The lpSpaces (pg. 196)  
6.3 Power Series (pg. 206)  
6.4 Applications to Finance (pg. 215)  
7 Discrete Probability Theory (pg. 231)  
7.1 The Notion of Randomness (pg. 231)  
7.2 Sample Spaces (pg. 233)  
7.3 Combinatorics (pg. 247)  
7.4 Random Variables (pg. 252)  
7.5 Expectations of Discrete Distributions (pg. 264)  
7.6 Discrete Probability Density Functions (pg. 287)  
7.7 Generating Random Samples (pg. 301)  
7.8 Applications to Finance (pg. 307)  
8 Fundamental Probability Theorems (pg. 347)  
8.1 Uniqueness of the m.g.f. and c.f. (pg. 347)  
8.2 Chebyshev’s Inequality (pg. 349)  
8.3 Weak Law of Large Numbers (pg. 352)  
8.4 Strong Law of Large Numbers (pg. 357)  
8.5 De Moivre–Laplace Theorem (pg. 368)  
8.6 The Normal Distribution (pg. 377)  
8.7 The Central Limit Theorem (pg. 381)  
8.8 Applications to Finance (pg. 386)  
9 Calculus I: Differentiation (pg. 417)  
9.1 Approximating Smooth Functions (pg. 417)  
9.2 Functions and Continuity (pg. 418)  
9.3 Derivatives and Taylor Series (pg. 450)  
9.4 Convergence of a Sequence of Derivatives (pg. 478)  
9.5 Critical Point Analysis (pg. 488)  
9.6 Concave and Convex Functions (pg. 494)  
9.7 Approximating Derivatives (pg. 504)  
9.8 Applications to Finance (pg. 505)  
10 Calculus II: Integration (pg. 559)  
10.1 Summing Smooth Functions (pg. 559)  
10.2 Riemann Integration of Functions (pg. 560)  
10.3 Examples of the Riemann Integral (pg. 574)  
10.4 Mean Value Theorem for Integrals (pg. 579)  
10.5 Integrals and Derivatives (pg. 581)  
10.6 Improper Integrals (pg. 587)  
10.7 Formulaic Integration Tricks (pg. 592)  
10.8 Taylor Series with Integral Remainder (pg. 598)  
10.9 Convergence of a Sequence of Integrals (pg. 602)  
10.10 Numerical Integration (pg. 609)  
10.11 Continuous Probability Theory (pg. 613)  
10.12 Applications to Finance (pg. 641)  
References (pg. 685)  
Index (pg. 689) 
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