| Foreword | 5 |
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| Acknowledgements | 11 |
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| Contents | 13 |
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| Part I Foundations | 21 |
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| The strength of nonstandard analysis | 22 |
| The virtue of simplicity | 46 |
| Analysis of various practices of referring in classical or non standard mathematics | 52 |
| Stratified analysis? | 66 |
| ERNA at work | 83 |
| The Sousa Pinto approach to nonstandard generahsed functions | 95 |
| Neutrices in more dimensions | 111 |
| Part II Number theory | 136 |
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| Nonstandard methods for additive and combinatorial number theory. A survey | 137 |
| Nonstandard methods and the Erdos- Turan conjecture | 151 |
| Part III Statistics, probability and measures | 161 |
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| Nonstandard likelihood ratio test in exponential families | 162 |
| A finitary approach for the representation of the infinitesimal generator of a markovian semigroup | 187 |
| On two recent applications of nonstandard analysis to the theory of financial markets | 194 |
| Quantum Bernoulli experiments and quantum stochastic processes | 206 |
| Applications of rich measure spaces formed from nonstandard models | 223 |
| More on S- measures | 234 |
| A Radon- Nikodym theorem for a vector- valued reference measure | 244 |
| Differentiability of Loeb measures | 255 |
| Differential systems and equations | 267 |
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| The power of Gateaux differentiability | 268 |
| MO£WM^^(£L^M = ||,(,)_,(,)|| | 268 |
| 278 | 268 |
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| Nonstandard Palais- Smale conditions | 286 |
| Averaging for ordinary differential equations and functional differential equations | 301 |
| Path- space measure for stochastic differential equation with a coefficient of polynomial growth | 321 |
| Optimal control for Navier- Stokes equations | 332 |
| Local- in- time existence of strong solutions of the n- dimensional Burgers equation via discretizations | 364 |
| Infinitesimals and education | 382 |
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| Calculus with infinitesimals | 383 |
| Pre- University Analysis | 409 |
