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Finance Mathematicsis devoted to financial markets both with discrete and continuous time, exploring how to make the transition from discrete to continuous time in option pricing. This book features a detailed dynamic model of financial markets with discrete time, for application in real-world environments, along with Martingale measures and martingale criterion and the proven absence of arbitrage.With a focus on portfolio optimization, fair pricing, investment risk, and self-finance, the authors provide numerical methods for solutions and practical financial models, enabling you to solve problems both from mathematical and from financial point of view.Calculations of Lower and upper prices, featuring practical examplesThe simplest functional limit theorem proved for transition from discrete to continuous timeLearn how to optimize portfolio in the presence of risk factors Yuliya Mishura is the Head of the Department of Probability, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko Kyiv National University, Professor. Key qualifications: : Stochastic analysis, theory of stochastic processes, stochastic differential equations, numerical schemes, financial mathematics, risk processes, statistics of stochastic processes, models with long-range dependence. Member of Actuarial Society of Ukraine, of American Mathematical Society, of European Mathematical Society and of International Statistical Institute, the Head of Technical Committee of Standardization TC-70 'Application of Statistical Methods".

It is very difficult to motivate students when it comes to a school subject like Mathematics. Teachers spend a lot of time trying to find something that will arouse interest in students. It is particularly difficult to find materials that are motivating enough for students that they eagerly wait for the next lesson. One of the solutions may be found in Vedic Mathematics. Traditional methods of teaching Mathematics create fear of this otherwise interesting subject in the majority of students. Fear increases failure. Often the traditional, conventional mathematical methods consist of very long lessons which are difficult to understand. Vedic Mathematics is an ancient system that is very flexible and encourages the development of intuition and innovation. It is a mental calculating tool that does not require a calculator because the calculator is embedded in each of us. Starting from the above problems of fear and failure in Mathematics, the goal of this paper is to do research with the control and the experimental group and to compare the test results. Two tests should be done for each of the groups. The control group would do the tests in the conventional way. The experimental group would do the first test in a conventional manner and then be subjected to different treatment, that is to say, be taught on the basis of Vedic Mathematics. After that, the second group would do the second test according to the principles of Vedic Mathematics. Expectations are that after short lectures on Vedic mathematics results of the experimental group would improve and that students will show greater interest in Mathematics.

Citation: Gardiner, Mary Maud. Nature's mathematics. Senior thesis, Kansas State Agricultural College, 1893. ; Morse Department of Special Collections ; Introduction: We generally think of nature as being free from all mathematical exactness and regular arrangement – that nature never places herself in straight lines and exact angles. We feel that she is free from square and circles and of all things suggestive of mathematical government; that she is careless and easy and restricted to no such stiff ways as those of man, but picturesque in her irregularity, and purposeless in the promiscuous scattering of her elements over land and sea and sky. Such is the impression of the casual observer. But when we come to study nature more carefully, we find that it is not a miscellaneous collection of things without definite laws or regulations. We find these elements in circles, pentagons, ellipses and other geometrical forms.

One can identify at least three different types of relationships between mathematics and crises. First, mathematics can picture a crisis. This is in accordance with the classic interpretation of mathematical modelling, which highlights that a mathematical model provides a representation of a piece of reality, a reality that could be a critical situation such as, for instance, a pandemic. Second, mathematics can constitute a crisis, meaning that mathematics can form an intrinsic part of the very dynamics of a crisis. This phenomenon can be illustrated by the economic crises that spread around the world in 2008. Third, mathematics can format a crisis. This final formulation refers to a situation where a mathematical reading of a crisis brings about ways of acting in the critical situation that might be adequate, but also counterproductive, if not catastrophic. This is illustrated with reference to the potential crises due to climate changes. As a conclusion, the paper addresses the politics of crises, which refers to the power that can be acted out through a crisis discourse in which mathematics may come to play a deplorable role.