Mathematica Day at the
University of Warsaw

9 December 2017


Schedule

Please note that all talks will be given in Polish.

Conference, December 9, 2017

  • 8:30

    Registration

  • 9:00
    Opening Words

    Piotr Wendykier, Consultant, Wolfram Research and

    Zbigniew Galon, Chairman of the Board, Gambit

  • 9:30
    Mathematica and the Pricing of Financial Options

    The pricing of financial options is one of the most important and difficult problems in mathematical finance. Mathematica has a large number of sophisticated functions for modeling the movements of stock prices (including a function that can obtain financial data from the internet), for computing the prices of a variety of options in the classic Black–Scholes model and for simulating a variety of discontinuous stochastic processes that can provide more accurate answers than the ones given by the Black–Scholes model. We will illustrate several topics in this area. This talk should be of interest to all students interested in mathematical finance, both undergraduate and research level, and also to anyone interested in options or other financial derivatives.

    Andrzej Kozłowski

    Senior Lecturer, University of Warsaw

  • 10:30
    Mathematica and Neuroscience: An Application of the Mathematica Software to Simulate the Activity of Biologically Realistic Neural Networks

    Neuroscience, in recent years, has become one of the most intensively explored fields in science. It is hard to be surprised—both the new measurement techniques of brain activity and the ever-increasing computing resources give us the hope that in the coming years, we will understand much better the relation of the brain's biophysics and the human mind. The question of this mind-body relationship, as it is known, has ignited the minds of philosophers and scientists for many centuries. It turns out that the Wolfram Language and the Mathematica environment can be successfully used in simulations of biologically realistic neural networks. During the lecture, both basic, didactic procedures to simulate the activity of nerve cells and results of advanced neuronal research, performed in large part in the Mathematica environment, will be presented.

    Franciszek Rakowski

    Assistant Professor, Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw

  • 11:00
    Neural Networks in the Wolfram Language

    This talk will give a high-level overview of the neural network framework in the Wolfram Language. I will demonstrate application examples in the fields of image and audio processing and describe the Neural Net Repository—a public resource hosting a collection of neural network models.

    Piotr Wendykier

    Consultant, Wolfram Research

  • 11:30

    Lunch

  • 12:30
    Application of the System Mathematica in the Study of the Circular Restricted Four-Body Problem

    In the present talk, we demonstrate the application of Mathematica in the study of the circular restricted four-body problem. Recall that three massive particles P0, P1, P2 move in the plane on circular orbits around their common center of mass and form a central configuration at any instant of time. This configuration corresponds either to the Lagrange triangle or to the Euler collinear solution to the three-body problem. Differential equations determining the motion of the particle P3 of negligible mass in the gravitational field of the particles P0, P1, P2 are nonlinear, and their general solution cannot be found in symbolic form. So we look for the exact particular solutions, such as the relative equilibria, and investigate their stability on the basis of the KAM theory. Realization of this task includes several steps—namely, derivation of the equations of motion, search for the relative equilibrium positions of the particle P3 for different values of the system parameters, normalization of the Hamiltonian function in the neighborhood of each equilibrium solution and application of theorems of the KAM theory to conclude on stability or instability of the equilibrium positions. Here we discuss the most important and useful algorithms for solving such problems and demonstrate the results obtained with the aid of the computer algebra system Mathematica.

    Alexander Prokopenya

    Professor, Warsaw University of Live Sciences

  • 13:00
    Mathematica in Teaching: Green's and Stokes's Theorems

    In this talk, I shall explain how Mathematica can be used to explain Green's and Stokes's theorems. Stokes's theorem is one of the fundamental theorems of vector analysis relating line integrals and surface integrals of vector fields. Stokes's theorem is also known as the Kelvin–Stokes theorem or the curl theorem. It was discovered around 1850. Stokes's theorem is based on Green's theorem, relating line integrals to double integrals over the region. The talk will be useful to students and lecturers.

    Galina Filipuk

    Assistant Professor, University of Warsaw

  • 13:30
    Modeling Cochlea—A System with Localized Resonances

    A cochlea has the remarkable property of vibrating at a specific location depending on frequency. Using the numerical and analytical capabilities of Mathematica, a mechanical cochlea model was created having localized, frequency-dependent eigenmodes. Its analysis leads to a new class of wave equations.

    Ernest Aleksy Bartnik

    Professor, University of Warsaw

  • 14:00
    Illustrating Topology with Mathematica

    We demonstrate how the combination of Mathematica's graphic, analytic and algebraic capabilities can be used to introduce students to advanced concepts from differential and algebraic topology. Our illustration will be the Morse–Smale–Witten theory on the torus and other closed surfaces. In particular, we will show how to compute the Euler characteristic of a closed smooth hypersurface in 3D given by a complicated algebraic equation.

    Andrzej Kozłowski

    Senior Lecturer, University of Warsaw

  • 14:30

    Coffee break

  • 15:00
    C++ Integration into the Wolfram Language

    The Wolfram Language is a very powerful tool that allows you to perform sophisticated computations with just one line of code. Sometimes, to optimize the efficiency of your application, you may want to control it at a lower level, closer to the machine code—for example, by writing it in C or C++. With help from LibraryLink, it is possible to combine the best of both worlds and use C/C++ library functions directly from the Wolfram Language. In my talk, I will guide you through that process.

    Rafał Chojna

    Consultant, Wolfram Research

  • 15:30
    UX 101: Building User-Friendly Interfaces with the Wolfram Language

    If you are planning to create an application, big or small, you'll need to design a user interface. This introduction to user experience design will help you avoid common mistakes. You will learn about general guidelines you can follow while building a user-friendly interface. We will also see real-life examples we can learn from, because UX design is not about bells and whistles but about helping users achieve their goals. We will focus on interfaces that can be built with the Wolfram Language, but key principles of user-centered approach apply to any technology.

    Paweł Mucha

    Consultant, Wolfram Research

  • 16:00
    My Impressions after a Summer Internship at Wolfram Research

    This year, I did a summer internship at Wolfram Research. I will tell you what my work looked like and what my responsibilities were. My task was to improve RAWTools—a Mathematica paclet for extracting data from RAW files (i.e. unprocessed by a camera). I am going to show which tools were useful for implementing it.

    Konrad Majewski

    Student, University of Warsaw

  • 16:30
    Closing Words

    Rafał Chojna

    Consultant, Wolfram Research

In Association With
GAMBIT, Software and Training Center Ltd. Faculty of Mathematics, Informatics and Mechanics, University of Warsaw