# Articles — Math

Articles tagged Math

Show all Articles FSU-MATH2400-Project4
This project introduces the idea of recursive sequences. Students then prove that a given recursive sequence converges and find its limit. The final portion of the project is a derivation and investigation of the Fibonacci Sequence and the Golden Ratio.
Sarah Wright MOOC Dropout Prediction with Model Stacking
We are asked to predict the probability of the event that a student will drop out a course. We firstly extracted many features from the huge dataset. Then we used ensemble learning machine and model stacking technique to get the final result, which ranked the 1st in 68 teams.
Qi Zhao Charge to Mass Ratio of the Electron
For an electron moving in a circular path in a magnetic field, if we know the magnetic field strength, accelerating voltage, and radius of the electron's trajectory, then we can make an estimation of the electron's charge to mass ratio. We calculated an average charge to mass ratio of $$2.08 \times 10^{11} \pm 1.81 \times 10^8$$ Coulombs per kilogram.
Jake Rugh SOLAR SALES ON YOUR TRIP TO MARS
We study Logarithmically Spiral Trajectories and, in particular, we look for a solution to minimize the transit time of a Spacecraft propelled by a Solar Sail, while simultaneously minimizing the area of the Solar Sail, which would allow us to carry more payload on board. We start by analyzing the forces that act on the Spacecraft taking into account that its propellant is a Solar Sail; we use the studied forces to deduce the motion equations. We then solve this motion equation with a Runge-Kutta 4 method and transform the problem of minimizing time and area to a Non-linear Optimization problem. When solving the NLP we also try to minimize the relative final speed of th spacecraft with the destination planet in order to guarantee the possibility of a safe landing on its surface. The model improves when an angle parameter α (describing the angle formed by the Solar Sail with the colliding photons) is defined as a piecewise constant function and optimized whose values are optimized in every interval to minimize transit time and Area. Using the developed model to optimize the trajectory to be followed for sending from Earth to Mars a 2000kg-spacecraft propelled by a Solar Sail, subject to the condition that at trajectory start Mars and Earth were at their closest approach, and the Arrival Relative Velocity is less than 9km/s, give us a minimal transit time of 500days and a minimal area for the Solar Sail of 183158m2, meaning that the maximal payload would be 718kg. Compared with different number of partitions of α, the optimum stays stable. This gives a solid optimal trajectory and a great result for the numerical method used. Actually, waiting until the best moment to throw the Spacecraft, id est, Mars is at 1.14 radians respectively to Earth initial position, the minimal sail area 145950 m2 and, therefore, ables to transport until 978 kg of payload with the same transit time. In addition and to conclude we tried the model to optimize the inverse trajectory.
Marco Praderio Bova, Eneko Martin Martinez, & Maria dels Àngels Guinovart Llort FSU-MATH2400-Project2
This is a project for Calculus 2 students at Fitchburg State University. This project walks students through two examples of using definite integrals to determine the volume of objects: a bundt cake serves as the solid of revolution and the students build a structure from play dough that is not a solid of revolution.
Sarah Wright