Mathematical logicMathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.
Mathematical modelling of infectious diseasesMathematical models can project how infectious diseases progress to show the likely outcome of an epidemic (including in plants) and help inform public health and plant health interventions. Models use basic assumptions or collected statistics along with mathematics to find parameters for various infectious diseases and use those parameters to calculate the effects of different interventions, like mass vaccination programs. The modelling can help decide which intervention(s) to avoid and which to trial, or can predict future growth patterns, etc.
Project Orion (nuclear propulsion)Project Orion was a study conducted in the 1950s and 1960s by the United States Air Force, DARPA, and NASA into the viability of a nuclear pulse spaceship that would be directly propelled by a series of atomic explosions behind the craft. Early versions of the vehicle were proposed to take off from the ground; later versions were presented for use only in space. The design effort took place at General Atomics in San Diego, and supporters included Wernher von Braun, who issued a white paper advocating the idea.
Computer simulationComputer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict. Computer simulations have become a useful tool for the mathematical modeling of many natural systems in physics (computational physics), astrophysics, climatology, chemistry, biology and manufacturing, as well as human systems in economics, psychology, social science, health care and engineering.
Mathematical and theoretical biologyMathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to prove and validate the scientific theories. The field is sometimes called mathematical biology or biomathematics to stress the mathematical side, or theoretical biology to stress the biological side.
SimulationA simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of models; the model represents the key characteristics or behaviors of the selected system or process, whereas the simulation represents the evolution of the model over time. Often, computers are used to execute the simulation. Simulation is used in many contexts, such as simulation of technology for performance tuning or optimizing, safety engineering, testing, training, education, and video games.
Fusion rocketA fusion rocket is a theoretical design for a rocket driven by fusion propulsion that could provide efficient and sustained acceleration in space without the need to carry a large fuel supply. The design requires fusion power technology beyond current capabilities, and much larger and more complex rockets. Fusion nuclear pulse propulsion is one approach to using nuclear fusion energy to provide propulsion. Fusion's main advantage is its very high specific impulse, while its main disadvantage is the (likely) large mass of the reactor.
EchinodermAn echinoderm (ᵻˈkaɪnəˌdɜrm,_ˈɛkə-) is any member of the phylum Echinodermata (ᵻˌkaɪnoʊˈdɜrmətə). The adults are recognisable by their (usually five-point) radial symmetry, and include starfish, brittle stars, sea urchins, sand dollars, and sea cucumbers, as well as the sea lilies or "stone lilies". Adult echinoderms are found on the sea bed at every ocean depth, from the intertidal zone to the abyssal zone. The phylum contains about 7,000 living species, making it the second-largest grouping of deuterostomes, after the chordates.
Ion thrusterAn ion thruster, ion drive, or ion engine is a form of electric propulsion used for spacecraft propulsion. It creates thrust by accelerating ions using electricity. An ion thruster ionizes a neutral gas by extracting some electrons out of atoms, creating a cloud of positive ions. Ion thrusters are categorized as either electrostatic or electromagnetic. Electrostatic thruster ions are accelerated by the Coulomb force along the electric field direction.
Mathematical financeMathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio management on the other. Mathematical finance overlaps heavily with the fields of computational finance and financial engineering.
