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.
Fluvial processesIn geography and geology, fluvial processes are associated with rivers and streams and the deposits and landforms created by them. When the stream or rivers are associated with glaciers, ice sheets, or ice caps, the term glaciofluvial or fluvioglacial is used. Fluvial processes include the motion of sediment and erosion or deposition on the river bed. The movement of water across the stream bed exerts a shear stress directly onto the bed.
ValleyA valley is an elongated low area often running between hills or mountains, which will typically contain a river or stream running from one end to the other. Most valleys are formed by erosion of the land surface by rivers or streams over a very long period. Some valleys are formed through erosion by glacial ice. These glaciers may remain present in valleys in high mountains or polar areas. At lower latitudes and altitudes, these glacially formed valleys may have been created or enlarged during ice ages but now are ice-free and occupied by streams or rivers.
Floridan aquiferThe Floridan aquifer system, composed of the Upper and Lower Floridan aquifers, is a sequence of Paleogene carbonate rock which spans an area of about in the southeastern United States. It underlies the entire state of Florida and parts of Alabama, Georgia, Mississippi, and South Carolina. The Floridan aquifer system is one of the world's most productive aquifers and supplies drinking water for nearly 10 million people.
OverdraftingOverdrafting is the process of extracting groundwater beyond the equilibrium yield of an aquifer. Groundwater is one of the largest sources of fresh water and is found underground. The primary cause of groundwater depletion is the excessive pumping of groundwater up from underground aquifers. There are two sets of yields: safe yield and sustainable yield. Safe yield is the amount of groundwater that can be withdrawn over a period of time without exceeding the long-term recharge rate or affecting the aquifer integrity.
SedimentSediment is a naturally occurring material that is broken down by processes of weathering and erosion, and is subsequently transported by the action of wind, water, or ice or by the force of gravity acting on the particles. For example, sand and silt can be carried in suspension in river water and on reaching the sea bed deposited by sedimentation; if buried, they may eventually become sandstone and siltstone (sedimentary rocks) through lithification.
Mathematical economicsMathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity.
Mathematical psychologyMathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior (in practice often constituted by task performance). The mathematical approach is used with the goal of deriving hypotheses that are more exact and thus yield stricter empirical validations.
Sensitivity analysisSensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be divided and allocated to different sources of uncertainty in its inputs. A related practice is uncertainty analysis, which has a greater focus on uncertainty quantification and propagation of uncertainty; ideally, uncertainty and sensitivity analysis should be run in tandem.
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.
