Numeral notation specifies how a number is written, including its digit alphabet, base and separators. The same integer can appear as decimal $13$, binary $1101_2$ or hexadecimal ${\mathrm{D}}_{16}$. A base marker distinguishes the written numeral from an otherwise identical string in another numeral system.

This differs from expression notation, which also describes operations on represented numbers. For example 0x10 names one integer in a programming convention, while $2^4$ gives an expression evaluating to that same integer. Keeping representation separate from value is important in algorithms involving digit constraints or input length.

Order theory studies binary relations describing precedence or comparison. A partial order is reflexive, antisymmetric and transitive; a total order additionally compares every pair. A partially ordered set records a set together with its chosen order.

Set inclusion gives a partial order on the subsets of $\{1,2\}$. The subsets $\{1\}$ and $\{2\}$ are incomparable, while their least upper bound is their union. The usual order on the real numbers is total. Distinguishing a maximum from a merely maximal element is useful whenever incomparable alternatives occur, including dependencies, divisibility and optimization.

Nanotechnology studies and controls matter whose important dimensions are on the nanoscale, conventionally about $1$–$100$ nanometres. A nanometre is $10^{-9}$ metres. The scientific interest comes from changes in behaviour at these dimensions, including the increasing role of surfaces and, in suitable systems, quantum confinement.^[ref]

For example, subdividing a fixed volume into smaller nanoparticles increases the exposed surface area, changing how much material can participate in a surface reaction. Nanostructures can also alter electrical conductivity, interaction with light and mechanical properties by controlling geometry rather than changing only chemical chemical composition. Useful nanotechnology therefore combines fabrication with measurements of structure and properties, such as electron microscopy or atomic force microscopy.^[ref]

A microelectromechanical system combines small mechanical structures with electrical sensing or actuation. Fabrication methods related to semiconductor device fabrication can create suspended beams, membranes and movable masses together with their electrodes. Sensors and actuators can consequently be integrated into compact devices.

A capacitive accelerometer illustrates the mechanism. A suspended proof mass moves relative to its support under acceleration. In a simple spring model, a slowly varying support acceleration $a$ produces a relative displacement $x\approx -ma/k$, where $m$ is the mass and $k$ is the spring constant. Measuring a change of capacitance then measures that displacement. The ADXL335 uses suspended polysilicon structures and a differential capacitor to turn motion into an electrical signal.^[ref]

For an idealized pair of parallel-plate capacitors with equal area $A$ and gaps $g\mp x$, the capacitance difference isThis model explains why a small mechanical displacement can produce a signed electrical measurement; it is not a detailed model of every commercial MEMS geometry.

A fluid used to carry heat away from a system.

Nuclear engineering designs and studies systems that use nuclear reactions or manage materials with radioactivity. Its subjects include nuclear reactors, radiation detection, radiation shielding, nuclear fuel, the behaviour of structural materials under irradiation, and radioactive waste management.

A nuclear power plant shows why several areas of engineering must work together. Nuclear fission releases energy; a coolant transports the resulting heat; a heat engine converts part of that heat to mechanical work; an electrical generator produces electrical energy. In a pressurized water reactor, a heat exchanger transfers heat from the pressurized reactor coolant to a separate circuit that produces steam. Thus neutron physics, heat transfer, fluid mechanics and materials science constrain the same design.^[ref]

Manufacturer of scientific instruments, including atomic force microscopes.

A sensor converts a physical quantity into an observable signal. A temperature sensor might produce a voltage or resistance change that a measuring system converts into a temperature estimate. A useful model separates sensitivity, offset, noise, calibration and dynamic response: a large output change does not guarantee accuracy if the calibration drifts. Sensors also load the system they measure, for example by drawing heat or electrical current. The complete measurement chain includes the sensor, readout electronics and the model mapping the signal back to the intended quantity.

Official website: www.analog.com

Detection and inference about remote objects using transmitted radio waves and their returned electromagnetic radiation. A received signal depends on propagation, directional antenna gain, target scattering and receiver sensitivity.

Competitive programming asks participants to design and implement algorithms for specified computational problems, usually with constraints on time complexity and space complexity. A successful solution combines a correctness argument with an implementation that fits the available resources.

Organic chemistry studies carbon-based molecular structures and their transformations, with emphasis on connectivity, functional groups, and stereochemistry. Carbon's ability to form chains, rings, and multiple bonds supports a very large range of molecular architectures.

A reaction can change one functional group while preserving the rest of a framework, or form a new carbon-carbon bond that enlarges it. Following electron movement and testing competing mechanisms makes these transformations predictable rather than a catalogue of isolated recipes.

Coordination chemistry studies coordination complexes, including their ligands in coordination chemistry, structures and reactions.

Isomers have the same molecular formula but different arrangements of their atoms. Constitutional isomers differ in connectivity; stereoisomers retain connectivity but differ in spatial arrangement.

For example, ethanol and dimethyl ether share ${\mathrm{C}}_2{\mathrm{H}}_6\mathrm{O}$ but connect their atoms differently. Two enantiomers instead have mirror-related spatial structures. Formula, connectivity, and stereochemistry therefore encode different levels of chemical identity.