Applied mathematics

thumb|alt=Lorenz cipher machine with twelve rotors mechanism|upright=1.5| Lorenz cipher machine, used in [[World War II to encrypt communications of the German High Command]] Cryptography, or cryptology, is the practice and study of techniques for secure communication in the presence of adversarial behavior. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, information security, electrical engin

thumb|upright=1.05|A modern instrument for geodetic measurements using satellites

discipline of mathematics

description of a system using mathematical concepts and language

thumb|One of the possible modes of Vibrations of a circular drum|vibration of a circular drum (see other modes) thumb|upright|Car suspension: Designing vibration control is undertaken as part of Acoustical engineering|acoustic, automotive or mechanical [[engineering.]]

alt=A set of number blocks. The blocks 1, 2, and 3 are in the foreground; six other blocks can be seen in the background|thumb|Number blocks, which can be used for counting Counting is the process of determining the number of elements of a finite set of objects; that is, determining the size of a set. The traditional way of counting consists of continually increasing a (mental or spoken) counter by a unit for every element of the set, in some order, while marking (or displacing) those elements to avoid visiting the same element more than once, until no unmarked elements are left; if the counte

thumb|upright=1.5|Reconstruction of the appearance of cyclometer, a device used to break the encryption of an early version of the [[Enigma machine. Based on sketches in Marian Rejewski's memoirs.]]

area of mathematics

field concerned with constructing mathematical models and quantitative analysis techniques and using computers to analyze and solve scientific problems

uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions

thumb|300px|Figure 1.  The green line represents an overfitted model and the black line represents a regularized model. While the green line best follows the training data, it is too dependent on that data and is likely to have a higher error rate on new unseen data, illustrated by black-outlined dots, compared to the black line. thumb|300x300px|Figure 2.  Noisy (roughly linear) data is fitted to a linear function and a polynomial function. Although the polynomial function is a perfect fit, the linear function can be expected to generalize better: If the two functions were used to ex

visible regularity of form found in the natural world

approach to psychological research that is based on mathematical modeling of perceptual, cognitive and motor processes

academic discipline

relationship between mathematics and art

right|thumb|A solution to a discretized partial differential equation, obtained with the finite element method.

interdiscplinary field of research

mathematical model describing the response of a brittle material to mechanical stresses and to define shear strength of soils and rocks

branch of applied mathematics

estimating the maximum of a discrete uniform distribution from sampling without replacement, historically from predicting German tank production based on ascending serial numbers in tanks lost in combat

American academic

framework to describe phase transitions

group of areas of study that includes, in addition to mathematics, those academic disciplines that are primarily mathematical in nature

distance from a point to the boundary of a set

analysis of datasets using techniques from topology

award

mathematics inspired by physics

problem of finding a point minimizing the sum of weighted distances from given (point, weight) pairs

Wikimedia disambiguation page

matrix used in finite element analysis

branch of applied mathematics

or Bass model, a mathematical marketing model

problem-solving technique in applied mathematics using order-of-magnitude approximations

subfield of topology with an overlap with areas of computer science

thumb|The sequence ATGG has two 3-mers: ATG and TGG. In bioinformatics, '''k-mers' are substrings of length k contained within a biological sequence. Primarily used within the context of computational genomics and sequence analysis, in which k-mers are composed of nucleotides (i.e. A, T, G, and C), k-mers are capitalized upon to assemble DNA sequences, improve heterologous gene expression, identify species in metagenomic samples, and create attenuated vaccines. Usually, the term k''-mer refers to all of a sequence's subsequences of length k, such that the sequence AGAT would have four monomers

frequency-domain analysis method

in thermal equilibrium, each phase of physical matter comes to an end at a transitional point, or spatial interface, called a phase boundary, due to the immiscibility of said matter with the matter on the other side of said boundary

formulation of classical mechanics in which one Legendre-transforms some, but not all, of generalized velocities into generalized momenta

organization

treatise by John Wilkins published 1648