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Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions).
Alexandrov's uniqueness theorem (discrete geometry) Alperin–Brauer–Gorenstein theorem (finite groups) Alspach's theorem (graph theory) Amitsur–Levitzki theorem (linear algebra) Analyst's traveling salesman theorem (discrete mathematics) Analytic Fredholm theorem (functional analysis) Anderson's theorem (real analysis)
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic [1] – do not vary smoothly in this way, but have distinct, separated values. [2]
Download as PDF; Printable version; In other projects ... Theorems in discrete geometry ... (1 C, 54 P) Pages in category "Theorems in discrete mathematics"
The mass of an object of known density that varies incrementally, the moment of inertia of such objects, as well as the total energy of an object within a discrete conservative field can be found by the use of discrete calculus. An example of the use of discrete calculus in mechanics is Newton's second law of motion: historically stated it ...
Discrete optimization is a branch of optimization in applied mathematics and computer science. As opposed to continuous optimization , some or all of the variables used in a discrete optimization problem are restricted to be discrete variables —that is, to assume only a discrete set of values, such as the integers .
From the example above, one solution is k = 4, but it is not the only solution. Since 3 16 ≡ 1 (mod 17)—as follows from Fermat's little theorem—it also follows that if n is an integer then 3 4+16n ≡ 3 4 × (3 16) n ≡ 13 × 1 n ≡ 13 (mod 17). Hence the equation has infinitely many solutions of the form 4 + 16n.
A discrete subgroup H of G is cocompact if there is a compact subset K of G such that HK = G. Discrete normal subgroups play an important role in the theory of covering groups and locally isomorphic groups. A discrete normal subgroup of a connected group G necessarily lies in the center of G and is therefore abelian. Other properties: