By Steven G. Krantz

Transparent, rigorous definitions of mathematical phrases are the most important to sturdy clinical and technical writing-and to knowing the writings of others. Scientists, engineers, mathematicians, economists, technical writers, machine programmers, in addition to academics, professors, and scholars, all have the necessity for understandable, operating definitions of mathematical expressions. to satisfy that want, CRC Press proudly introduces its Dictionary of Algebra, mathematics, and Trigonometry- the second one released quantity within the CRC finished Dictionary of arithmetic. greater than 3 years in improvement, best lecturers and execs from prestigious associations worldwide carry you greater than 2,800 particular definitions, written in a transparent, readable variety, entire with substitute meanings, and similar references.From Abelian cohomology to 0 ring and from the very easy to the hugely complex, this exact lexicon comprises phrases linked to mathematics, algebra, and trigonometry, with traditional overlap into geometry, topology, and different similar areas.Accessible but rigorous, concise yet entire, the Dictionary of Algebra, mathematics, and Trigonometry is your key to accuracy in writing or figuring out clinical, engineering, and mathematical literature.

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**Extra info for Dictionary of Algebra, Arithmetic, and Trigonometry **

**Sample text**

Then M is also connected and G is homeomorphic to the direct product of M with a Euclidean space Rn . Cartan-Weyl Theorem A theorem that assists in the characterization of irreducible representations of complex semisimple Lie algebras. Let G be a complex semisimple Lie algebra, H a Cartan subalgebra, the root system of G relative to H, α = σ ∈ rσ σ , rσ ∈ R, a complexvalued linear functional on H, and ρ : G → GLn (C) a representation of G. The functional α is a weight of the representation if the space of vectors v ∈ Cn that satisfy ρ(h)v = α(h)v for all h ∈ H is nontrivial; Cn decomposes as a direct sum of such spaces associated with weights α1 , .

See complex number. (2) A set of elements from a group (not necessarily forming a group in their own right). (3) A sequence of modules {C i : i ∈ Z}, together with, for each i, a module homomorphism δ i : C i → C i+1 such that δ i−1 ◦ δ i = 0. Diagramatically, we have δ i−2 δ i−1 δi δ i+1 . . −→ C i−1 −→ C i −→ C i+1 −→ . . where the composition of any two successive δ j is zero. complex algebraic variety riety. , the study of geometric shapes through the use of coordinate systems, but within a complex vector space rather than the more usual real vector space so that the coordinates are complex numbers rather than real numbers.

By the First Isomorphism Theorem, the coimage of φ is isomorphic to the image of φ, as a consequence of which the term coimage is not often used. cokernel Let φ : M → N be a homomorphism between two modules M and N . Then the factor module N/ im φ (where im φ denotes the image of φ) is called the cokernel of φ, denoted coker φ. collecting terms The name given to the process of rearranging an expression so as to combine or group together terms of a similar nature. For example, if we rewrite x 2 + 2x + 1 + 3x 2 + 5x as 4x 2 + 7x + 1 we have collected together the x 2 terms and the x terms; if we rewrite x 2 +y 2 +2x−2y as x 2 + 2x + y 2 − 2y we have collected together all the terms involving x, and all the terms involving y.