Source : Webster's Revised Unabridged Dictionary (1913)

Analysis \A*nal"y*sis\, n.; pl. {Analyses}. [Gr. ?, fr. ? to
   unloose, to dissolve, to resolve into its elements; ? up + ?
   to loose. See {Loose}.]
   1. A resolution of anything, whether an object of the senses
      or of the intellect, into its constituent or original
      elements; an examination of the component parts of a
      subject, each separately, as the words which compose a
      sentence, the tones of a tune, or the simple propositions
      which enter into an argument. It is opposed to
      {synthesis}.

   2. (Chem.) The separation of a compound substance, by
      chemical processes, into its constituents, with a view to
      ascertain either (a) what elements it contains, or (b) how
      much of each element is present. The former is called
      {qualitative}, and the latter {quantitative analysis}.

   3. (Logic) The tracing of things to their source, and the
      resolving of knowledge into its original principles.

   4. (Math.) The resolving of problems by reducing the
      conditions that are in them to equations.

   5.
      (a) A syllabus, or table of the principal heads of a
          discourse, disposed in their natural order.
      (b) A brief, methodical illustration of the principles of
          a science. In this sense it is nearly synonymous with
          synopsis.

   6. (Nat. Hist.) The process of ascertaining the name of a
      species, or its place in a system of classification, by
      means of an analytical table or key.

   {Ultimate}, {Proximate}, {Qualitative}, {Quantitative}, and
   {Volumetric analysis}. (Chem.) See under {Ultimate},
      {Proximate}, {Qualitative}, etc.

Mathematics \Math`e*mat"ics\, n. [F. math['e]matiques, pl., L.
   mathematica, sing., Gr. ? (sc. ?) science. See {Mathematic},
   and {-ics}.]
   That science, or class of sciences, which treats of the exact
   relations existing between quantities or magnitudes, and of
   the methods by which, in accordance with these relations,
   quantities sought are deducible from other quantities known
   or supposed; the science of spatial and quantitative
   relations.

   Note: Mathematics embraces three departments, namely: 1.
         {Arithmetic}. 2. {Geometry}, including {Trigonometry}
         and {Conic Sections}. 3. {Analysis}, in which letters
         are used, including {Algebra}, {Analytical Geometry},
         and {Calculus}. Each of these divisions is divided into
         pure or abstract, which considers magnitude or quantity
         abstractly, without relation to matter; and mixed or
         applied, which treats of magnitude as subsisting in
         material bodies, and is consequently interwoven with
         physical considerations.

Source : WordNet®

analysis
     n 1: an investigation of the component parts of a whole and their
          relations in making up the whole
     2: the abstract separation of a whole into its constituent
        parts in order to study the parts and their relations
        [syn: {analytic thinking}] [ant: {synthesis}]
     3: a form of literary criticism in which the structure of a
        piece of writing is analyzed
     4: the use of closed-class words instead of inflections: e.g.,
        `the father of the bride' instead of `the bride's father'
     5: a branch of mathematics involving calculus and the theory of
        limits; sequences and series and integration and
        differentiation
     6: a set of techniques for exploring underlying motives and a
        method of treating various mental disorders; based on the
        theories of Sigmund Freud; "his physician recommended
        psychoanalysis" [syn: {psychoanalysis}, {depth psychology}]
     [also: {analyses} (pl)]