The Collaborative International Dictionary of English v.0.48:

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.
   [1913 Webster]

   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.
         [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

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.
      [1913 Webster]

   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.
      [1913 Webster]

   3. (Logic) The tracing of things to their source, and the
      resolving of knowledge into its original principles.
      [1913 Webster]

   4. (Math.) The resolving of problems by reducing the
      conditions that are in them to equations.
      [1913 Webster]

   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.
          [1913 Webster]

   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.
      [1913 Webster]

   Ultimate, Proximate, Qualitative, Quantitative, and
   Volumetric analysis. (Chem.) See under Ultimate,
      Proximate, Qualitative, etc.
      [1913 Webster]

WordNet (r) 3.0 (2006):

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:
       analysis, analytic thinking] [ant: synthesis,
       synthetic thinking]
    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, analysis, depth
       psychology]

Moby Thesaurus II by Grady Ward, 1.0:

240 Moby Thesaurus words for "analysis":
   Baconian method, Boolean algebra, Euclidean geometry,
   Fourier analysis, Lagrangian function, a fortiori reasoning,
   a posteriori reasoning, a priori reasoning, abstraction,
   accounting, airing, algebra, algebraic geometry, alteration,
   analytic geometry, anatomization, anatomy, arithmetic, arrangement,
   assay, associative algebra, atomization, audit,
   automatic electronic navigation, binary arithmetic, braking,
   breakdown, breakup, buzz session, calculus, canvassing, cataloging,
   categorization, change, checkup, circle geometry,
   circumstantiation, classification, codification, colloquium,
   comment, commentary, commentation, computation, conference,
   consideration, coordination, critical review, criticism, critique,
   debate, debating, decomposition, deduction, deductive reasoning,
   deliberation, demarcation, depth interview, depth psychology,
   descriptive geometry, desynonymization, diaeresis, dialectic,
   dialogue, differencing, differential calculus, differentiation,
   discrimination, discussion, disequalization, disintegration,
   disjunction, dissection, distinction, distinguishment,
   diversification, division, division algebra, doctrinairism,
   doctrinality, doctrinarity, dream analysis, dream symbolism,
   editorial, enquiry, epagoge, equivalent algebras, examination,
   exchange of views, explanation, fact distribution, filing,
   forecasts, forum, game theory, generalization, geodesy, geometry,
   gloss, grading, graphic algebra, group analysis, group theory,
   grouping, higher algebra, higher arithmetic, hyperbolic geometry,
   hypothesis and verification, indexing, individualization,
   individuation, induction, inductive reasoning, inference,
   infinitesimal calculus, inquest, inquirendo, inquiring,
   inquiring mind, inquiry, inquisition, inspection,
   integral calculus, interpretation, interpretation of dreams,
   intuitional geometry, invariant subalgebra, inverse geometry,
   investigation, itemization, joint discussion, judgement, leader,
   leading article, line geometry, linear algebra, logical analysis,
   logical discussion, manipulation, mathematical physics,
   matrix algebra, mere theory, metageometry, modification,
   modular arithmetic, n-tuple linear algebra, natural geometry,
   nilpotent algebra, nonlinear calibrations, notice, number theory,
   open discussion, open forum, opinion, output measurement,
   panel discussion, particularization, perlustration,
   personalization, philosophical induction, pigeonholing, placement,
   plane trigonometry, political arithmetic, processing,
   projective geometry, proper subalgebra, psychanalysis,
   psychoanalysis, psychoanalytic method, psychoanalytic therapy,
   psychognosis, psychognosy, psychology of depths,
   quaternian algebra, ranging, ranking, rap, rap session, rating,
   record keeping, reducible algebra, remark, report, resolution,
   review, running commentary, scan, scrutiny, segregation, seminar,
   separation, set theory, severalization, severance, simple algebra,
   solid geometry, sorting, specialization, specification,
   speculation, speculative geometry, spherical trigonometry,
   statistics, steering, stratification, study, subalgebra,
   subdivision, supersonic flow detection, survey, syllogism,
   syllogistic reasoning, symposium, synthesis, systems analysis,
   tabulation, taxonomy, the couch, theoretic, theoretical basis,
   theoretics, theoria, theoric, theorization, theory, topology,
   town meeting, treatment, trig, trigonometry, typology,
   universal algebra, universal geometry, variation, vector algebra,
   ventilation, view, write-up, zero algebra