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AM Mathematics AM3KV AM Mathematics Mathematics AM Common subdivisions AM2 AM2 . Common subdivisions . Logic AM2 GW * For mathematical forms of presentation, see AM3 4. * Add to AM2 numbers 2/9 from Auxiliary Schedule 1, AM2 L Agents with the adjustments indicated below. M . Machines in mathematics . By level of presentation * The general class for machine computation is under * Use these distinctions only if they are helpful to the Operations (AM7 H2M). Use this class only if needed library concerned. to qualify concepts appearing earlier in the schedule 3EM . Collegiate level than AM7 H or for completely general works on the 3EO . Advanced level, research level subject. 3MC . Aids to study N . Computers in mathematics * For computer programs, see Operations P . Programs in mathematics AM7 H2M. Conceptual agents 3MY . Digests, abridgements S . Symbols, notation in mathematics 3N . Mathematical tables Forms of mathematical presentation * And similar compilations. * The primary use of the concepts below is in qualifying . By degree of accuracy specific mathematical topics (e.g. Groups - Word 3NK . Figure tables problems ASA 3KR). Use the classes below on their * Four-figure, five-figure, etc. tables. own only for truly general studies of the concepts . By function involved. 3NL . General tables, ready-reckoners AM3 4 . Mathematical presentation 3NM . Conversion tables . Properties 3NO . Logarithmic & elementary function tables 5 . Errors 3NP . Higher function tables 6 . Error bounds 3X . Mathematical recreations, mathematical puzzles, 9 . Statements mathematical games A . Theory, abstract theory * Exposition of the abstract principles of a topic. For 7 . History of mathematics abstract mathematical theory as a method (and itself . Periods in history of mathematics the topic studied) see AM3 N. * Add to AM2 7 letters A/V from Auxiliary AX . Hypotheses Schedule 4B. B . Theories special to a context 8 . Places in history of mathematics * For use when qualifying a specific topic studied. * Add to AM2 8 letters A/Z from Auxiliary * See also Models AM3 L Schedule 2. * Add to -3C letters H/W in Auxiliary Schedule . By cultural group AM1, e.g. -3CW B Potential theory 8BT . Ethnomathematics * An alternative (not recommended) to this division 9 . Biography of mathematicians by concept is to arrange theories A/Z by name. * For names of individuals used to characterize D . Axioms, postulates properties, etc., see AP2. * For axiomatic method, see Mathematical logic, 9B . Relations with other subjects AM4 F. 9C . Comparison with other subjects E . Special axioms A . Philosophy of mathematics * Add to AM3 E letters B/H following AM5 3E so * For quasi-philosophical doctrines underlying far as applicable, e.g. -3EF Axioms of choice. mathematical methodology, see Foundations of F . Theorems mathematics AM3 P. G . Lemmas * Add to AM2 letters A/J following A in AA/AJ. H . Formulae Some prominent concepts are given below for I . Demonstrations convenience. J . Proofs BA . Schools of philosophy in mathematics * For proof theory as a subject, see AM4 P. * For philosophical schools in mathematical logic, see AM4 2BA. JKP . Problems * Will generally be used only as a qualifier of another COP . Mathematical Platonism topic, e.g. in collections of problems for students. * See also Logicism AM3 R * For problem solving as a subject, see AM4 FV. GW . Logic KR . Word problems * See Mathematical logic AM4 KS . Incorrectly posed problems KV . Problems special to a context 1 AM3L AM4994 Mathematical logic Mathematics AM Mathematics AM Forms of mathematical presentation Methodologies in general AM3 M . Problems AM3 JKP Foundations of mathematics AM3 P . Problems special to a context AM3 KV Schools of thought . Inductive mathematics AM3 W AM3 L . Models * Representations assisting interpretation of a subject. AM4 Mathematical logic * For model theory as a subject, see AM4 Q. * Usually treated as nearly synonymous with symbolic * For models as mathematical relations, see logic. But for general studies of symbolic logic per se in AM9 S3L. mathematical logic, see AM4 9Y. For symbolic logic in LX . Simulation general, see AL9 Y. * Probabilistic modelling. * As a subclass of mathematics the structure sought is one consistent with that in other subclasses of mathematics. The order of the mathematical concepts is therefore Methodologies in mathematics exactly the same. * But in order to make the purely logical part completely consistent with logic in general (AL) the notation has M . Methodologies in general been modified slightly. Division is directly by the N . Abstract mathematical theory scheduled class AM/AW and does not use the provisions * As a subject; for theory as a form of presentation, of Auxiliary Schedule AM1. The effect of this is to see AM3 A. shorten classmarks both here (in AM4) and in AL3 3X (Mathematics of logic); but it does this at the expense of . Philosophical methodologies dropping the facility in Auxiliary Schedule AM1 (at * Approaches to mathematics as a whole. -H/-W) for specifying types of mathematical concepts. In both AM4 and AL3 3X concepts are primarily logical ones and when Types of these are required they P . Foundations of mathematics, metamathematics are got by enumeration at the end of the relevant class; * The term `metamathematics' is used loosely, e.g. AM4 QR/AM4 RET Types of (logical) models; sometimes being treated as a particular AM4 RH/RW Types of formal deductive systems. In development of Formalism, sometimes more the last example, division via Auxiliary Schedule AM1 narrowly still, as equivalent to proof theory. It is is utilized for some of the types. used here in its widest sense. * Add to AM4 numbers 2/8 following AM in AM2/AM8. * See also Philosophy of mathematics AM2 A. * Add to AM4 9 number 9 following AM at AM9 and . Schools of thought letters M/W following A in AM/AW. A selection is * General studies only. A particular topic in logic given below of some prominent concepts. or mathematics as treated by a particular 2A . Philosophy of mathematical logic schoool goes with the topic. 2BA . Schools of philosophy in mathematical logic R . Logicism, logicalists 2L . Agents * See also Mathematical Platonism, 2N . Computers AM2 COP 2P . Programs S . Formalism 34 . Forms of mathematical presentation * For Metamathematics, see AM3 P and the * Many of these (e.g. statements) have a special note there. significance in logic and these are enumerated in their * For properties of formal languages, see appropriate positions. In case of doubt, the latter Mathematical logic, AM4 AD. should be preferred to the terms synthesized here. Proof theory 3D . Axioms in mathematical logic * See AM4 P * For axiomatic method see AM4 F. Model theory 3M . Methodologies * See AM4 Q 3P . Foundations of mathematical logic, T . Constructivism & intuitionism metamathematics in mathematical logic U . Constructivism * See also Proof theory AM4 P; Model theory * See also Recursion theory AM4 H3A AM4 Q. V . Intuitionism 3R . Logicism in mathematical logic * See also Intuitionist logic AM4 RF 3S . Formalism in mathematical logic V3D . Axioms 3T . Constructivism & intuitionism V3E . Constructability postulate, effective 5 . Set theory in mathematical logic constructability postulate 62 . Mathematical methods by various characteristics W . Inductive mathematics 74 . Mathematical operations & processes * For mathematical induction see AM4 T. * See also Recursion theory AM4 H3A 8J . Mathematical relations 993 . Forms 994 . Mathematical relations by various characteristics 2 AM49MN Deductive logic in mathematics AM4GLM Mathematics AM Foundations of mathematics AM3 P Methodologies in general AM3 M Mathematical logic AM4 Foundations of mathematics AM3 P Deductive logic in mathematics AM4 A Mathematical logic AM4 Logical properties AM4 AD Mathematical relations AM4 8J . Equivalence in mathematical logic AM4 BB . Mathematical relations by various characteristics AM4 994 . Identity in mathematical logic AM4 BC AM4 9MN Mathematical properties AM4 BE . Opposition 9PA Parts, elements & entities in mathematics BH . Truth 9R5 Mathematical systems, branches BH8 L . Truth functions BV Properties special to a given context * For example, stability of models AM4 QBV. 9WZ Systems in mathematical logic * From this point onwards, the schedule for CL Logical operations mathematical logic is basically an expansion of that D . Reasoning for general logic (AL), with additional material . Elements incorporating mathematical operations, relations, etc. DF . Fallacies and expanding particular classes (e.g. algorithms). DL . Paradoxes * It is important to note that, apart from the expanded DP . Contradictions classes, the following schedule is only a selection of EB . Analysis in mathematical logic the concepts in AL. This selection is designed to ED . Interpretation show the scope and structure of the class and to indicate the concepts particularly relevant to EF . Formalization mathematical logic.But all the detail in AL is EH . Implication available here and this class should be used in F . Axiomatics in mathematical logic conjunction with AL. * For axioms as statements (used in qualifying * Add to AM4 numbers 9X/9Y and letters A/W other concepts), see AM3 D. following AL in ALA/ALW. F3E . Axioms 9X . Classical logic in mathematics F3F . Theorems * Classical logic in general is at AL9 X. F3H . Formulae 9Y . Symbolic logic in mathematics FH . Syntax, rules of syntax * For works considering symbolic logic as an FJ . Formation rules element in mathematical logic, rather than FK
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