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This is a list of mathematical logic topics. For traditional syllogistic logic, see the list of topics in logic . See also the list of computability and complexity topics for more theory of algorithms .
Fundamentals of mathematical logic. A K Peters, Ltd. ISBN 1-56881-262-0. Andrews, Peter B. (2002). An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof (2nd ed.). Boston: Kluwer Academic Publishers. ISBN 978-1-4020-0763-7. Barwise, Jon, ed. (1989). Handbook of Mathematical Logic. Studies in Logic and the Foundations of ...
Mathematical induction is a method for proving that a statement () is true for every natural number, that is, that the infinitely many cases (), (), (), (), … all hold. This is done by first proving a simple case, then also showing that if we assume the claim is true for a given case, then the next case is also true.
He has also taught the history of mathematics and probability theory. In 1997 Cambridge University Press published his book Introduction to mathematical reasoning: numbers, sets and functions. [6] As a research mathematician, Eccles specialised in topology and homotopy theory, publishing numerous journal papers in this area of study.
Deductive reasoning plays a central role in formal logic and mathematics. [1] In mathematics, it is used to prove mathematical theorems based on a set of premises, usually called axioms. For example, Peano arithmetic is based on a small set of axioms from which all essential properties of natural numbers can be inferred using deductive reasoning.
Mathematical reasoning requires rigor. This means that the definitions must be absolutely unambiguous and the proofs must be reducible to a succession of applications of inference rules, [e] without any use of empirical evidence and intuition.
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major motivating factor for the development of computer science.
The Principles and Standards for School Mathematics was developed by the NCTM. The NCTM's stated intent was to improve mathematics education. The contents were based on surveys of existing curriculum materials, curricula and policies from many countries, educational research publications, and government agencies such as the U.S. National Science Foundation. [3]