Projects

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Learning Discrete Mathematics and Computer Science
via Primary Historical Sources

All Projects

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Sixteen projects developed before 2008 are posted at http://www.math.nmsu.edu/hist_projects/

Projects developed since 2008 are listed below. With each project there is a list of suggested courses where the project may be used and a list of topics covered in the project.

Projects related to Course Mathematical Logic are:

Project 3: Deduction through the Ages: A History of Truth 2013-03-08 Blog
Courses: An introductory discrete mathematics course, A course in discrete mathematics for beginning computer science majors
Topic: Elementary propositional logic, truth tables, the truth table of an implication

Project 13: Henkin's Method and the Completeness Theorem 2010-11-26 Blog
Courses: Mathematical Logic (advanced)
Topic: syntax of first-order logic, axioms and rules of inference, formal concept of proof, deduction theorem, satisfiability and validity, soundness, Henkin's method, completeness, Loewenheim-Skolem theorem, first-order logic with equality

Project 14: Peano Arithmetic 2010-12-12 Blog
Courses: Mathematical Logic (advanced)
Topic: Peano postulates, consistency and independence of Peano postulates, recursive definition of addition and multiplication, properties of addition and multiplication, first-order arithmetic

Project 15: Goedel's Incompleteness Theorems 2011-01-05 Blog
Courses: Mathematical Logic (advanced)
Topic: Self-referential statements and paradoxes, first-order languages and first-order theories, models, Peano arithmetic (PA), diagonalization lemma, incompleteness of PA (Goedel's first incompletenss theorem), unprovability of consistency (Goedel's second incompleteness theorem).

Project 16: Undecidability of First-Order Logic Blog
Courses: Mathematical Logic (advanced)
Topic: Different formulations of the decision problem, models, isomorphic models, intended model, one-way infinite line, two-way infinite line, upper half-plane, Turing machines, halting problem, undecidability of first-order satisfiability

Note: If you would like to use any of the projects please let us know and we will e-mail you a .tex file of the project which you can modify to better suit your class needs.