|
Mathematics is about structure, about reasoning, and about modeling. This course braids these three threads together. Mathematical logic began as the study of the reasoning used in mathematics, but it turns out to be useful in describing the mathematical concept of structure and in modeling automated reasoningthat is, modeling computation. The logical approach to structure gives an alternate perspective on such other mathematical subjects as combinatorics and abstract algebra. This, for the most part, is described by the area of model theory, which is the focus of Unit 1. In Unit 2, we will look at modeling computation. The central fact of these models, from a logical standpoint, is that once we can handle a computation as a definable mathematical object, we can prove that certain computations are impossible. The most famous such proof is Gödel’s Incompleteness Theorem, showing that it is impossible to compute truth in a system sufficiently strong to describe natural number arithmetic. Details:
http://www.saylor.org/courses/ma201/
Categories:
Mathematics
|
|
AlternativesIf you know any alternatives, please let us know. PrerequisitesIf you can suggest any prerequisite, please let us know. Paths
See all Education Paths Certification Exams-- there are no exams to get certification after this course --If your company does certification for those who completed this course then register your company as certification vendor and add your exams to the Exams Directory. StudentsPeople who learned this course or plan to learn. These people added the course to their Education Passport or their Personal Education Path. 
Alberto Mesa
Andrey Kirillov
Daniel Pastushchak
| ||