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Formal mathematical logic is the foundation on which all of mathematics and mathematical reasoning is built. This [course_title] starts off with the introduction to propositional calculus, the basics to the course; then it focuses on the first-order logic and model theory. Topics covered include the metatheorems dealing with the properties of soundness, completeness, decidability, and consistency. The final part of the course is about formal number theory.
Assessment
This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.
Certification
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Course Credit: Open Culture
Course Curriculum
| Module: 01 | |||
| Mod-01 Lec-01 Sets and Strings | 00:44:00 | ||
| Mod-01 Lec-02 Lecture-02-Syntax of Propositional Logic | 00:46:00 | ||
| Mod-01 Lec-03 Lecture-03-Unique Parsing | 00:52:00 | ||
| Mod-01 Lec-04 Lecture-04-Semantics of PL | 00:47:00 | ||
| Mod-01 Lec-05 Lecture-05-Consequences and Equivalences | 00:44:00 | ||
| Mod-01 Lec-06 Five results about PL | 00:41:00 | ||
| Module: 02 | |||
| Mod-01 Lec-07 Lecture-07-Calculations and Informal Proofs | 00:46:00 | ||
| Mod-01 Lec-08 Lecture-08-More Informal Proofs | 00:48:00 | ||
| Mod-01 Lec-09 Lecture-09-Normal forms | 00:51:00 | ||
| Mod-01 Lec-10 Lecture-10-SAT and 3SAT | 00:45:00 | ||
| Mod-01 Lec-11 Lecyture-11-Horn-SAT and Resolution | 00:55:00 | ||
| Mod-01 Lec-12 Lecture-12-Resolution | 00:47:00 | ||
| Module: 03 | |||
| Mod-01 Lec-13 Lecture-13-Adequacy of Resolution | 00:53:00 | ||
| Mod-01 Lec-14 Lecture-14-Adequacy and Resolution Strategies | 00:48:00 | ||
| Mod-01 Lec-15 Lecture-15-Propositional Calculus (PC) | 00:50:00 | ||
| Mod-01 Lec-16 Lecture-16-Some Results about PC | 00:49:00 | ||
| Mod-01 Lec-17 Lecture-17-Arguing with Proofs | 00:47:00 | ||
| Mod-01 Lec-18 Lecture-18-Adequacy of PC | 00:51:00 | ||
| Module: 04 | |||
| Mod-01 Lec-19 Lecture-19-Compactness & Analytic Tableau | 00:50:00 | ||
| Mod-01 Lec-20 Lecture-20-Examples of Tableau Proofs | 00:45:00 | ||
| Mod-01 Lec-21 Lecture-21-Adequacy of Tableaux | 00:46:00 | ||
| Mod-01 Lec-22 Lecture-22-Syntax of First order Logic (FL) | 00:47:00 | ||
| Mod-01 Lec-23 Lecture-23-Symbolization & Scope of Quantifiers | 00:48:00 | ||
| Mod-01 Lec-24 Lecture-24-Hurdles in giving Meaning | 00:45:00 | ||
| Module: 05 | |||
| Mod-01 Lec-25 Lecture-25-Semantics of FL | 00:50:00 | ||
| Mod-01 Lec-26 Lecture-26-Relevance Lemma | 00:48:00 | ||
| Mod-01 Lec-27 Lecture-27-Validity, Satisfiability & Equivalence | 00:49:00 | ||
| Mod-01 Lec-28 Lecture-28-Six Results about FL | 00:48:00 | ||
| Mod-01 Lec-29 Lecture-29-Laws, Calculation & Informal Proof | 00:47:00 | ||
| Mod-01 Lec-30 Lecture-30-Quantifier Laws and Consequences | 00:49:00 | ||
| Module: 06 | |||
| Mod-01 Lec-31 Lecture-31-More Proofs and Prenex Form | 00:51:00 | ||
| Mod-01 Lec-32 Lecture-32-Prenex Form Conversion | 00:46:00 | ||
| Mod-01 Lec-33 Lecture-33-Skolem Form | 00:53:00 | ||
| Mod-01 Lec-34 Lecture-34-Syntatic Interpretation | 00:50:00 | ||
| Mod-01 Lec-35 Lecture-35-Herbrand’s Theorem | 00:45:00 | ||
| Mod-01 Lec-36 Lecture-36-Most General Unifiers | 00:51:00 | ||
| Module: 07 | |||
| Mod-01 Lec-37 Lecture-37-Resolution Rules | 00:46:00 | ||
| Mod-01 Lec-38 Lecture-38-Resolution Examples | 00:49:00 | ||
| Mod-01 Lec-39 Lecture-39-Ariomatic System FC | 00:46:00 | ||
| Mod-01 Lec-40 Lecture-40-FC and Semidecidability of FL | 00:49:00 | ||
| Mod-01 Lec-41 Lecture-41-Analytic Tableau for FL | 00:47:00 | ||
| Mod-01-Lec-42 Lecture-42-Godels Incompleteness Theorems | 00:48:00 | ||
| Assessment | |||
| Submit Your Assignment | 00:00:00 | ||
| Certification | 00:00:00 | ||
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