Free online courseMathematical Logic
Duration of the online course: 12 hours and 19 minutes
New course
Explore Mathematical Logic in this free course covering key concepts in calculus, such as sentential logic, compactness, Gödel's theorem, and more.
Course Description
Delve into the comprehensive world of Mathematical Logic with this free online course tailored for those interested in enhancing their understanding of calculus-based logic. Designed for basic study levels, this course meticulously covers an array of subjects structured to provide a thorough foundation in logic. Starting with an introduction to mathematical logic, the course progresses through critical concepts such as sentential logic and truth assignments.
Students will explore the completeness of sentential logic, structural induction, recursion, and the language of first-order logic. The course takes a deep dive into complex topics like elementary classes, logical implication, and definable sets. Alongside, there is a significant focus on structural analysis, including homomorphisms and preservation results.
The course discusses the nuance of non-definability results using automorphisms and substructures. Learners will benefit from an extensive study of compactness and its applications, with sections dedicated to the compactness in sentential logic, topological compactness, and its relevance to graph coloring.
A critical section on syntactical and logical axioms equips students to understand the intricacies of tautologies in first-order logic, metatheorems, and the soundness theorem. The exploration of Gödel's completeness theorem and term models will further enhance the analytical prowess of the participants.
Concluding with an insightful summary, this course is an excellent opportunity for learners to grasp the complexities of mathematical logic and its various applications in calculus. Whether you're looking to solidify your mathematical foundation or expand your knowledge, this course is a valuable resource for academic and personal growth.
Course content
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Video class: 1. Introduction to Mathematical Logic
0h13m
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Video class: 2. Logic. Strings
0h03m
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Video class: 3. Logic. The Language Of Sentential Logic
0h09m
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Video class: 4. Logic. Truth Assignments
0h16m
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Video class: 5. Logic. Tautological Implication
0h17m
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Video class: 6. Logic. The completeness of the language for sentential logic
0h21m
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Video class: 7. Logic. Generating sets out of functions
0h24m
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Video class: 8. Logic. Structural induction and Recursion
0h16m
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Video class: 9. Logic. The Language of First Order Logic
0h20m
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Video class: 10. Logic. Structures
0h11m
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Video class: 11. Logic. Free Variables
0h14m
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Video class: 12. Logic. Interpretation of Terms
0h10m
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Video class: 13. Logic. Interpretation of Formulas
0h12m
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Video class: 14. Logic. Elementary Classes
0h22m
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Video class: 15. Logic. Elementary Equivalence
0h11m
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Video class: 16. Logic. Logical Implication
0h09m
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Video class: 17. Logic. Definable Sets
0h12m
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Video class: 18. Logic. Homomorphisms
0h15m
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Video class: 19. Logic. Preservation results
0h22m
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Video class: 20. Logic. Non-definability results using automorphisms
0h13m
This free course includes:
12 hours and 19 minutes of online video course
Exercises to train your knowledge
Certificate of course completion
100% free, from content to certificate
This online course can only be accessed through the Cursa App. Download it using the QR code or the links below:
This online course can only be accessed through the Cursa app. Install it using the links below:
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