About the course

Mathematics is built on a formal system, including logic and the axioms of set theory. The study of the foundations of mathematics focuses on this formal system and possible alternative.

　　Algebraic Logic - Algebraic logic offers algebraic descriptions of models appropriate for the study of various logics. The classical example is the equivalence of propositional calculus and Boolean algebras. We are interested in residuated lattices (which include Boolean algebras, Heyting algebras and MV-algebras, for instance) and the corresponding logics. We also study decidability and the properties of proofs in substructural logics, i.e., logics that lack one of the usual structural rules.

　　Set Theory- Set theory constitutes a foundation for all of mathematics. In its inception, set theory dealt with axiomatics, clarifying and studying the axioms on which mathematics is based, and discovering their consequences as well as their limitations. Modern set theory continues this line of investigation as well as others, in particular, giving precise methods for studying real analysis, measure theory, and topology. The main tools of modern set theory are cardinal invariants, combinatorics, forcing, forcing axioms, inner models, and large cardinal axioms. At DU, we work on set theory involving all of the above. Of particular interest are ultrafilters and their applications in logic, set theory and topology, including the Stone–Čech compactification of the natural numbers. The classification of ultrafilters up to Tukey (cofinal) type is one current focus of research. This study is connecting Ramsey theory to ultrafilters in an interesting manner.

　　Automated Deduction- Automated deduction is a field of artificial intelligence focused on rigorous, computer assisted proofs of mathematical theorems. Automated deduction can provide early insights into increasingly more technical areas of mathematics and also establish original, state-of-the-art theorems. While some human guidance is usually necessary to obtain complicated proofs by automated deduction, the proofs can then be routinely checked for correctness. We are mostly using automated deduction in the area of nonassociative mathematics. Many proofs we obtained were humanized for publication in standard mathematical research journals. Other proofs are too long (tens of thousands of steps) but they nevertheless impact the field. Furthermore, feedback from working mathematicians helps researchers in automated deduction and leads to software improvements. Scholarships - View all scholarships Internships

　　

Start dates and prices

Course fees are indicative and should be used as a guide. Speak to a counsellor to get an accurate price.

　　Duration: 3 Year(s)Fees: Not available

Intake	Location
Winter (January), 2024	Denver
Fall (September), 2024	Denver
Winter (January), 2025	Denver
Fall (September), 2025	Denver
Winter (January), 2026	Denver

　　

How to apply

Entry requirements for University of Denver

Bachelors degree: All graduate applicants must hold an earned baccalaureate from a regionally accredited college or university or the recognized equivalent from an international institution.

　　Grade point average: The minimum undergraduate GPA for admission consideration for graduate study at the University of Denver is a cumulative 2.5 on a 4.0 scale or a 2.5 on a 4.0 scale for the last 60 semester credits or 90 quarter credits (approximately two years of work) for the baccalaureate degree. An earned master?s degree or higher from a regionally accredited institution supersedes the minimum standards for the baccalaureate. For applicants with graduate coursework but who have not earned a master?s degree or higher, the GPA from the graduate work may be used to meet the requirement. The minimum GPA is a cumulative 3.0 on a 4.0 scale for all graduate coursework undertaken.

　　Program GPA requirement: The minimum undergraduate GPA for admission consideration for this program is a cumulative 2.5 on a 4.0 scale

　　The minimum GPA is a cumulative 3.0 on a 4.0 scale for all graduate coursework undertaken.

　　Minimum TOEFL Score: 80 (iBT) or 550 (paper-based)

　　Minimum IELTS Score: 6.5

　　

English language requirements

　　6.5

　　Overall IELTS band score

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　　TOEFL Internet based overall score: 80.0

　　

Application deadline:

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Further information

Career outcomes

　　

Reviews and rankings

World ranking

　　501st / 1250

　　THE World ranking

　　

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