Denver,
CO,
United States
Type
Private
Degrees offered
Bachelor's Degree
PhD in Mathematics- Algebra and Number Theory in Denver United States | University of Denver
University of Denver
|
Denver United States
Visit institution website
for more information
Qualification
Doctor of Philosophy
Languages
English
Delivery Mode
On-Campus
Tuition (2025)
USD
51,090
Attendance
Full-time
Full-time Duration
36 months
Whenever the associative property (xy)z = x(yz) breaks down, we venture into nonassociative mathematics. This field typically divides into two main branches: nonassociative algebras (including Lie and Jordan algebras) and the study of quasigroups and loops (which encompasses aspects of latin square theory).
Our research at DU primarily concentrates on quasigroups and loops. A quasigroup consists of a set equipped with a binary operation where the equation x·y=z always has exactly one solution when any two variables are known. Loops extend this concept by including an identity element.
Loop theory employs diverse methods drawn from group theory, combinatorial mathematics, universal algebra, and computer-assisted proof systems. Much of the research centers on specific loop varieties, like Moufang loops that obey the identity ((xy)x)z = x(y(xz))).
Destination of Study
Subjects of Study
Language Requirements
English
IELTS 6.5
Qualification Requirements
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 masters 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 masters 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
Minimum TOEFL Score Internetbased test 80
Minimum IELTS Score 6.5
Minimum C1 Advanced Score 176
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 masters 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 masters 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
Minimum TOEFL Score Internetbased test 80
Minimum IELTS Score 6.5
Minimum C1 Advanced Score 176
Tuition
USD
51,090