Campuses:
This is archival data. This system was retired as of August 21, 2023 and the information on this page has not been updated since then. For current information, visit catalogs.umn.edu.
Twin Cities Campus
Mathematics Ph.D.School of Mathematics
College of Science and Engineering
Link to a list of faculty for this program.
Contact Information
127 Vincent Hall, 206 Church Street SE, Minneapolis, MN 55455 (612-624-6391; fax: 612-624-6702)
Email:
gradprog@math.umn.edu
Website: https://cse.umn.edu/math
Along with the program-specific requirements listed below, please read the
General Information section of
this
website for requirements that apply to all major fields.
The School of Mathematics offers a PhD in mathematics and a PhD in mathematics with emphasis in applied mathematics.
Special areas of research include ordinary and partial differential equations; probability; real, complex, harmonic, functional, and numerical analysis; differential and algebraic geometry; topology; number theory; commutative algebra; group theory; logic; combinatorics; mathematical physics; and applied and industrial mathematics, mathematical biology, and dynamical systems.
Program Delivery
Prerequisites for Admission
The preferred undergraduate GPA for admittance to the program
is 3.00.
Undergraduate degree in mathematics or equivalent.
Other requirements to be completed before admission:
Applicants should have the prerequisite material of abstract algebra, analysis, and topology.
GRE scores are not required for admission.
To receive full consideration for financial support, applicants for whom English is not their native language should have an English Language Proficiency (ELP) score of at least a 2, which is a total score of 100 or higher and a speaking score of 23 or higher on the TOEFL iBT or a total score of 7 or higher with a speaking score of 7 or higher on the IELTS.
Special Application Requirements:
Applications are accepted for fall semester only. The application deadline is December 15.
International applicants must submit score(s) from one of the following tests:
Key to test
abbreviations
(TOEFL, IELTS).
For an online application or for more information about graduate education admissions, see the
General Information section of this
website.
Program Requirements
25
credits are required in the major.
12 credits are required outside the major. 24 thesis credits are required.
This program may be completed with a minor.
Use of 4xxx courses towards program requirements is not permitted.
A minimum GPA of 3.00
is required for students to remain in good standing.
Courses offered on both the A-F and S/N grading basis must be taken A-F, with a minimum grade of B earned for each course.
Students choose a program of coursework in consultation with their advisor and the director of graduate studies that best prepares them for research in mathematics.
Teaching Preparation (1 credit)
Complete the following course:
MATH 8001 - Preparation for College Teaching
(1.0 cr)
Major Core Coursework (12 credits)
Select a minimum of 12 credits from the following in consultation with the advisor:
MATH 8201 - General Algebra
(3.0 cr)
MATH 8301 - Manifolds and Topology
(3.0 cr)
MATH 8401 - Mathematical Modeling and Methods of Applied Mathematics
(3.0 cr)
MATH 8441 - Numerical Analysis and Scientific Computing
(3.0 cr)
MATH 8601 - Real Analysis
(3.0 cr)
MATH 8651 - Theory of Probability Including Measure Theory
(3.0 cr)
MATH 8701 - Complex Analysis
(3.0 cr)
Major Depth Coursework (6 credits)
Select a minimum of 6 credits from the following in consultation with the advisor:
MATH 8202 - General Algebra
(3.0 cr)
MATH 8302 - Manifolds and Topology
(3.0 cr)
MATH 8402 - Mathematical Modeling and Methods of Applied Mathematics
(3.0 cr)
MATH 8442 - Numerical Analysis and Scientific Computing
(3.0 cr)
MATH 8602 - Real Analysis
(3.0 cr)
MATH 8652 - Theory of Probability Including Measure Theory
(3.0 cr)
MATH 8702 - Complex Analysis
(3.0 cr)
Major Elective Coursework (6 credits)
Select a minimum of 6 credits from the following list in consultation with the advisor. Additional core and depth courses may be used to meet the elective coursework requirement.
MATH 8141 - Applied Logic
(3.0 cr)
MATH 8142 - Applied Logic
(3.0 cr)
MATH 8151 - Axiomatic Set Theory
(3.0 cr)
MATH 8152 - Axiomatic Set Theory
(3.0 cr)
MATH 8166 - Recursion Theory
(3.0 cr)
MATH 8167 - Recursion Theory
(3.0 cr)
MATH 8172 - Model Theory
(3.0 cr)
MATH 8173 - Model Theory
(3.0 cr)
MATH 8190 - Topics in Logic
(1.0-3.0 cr)
MATH 8201 - General Algebra
(3.0 cr)
MATH 8202 - General Algebra
(3.0 cr)
MATH 8207 - Theory of Modular Forms and L-Functions
(3.0 cr)
MATH 8208 - Theory of Modular Forms and L-Functions
(3.0 cr)
MATH 8211 - Commutative and Homological Algebra
(3.0 cr)
MATH 8212 - Commutative and Homological Algebra
(3.0 cr)
MATH 8245 - Group Theory
(3.0 cr)
MATH 8246 - Group Theory
(3.0 cr)
MATH 8251 - Algebraic Number Theory
(3.0 cr)
MATH 8252 - Algebraic Number Theory
(3.0 cr)
MATH 8253 - Algebraic Geometry
(3.0 cr)
MATH 8254 - Algebraic Geometry
(3.0 cr)
MATH 8270 - Topics in Algebraic Geometry
(1.0-3.0 cr)
MATH 8271 - Lie Groups and Lie Algebras
(3.0 cr)
MATH 8272 - Lie Groups and Lie Algebras
(3.0 cr)
MATH 8280 - Topics in Number Theory
(1.0-3.0 cr)
MATH 8300 - Topics in Algebra
(1.0-3.0 cr)
MATH 8301 - Manifolds and Topology
(3.0 cr)
MATH 8302 - Manifolds and Topology
(3.0 cr)
MATH 8306 - Algebraic Topology
(3.0 cr)
MATH 8307 - Algebraic Topology
(3.0 cr)
MATH 8360 - Topics in Topology
(1.0-3.0 cr)
MATH 8365 - Riemannian Geometry
(3.0 cr)
MATH 8366 - Riemannian Geometry
(3.0 cr)
MATH 8370 - Topics in Differential Geometry
(1.0-3.0 cr)
MATH 8380 - Topics in Advanced Geometry
(1.0-3.0 cr)
MATH 8385 - Calculus of Variations and Minimal Surfaces
(3.0 cr)
MATH 8386 - Calculus of Variations and Minimal Surfaces
(3.0 cr)
MATH 8387 - Mathematical Modeling of Industrial Problems
(3.0 cr)
MATH 8388 - Mathematical Modeling of Industrial Problems
(3.0 cr)
MATH 8390 - Topics in Mathematical Physics
(1.0-3.0 cr)
MATH 8401 - Mathematical Modeling and Methods of Applied Mathematics
(3.0 cr)
MATH 8402 - Mathematical Modeling and Methods of Applied Mathematics
(3.0 cr)
MATH 8431 - Mathematical Fluid Mechanics
(3.0 cr)
MATH 8432 - Mathematical Fluid Mechanics
(3.0 cr)
MATH 8441 - Numerical Analysis and Scientific Computing
(3.0 cr)
MATH 8442 - Numerical Analysis and Scientific Computing
(3.0 cr)
MATH 8445 - Numerical Analysis of Differential Equations
(3.0 cr)
MATH 8446 - Numerical Analysis of Differential Equations
(3.0 cr)
MATH 8450 - Topics in Numerical Analysis
(1.0-3.0 cr)
MATH 8470 - Topics in Mathematical Theory of Continuum Mechanics
(1.0-3.0 cr)
MATH 8501 - Differential Equations and Dynamical Systems I
(3.0 cr)
MATH 8502 - Differential Equations and Dynamical Systems II
(3.0 cr)
MATH 8503 - Bifurcation Theory in Ordinary Differential Equations
(3.0 cr)
MATH 8505 - Applied Dynamical Systems and Bifurcation Theory I
(3.0 cr)
MATH 8506 - Applied Dynamical Systems and Bifurcation Theory II
(3.0 cr)
MATH 8520 - Topics in Dynamical Systems
(1.0-3.0 cr)
MATH 8530 - Topics in Ordinary Differential Equations
(1.0-3.0 cr)
MATH 8540 - Topics in Mathematical Biology
(1.0-3.0 cr)
MATH 8571 - Theory of Evolutionary Equations
(3.0 cr)
MATH 8572 - Theory of Evolutionary Equations
(3.0 cr)
MATH 8580 - Topics in Evolutionary Equations
(1.0-3.0 cr)
MATH 8581 - Applications of Linear Operator Theory
(3.0 cr)
MATH 8582 - Applications of Linear Operator Theory
(3.0 cr)
MATH 8583 - Theory of Partial Differential Equations
(3.0 cr)
MATH 8584 - Theory of Partial Differential Equations
(3.0 cr)
MATH 8590 - Topics in Partial Differential Equations
(1.0-3.0 cr)
MATH 8600 - Topics in Advanced Applied Mathematics
(1.0-3.0 cr)
MATH 8601 - Real Analysis
(3.0 cr)
MATH 8602 - Real Analysis
(3.0 cr)
MATH 8640 - Topics in Real Analysis
(3.0 cr)
MATH 8641 - Spatial Ecology
(3.0 cr)
MATH 8651 - Theory of Probability Including Measure Theory
(3.0 cr)
MATH 8652 - Theory of Probability Including Measure Theory
(3.0 cr)
MATH 8654 - Fundamentals of Probability Theory and Stochastic Processes
(3.0 cr)
MATH 8655 - Stochastic Calculus with Applications
(3.0 cr)
MATH 8659 - Stochastic Processes
(3.0 cr)
MATH 8660 - Topics in Probability
(1.0-3.0 cr)
MATH 8668 - Combinatorial Theory
(3.0 cr)
MATH 8669 - Combinatorial Theory
(3.0 cr)
MATH 8680 - Topics in Combinatorics
(1.0-3.0 cr)
MATH 8701 - Complex Analysis
(3.0 cr)
MATH 8702 - Complex Analysis
(3.0 cr)
MATH 8790 - Topics in Complex Analysis
(1.0-3.0 cr)
MATH 8801 - Functional Analysis
(3.0 cr)
MATH 8802 - Functional Analysis
(3.0 cr)
MATH 8990 - Topics in Mathematics
(1.0-6.0 cr)
MATH 8991 - Independent Study
(1.0-6.0 cr)
MATH 8992 - Directed Reading
(1.0-6.0 cr)
MATH 8993 - Directed Study
(1.0-6.0 cr)
MATH 8994 - Topics at the IMA
(1.0-3.0 cr)
Outside Coursework (12 credits)
A minimum of 12 credits in a minor or supporting program that supports the thesis research are required. If a supporting program is chosen, additional core, depth, or elective MATH courses outside the student's primary research area may be used to meet the outside coursework requirement. Coursework is selected with the advisor and director of graduate studies.
Thesis Credits (24 credits)
Take 24 doctoral thesis credits after passing the preliminary oral exam.
MATH 8888 - Thesis Credit: Doctoral
(1.0-24.0 cr)
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Credits: | 1.0 [max 1.0] |
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Grading Basis: | A-F or Aud |
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Typically offered: | Periodic Spring |
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Grading Basis: | A-F or Aud |
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Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Spring |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 1.0 -3.0 [max 12.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall & Spring |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Spring |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall & Spring |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
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Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Spring |
Credits: | 1.0 -3.0 [max 12.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Fall & Spring |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Spring |
Credits: | 1.0 -3.0 [max 12.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall & Spring |
Credits: | 1.0 -3.0 [max 12.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Fall & Spring |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Spring |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 1.0 -3.0 [max 12.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall & Spring |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Spring |
Credits: | 1.0 -3.0 [max 12.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Fall & Spring |
Credits: | 1.0 -3.0 [max 12.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall & Spring |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 1.0 -3.0 [max 12.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Spring |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 3.0 [max 3.0] |
Typically offered: | Periodic Fall |
Credits: | 3.0 [max 3.0] |
Typically offered: | Every Fall |
Credits: | 3.0 [max 3.0] |
Typically offered: | Every Spring |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Spring |
Credits: | 1.0 -3.0 [max 12.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Fall & Spring |
Credits: | 1.0 -3.0 [max 12.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall & Spring |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Spring |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 1.0 -3.0 [max 12.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall & Spring |
Credits: | 1.0 -3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall & Spring |
Credits: | 1.0 -3.0 [max 12.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Fall & Spring |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Spring |
Credits: | 1.0 -3.0 [max 12.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Spring |
Credits: | 1.0 -3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Fall & Spring |
Credits: | 1.0 -3.0 [max 12.0] |
Typically offered: | Every Fall & Spring |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Spring |
Credits: | 3.0 [max 12.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | S-N or Aud |
Typically offered: | Periodic Fall |
Credits: | 3.0 [max 3.0] |
Typically offered: | Every Fall |
Credits: | 3.0 [max 3.0] |
Typically offered: | Every Spring |
Credits: | 3.0 [max 3.0] |
Typically offered: | Periodic Spring |
Credits: | 3.0 [max 3.0] |
Typically offered: | Every Fall |
Credits: | 3.0 [max 3.0] |
Typically offered: | Every Fall |
Credits: | 1.0 -3.0 [max 12.0] |
Typically offered: | Every Fall & Spring |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Spring Even Year |
Credits: | 1.0 -3.0 [max 12.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Fall & Spring |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Spring |
Credits: | 1.0 -3.0 [max 12.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Every Fall |
Credits: | 3.0 [max 3.0] |
Grading Basis: | A-F or Aud |
Typically offered: | Periodic Spring |
Credits: | 1.0 -6.0 [max 24.0] |
Grading Basis: | S-N or Aud |
Typically offered: | Every Fall & Spring |
Credits: | 1.0 -6.0 [max 24.0] |
Typically offered: | Every Fall, Spring & Summer |
Credits: | 1.0 -6.0 [max 24.0] |
Grading Basis: | S-N or Aud |
Typically offered: | Every Fall & Spring |
Credits: | 1.0 -6.0 [max 24.0] |
Grading Basis: | S-N or Aud |
Typically offered: | Every Spring |
Credits: | 1.0 -3.0 [max 6.0] |
Typically offered: | Every Fall & Spring |
Credits: | 1.0 -24.0 [max 100.0] |
Grading Basis: | No Grade |
Typically offered: | Every Fall & Spring |