| Program start date | Application deadline |
| 2023-12-15 | - |
Program Overview
The Ph.D. in Mathematics at the University of Wisconsin-Madison offers advanced training in mathematics, culminating in a dissertation with original research. Students specialize in areas such as algebra, analysis, or applied mathematics, and complete coursework, qualifying exams, and a preliminary exam before embarking on their dissertation research. The program emphasizes independent research, collaboration, and ethical conduct, preparing graduates for careers in academia, government, industry, or non-profit organizations.
Program Outline
Degree Overview:
Overview:
The Ph.D. in Mathematics at the University of Wisconsin-Madison offers advanced graduate-level training in mathematics and culminates in the completion of a dissertation containing original research.
Objectives:
- To develop a comprehensive understanding of basic and advanced graduate mathematics.
- To conduct significant original research in a chosen area of mathematics.
- To demonstrate competence in presenting and communicating complex mathematical ideas.
- To cultivate ethical and professional conduct within the field of mathematics.
Program Description:
The program provides students with flexibility in their research specialization, covering a wide range of areas including:
- Algebra, Algebraic Geometry, Combinatorics, and Number Theory
- Analysis, Differential Equations, and Probability
- Applied and Computational Mathematics
- Logic
- Geometry, Topology, and Dynamics
- Mathematics Education
Outline:
Program Structure:
The curriculum consists of a combination of coursework and research, typically completed within eight years.
Coursework:
- Students complete a total of 51 graduate credits, which includes courses in mathematics and a doctoral minor or graduate certificate.
- Coursework must align with the student's chosen area of specialization.
- Courses numbered above 700 are considered graduate-level.
- Courses below 700 may be approved by the academic advisor.
Qualifying Examinations:
- Two qualifying exams must be passed by the beginning of the fourth semester.
- One qualifying exam must be passed by the beginning of the sixth semester.
Preliminary Examination (Specialty Exam):
- Must be passed by the end of the eighth semester.
Dissertation:
- Students complete original research and write a dissertation under the guidance of a faculty advisor.
- The dissertation must make a substantial contribution to the field of mathematics.
Assessment:
Methods:
- Coursework grades
- Qualifying exams
- Preliminary exam
- Dissertation defense
Criteria:
- Minimum GPA of 3.00
- Satisfactory performance on qualifying exams and preliminary exam
- Successful defense of the dissertation
Teaching:
Teaching Methods:
- Lectures
- Seminars
- Guided research
Faculty:
- Renowned faculty with expertise in various areas of mathematics
Unique Approaches:
- Emphasis on independent research
- Opportunities for students to present research findings at conferences and seminars
- Interdisciplinary collaborations with other departments and research centers
Careers:
Potential Career Paths:
- Academia (research and teaching)
- Government agencies
- Private industry (e.g., data science, finance, software development)
- Non-profit organizations
Opportunities and Outcomes:
- The program prepares students for successful careers in research, teaching, or applied mathematics.
- Graduates are highly sought after by employers in various sectors.
- Alumni have made significant contributions to the advancement of mathematical knowledge and its applications.