Best institutions to study Topology and Foundations
A program that focuses on the properties of unaltered geometric configurations under conditions of continuous, multi-directional transformations.
1 U.S. institutions graduated 3 Topology and Foundations students in 2024–25 (IPEDS). It is CIP 27.0105, a specialization of Mathematics (CIP 27.01), and leads most directly to the Mathematicians occupation (BLS SOC 15-2021).
About Topology and Foundations programs
A program that focuses on the properties of unaltered geometric configurations under conditions of continuous, multi-directional transformations. Includes instruction in mathematical logic, proof theory, model theory, set theory, combinatorics, continua, homotopy, homology, links, and transformation actions.
Source: National Center for Education Statistics, Classification of Instructional Programs (CIP 2020).
The Topology and Foundations program, part of the Mathematics field, explores the properties of geometric configurations under continuous transformations. This program is designed for students interested in advanced mathematical concepts, including mathematical logic, proof theory, and set theory. It offers an in-depth understanding of the foundational aspects of mathematics, making it ideal for those pursuing research or academic careers in this discipline.
Students will gain core skills in mathematics, critical thinking, and problem-solving. Coursework typically covers topics such as combinatorics, homotopy, and homology, equipping graduates with the knowledge necessary to develop new mathematical principles and advance the field.
Credentials awarded
What Topology and Foundations graduates earned in 2024–25, by award level (IPEDS completions).
- Doctor's degree - research/scholarship3 graduates / yr · 1 institution100%
Graduates over time
Topology and Foundations completions reported to IPEDS each year, all award levels combined.
| Year | Graduates |
|---|---|
| 2013 | 2 |
| 2014 | 3 |
| 2015 | 2 |
| 2016 | 0 |
| 2017 | 3 |
| 2018 | 1 |
| 2019 | 2 |
| 2020 | 3 |
| 2021 | 2 |
| 2022 | 3 |
| 2023 | 0 |
| 2024 | 2 |
| 2025 | 3 |
Top 1 institutions for Topology and Foundations, ranked by graduates
Graduates (IPEDS completions), 2024–25. Award levels show which credentials each institution confers in this specialization.
| # | Institution | Graduates / yr | Grad rate | Net price | Field earnings* (1 yr) |
|---|---|---|---|---|---|
| 1 | University of California - Berkeley Berkeley, CAPublicDoctoral | 3 | 93% | — | $46,674 |
* Median earnings 1 year after graduation for the broader Mathematics field (CIP 27.01) at these institutions; College Scorecard does not publish earnings at the 6-digit level.
Offered in 1 states
Where Topology and Foundations graduates come from. Each state links to all Mathematics programs offered there.
| State | Institutions | Graduates / yr | Top institution by graduates |
|---|---|---|---|
| California | 1 | 3 | University of California - Berkeley3 / yr |
Careers & outlook
The payoff after graduation: occupation 15-2021, Mathematicians, and its national outlook.
Graduates of the Topology and Foundations program can pursue careers as mathematicians, with additional opportunities as natural sciences managers or postsecondary mathematics teachers. The job outlook shows little or no change, with an estimated 100 annual openings and a median wage of $121,680. A typical education requirement for these roles is a master's degree.
Top-paying metros
Career pathways for CIP 27.0105
The occupations the NCES crosswalk maps this 6-digit code to, with BLS pay and 10-year outlook.
| Occupation | US median pay | Growth | Openings / yr | Typical entry education |
|---|---|---|---|---|
Mathematiciansprimary SOC 15-2021 | $126,710 | -0.7% Little or no change | ~100 | Master's degree |
Natural Sciences Managers SOC 11-9121 | $167,220 | +3.7% About as fast as average | ~8,500 | Bachelor's degree |
Mathematical Science Teachers, Postsecondary SOC 25-1022 | $79,940 | +2.3% About as fast as average | ~4,400 | Doctoral or professional degree |
Job Zone Five: Extensive Preparation Needed
- Education
- Most of these occupations require graduate school. For example, they may require a master's degree, and some require a Ph.D., M.D., or J.D. (law degree).
- Experience
- Extensive skill, knowledge, and experience are needed for these occupations. Many require more than five years of experience. For example, surgeons must complete four years of college and an additional five to seven years of specialized medical training to be able to do their job.
- Training
- Employees may need some on-the-job training, but most of these occupations assume that the person will already have the required skills, knowledge, work-related experience, and/or training.
Related careers
Skills & knowledge in Topology and Foundations programs
From the U.S. Dept. of Labor for the occupation this specialization most leads to.
Skills you'll build
Knowledge areas
Abilities that matter most
Day-to-day work activities
What graduates do on the job
- Mentor others on mathematical techniques.
- Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.
- Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
- Disseminate research by writing reports, publishing papers, or presenting at professional conferences.
- Assemble sets of assumptions, and explore the consequences of each set.
- Perform computations and apply methods of numerical analysis to data.
Tools and technology used
Other Mathematics specializations
The 5 other 6-digit CIP codes under Mathematics (CIP 27.01).
- MathematicsCIP 27.010123,537 graduates / yr1,300 institutions
- MathematicsCIP 27.0199344 graduates / yr29 institutions
- Analysis and Functional AnalysisCIP 27.0103limited data7 graduates / yr1 institutions
Show 2 more CIP codes with no U.S. programs reported+
- Algebra and Number Theory27.0102
- Geometry/
Geometric Analysis27.0104
No institution reported completions for these codes in the latest IPEDS year, so they have no page.
Common questions
What is the focus of the Topology and Foundations program?+
The program focuses on the properties of geometric configurations under continuous transformations and includes various advanced mathematical topics.
What skills will I develop in this program?+
You will develop skills in mathematics, critical thinking, and problem-solving, along with knowledge in areas like logic and set theory.
What careers can I pursue with this degree?+
Graduates can become mathematicians, natural sciences managers, or postsecondary mathematics teachers.
What is the job outlook for mathematicians?+
The job outlook shows little or no change, with about 100 annual openings and a median wage of $121,680.
What is the CIP code for Topology and Foundations?+
Topology and Foundations is CIP 27.0105 in the NCES Classification of Instructional Programs (CIP 2020), a 6-digit specialization within Mathematics (CIP 27.01). NCES defines it as: A program that focuses on the properties of unaltered geometric configurations under conditions of continuous, multi-directional transformations. Includes instruction in mathematical logic, proof theory, model theory, set theory, combinatorics, continua, homotopy, homology, links, and transformation actions.
How many institutions offer Topology and Foundations programs?+
1 U.S. institutions reported Topology and Foundations graduates in IPEDS 2024–25, across 1 states, awarding 3 credentials in the year. That is 0.0% of all Mathematics graduates.
How much do Topology and Foundations graduates earn?+
Earnings are not published at the 6-digit CIP level by any federal source. The Mathematicians occupation, which Topology and Foundations most directly leads to, pays a median of $126,710 a year nationally (BLS OEWS May 2025), and graduates of the broader Mathematics field report median earnings of $46,674 one year after graduation (College Scorecard).
About the data on this page
Every figure comes from an official federal or public source. Here is each one and the release it is currently on.
Program definitions are from the NCES Classification of Instructional Programs (CIP 2020). Skills, knowledge, abilities, work activities, tools, and job zones are from the O*NET database by the U.S. Department of Labor, used under the CC BY 4.0 license.
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