Mathematics
Degrees ...BA, MA, MS, PhD
The undergraduate degree in mathematics emphasizes knowledge and awareness of:
- basic real analysis of one variable;
- calculus of several variables and vector analysis;
- basic linear algebra and theory of vector spaces;
- the structure of mathematical proofs and definitions; and
- at least one additional specialized area of mathematics.
In addition, students completing a degree in mathematics are expected to acquire the ability and skills to:
- use techniques of differentiation and integration of one and several variables;
- solve problems using differentiation and integration;
- solve systems of linear equations;
- give direct proofs, proofs by contradiction, and proofs by induction;
- formulate definitions;
- read mathematics without supervision; and
- utilize mathematics.
Bachelor's Degree Program +
The requirements for the major in mathematics are currently under review by the Department of Mathematics. For more information, contact the department.
The department of mathematics offers two plans for earning a BA in mathematics. For each plan students must complete the general requirements of the College of Arts and Sciences as well as the required courses listed below.
To earn an undergraduate degree in mathematics plans I and II, students must take Calculus 1, 2, and 3 plus 24 credit hours of courses numbered 3000 or above with 9 credit hours at the 4000-level or above, with a grade of C- or better and with 2.00 (C) average for all attempted work in mathematics. The 24 credit hours must be fulfilled by a minimum of eight courses.
Note: Any APPM course that is cross-listed as a MATH course is considered by the Department of Mathematics to be a mathematics course.
Mathematics Plan I +
| Required Courses | Semester Hours |
| Calculus 1, 2, and 3 | 12-14 |
| MATH 3000 Introduction to Abstract Mathematics or MATH 3200 Introduction to Abstract Mathematics through Topology | 3 |
| MATH 3130 Introduction to Linear Algebra | 3 |
| MATH 3140 Abstract Algebra 1 | 3 |
| MATH 4310 Introduction to Analysis | 3 |
| A two-semester upper-division sequence approved by the Department of Mathematics and upper-division math electives | 12 |
Graduating in Four Years +
Consult the Four-Year Guarantee Requirements for information on eligibility. The concept of "adequate progress" as it is used here only refers to maintaining eligibility for the four-year guarantee; it is not a requirement for the major. To maintain adequate progress in mathematics Plan I, students should meet the following requirements:
| Declare major by the beginning of the second semester. | |
| Complete Calculus 1, 2, and 3, and either MATH 3000, 3200, or 3130 by the end of the fourth semester. | |
| Complete either MATH 3000 or 3200 and MATH 3130, 3140, and at least two optional upper-division 3-credit mathematics courses by the end of the sixth semester. | |
| Complete MATH 4310, at least three optional upper-division 3-credit mathematics courses, and have begun an approved two-semester upper-division sequence by the end of the seventh semester. | |
| Complete a total of eight upper-division 3-credit mathematics courses including an approved two-semester upper-division sequence by the end of the eighth semester. |
Note: At least three of the eight courses must be at the 4000 level.
Mathematics Plan II +
| Required Courses | Semester Hours |
| Calculus 1, 2, and 3 | 12-14 |
| MATH 3130 Introduction to Linear Algebra | 3 |
| MATH 4430 Ordinary Differential Equations | 3 |
| MATH 4650 Intermediate Numerical Analysis | 3 |
| One of the following courses: MATH 4510 Introduction to Probability, MATH 4470 Introduction to Partial Differential Equations, MATH 4450 Introduction to Complex Variables, MATH 4330 Fourier Analysis, or MATH 4120 Introduction to Operations Research | 3 |
| A two-semester upper-division sequence approved by the Department of Mathematics and upper-division math electives | 12 |
Graduating in Four Years +
Consult the Four-Year Guarantee Requirements for information on eligibility. The concept of "adequate progress" as it is used here only refers to maintaining eligibility for the four-year guarantee; it is not a requirement for the major. To maintain adequate progress in mathematics, students should meet the following requirements:
| Declare the major by the beginning of the second semester. | |
| Complete Calculus 1, 2, and 3, and MATH 3130 by the end of the fourth semester. | |
| Complete MATH 4430 and 4650; at least one of the following: MATH 4330, 4450, 4470, or 4510; and at least one additional 3-credit hour upper-division elective by the end of the sixth semester. | |
| Complete at least three optional upper-division 3-credit mathematics courses and begin an approved two-semester upper-division sequence by the end of the seventh semester. | |
| Complete a total of eight upper-division 3-credit mathematics courses, including an approved two-semester upper-division sequence by the end of the eighth semester. |
Secondary Licensure +
The program for obtaining a secondary teaching license is handled by the School of Education and this program has requirements in addition to those needed for a mathematics degree. Teacher licensure candidates should talk to an advisor in the School of Education.
Residency Requirement +
For the BA degree in mathematics, all students must have completed at least 12 credit hours of upper-division mathematics courses, with grades of C (2.00) or better, taken in the College of Arts and Sciences on the Boulder campus. Additional courses transferred from other universities or from other campuses of the University of Colorado that are used to meet the minimum 24-hour upper-division requirement must be approved by the Department of Mathematics. Courses accepted as mathematics credit but excluded from the minimum 24-hour upper-division requirement still count in the 45 maximum hours allowed in mathematics.
Undergraduate students planning to do graduate work in mathematics should take MATH 3140, 4310, and 4320, as well as fulfill the arts and sciences language requirement with German, French, or Russian.
Minor Program +
A minor is offered in mathematics. Declaration of a minor is open to any student enrolled at CU-Boulder, regardless of college or school. For minor information see www.colorado.edu/artssciences/students/undergraduate/academics/minors.html.
Mathematics Modules Program +
The Department of Mathematics is no longer offering the flexibly-paced courses formerly known as the Mathematics Modules.
The content of those courses is now covered in lecture-based formatted courses. Students may contact the Department of Mathematics for further information.
Graduate Degree Programs +
The Department of Mathematics offers programs leading to the degrees MA or PhD in mathematics and MS in applied mathematics. Students interested in any of these programs should read carefully the material describing the university requirements in the Graduate School section. The student is responsible for satisfying these requirements at the proper time.
The prerequisite for graduate work in mathematics is at least 30 credit hours in mathematics, including two semesters of advanced calculus (undergraduate real analysis, beyond calculus), a semester of linear algebra, and a semester of either modern algebra or differential equations, with a grade of B or better. GRE scores are required to be considered for financial support.
The basic requirements for the various degrees are summarized here, and full details are available in the department office or online at math.colorado.edu. For fulfillment of all course requirements, mathematics courses must be numbered 5000 or higher excluding MATH 5800. No language is required of master's students.
To earn an MA degree under the thesis plan, a student must complete 24 credit hours of graduate course work at the 5000-level or above, including two courses that are approved full-year courses, and 6 credit hours of thesis work. For the nonthesis plan, 30 credit hours of course work, 24 of which must be at the 5000-level or above, are required. Two of those courses must be approved full-year courses. No more than 6 credit hours of seminars or independent study may be included in the 30-hour requirement.
For the MS degree in applied mathematics, 30 credit hours of graduate course work, 24 of which must be at the 5000-level or above, are required. Of these, 6 to 12 credit hours must be in an approved minor program outside the mathematics department.
To earn an MA degree or an MS degree, a student must pass a master's examination based on the particular program of the student.
Before being admitted to candidacy for the PhD degree in mathematics, a student must pass examinations in real analysis, modern algebra, and pass a comprehensive exam. The basic requirements for a PhD degree in mathematics are as follows: demonstrate reading knowledge of French, German, or Russian (see departmental requirement sheet for language options); demonstrate competence in a modern scientific programming language; complete at least 30 credit hours of graduate course work and 30 credit hours of thesis; prepare a written thesis that contains substantial original contributions to mathematics; and successfully complete a final examination. For more current and precise details, contact the mathematics office or go to the department website at math.colorado.edu.
