The undergraduate degree in mathematics emphasizes knowledge and awareness of:
- Calculus of several variables and vector analysis.
- The structure of mathematical proofs and definitions.
- Basic linear algebra and the theory of vector spaces.
- Basic real analysis of one variable.
- 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:
- Move from concrete to abstract thinking and back with facility.
- Recognize patterns and connections between areas of mathematics and between mathematics and other subjects.
- Organize and construct a logical argument, provide evidence to support arguments and articulate arguments clearly and succinctly, both verbally and in writing.
Program Tracks
The mathematics program offers five tracks that lead to the BA degree. All five tracks require Calculus 1, Calculus 2, Calculus 3, MATH 2001, MATH 2135 and MATH 3001.
Comprehensive Track
The comprehensive track emphasizes theoretical mathematics, and is aimed at students seeking a general background in mathematics or intending to pursue graduate work in mathematics.
Applicable Track
The applicable track is aimed at students seeking a background in applied and/or applicable mathematics.
Secondary Education Track
The secondary education track is designed to align with the Colorado licensure requirements for mathematics secondary education, and the university does offer a program for obtaining secondary education mathematics teaching licensure.
Computational Track
The computational track is designed for students with an interest in the intersection of mathematics and computer science.
Statistics Track
The statistics track is designed for students seeking a background in statistics and/or data science.
Requirements
Program Requirements
To earn a BA in mathematics, a student must complete the general requirements of the College of Arts and Sciences, as well as the six mathematics core courses and the five additional courses for one of the five tracks (described on the Program Tracks tab).
Students must earn a grade of C- or better in each of the mathematics core courses and the five additional courses, and have at least a C average for all attempted work in mathematics.
Required Core Courses
The following courses are required of all mathematics majors, regardless of track.
| Code | Title | Credit Hours |
|---|---|---|
| Required Courses | ||
| MATH 1300 | Calculus 1 | 4-5 |
| or MATH 1310 | Calculus for Life Sciences | |
| or APPM 1350 | Calculus 1 for Engineers | |
| MATH 2300 | Calculus 2 | 4-5 |
| or APPM 1360 | Calculus 2 for Engineers | |
| MATH 2400 | Calculus 3 | 4-5 |
| or APPM 2350 | Calculus 3 for Engineers | |
| MATH 2001 | Introduction to Discrete Mathematics | 3 |
| or MATH 2002 | Number Systems: An Introduction to Higher Mathematics | |
| MATH 2135 | Introduction to Linear Algebra for Mathematics Majors | 3 |
| MATH 3001 | Analysis 1 | 3 |
| Program Track Coursework | 15-16 | |
| Total Credit Hours | 36-40 | |
Program Tracks
Comprehensive Track
Aimed at students seeking a general background in mathematics or intending to pursue graduate work in mathematics, in addition to the coursework required of all mathematics majors, the comprehensive track requires the following courses.
Required Courses and Credits
| Code | Title | Credit Hours |
|---|---|---|
| Required Courses | ||
| MATH 3140 | Abstract Algebra 1 | 3 |
| MATH 4140 | Abstract Algebra 2 | 3 |
| or MATH 4001 | Analysis 2 | |
| Electives | ||
| Three upper-division MATH or approved APPM courses (at least one at the 4000-level) | 9 | |
| Total Credit Hours | 15 | |
Graduating in Four Years
Consult the Four-Year Guarantee Requirements for information on eligibility. The concept of "adequate progress," as it is used here, 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.
- By the beginning of the second semester, declare the major.
- By the end of the fourth semester, complete Calculus 1, Calculus 2, Calculus 3, MATH 2001 or MATH 2002, MATH 2135, and MATH 3001.
- By the end of the sixth semester, complete MATH 3140, MATH 4140 or MATH 4001, and one additional approved MATH or APPM course.
- By the end of the eighth semester, complete the major.
Applicable Track
Aimed at students seeking a background in applied and/or applicable mathematics, in addition to the coursework required of all mathematics majors, the applicable track requires the following courses.
Required Courses and Credits
| Code | Title | Credit Hours |
|---|---|---|
| Required Courses | ||
| MATH 4510 | Introduction to Probability Theory | 3 |
| MATH 3430 | Ordinary Differential Equations | 3 |
| MATH 4520 | Introduction to Mathematical Statistics | 3 |
| or MATH 4470 | Partial Differential Equations | |
| Electives | ||
| Two upper-division MATH or approved APPM courses | 6 | |
| Total Credit Hours | 15 | |
Graduating in Four Years
Consult the Four-Year Guarantee Requirements for information on eligibility. The concept of "adequate progress," as it is used here, 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.
- By the beginning of the second semester, declare the major.
- By the end of the fourth semester, complete Calculus 1, Calculus 2, Calculus 3, MATH 2001 or MATH 2002, MATH 2135, and MATH 3001.
- By the end of the sixth semester, complete MATH 4510 ,MATH 3430 ,and either MATH 4520 or MATH 4470.
- By the end of the eighth semester, complete the major.
Secondary Education Track
Aimed at students intending to teach mathematics at the secondary level, in addition to the coursework required of all mathematics majors, the secondary education track requires the following courses.
Required Courses and Credits
| Code | Title | Credit Hours |
|---|---|---|
| Required Courses | ||
| MATH 3110 | Introduction to Theory of Numbers | 3 |
| or MATH 3140 | Abstract Algebra 1 | |
| MATH 3120 | Functions and Modeling | 3 |
| MATH 3210 | Euclidean and Non-Euclidean Geometry | 3 |
| MATH 3510 | Introduction to Probability and Statistics | 3 |
| MATH 4820 | History of Mathematical Ideas | 3 |
| Total Credit Hours | 15 | |
Note: Completion of the secondary education track does not provide the student a teaching license.
Graduating in Four Years
Consult the Four-Year Guarantee Requirements for information on eligibility. The concept of "adequate progress," as it is used here, 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.
- By the beginning of the second semester, declare the major.
- By the end of the fourth semester, complete Calculus 1, Calculus 2, Calculus 3, MATH 2001 or MATH 2002, MATH 2135, MATH 3001, and MATH 3120 .
- By the end of the sixth semester, complete MATH 3510, MATH 3210, and either MATH 3110 or MATH 3140.
- By the end of the eighth semester, complete the major.
Computational Track
Aimed at students interested in both mathematics and computation, in addition to the coursework required of all mathematics majors, the computational track requires the following courses.
Ancillary Courses
| Code | Title | Credit Hours |
|---|---|---|
| Ancillary Courses 1 | ||
| CSCI 1300 | Computer Science 1: Starting Computing | 4 |
| CSCI 2270 | Computer Science 2: Data Structures | 4 |
| Total Credit Hours | 8 | |
| 1 | CSCI 1300 and CSCI 2270 do not count toward hours in the major and are not part of the major GPA. |
Required Courses and Credits
| Code | Title | Credit Hours |
|---|---|---|
| Required Courses | ||
| CSCI 3104 | Algorithms | 4 |
| MATH 3430 | Ordinary Differential Equations | 3 |
| MATH/APPM 4650 | Intermediate Numerical Analysis 1 | 3 |
| Electives | ||
| Two MATH or approved APPM or approved CSCI courses, at least one of which must be at the 4000-level. | 6 | |
| Total Credit Hours | 16 | |
Graduating in Four Years
Consult the Four-Year Guarantee Requirements for information on eligibility. The concept of "adequate progress," as it is used here, 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.
- By the beginning of the second semester, declare the major.
- By the end of the fourth semester, complete Computer Science 1, Computer Science 2, Calculus 1, Calculus 2, Calculus 3, MATH 2001 or MATH 2002, MATH 2135, and MATH 3001 .
- By the end of the sixth semester, complete CSCI 3104, MATH 3430, MATH 4650/APPM 4650 and one of the additionally required upper-division MATH classes.
- By the end of the eighth semester, complete the major.
Statistics Track
Aimed at students seeking a background in statistics and/or data science, in addition to the coursework required of all mathematics majors, the statistics track requires the following courses.
Required Courses and Credits
| Code | Title | Credit Hours |
|---|---|---|
| Required Courses | ||
| MATH 4510 | Introduction to Probability Theory | 3 |
| MATH 4520 | Introduction to Mathematical Statistics | 3 |
| MATH 4540 | Introduction to Time Series | 3 |
| Electives | ||
| Two of the following courses: | 6 | |
| Markov Processes, Queues, and Monte Carlo Simulations | ||
APPM 4590 | ||
| Introduction to Stochastic Processes | ||
| Statistical Methods and Application I | ||
| Statistical Methods and Applications II | ||
| Statistical Learning | ||
| Total Credit Hours | 15 | |
Graduating in Four Years
Consult the Four-Year Guarantee Requirements for information on eligibility. The concept of "adequate progress," as it is used here, 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.
- By the beginning of the second semester, declare the major.
- By the end of the fourth semester, complete Calculus 1, Calculus 2, Calculus 3, MATH 2001 or MATH 2002, MATH 2135, and MATH 4510.
- By the end of the sixth semester, complete MATH 3001, MATH 4520, and MATH 4540.
- By the end of the eighth semester, complete the major.
Recommended Four-Year Plan of Study
Through the required coursework for the major, students will complete the QRMS component of the Gen Ed Skills Requirement and, depending on the track of study, potentially some credit hours in the Natural Sciences and Arts & Humanities areas of the Gen Ed Distribution Requirement.
| Year One | ||
|---|---|---|
| Fall Semester | Credit Hours | |
| MATH 1300 | Calculus 1 | 5 |
| Gen. Ed. Distribution/diversity course (example: Social Sciences/Global Perspective) | 3 | |
| Gen. Ed. Skills course (example: Lower-division Written Communication) | 3 | |
| Elective | 3 | |
| Credit Hours | 14 | |
| Spring Semester | ||
| MATH 2300 | Calculus 2 | 5 |
| Gen. Ed. Distribution course (example: Natural Sciences with Lab) | 4 | |
| Gen. Ed. Distribution/Diversity course (example: Arts & Humanities/US Perspective) | 3 | |
| Elective | 3 | |
| Credit Hours | 15 | |
| Year Two | ||
| Fall Semester | ||
| MATH 2400 | Calculus 3 | 5 |
| MATH 2001 or MATH 2002 | Introduction to Discrete Mathematics or Number Systems: An Introduction to Higher Mathematics | 3 |
| Gen. Ed. Distribution course (example: Natural Sciences) | 3 | |
| Elective | 3 | |
| Elective | 3 | |
| Credit Hours | 17 | |
| Spring Semester | ||
| MATH 2135 | Introduction to Linear Algebra for Mathematics Majors | 3 |
| Gen. Ed. Distribution course (example: Natural Sciences) | 3 | |
| Gen. Ed. Distribution course (example: Social Sciences) | 3 | |
| Elective | 3 | |
| Elective | 3 | |
| Credit Hours | 15 | |
| Year Three | ||
| Fall Semester | ||
| MATH Upper Division Elective | 3 | |
| Gen. Ed. Skills course (example: Upper-division Written Communication) | 3 | |
| Gen. Ed. Distribution course (example: Arts & Humanities) - Upper-division | 3 | |
| Upper-division Elective | 3 | |
| Upper-division Elective | 3 | |
| Credit Hours | 15 | |
| Spring Semester | ||
| MATH 3001 | Analysis 1 | 3 |
| Gen. Ed. Distribution course (example: Arts & Humanities) | 3 | |
| Gen. Ed. Distribution course (example: Social Sciences) | 3 | |
| Upper-division Elective | 3 | |
| Upper-division Elective | 3 | |
| Credit Hours | 15 | |
| Year Four | ||
| Fall Semester | ||
| MATH Upper Division Elective | 3 | |
| MATH Upper Division Elective | 3 | |
| Gen. Ed. Distribution course (Natural Sciences) | 3 | |
| Upper-division Elective | 3 | |
| Upper-division Elective | 3 | |
| Credit Hours | 15 | |
| Spring Semester | ||
| MATH Upper Division Elective | 3 | |
| MATH Upper Division Elective | 3 | |
| Gen. Ed. Distribution course (example: Arts & Humanities) | 3 | |
| Gen. Ed. Distribution course (example: Social Sciences) | 3 | |
| Upper-division Elective | 3 | |
| Credit Hours | 15 | |
| Total Credit Hours | 121 | |
Bachelor's–Accelerated Master's Degree Program(s)
The bachelor's–accelerated master's (BAM) degree program options offer currently enrolled CU Boulder undergraduate students the opportunity to receive a bachelor's and master's degree in a shorter period of time. Students receive the bachelor's degree first but begin taking graduate coursework as undergraduates (typically in their senior year).
Because some courses are allowed to double count for both the bachelor's and the master's degrees, students receive a master's degree in less time and at a lower cost than if they were to enroll in a stand-alone master's degree program after completion of their baccalaureate degree. In addition, staying at CU Boulder to pursue a bachelor's–accelerated master's program enables students to continue working with their established faculty mentors.
BA in Mathematics, MA in Mathematics or MS in Applied Mathematics
Each of the BAM degree programs offered by the Department of Mathematics allows highly motivated and successful students to experience graduate-level coursework earlier in their education than would otherwise be possible, and also allows them to obtain a master's degree in a reduced time period. Students are allowed to count 6 hours of graduate-level mathematics department coursework towards both their undergraduate and graduate degree requirements.
Admissions Requirements
In order to gain admission to the BAM programs named above, a student must meet the following criteria:
- Have a cumulative GPA of 3.0 or higher.
- Have completed a minimum of 45 credit hours of coursework.
- If a transfer student, have completed a minimum of 24 credit hours at CU Boulder.
- Have completed a minimum of two upper-division courses from the Department of Mathematics.
The earliest admission to the program is after the successful completion of at least total 45 credit hours and a minimum of two upper-division courses from the Department of Mathematics. Students must have at least one year of coursework remaining towards the completion of their undergraduate degree in order to be admitted to the program. Students admitted to the program may not pursue a double degree or a double major; however, outside minors are allowed.
Program Requirements
Students may take up to and including 12 hours while in the undergraduate program which can later be used toward the master's degree. However, only 6 credits may be double counted toward the bachelor's degree and the master's degree. Students must apply to graduate with the bachelor's degree, and apply to continue with the master's degree, early in the semester in which the undergraduate requirements will be completed.
If you are interested in the BAM degree program, please contact the mathematics graduate program for more information.