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.

Required Courses
MATH 1300Calculus 14-5
or MATH 1310 Calculus for Life Sciences
or APPM 1350 Calculus 1 for Engineers
MATH 2300Calculus 24-5
or APPM 1360 Calculus 2 for Engineers
MATH 2400Calculus 34-5
or APPM 2350 Calculus 3 for Engineers
MATH 2001Introduction to Discrete Mathematics3
or MATH 2002 Number Systems: An Introduction to Higher Mathematics
MATH 2135Introduction to Linear Algebra for Mathematics Majors3
MATH 3001Analysis 13
Program Track Coursework15-16
Total Credit Hours36-40

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

Required Courses
MATH 3140Abstract Algebra 13
MATH 4140Abstract Algebra 23
or MATH 4001 Analysis 2
Electives
Three upper-division MATH or approved APPM courses (at least one at the 4000-level)9
Total Credit Hours15

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 2002MATH 2135, and MATH 3001.
  • By the end of the sixth semester, complete MATH 3140MATH 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

Required Courses
MATH 4510Introduction to Probability Theory3
MATH 3430Ordinary Differential Equations3
MATH 4520Introduction to Mathematical Statistics3
or MATH 4470 Partial Differential Equations
Electives
Two upper-division MATH or approved APPM courses6
Total Credit Hours15

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.

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

Required Courses
MATH 3110Introduction to Theory of Numbers3
or MATH 3140 Abstract Algebra 1
MATH 3120Functions and Modeling3
MATH 3210Euclidean and Non-Euclidean Geometry3
MATH 3510Introduction to Probability and Statistics3
MATH 4820History of Mathematical Ideas3
Total Credit Hours15

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.

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

Ancillary Courses 1
CSCI 1300Computer Science 1: Starting Computing4
CSCI 2270Computer Science 2: Data Structures4
Total Credit Hours8

Required Courses and Credits

Required Courses
CSCI 3104Algorithms4
MATH 3430Ordinary Differential Equations3
MATH/APPM 4650Intermediate Numerical Analysis 13
Electives
Two MATH or approved APPM or approved CSCI courses, at least one of which must be at the 4000-level. 6
Total Credit Hours16

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 2002MATH 2135, and MATH 3001 .
  • By the end of the sixth semester, complete CSCI 3104MATH 3430MATH 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

Required Courses
MATH 4510Introduction to Probability Theory3
MATH 4520Introduction to Mathematical Statistics3
MATH 4540Introduction to Time Series3
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 Hours15

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.

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.

Plan of Study Grid
Year One
Fall SemesterCredit 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 Hours14
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 Hours15
Year Two
Fall Semester
MATH 2400 Calculus 3 5
MATH 2001
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 Hours17
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 Hours15
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 Hours15
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 Hours15
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 Hours15
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 Hours15
 Total Credit Hours121

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.