# Major/Minor Requirements

Mathematics is a subject with many facets and many applications. The School of Mathematics offers BA and BSMath degree programs that allow many choices. We offer specializations in actuarial mathematics, computer applications, mathematical biology, and mathematics education. However, many of our math majors do not choose a specialization, and, of course, some students make course choices that prepare them well for graduate study in pure and applied mathematics. We also offer courses in mathematics that apply to industry and courses that could lead to careers in business or finance.

See the main differences between the BA, offered through the College of Liberal Arts (CLA), and the BS, offered through the College of Science and Engineering (CSE) and the requirements to be admitted to the major below.

All mathematics majors must complete one of the following two introductory sequences:

Sequence 1:

- MATH 1271/1371/1571H Calculus I
- MATH 1272/1372/1572H Calculus II
- MATH 2243/2373/2574H Linear algebra and differential equations
- MATH 2263/2374/2573H Multivariable calculus and vector analysis
- MATH 2283/3283W Sequences, series and foundations

Sequence 2 (Honors students only):

- Credit equivalent to Calculus I and II (typically Advanced Placement)
- MATH 3592H Honors Mathematics I
- MATH 3593H Honors Mathematics II

Note that MATH 3283W counts as an upper-division writing intensive course toward the liberal education writing requirement but NOT as an upper-division MATH course toward the major.

CLA students must take six upper-division MATH courses, complete a senior project, and take a foreign language. To declare a Major in Mathematics, students must have successfully completed 3 courses:

- MATH 1271/1371/1571H Calculus I
- MATH 1272/1372/1572H Calculus II
- One 2xxx level Calculus course:
- 2243/2373/2574H (Linear Algebra & Differential Equations) or
- 2263/2374/2573H (Multivariable Calculus)

Among their six upper-division MATH courses, CLA students must choose two algebra courses and two analysis courses from the following lists:

Algebra List

Of the two algebra courses, at least one must be chosen from the Theoretical Algebra list:

Theoretical Algebra

- MATH 4281 Introduction to Modern Algebra
- MATH 5248 Cryptology and Number Theory
- MATH 5251 Error-correcting Codes, Finite Fields, Algebraic Curves
- MATH 5285H Honors: Fundamental Structures of Algebra I
- MATH 5286H Honors: Fundamental Structures of Algebra II
- MATH 5385 Introduction to Computational Algebraic Geometry

Applied Algebra

- MATH 4242 Applied Linear Algebra
- MATH 5705 Enumerative Combinatorics
- MATH 5707 Graph Theory and Non-enumerative Combinatorics
- MATH 5711 Linear Programming and Combinatorial Optimization
- MATH 5485 Introduction to Numerical Methods I

Analysis List

- MATH 4567 Fourier Analysis
- MATH 4603 Advanced Calculus I
- MATH 4604 Advanced Calculus II
- MATH 5486 Introduction to Numerical Methods II
- MATH 5525 Introduction to Ordinary Differential Equations
- MATH 5535 Dynamical Systems and Chaos
- MATH 5583 Complex Analysis
- MATH 5587 Elementary Partial Differential Equations I
- MATH 5588 Elementary Partial Differential Equations II
- MATH 5615 Honors: Introduction to Analysis I
- MATH 5616 Honors: Introduction to Analysis II
- MATH 5651 Basic Theory of Probability and Statistics
- STAT 5101 (equivalent to MATH 5651)
- MATH 5652 Stochastic Processes
- MATH 5654 Prediction and Filtering

Note that MATH 3283W, 4067W, 49xx, and 59xx do not count toward the upper-division MATH course requirement.

STAT 5102 can count toward the upper-division MATH course requirement, but not the Analysis requirement.

CLA math majors must complete a Senior Project: either MATH 4995 or MATH 4997W. See a math faculty adviser well in advance of the senior year to formulate a plan for completing the project. More information, forms, and other resources are available on the Senior Project page.

CSE students must take eight upper-division MATH courses, complete a pair of technical elective courses, and take Physics and Computer Science courses. To be admitted to Upper Division CSE as a Math Major, students must have successfully completed 5 courses:

- MATH 1271/1371/1571H Calculus I
- MATH 1272/1372/1572H Calculus II
- One 2xxx level Calculus course:
- Linear Algebra & Differential Equations (2243/2373/2574H) or
- Multivariable Calculus (2263/2374/2573H)

- & 5. Two Calculus-based Physics courses:
- PHYS 1301W/1401V/1501V
- PHYS 1302W/1402V/1502V

Among their eight upper-division MATH courses, CSE students must choose two algebra courses and two analysis courses from the following lists:

Algebra List

Of the two algebra courses, at least one must be chosen from the Theoretical Algebra list:

- MATH 4281 Introduction to Modern Algebra
- MATH 5248 Cryptology and Number Theory
- MATH 5251 Error-correcting Codes, Finite Fields, Algebraic Curves
- MATH 5285H Honors: Fundamental Structures of Algebra I
- MATH 5286H Honors: Fundamental Structures of Algebra II
- MATH 5385 Introduction to Computational Algebraic Geometry

Applied Algebra

- MATH 4242 Applied Linear Algebra
- MATH 5705 Enumerative Combinatorics
- MATH 5707 Graph Theory and Non-enumerative Combinatorics
- MATH 5711 Linear Programming and Combinatorial Optimization
- MATH 5485 Introduction to Numerical Methods I

- MATH 4567 Fourier Analysis
- MATH 4603 Advanced Calculus I
- MATH 4604 Advanced Calculus II
- MATH 5486 Introduction to Numerical Methods II
- MATH 5525 Introduction to Ordinary Differential Equations
- MATH 5535 Dynamical Systems and Chaos
- MATH 5583 Complex Analysis
- MATH 5587 Elementary Partial Differential Equations I
- MATH 5588 Elementary Partial Differential Equations II
- MATH 5615 Honors: Introduction to Analysis I
- MATH 5616 Honors: Introduction to Analysis II
- MATH 5651 Basic Theory of Probability and Statistics
- STAT 5101 (equivalent to MATH 5651)
- MATH 5652 Stochastic Processes
- MATH 5654 Prediction and Filtering

Note that MATH 3283W, 4067W, 49xx, and 59xx do not count toward the upper-division MATH course requirement.

STAT 5102 can count toward the upper-division MATH course requirement, but not the Analysis requirement.

- At least one semester of Computer Science. Typical choices include:
- CSCI 1103 Java
- CSCI 1113 C/C++
- CSCI 1133 Python

- Three semesters of Physics:
- PHYS 1301W/1401V/1501V Physics I
- PHYS 1302W/1402V/1502V Physics II
- PHYS 2303 or PHYS 2311 or PHYS 2403H or PHYS 2503

Note: Students in the Actuarial and Mathematical Biology specializations need only take two semesters of Physics.

- Technical Elective Package. Two courses satisfying the following requirements:
- At least three credits each
- Numbered 3xxx or higher
- Calculus I is a prerequisite
- Must have a theme or connection, requiring approval by a math faculty adviser. For example, two courses from the same department.

Each sub-plan below, including "no specialization," represents a specific route toward satisfying the general requirements described above.

- Introductory sequence as described above (the first three courses are required prior to admission to the major)
- Senior project as described above

- Two courses from the Algebra list
- Two courses from the Analysis list
- Two additional upper-division MATH courses

- One course from the Theoretical Algebra list
- MATH 4242 Applied Linear Algebra
- MATH 5651 Basic Theory of Probability and Statistics or STAT 5101
- MATH 5652 Stochastic Processes
- MATH 4065 Theory of Interest
- MATH 5067 Actuarial Mathematics I
- MATH 5068 Actuarial Mathematics II
- One CSCI course
- ECON 1101, 1102, 3101, 4261
- ACCT 2050, FINA 3001
- Two of INS 4100, 4101, 4200
- Recommended: MATH 4067W Actuarial Mathematics in Practice

- One course from the Theoretical Algebra list
- MATH 5485 Numerical Methods I
- MATH 5486 Numerical Methods II
- One course from the Analysis list
- MATH 5165 Mathematical Logic I
- One additional computing-related MATH course (4242, 5166, 5248, 5251, 5285H, 5286H, 5385, 5705, 5707, 5711)
- Two 1xxx-level CSCI courses (for example 1103-1913 or 1113-1913 or 1133-1933)
- CSCI 2011/2011H
- Two upper-division CSCI courses (4011, 4041, 4107, 4511W, 5107, 5108, 5403, 5421, 5451, 5511, 5512, 5521)

- Mathematical Biology: Genomics
- MATH 4428 Mathematical Modeling
- One course from the Theoretical Algebra list
- MATH 4242 Applied Linear Algebra
- MATH 5525 Intro to Ordinary Differential Equations or MATH 5535 Dynamical Systems & Chaos
- MATH 5651 Basic Theory of Probabilty and Statistics or STAT 5101
- One additional upper-division MATH course (for example: MATH 5445 Mathematical Analysis of Biological Networks)
- CSCI 5461 or 5481 (note the CSCI prerequisites for these courses)
- BIOL 1009/1009H General Biology (regular/Honors)
- GCD 3022 Genetics
- One of the following: (note the prerequisites for PBIO, EEB, GCD courses)
- PBIO 5301 Plant Genomics
- EEB 5042 Quantitative Genetics
- GCD 4143 Human Genetics
- GCD 4151 Molecular Biology of Cancer
- CSCI 5461/5481 (the one not taken above)
- MATH 5445 Mathematical Analysis of Biological Networks (recommended)

- Mathematical Biology: Physiology
- MATH 4428 Mathematical Modeling
- One course from the Theoretical Algebra list
- MATH 4242 Applied Linear Algebra
- MATH 5525 Intro to Ordinary Differential Equations or MATH 5535 Dynamical Systems & Chaos
- MATH 5651 Basic Theory of Probability and Statistics or STAT 5101
- MATH 5445 Mathematical Analysis of Biological Networks or MATH 5447 Theoretical Neuroscience
- BIOL 1009/1009H General Biology (regular/Honors)
- PHSL 3061 Principles of Physiology
- PHYS 1201W and PHYS 1202W
- CHEM 1061, 1065, 1062, 1066
- One of the following: (note the prerequisites for PHSL and NSC courses)
- PHSL 4700 (was BIOL 4700) Cell Physiology
- PHSL 5444 Muscle
- NSC 5202 Theoretical Neuroscience: Systems and Information Processing (note the prerequisites for this course)
- MATH 5445 or MATH 5447 (the one not taken above)

- MATH 4281 or MATH 5248 or MATH 5251 or MATH 5285H
- MATH 4707 or MATH 5705 or MATH 5707 (Note: MATH 4707 Introduction to Combinatorics and Graph Theory satisfies the Algebra requirement only for the Math Ed specialization.)
- MATH 5335 Geometry I
- MATH 4653 Elementary Probability (MATH 5651 or STAT 5101 may be substituted.)
- Two courses from the Analysis list

- Introductory sequence as described above [the first three courses are required prior to admission to the major]
- Three semesters of physics as described above [the first two courses are required prior to admission to the major]
- One semester of Computer Science as described above.

- Two courses from the Algebra list
- Two courses from the Analysis list
- Four additional upper-division MATH courses
- Technical electives as described above

- One course from the Theoretical Algebra list
- MATH 4242 Applied Linear Algebra
- MATH 5651 Basic Theory of Probability and Statistics or STAT 5101
- MATH 5652 Stochastic Processes
- MATH 4065 Theory of Interest
- MATH 5067 Actuarial Mathematics I
- MATH 5068 Actuarial Mathematics II
- One additional upper-division MATH course (recommended: MATH 4428, 5485, 5075, 5076)
- ECON 1101, 1102, 3101, 4261 (note: 3101 and 4261 satisfy the technical elective requirement)
- ACCT 2050, FINA 3001
- Two of INS 4100, 4101, 4200
- Recommended: MATH 4067W Actuarial Mathematics in Practice

- One course from the Theoretical Algebra list
- MATH 5485 Numerical Methods I
- MATH 5486 Numerical Methods II
- One course from the Analysis list
- MATH 5165 Mathematical Logic I
- One additional computing-related MATH course (4242, 5166, 5248, 5251, 5285H, 5286H, 5385, 5705, 5707, 5711)
- Two additional upper-division MATH courses
- Two 1xxx-level CSCI courses (for example 1103-1913 or 1113-1913 or 1133-1933)
- CSCI 2011/2011H
- Two upper-division CSCI courses (4011, 4041, 4107, 4511W, 5107, 5108, 5403, 5421, 5451, 5511, 5512, 5521), which satisfy the technical elective requirement

- Mathematical Biology: Genomics
- MATH 4428 Mathematical Modeling
- One course from the Theoretical Algebra list
- MATH 4242 Applied Linear Algebra
- MATH 5525 Intro to Ordinary Differential Equations or MATH 5535 Dynamical Systems & Chaos
- MATH 5651 Basic Theory of Probabilty and Statistics or STAT 5101
- Three additional upper-division MATH courses (for example: MATH 5445 Mathematical Analysis of Biological Networks)
- CSCI 5461 or 5481 (note the CSCI prerequisites for these courses)
- BIOL 1009/1009H General Biology (regular/Honors)
- GCD 3022 Genetics
- One of the following: (note the prerequisites for PBIO, EEB, GCD courses)
- PBIO 5301 Plant Genomics
- EEB 5042 Quantitative Genetics
- GCD 4143 Human Genetics
- GCD 4151 Molecular Biology of Cancer
- CSCI 5461/5481 (the one not taken above)
- MATH 5445 Mathematical Analysis of Biological Networks (recommended)

- Mathematical Biology: Physiology
- MATH 4428 Mathematical Modeling
- One course from the Theoretical Algebra list
- MATH 4242 Applied Linear Algebra
- MATH 5525 Intro to Ordinary Differential Equations or MATH 5535 Dynamical Systems & Chaos
- MATH 5651 Basic Theory of Probability and Statistics or STAT 5101
- MATH 5445 Mathematical Analysis of Biological Networks or MATH 5447 Theoretical Neuroscience
- Two additional upper-division MATH courses
- BIOL 1009/1009H General Biology (regular/Honors)
- PHSL 3061 Principles of Physiology
- CHEM 1061, 1065, 1062, 1066
- One of the following: (note the prerequisites for PHSL and NSC courses)
- PHSL 4700 (was BIOL 4700) Cell Physiology
- PHSL 5444 Muscle
- NSC 5202 Theoretical Neuroscience: Systems and Information Processing (note the prerequisites for this course)
- MATH 5445 or MATH 5447 (the one not taken above)

- MATH 4281 or MATH 5248 or MATH 5251 or MATH 5285H
- MATH 4707 or MATH 5705 or MATH 5707 (Note: MATH 4707 Introduction to Combinatorics and Graph Theory satisfies the Algebra requirement only for the Math Ed specialization.)
- MATH 5335 Geometry I
- MATH 4653 Elementary Probability (MATH 5651 or STAT 5101 may be substituted.)
- Two courses from the Analysis list
- Two additional upper-division MATH courses (recommended: MATH 5336, 4242, 5652, STAT 5102)
- Technical elective as described above

The minor in Mathematics is offered through CLA. To apply for the Mathematics Minor, send an email request to ugrad@math.umn.edu. The applications are reviewed and approved by the DUGS for Mathematics. Requirements:

- Introductory sequence as described above
- Two upper-division MATH courses

Here are course recommendations for students considering graduate study in mathematics:

- MATH 3592H/3593H or MATH 1571H/1572H/2573H/2574H/3283W
- MATH 5615H/5616H Honors: Introduction to Analysis I/II
- MATH 5285H/5286H Honors: Fundamental Structures of Algebra I/II
- MATH 5165/5166 Mathematical Logic I/II
- MATH 5345H Honors: Introduction to Topology
- MATH 5378 Differential Geometry
- MATH 5467 Introduction to the Mathematics of Image and Data Analysis
- MATH 5485/5486 Introduction to Numerical Methods I/II
- MATH 5587/5588 Elementary Partial Differential Equations I/II
- MATH 5583 Complex Analysis
- MATH 5651 Basic Theory of Probability and Statistics or STAT 5101
- MATH 8xxx - see registration procedure for 8xxx MATH courses

MATH 3283W, 4067W, 49xx, and 59xx do not count as upper-division MATH courses, but STAT 5101 and STAT 5102 do.

This document addresses only the major requirements; it does not discuss liberal education requirements or the CLA foreign language requirement.

All courses that are in the major or are prerequisite to courses in the major must be passed with a grade of C- or better.