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- The Mathematics Major
- Lower Division Requirements
- Upper Division Requirements
- Additional Requirements for BSMath Degree in CSE (was IT)
- Requirements for the BA in CLA
- Specializations
- Actuarial
- Mathematics Education
- Computer Applications
- Graduate School Track
- The Mathematics Minor
The Mathematics Major
Mathematics is a subject with many facets and many applications. The School of Mathematics offers a
major that allows many choices. We have well-defined tracks in: mathematics applicable to industry and
the biological sciences, mathematics applicable to computer science, mathematics useful in actuarial
practice, and mathematics necessary for certification as a secondary mathematics teacher. We of course
have programs that lead to graduate study in both pure and applied mathematics, and we offer a general
major for those students who do not choose to specialize. We offer coursework that could lead to a
career in business or finance. The Actuarial, Education and Computer Science specializations are
recorded on the transcript and noted on the diploma. At the moment of writing, the other
specializations are not so formally recognized. However, they all exist in the School of Mathematics
and, as will be made clear in the descriptions of the different programs, they tend to require more
coursework (and more credits) than the minimum needed to complete the general major. Students who do
not choose a specialized major are able to graduate with the minimum 120 credits if they plan their
programs carefully.
We offer mathematics majors in both the College of Science & Engineering (CSE) and the College of Liberal Arts.
What basic differences are there between the majors in CLA and in CSE? CSE mathematics majors face
broader technical requirements, and must take Physics and Computer Science. Everyone graduating from
CLA is advised to take at least one course in Computer Science and also must be proficient in a foreign
language. CLA students must also complete a Senior Project in the major. CLA majors must take at least
six upper division courses while CSE majors must take at least eight of them. In
addition, CSE majors must take a "Technical Elective" as described below.
All of these different requirements and approaches to the subject are described in detail in this
handout.
This document addresses only the mathematics departmental requirements for the major. In
particular, it does not discuss the University's liberal education requirements or the foreign
language requirement in CLA. The Undergraduate Catalogue or College Advising Office is the proper
source of information on these and other Collegiate and all-University requirements.
All courses that are required for the major or as prerequisites for major courses must be passed
with a grade of at least C-.
Lower Division Requirements
All mathematics majors must start by taking two years of calculus or their equivalent. This
requirement is satisfied by taking one of the sequences listed below. It may be satisfied in part by
receiving credit through the Advanced Placement Exam. These courses cover single and multivariable
calculus, introductory linear algebra, and differential equations.
1271-1272-2243-2263 (for CLA or CSE students) --or-- 1371-1372-2373-2374 (for CSE students only)
--or-- 1571H-1572H-2573H-2574H (for CSE honors students)--or--3592H-3593H (Advanced Placement and Math
Honors).
All students in the major who have not taken the Honors Calculus must start their approach
to proofs by taking one of the following courses:
2283 Sequences, Series and Foundations --or-- 3283 The writing-intensive version of
Math 2283.
This requirement is waived for students who have completed the CSE honors calculus
sequence or the Advanced Placement sequence.
Note that, while Math 3283 is a 3-xxx level course, and so satisfies the requirement of a
writing-intensive course in the major, it may not be counted as part of the Upper Division Math
Requirements.
Additional Requirements: CSE majors must take at least one semester of Computer Science, as
discussed below, and must also take Physics. (CLA majors are strongly advised to take at least one
semester of Computer Science.)
- Computer Science: At least one semester. The most common choices include:
- CSci 1103: Introduction to Computer Programming in Java: For students with little or
no programming experience who expect to be able to design web pages and do other web-related
tasks.
- CSci 1107: Introduction to FORTRAN Programming for Scientists and Engineers. For
students with limited programming experience who expect to take Numerical Analysis courses or to be
involved with scientific computing.
- CSci 1113: Introduction to C/C++ Programming for Scientists and Engineers. A somewhat
higher level course for the same audience as CSci 1107. Students with little or no programming
experience often have difficulty in this course. Such students who want to learn C/C++ might consider
taking CSci 1107 first.
- CSci 1901 or 1901-1902: Structure of Computer Programs I, II. For
students who want a deeper grasp of programming. After the two semesters the student should have
mastered Java at a deeper level than 1103, and be prepared to master C/C++ or FORTRAN.
- Physics: Three semesters, except that students in the Actuarial or Mathematical Biology tracks
need only take two semesters. The courses most commonly taken are: Phys 1301-1302 plus one of the
following: 2303, 2311, or 2503. The CSE Honors Physics, Phys 1401H-1402H-2403H also satisfies the
requirement. Transfer students with precisely one year of transferable physics should consult the
physics department as to what course or courses to take.
Upper Division Math Requirements
Each Math major in CLA or CSE must take two courses from the algebra list and two courses from the
analysis list.
Algebra List:
At least one of the courses on this list must be chosen from column X.
| COLUMN X | COLUMN Y
| | Math 4281: Introduction to Modern Algebra | Math 4242: Applied Linear Algebra
| | Math 5248: Cryptography and Number Theory | Math 5705: Enumerative Combinatorics
| | Math 5251: Error-Correcting Codes, Finite Fields, Algebraic Curves | Math 5707:Graph Theory and Non-enumerative Combinatorics
| | Math 5285: Honors: Fundamental Structures of Algebra I | Math 5711: Linear Programming and Combinatorial Optimization
| | Math 5286: Honors: Fundamental Structures of Algebra II | Math 5485: Introduction to Numerical Methods I
| | Math 5385: Introduction to Computational Algebraic Geometry |
|
Analysis List:
Math 4567 Applied Fourier Analysis
Math 4603 Advanced Calculus I
Math 4604 Advanced Calculus II
Math 4606 Advanced Calculus (4603 and 4606 may not both be used to satisfy the analysis requirement.)
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
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 (or the equivalent Stat 5101)
Math 5652 Stochastic Processes
Math 5654 Prediction and Filtering
Additional Requirements for the BSMath Degree in CSE
Technical Elective Package: Two courses of at least 3 credits each, not necessarily in the Mathematics
Department, but constrained by these three requirements:
- A prerequisite for the courses shall be Calculus I (Math 1271 or 1371) or higher.
- The courses shall be numbered 3XXX or higher.
- The courses shall have a "theme" or "connection". Courses in the same department are
assumed to be linked. If the courses are in different departments, they must have visible "connections" in the subject matter, or to the
student's special interests/career plans. For example, a student who has abandoned a major in some engineering department will be allowed to
offer EE 3025-3161 (same department), but not the interdepartmental mix of EE 3061-Stat 3021 (no visible connections). An acceptable package for
anyone would be Math 5651-Stat 5041 (obvious connections in the subject matter). On the other hand, a known actuarial student might offer the
diverse package of Econ 3101-Stat 3021 (career-related). Advisor approval of the package is required for the technical elective. If the package
is questionable, and receives advisor approval, the student should ask the advisor to make a note of that fact in his or her file. Where a
dispute arises, and the DUGS is called to arbitrate, he or she will honor such written approval.
Credit and coursework requirements
The student must complete at least 120 credits.
In addition to the Lower Division Requirements, the CSE student must
complete eight upper division mathematics courses of at least 3 credits each, including two from the algebra list and two from the analysis list.
Courses from other departments that count as part of the eight course upper division requirement are:
Stat 5101 Theory of Statistics I (mentioned above as equivalent to Math 5651
Stat 5102 Theory of Statistics II (which is different
from Math 5652)
No other courses from other departments may be used to satisfy the eight course upper division
requirement, though they may be used as part of the Technical Elective.
The following courses may not be used to satisfy any upper division requirement in mathematics and may not be used to satisfy any part of the Technical
Elective:
Math 3113 or 4113 Topics in Elementary Mathematics I
Math 3116 or 4116 Topics in Elementary Math II: Short Course
Math 3118 or 4118 Topics in Elementary Mathematics II
Math 4005 Calculus Refresher
Note again that while Math 3283 is a 3-xxx level course, and so satisfies the requirement of a writing-intensive course
in the major, it may not be counted as part of the Upper Division Math Requirement or as technical elective.
Requirements for the BA in CLA
All CLA students must complete a Senior Project. See a mathematics advisor to discuss procedures for working on that project.
An information sheet and the actual application form for the Senior Project are available from Registration Forms. Click here for a CLA Math Senior Project template and timeline.
Credit and coursework requirements. The student must complete at least 120 credits, including at least 41 in the major. In addition to the
Lower Division Requirements, the student must complete six upper division mathematics courses of at least 3 credits each, including two from
the algebra list and two from the analysis list. The courses available for satisfying the six-course upper division requirement are the same
as those available for the BSMath degree, as described on the previous page.
Specializations: BA-Math or BS-Math
The School of Mathematics offers specializations in actuarial mathematics, computer applications and in preparation for teaching
mathematics in the secondary school. These specializations earn a designation that appears on the diploma. At this time, these three
specializations are the only active sub-plans for either the CLA or the CSE Mathematics Major. There is a track that is designed as an
optimal preparation for graduate study in mathematics, but no special designation appears on the diploma. Students in any of these
specializations must meet the requirements of the major in their college as described above (with some exceptions noted in the
descriptions of the specializations).
Actuarial
These are the additional requirements to obtain a specialization in Actuarial Science (both CLA and CSE):
- All Actuarial Math students must take one of CSci 1103 (Java) or CSci 1113 (Programming in C/C++)
- Economics : 1101-1102 (or 1104-1105), 3101, 4261 (Principles of Macroeconomics and Microeconomics,
Intermediate Microeconomics, Introduction to Econometrics). Econ 3101-4261 can be used as the technical elective for CSE students.
- Business : Acct 2050, Fina 3001, and 2 out of 3 of Ins 4100, 4101, 4200.
- Probability and Statistics : Math 5651 or Stat 5101, and either Math 5652 or Stat 5102. Note: Math 5651 and Stat 5101
are considered identical; either is a sufficient prerequisite for either sequel; either can be used as part of the analysis requirement.
Of the sequels, we recommend Math 5652 over Stat 5102. A secondary advantage to this choice is that Math 5652 will complete the analysis
requirement but Stat 5102 will not.
- Actuarial Mathematics : The student must complete Math 4065, Theory of Interest and Math 5067-5068, Actuarial Mathematics I and II.
- Algebra : Math 4242, Applied Linear Algebra. It is strongly recommended that the student also take 5711 (Optimization:
cross-listed with/meets with IE5531). Either one of these courses counts as part of the Algebra Requirement. Note: students in the
Actuarial Specialization must also take an Algebra course from Column X.
Note again that CSE students in the actuarial specialization are not required to take the third semester of Physics.
CSE students (and CLA students who have room in their programs) might use some of the following as technical electives or to fill out their program:
Math 4428, Mathematical Modeling
Math 5485, Numerical Methods I
Math 5705 or 5707, Combinatorics A or B
Math 5075/5076, Mathematics of Options, Futures and Derivatives
Stat 5302,Applied Regression Analysis
Fina 4241, Corporate Financing Decisions
Fina 4121, Financial Markets and Interest Rates;
Econ 3101, Intermediate Microeconomics;
Econ3102, Intermediate Macroeconomics
CSci 4061, Introduction to Operating System
CSci 5103, Operating Systems
CSci 5301/2, Numerical Analysis.
Mathematics Education
These are the additional requirement to obtain a specialization in Secondary Mathematics Education:
- CLA majors must take seven upper division mathematics courses satisfying major requirements.
- Each student must include the following four courses in the major program:
Math 5651: Basic Theory of Probability and Statistics or the equivalent Stat 5101: Theory of Statistics I, or Math 4653: Elementary Probability
Math 4281: Introduction to Modern Algebra or Math 5285: Honors: Fundamental Structures of Algebra I or Math 4242: Applied Linear Algebra.
Math 5335 Geometry I
Math 4707 or 5707 or 5705 (Combinatorics) NOTE: Math 4707 will be accepted as an algebra course only for students completing this specialization.
If a student takes MATH 4242, then the student must also choose a Column X algebra course. Note that, of the courses above in the Mathematics Education sub-plan, only MATH 5651 and STAT 5101 are on the analysis list. A total of two analysis courses must be chosen.
There are other courses that are recommended but not required. These include Math 5652: Stochastic Processes or Stat 5102: Theory of Statistics II, which are strongly recommended. Another strong recommendation is Math 5336: Geometry II.
All students who attempt this specialization should consult the staff in Mathematics Education about other
courses that must be completed in order to obtain secondary licensure in Minnesota. To start this, call
(612) 625-6501 and ask for a referral for information on the program in Mathematics Education. This
consultation should be done by the end of the junior year or at the very beginning of the senior year.
Computer Applications
These are the additional requirements for an emphasis in Computer Applications.
If the course for this category is from the algebra list, then it must be in addition to the two courses from that list that are required for all mathematics majors.
Note: Students who complete this emphasis will also satisfy the requirements for a minor in Computer Science.
Graduate School Track
(No claim is made or implied that taking another track and doing well precludes going to graduate school. In some sense this is a "Pure Mathematics" track.)
- Lower Division:
First year calculus;
Most preferable: Math 3592H, 3593H: Honors Mathematics
Next: Math 1571H, 1572H: Honors Calculus
Next: Math 1371, 1372: CSE Calculus
Next: Math 1281, 1282: Calculus for the Biological Sciences
Next: Math 1271, 1272: Standard calculus
Second year calculus: Continue the sequence that the student is in: Math 2573H & Math 2574H or Math 2373, Math 2374 or Math 2243, 2263.
Plus Math 3283W: Sequences, Series and Foundations - Writing Intensive (for those students who have not taken the Honors sequence)
Some of the students who choose this option will enter with some sort of advanced placement. Individual consultation will be necessary to place them properly.
- Analysis and Algebra requirements:
One of the sequences Math 5615-5616 Honors: Introduction to Analysis I, II and Math 5285-5286 Honors: Fundamental
Structures of Algebra I, II are strongly recommended. Many students in this track may wish to take both of these sequences.
If Math 5615-5616 is taken and Math 5285-5286 is not taken, the algebra requirement must be chosen from Math 4281, Introduction to Modern Algebra and one of Math 5385, Introduction to Computational Algebraic Geometry or one of Math 5705: Enumerative Combinatorics or Math 5707: Graph Theory and Non-Enumerative Combinatorics.
If Math 5285-5286 is taken and Math 5615-5616 is not taken, the analysis requirement must be chosen from Math 5525, Introduction to Ordinary Differential Equations, Math 5535, Dynamical Systems and Chaos, Math 5588, Elementary Partial Differential Equations II, Math 5652, Introduction to Stochastic Processes, and Math 5654, Prediction and Filtering.
- Other mathematics courses to make a total of ten, including the technical elective (for CLA majors replace "ten" by "eight") 5-xxx or higher level mathematics courses must be chosen from the courses listed above (in section 2) or from among the following courses:
Math 5165-5166, Mathematical Logic I, II
Math 5345, Introduction to Topology
Math 5378, Differential Geometry
Math 5467, Introduction to the Mathematics of Wavelets
Math 5485-5486, Introduction to Numerical Methods I, II
Math 5587, Elementary Partial Differential Equations I
Math 5583, Complex Analysis
Math 5651, Basic Theory of Probability and Statistics or Stat 5101
- Other requirements:
Students are expected to gain some expertise in and understanding of computer programming. Among the ways do this, taking CSci 1113, Introduction to C/C++ Programming for Scientists and Engineers and/or CSci 1901/1902, Structure of Computer Programming I, II are frequently used.
Physics: 3 semesters as described in the mathematics major description in the undergraduate catalogue (p.290 in the 2002-2004 undergraduate catalogue).
Either Math 4997W Senior Project (required for CLA majors) and/or at least one
8-xxx level course in mathematics.
The Mathematics Minor
A Minor in Mathematics consists of the standard five-part freshman-sophomore sequence (including Math 2283 or 3283) or the four-part honors sequence, and two courses at the 4xxx/5xxx level. Math 4900-4997 and 5900 cannot be used without special permission from a Math adviser. All of the courses must be approved courses for the major. Stat 5101 and/or Stat 5102 may be used as part of the Math Minor. Mathematics Minors are obtained by application through the Undergraduate Mathematics Office. Forms are available in 115 Vincent Hall (Ugrad Math Office). Math Minor applications must be approved by the DUGS for Mathematics. Approved applications must be filed with the appropriate office prior to application for graduation. The Ugrad Math Office will direct students to the proper office for submission of the approved Math Minor form.
Revised 3/30/05 by DLF as DUGS; Updated 2/7/11 cmc.
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