## Mathematics major requirements (B.A.)

The B.A. mathematics major is designed to meet
the needs of students with a wide variety of interests. All students
majoring in mathematics start with a basic core of required mathematics
courses. For the B.A. degree the student then builds on this foundation with a
selection of five upper-division courses, chosen from one of three
options. Students in the Teachers Option choose courses that meet
the requirements for state certification in mathematics. In the Applied Mathematics and Pure Mathematics options, students get a measure of depth by taking two year-long
sequences in mathematics.

### Required Courses

Students majoring in mathematics start with a core of five courses.

- MATH 1510 - Calculus I. (old nr: Math 142)
- MATH 1520 - Calculus II. (old nr: Math 143)
- MATH 2530 - Calculus III (old nr: Math 244) (must be taken at St. Louis
University
with a grade of at least “C”).
- MATH 2660 - Principles of Mathematics. (old nr: Math 266)
- MATH 3120 - Introduction to Linear Algebra. (old nr: Math 315)

Options for upper
division courses:

The
student pursuing a B.A. in mathematics must pass at
least five additional upper-division mathematics courses to complete the major under the guidelines of the Applied Mathematics option, the Pure Mathematics option, or the Teachers Option, described below. A GPA of 2.00 (“C” average) or
higher is required in upper-division mathematics courses counting
toward the major. The upper-division courses are built around
year-long sequences of courses in five areas of mathematics:

- MATH 3550, and 4550 or 4570 - Differential Equations; (old nrs: Math 355, 455, 457)
- MATH 4110, and 4120 or 4150 - Introduction to Abstract Algebra and Linear
Algebra or Number Theory; (old nrs: Math 411, 412, and 415)
- MATH 4210, and 4220 or 4230 - Introduction to Analysis and Metric
Spaces or Multivariable Analysis; (old nrs: Math 421, 422, and 423)
- MATH 4310, and 4320 or 4360 - Complex Variables. (old nrs: Math 451, 452, 453)
- MATH 3850 and 4800 or 4840 or 4870 - Foundations of Statistical Analysis and Probability Theory or Time Series or Applied Regression (Previous to Fall 2016, this sequence was 4810/401, 4820/402 - Probability and Statistics)

### Applied Mathematics

The Applied Mathematics option requires any two of the five year-long sequences listed above, plus a fifth upper-division mathematics course beyond the core
mathematics requirement. This option is appropriate for students planning on
careers in industry, government agencies, actuarial sciences, etc. The student's career ambitions should guide the selection of year-long sequences. For example, a career as an actuary will require expertise in probability and
statistics; a career as an applied mathematician, differential equations.

### Statistics Concentration

The Statistics Concentration (Available Fall 2016) requires

- MATH 3850 - Foundations of Statistical Analysis
- CSCI 1300 - Introduction to Object Oriented Programming
- MATH 4800 - Probability Theory
- MATH 4850 - Mathematical Statistics
- Two additional courses from the following:
- MATH 4210 - Introduction to Analysis
- MATH 4230 - Multivariable Analysis
- MATH 4840 - Time Series
- MATH 4860 Statistical Models
- MATH 4870 Applied Regression
- CSCI 5750 Machine Learning

### Pure
Mathematics

The Pure Mathematics option requires the two year-long sequences beginning with Introduction to Abstract Algebra and Introduction to Analysis, plus a fifth upper-division mathematics course beyond the core
mathematics requirement. This option is appropriate for students who intend to
go on to graduate school in mathematics, or who plan careers in cryptography, computer science, teaching, etc.

### Teachers
Option

The Teachers Option requires the following courses, which satisfy requirements for teacher certification.

- MATH 4050 - History of Mathematics (old nr: Math 405)
- MATH 4110 - Elements of Modern Algebra (old nr: Math 411)

or MATH 4210 - Real Analysis (old nr: Math 421)

- MATH 4410 - Foundations of Geometry (old nr: Math 441) or MATH 4470 - Non-Euclidean Geometry (old nr: Math 447)
- MATH 3850 Foundations of Statistical Analysis (Effective Fall 2016) [Old version MATH 4810 - Elementary Theory of Probability (old nr: Math 401)]
- One additional course chosen from the following:
- MATH 3550 - Differential Equations (old nr: Math 355)
- MATH 4800 - Elementary Theory of Probability (Effective Fall 2016)
- [MATH 4850 - Mathematical Statistics (old nr: Math 402) old version]
- MATH 4870 - Applied Regression (Effective Fall 2016)
- MATH 4150 - Number Theory (old nr: Math 415)
- (An appropriate upper-division mathematics elective
may be substituted, with the approval of the
student's mathematics mentor.)

## Mathematics major requirements (B.S.)

- Available Fall 2016

The B.S. mathematics major is designed to provide a strong grounding in mathematics for students considering graduate school in mathematics or a closely allied field. All students majoring in mathematics start with a basic core of required mathematics courses. For the B.S. degree the student then builds on this foundation with a selection of nine upper-division mathematics courses, chosen to include pure mathematics courses in real analysis and algebra, a statistics course at the upper division level, two completed upper division sequences including one in pure mathematics, and electives to complete the required nine upper division courses. Students must also take at least one course in computer programming and one course in another discipline that has a strong mathemtical or computational component, which cannot be a course counting for any other part of the B.S. requirements (for example, the B.S. core). The requirements for the B.S. in Mathematics follow the recommendations of the Mathematics Association of America for degree programs in mathematics that prepare students for graduate work.

### Required Courses

Students majoring in mathematics start with a core of five courses (18 hours).

- MATH 1510 - Calculus I. (old nr: Math 142)
- MATH 1520 - Calculus II. (old nr: Math 143)
- MATH 2530 - Calculus III (old nr: Math 244) (must be taken at St. Louis
University
with a grade of at least “C”).
- MATH 2660 - Principles of Mathematics. (old nr: Math 266)
- MATH 3120 - Introduction to Linear Algebra. (old nr: Math 315)

Students pursuing a B.S. in mathematics must pass at least nine further additional upper-division mathematics (beyond MATH 3120). A GPA of 2.00 ("C" average) or higher is required in upper-division mathematics courses counting toward the major (including MATH 3120). The additional upper-division courses are built around year-long sequences of courses in five areas of mathematics:

- MATH 3550, and 4550 or 4570 - Differential Equations; (old nrs: math 355, 455, 457)
- MATH 4110, and 4120 or 4150 - Introduction to Abstract Algebra and Linear Algebra or Number Theory; (old nrs: math 411, 412, and 415)
- MATH 4210, and 4220 or 4230 - Introduction to Analysis and Metric Spaces or Multivariable Analysis; (old nrs: Math 421, 422, and 423)
- MATH 4310, and 4320 or 4360 - Complex Variables (old nrs: Math 451, 452, 453)
- MATH 3850 and 4800 or 4840 or 4870 - Foundations of Statistical Analysis and Probability Theory or Time Series or Applied Regression (Previous to Fall 2016, this sequence was 4810/401, 4820/402 - Probability and Statistics)
- Other upper division courses are offered on an occasional basis.

### Pure Mathematics Requirement (6 hours)

The B.S. in Mathematics requires both MATH 4110 Introduction to Abstract Algebra and MATH 4210 Introduction to Real Analysis. (old nrs: Math 411, 421)

### Statistics Requirement (3 hours)

The B.S. in Mathematics requires at least one statistics course (with a MATH or STAT designation) at the 3000 or 4000 level.

### Sequence Requirement (6-9 hours)

Students are required to complete two upper division sequences, one of which must be in pure mathematics (a sequence starting with either MATH 4110 or MATH 4210). The other sequence will depend on the further educational and career plans of the individual student. (If the second selected sequence is a second pure mathematics sequence or a statistics sequence, then this requirement takes only a further 6 hours to complete rather than 9 hours).

### Mathematics Electives (9-12 hours)

Students select three or four upper division mathematics courses to bring the total number of additional mathematics courses beyond MATH 3120 to nine (27 hours), except for MATH 3270 and MATH 4050. Students can use these courses to customize their curriculum to their individual interests.

### Computer Programming (3-4 hours)

Students completing a B.S. in Mathematics must take at least one computer programming class. Options include CSCI 1060 Scientific Programming and CSCI 1300 Introduction to Object Oriented Programming.

### Allied Elective (3-4 hours)

Students will be required to take an additional course in another discipline that has a strong mathematical or computational component. Appropriate courses are available in computer science, economics, physics and other science and engineering disciplines. This course cannot be used to satisfy any of the other requirements for a B.S. degree. Introductory level (non-calculus based) statistics courses, including research methods, econometrics and biometrics courses, do not meet the "Allied Elective" requirement. A list of courses that satisfy the requirement is provided below. With pre-approval of the department chair, other courses may be allowed to satisfy the requirement.

List of permitted courses for the Allied Elective Requirement:

- The proposed 4000-level course in genomics (BIOL), if it is approved.
- CHEM 4300 Mathematical Technique in Chemistry
- Any 3 or 4 hour course in computer science (CSCI), in addition to the one course required for the B.S. in Mathematics.
- EAS 3330, EAS 3500, EAS 4330 (more advanced EAS classes that could satisfy the requirement already have at least one of these in the prerequisite sequence).
- Any 3 or 4 hour upper division (3000 or 4000 level) economics class (ECON) (paying attention to prerequisites), excluding ECON 3010.
- PHIL 4080 Advanced Symbolic Logic (noting that this course has a prerequisite of PHIL 4040).
- Any 3 or 4 hour course in Physics (PHYS) number 1610 or higher, not already counting toward the B.S. core requirement in laboratory sciences. (Note: PHYS 1610 should not be taken for credit if the student already has taken PHYS 1310 or equivalent for credit).
- Any 3 or 4 hour course in Engineering that has a calculus (at least MATH 1510) or Engineering Physics (PHYS 1610) prerequisite (paying attention to other prerequisites): AENG 2000 (or higher numbered courses with AENG 2000 in the prerequisite sequence), BME 3100, BME 3200, BME 3300, ECE 3140, ECE 3150, ECE 4120, ECE 4153, ECE 4151, ESCI 2100, ESCI 2150, ESCI 2300 (or higher numbered ESCI courses with at least one of ESCI 2100-2200 in the prerequisite sequence), MENG 2000, MENG 4530, MENG 4150.

## Mathematics Minor Requirements

There are three options for students minoring in mathematics: the traditional Mathematics Minor, the Engineering Mathematics Minor, and the Actuarial Mathematics Minor.

### Mathematics Minor

A minor in mathematics should consist of:

- MATH 1510 - Calculus I (old nr: Math 142)
- MATH 1520 - Calculus II (old nr: Math 143)
- MATH 2530 - Calculus III (old nr: Math 244)
- MATH 2660 - Principles of Mathematics (old nr: Math 266)
- MATH 3120 - Introduction to Linear Algebra (old nr: Math 315)
- one further course in upper-division mathematics chosen with attention to prerequisites.

### Engineering Mathematics Minor

Students seeking a minor in Engineering Mathematics must complete the three semesters of calculus and also complete four upper-division courses in subjects of importance to engineers, which include:

- MATH 3110 - Linear Algebra for Engineers (offered Spring semesters only) (old nr: Math 311)
- MATH 3240 - Numerical Analysis (offered occasionally) (old nr: Math 320)
- MATH 3270 - Advanced Mathematics for Engineers (old nr: Math 370)
- MATH 3550 - Differential Equations (old nr: Math 355)
- MATH 3600 - Combinatorics (offered occasionally) (old nr: Math 360)
- MATH 3810 - Probability and Statistics for Engineers (old nr: Math 403)
- MATH 3850 - Foundations of Statistical Analysis
- MATH 4310 - Introduction to Complex Variables (old nr: Math 451)
- MATH 4320 - Complex Variables II (old nr: Math 452)
- MATH 4360 - Geometric Topology (offered occasionally) (old nr: Math 453)
- MATH 4550 - Nonlinear Dynamics and Chaos (offered Spring semesters only)(old nr: Math 455)
- MATH 4570 - Partial Differential Equations (offered Fall semesters only) (old nr: Math 457)
- MATH 4650 - Cryptography (offered occasionally) (old nr: Math 465)
- MATH 4800 - Probability Theory
- MATH 4810 - Elementary Theory of Probability (old nr: Math 401)
- MATH 4820 - Introductory Mathematical Statistics (old nr: Math 402)
- MATH 4840 Time Series
- MATH 4870 Applied Regression

Other upper-division mathematics courses may fulfill the course requirement for the Engineering Mathematics Minor, subject to approval by the Department of Mathematics and Computer Science. Students must meet the prerequisites for all courses selected.

**Actuarial Mathematics Minor**

A minor in Actuarial Mathematics should consist of:

- MATH 1510 - Calculus I (old nr: Math 142)
- MATH 1520 - Calculus II (old nr: Math 143)
- MATH 2530 - Calculus III (old nr: Math 244)
- MATH 3110 Linear Algebra (old nr: Math 311)
- MATH 3760 Financial Mathematics (old nr: Math 363)
- MATH 3800 Elementary Theory of Probability (Available Fall 2016) [ Old version MATH 4810 Elementary Theory of Probability (old nr: Math 401)]
- one further course in upper-division mathematics chosen with attention to prerequisites.

Students interested in actuarial careers are encouraged to pursue a full mathematics major rather than the Actuarial Math Minor.