All students majoring in mathematics at Saint Louis University start with a basic core of required mathematics courses:

- MATH 1510: Calculus I
- MATH 1520: Calculus II
- MATH 2530: Calculus III (must be taken at Saint Louis University with a grade of at least C)
- MATH 2660: Principles of Mathematics
- MATH 3120: Introduction to Linear Algebra

## Major Requirements for the B.A.

The B.A. mathematics major is designed to meet the needs of students with a wide variety of interests. Along with the basic core of required courses, the student then selects five upper-division courses chosen from one of three options.

Students pursuing the teacher 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.

Students can also pursue a concentration in statistics.

A GPA of 2.0 (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: Differential Equations, plus MATH 4550 or MATH 4570
- MATH 4110: Introduction to Abstract Algebra, plus MATH 4120: Linear Algebra or MATH 4150: Number Theory
- MATH 4210: Introduction to Analysis, plus MATH 4220: Metric Spaces or
- MATH 4230: Multivariable Analysis
- MATH 4310: Complex Variables, plus MATH 4320 or MATH 4360
- MATH 3850: Foundations of Statistical Analysis, plus MATH 4800: Probability Theory, MATH 4840: Time Series or MATH 4870: Applied Regression

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 or actuarial sciences. 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.

The pure mathematics option requires the two year-long sequences beginning with MATH 4110: Introduction to Abstract Algebra and MATH 4210: 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 or teaching.

The teacher option requires the following courses, which satisfy requirements for teacher certification:

- MATH 4050: History of Mathematics
- MATH 4110: Elements of Modern Algebra or MATH 4210: Real Analysis
- MATH 4410: Foundations of Geometry or MATH 4470: Non-Euclidean Geometry
- MATH 3850: Foundations of Statistical Analysis

Students must also select one additional course chosen from the following:

- MATH 3550: Differential Equations
- MATH 4800: Elementary Theory of Probability
- MATH 4870: Applied Regression
- MATH 4150: Number Theory

An appropriate upper-division mathematics elective may be substituted, with the approval of the student's mathematics mentor.)

The statistics concentration requires that students take the following courses:

- MATH 3850: Foundations of Statistical Analysis
- CSCI 1300: Introduction to Object Oriented Programming
- MATH 4800: Probability Theory
- MATH 4850: Mathematical Statistics

Students must also take two additional courses selected 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

## Major Requirements for the B.S.

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.

Students select nine upper-division mathematics courses, which include pure mathematics courses in real analysis and algebra, a statistics course, two completed upper-division sequences (including one in pure mathematics), and electives.

Students must also take at least one course in computer programming and one course in another discipline that has a strong mathematical or computational component that cannot be a course counting for any other part of the B.S. requirements. 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.

Students pursuing a B.S. in mathematics must pass at least nine further additional upper-division mathematics beyond MATH 3120. A GPA of 2.0 (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: Differential Equations, plus MATH: 4550 or MATH: 4570
- MATH 4110: Introduction to Abstract Algebra, plus MATH 4120: Linear Algebra or MATH 4150: Number Theory
- MATH 4210: Introduction to Analysis, plus MATH 4220: Metric Spaces or
- MATH 4230: Multivariable Analysis
- MATH 4310: Complex Variables, plus MATH 4320 or MATH 4360
- MATH 4800: Probability and MATH 4850: Statistics

Other upper division courses are offered on an occasional basis.

The B.S. in Mathematics requires both MATH 4110: Introduction to Abstract Algebra and MATH 4210: Introduction to Real Analysis.

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

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 six hours to complete rather than nine hours.

Students select three or four upper division mathematics courses, which brings the total number of additional mathematics courses beyond MATH 3120 to nine. MATH 3270 and MATH 4050 do not fill this requirement. Students can use these courses to customize their curriculum to their individual interests.

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.

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. 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:

- CHEM 4300 Mathematical Technique in Chemistry
- Any three- or four-hour course in computer science, in addition to the one course required for the B.S. in Mathematics.
- The following courses in the Department of Earth and Atmospheric Sciences: EAS 3330: Physical Meteorology I, EAS 3500: Numerical Modeling Applications or EAS 4330: Climate Change and Variability (more advanced EAS classes that could satisfy the requirement already have at least one of these in the prerequisite sequence)
- Any three- or four-hour upper division (3000 or 4000 level) economics class, excluding ECON 3010
- PHIL 4080: Advanced Symbolic Logic (note that this course has a prerequisite of PHIL
4040)

Any three- or four-hour course in physics beyond PHYS 1610 or higher that’s not already being counted toward the B.S. core requirement in laboratory sciences. (PHYS 1610 should not be taken for credit if the student already has taken PHYS 1310 or equivalent for credit). - Any three or four-hour course in engineering that has a calculus (at least MATH 1510) or PHYS 1610: Engineering Physics prerequisite:
- AENG 2000: Introduction to Aeronautics and Astronomy (as well as higher numbered courses with AENG 2000 in the prerequisite sequence)
- BME 3100: Signals
- BME 3200: Mechanics
- BME 3300: Transport Fundamentals
- ECE 3140: Electromagnetic Fields
- ECE 3150: Linear Systems
- ECE 4120: Automatic Control Systems
- ECE 4151: Digital Signal Processing
- ECE 4153: Image Processing
- ESCI 2100: Statics
- ESCI 2150: Dynamics
- ESCI 2300: Thermodynamics (or higher numbered ESCI courses with either ESCI 2100 or ESCI 2200 in the prerequisite sequence)
- MENG 2000: Foundation to Engineering Design