Courses offered by the Department of Mathematics are designed to satisfy the needs of majors and nonmajors interested in mathematics primarily as part of a broad liberal education. They provide basic mathematical and statistical training for students in the social, biological, and physical sciences and in the professional schools; prepare teachers of mathematics; and provide advanced and graduate work for students specializing in the field.

**Preparation. **Students planning to major in mathematics at the university should take four years of high school mathematics including a year of mathematics as a senior. Courses in algebra, geometry, trigonometry, and more advanced topics should be included whether offered as separate courses or as a unit.

College transfer students who have completed a year of calculus should be able to satisfy the major requirements in mathematics at the University of Oregon in two years.

**Science Group Requirement.** The department offers courses that satisfy the science group requirement—MATH 105, 106, 107; MATH 211, 212, 213; MATH 231, 232, 233; MATH 241, 242, 243; MATH 246, 247; MATH 251, 252, 253; MATH 261, 262, 263; MATH 307. The 100-level courses present important mathematical ideas in an elementary setting, stressing concepts more than computation. They do not provide preparation for other mathematics courses but are compatible with further study in mathematics.

##### Enrollment in Courses

Beginning and transfer students must take a placement examination before enrolling in their first UO mathematics course; the examination is given during each registration period. Students who transfer credit for calculus to the university are excused from the examination.

To enroll in courses that have prerequisites, students must complete the prerequisite courses with grades of C– or better or P.

Students cannot receive credit for a course that is a prerequisite to a course they have already taken. For example, a student with credit in Calculus for Business and Social Science I (MATH 241) cannot later receive credit for College Algebra (MATH 111). For more information about credit restrictions, contact a mathematics advisor.

##### Bridge Requirement

Most upper-division courses include mathematical proof as a significant element. To prepare for this, students must satisfy the bridge requirement as a prerequisite to taking any 300- or 400-level course.

The bridge requirement is one of the following:

- Introduction to Proof (MATH 307)
- Elements of Discrete Mathematics I and II (MATH 231, 232)
- Calculus with Theory I and II (MATH 261, 262)

Note that this affects all majors because the bridge requirement must be satisfied before taking Elementary Analysis (MATH 315).

##### Program Planning

**Calculus Sequences.** The department offers four calculus sequences. Students need to consult an advisor in mathematics or in their major field about which sequence to take.

Calculus I,II,III (MATH 251, 252, 253) is the standard sequence recommended to most students in the physical sciences and mathematics. Calculus with Theory I,II,III (MATH 261, 262, 263) covers the same material as the standard sequence but includes theoretical background material and is for strong students with an interest in mathematics. Calculus for the Biological Sciences I,II (MATH 246, 247) covers comparable material as Calculus I,II but with an emphasis on modeling and applications to the life sciences. A one-year sequence can be formed by taking MATH 253 after MATH 247. Students interested in taking more advanced mathematics courses should take any of the sequences outlined above (MATH 251, 252, 253 or MATH 261, 262, 263 or MATH 246, 247, 253). The sequences are equivalent as far as department requirements for majors or minors and as far as prerequisites for more advanced courses.

The department’s fourth sequence is Calculus for Business and Social Science I, II (MATH 241, 242) and Introduction to Methods of Probability and Statistics (MATH 243), which is designed to serve the mathematical needs of students in the business, managerial, and social sciences. Choosing this sequence effectively closes the door to most advanced mathematics courses.

Mathematics majors usually take calculus in the freshman year, and should also satisfy the bridge requirement in their freshman year, if possible.

In the sophomore year, majors often take MATH 256, 281, 282, or MATH 315, 341, 342. Students interested in a physical science typically take the first sequence, while students in pure mathematics or in computer and information science find the second more appropriate. The sequences can be taken simultaneously, but it is possible to graduate in four years without taking both at once.

In the junior and senior years, students often take two mathematics courses a term, finishing MATH 256, 281, 282 or MATH 315, 341, 342 and completing the four required upper-division courses.

Students who are considering graduate school in mathematics should take at least one or two of the pure math sequences, MATH 413–415, 444–446, or 431–433. The choice merits discussion with an advisor.

#### Major Requirements

The department offers undergraduate preparation for positions in government, business, and industry and for graduate work in mathematics and statistics. Each student’s major program is individually constructed in consultation with an advisor.

Upper-division courses used to satisfy major requirements must be taken for letter grades, and only one D grade (D+ or D or D–) may be counted toward the upper-division requirement. At least 12 credits in upper-division mathematics courses must be taken in residence at the university.

Statistical Methods I,II (MATH 425, 426) cannot be used to satisfy requirements for a mathematics major.

For students who have completed MATH 261–263 with a grade of mid-C or better, the department will waive the requirement for MATH 315.

To qualify for a bachelor’s degree with a major in mathematics, a student must satisfy the requirements for one of the following options:

To qualify for a bachelor’s degree with a major in mathematics, a student must satisfy the requirements for one of the four options listed below. In all of these options, most courses require calculus as a prerequisite, and in each option some of the courses require satisfying the bridge requirement.

**Option One: Applied Mathematics.** Introduction to Differential Equations (MATH 256), Several-Variable Calculus I,II (MATH 281, 282), Elementary Analysis (MATH 315), Elementary Linear Algebra (MATH 341, 342), and four courses selected from Elementary Numerical Analysis I,II (MATH 351, 352), Functions of a Complex Variable I,II (MATH 411, 412), Ordinary Differential Equations (MATH 420), Partial Differential Equations: Fourier Analysis I,II (MATH 421, 422), Networks and Combinatorics (MATH 456), Discrete Dynamical Systems (MATH 457), Introduction to Mathematical Cryptography (MATH 458), Introduction to Mathematical Methods of Statistics I,II (MATH 461, 462), Mathematical Methods of Regression Analysis and Analysis of Variance (MATH 463)

**Option Two: Pure Mathematics.** Introduction to Differential Equations (MATH 256), Several-Variable Calculus I,II (MATH 281, 282), Elementary Analysis (MATH 315), Elementary Linear Algebra (MATH 341, 342), and four courses selected from Fundamentals of Abstract Algebra I,II,III (MATH 391, 392, 393), Geometries from an Advanced Viewpoint I,II (MATH 394, 395), Introduction to Analysis I,II,III (MATH 413, 414, 415), Introduction to Topology (MATH 431, 432), Introduction to Differential Geometry (MATH 433), Linear Algebra (MATH 441), Introduction to Abstract Algebra I,II,III (MATH 444, 445, 446), Stochastic Processes (MATH 467)

**Option Three: Secondary Teaching. **Elementary Analysis (MATH 315), Statistical Models and Methods (MATH 343), Number Theory (MATH 346), Elementary Linear Algebra (MATH 341), Fundamentals of Abstract Algebra I,II,III (MATH 391, 392, 393), Geometries from an Advanced Viewpoint I,II (MATH 394, 395), and Introduction to Programming and Algorithms (CIS 122) or another programming course approved by an advisor.

**Option Four: Design-Your-Own. **Introduction to Differential Equations (MATH 256), Several-Variable Calculus I,II (MATH 281, 282), Elementary Analysis (MATH 315), Elementary Linear Algebra (MATH 341, 342), and four courses chosen in consultation with an advisor from the lists of courses for the applied or pure mathematics options above.

It is important to get approval in advance; the four elective courses cannot be chosen arbitrarily. In some cases, upper-division courses can be substituted for the lower-division courses listed in the first sentence of this option.

Students are encouraged to explore the design-your-own option with an advisor. For example, physics majors typically fulfill the applied option. But physics students interested in the modern theory of elementary particles should construct an individualized program that includes abstract algebra and group theory. Another example: economics majors typically take statistics and other courses in the applied option. But students who plan to do graduate study in economics should consider the analysis sequence (MATH 413, 414, 415) and construct an individualized program that contains it.

##### Mathematics and Computer Science

The Department of Mathematics and the Department of Computer and Information Science jointly offer an undergraduate major in mathematics and computer science, leading to a bachelor of arts or a bachelor of science degree. This program is described in the **Mathematics and Computer Science** section of this catalog.

##### Recommended Mathematics Courses for Other Areas

Students with an undergraduate mathematics degree often change fields when enrolling in graduate school. Common choices for a graduate career include computer science, economics, engineering, law, medicine, and physics. It is not unusual for a mathematics major to complete a second major as well. The following mathematics courses are recommended for students interested in other areas:

**Actuarial Science.** Elementary Numerical Analysis I,II (MATH 351, 352); Introduction to Mathematical Methods of Statistics I,II (MATH 461, 462) and Mathematical Methods of Regression Analysis and Analysis of Variance (MATH 463). Courses in computer science, accounting, and economics are also recommended. It is possible to take the first few actuarial examinations (on calculus, statistics, and numerical analysis) as an undergraduate student.

**Biological Sciences.** Introduction to Mathematical Methods of Statistics I,II (MATH 461, 462)

**Computer and Information Science.** Elements of Discrete Mathematics I,II,III (MATH 231, 232, 233); Elementary Numerical Analysis I,II (MATH 351, 352) or Introduction to Mathematical Methods of Statistics I,II (MATH 461, 462); Networks and Combinatorics (MATH 456)

**Economics, Business, and Social Science.** Introduction to Mathematical Methods of Statistics I,II (MATH 461, 462). Students who want to take upper-division mathematics courses should take MATH 251–252 in place of MATH 241–242

**Physical Sciences and Engineering.** Elementary Numerical Analysis I,II (MATH 351, 352), Functions of a Complex Variable I,II (MATH 411, 412), Ordinary Differential Equations (MATH 420), Partial Differential Equations: Fourier Analysis I,II (MATH 421, 422)

##### Honors Program

Students preparing to graduate with honors in mathematics should notify the department’s honors advisor no later than the first term of their senior year. They must complete two of the following four sets of courses with at least a mid-B average (3.00 grade point average): MATH 413, 414; MATH 431, 432; MATH 444, 445; MATH 461, 467. They must also write a thesis covering advanced topics assigned by their advisor. The degree with departmental honors is awarded to students whose work is judged truly exceptional.

#### Minor Requirements

The minor is intended for any student, regardless of major, with a strong interest in mathematics. While students in such closely allied fields as computer and information science or physics often complete double majors, students with more distantly related majors such as psychology or history may find the minor useful.

To earn a minor in mathematics, a student must complete at least 30 credits in mathematics at the 200 level or higher, with at least 15 upper-division mathematics credits; MATH 425, 426 cannot be used toward the upper-division requirement. A minimum of 15 credits must be taken at the University of Oregon.

Only one D grade (D+ or D or D–) may be counted toward fulfilling the upper-division requirement. All upper-division courses must be taken for letter grades. The flexibility of the mathematics minor program allows each student, in consultation with a mathematics advisor, to tailor the program to his or her needs.

##### Preparation for Kindergarten through Secondary School Teaching Careers

The College of Education offers a fifth-year program for middle-secondary licensure in mathematics and for elementary teaching. For more information, see the **College of Education** section of this catalog.