# Course Options

We make an attempt here to divide the courses in our undergraduate curriculum roughly into classical mathematical areas. Any such division is subjective. Furthermore, because most areas of mathematics have interesting and deep relationships with many other areas of mathematics, this attempt at such a division may be sometimes misleading. But these general terms are often used, and it is useful to understand how mathematicians use them.

#### Analysis

The branch of mathematics dealing with calculus and its generalizations is called analysis. Courses in this area include advanced calculus, Introduction to Analysis (Math 316-317), Functions of a Complex Variable (Math 411-412), Differential Equations (Math 320 and 420), Fourier series (Math 421-422), and Numerical Analysis (Math 351-352). Someone interested in a career in technology, applied mathematics, physics, or economics will generally include plenty of analysis or applied analysis in his or her degree program, as well as numerical analysis (including approximate solution techniques and error analysis) and computer science.

#### Algebra

Most of mathematics which does not involve limits or continuity in some way can be generally thought of as belonging to the area of algebra. Our courses in this area include Math 341, Math 342 and Math 441 in linear algebra; two sequences of abstract algebra (Math 391-392 and Math 444-446); and number theory (Math 347-348).

#### Probability and Statistics

Besides Math 243 and Math 425 (which are aimed at mathematically unsophisticated students and thus unsuitable for majors), the department offers Math 461-463 on probability, inference, regression and analysis of variance, Math 467 on stochastic processes, and Math 343 on applied inference.

#### Topology, Geometry and Others

The department offers two terms of topology Math 431-432 and one term of differential geometry (Math 433) as well as two terms of more classical geometry (Math 394 and 395). There are also courses in combinatorics (Math 456), cryptography (Math 458), dynamical systems and chaos theory (Math 457), and occasional special courses.

Students planning on graduate work are encouraged to take courses in several fields to get some feeling for the breadth of mathematics.

## Courses Outside the Major

Language courses (French, German, and Russian are the classical languages of mathematics besides English, and many Ph.D. programs require some fluency in some of these languages) and a thorough grounding in English composition have always been valuable to mathematicians. A concentration in pedagogy or one of the sciences has also been useful when beginning a career. A strong background in economics, business, or finance is valuable, as is a background in computers science, although the situation is constantly changing. Students should have the goal of being able to relate mathematics to something outside of mathematics.

Physics courses (like Physics 251-253) make a natural complement to calculus courses both at the single variable and more advanced level, and we encourage all mathematics majors to take courses like this, especially those majors considering future careers in the physical sciences.

The discipline of economics is highly dependent on mathematics and quantitative methods, and majors who may want a career in the business or financial world should explore options in the Economics department as well as the business school.

Quantitative methods are finding increasing applications in biology as modern lab techniques produce mountains of data allow measurement of systems that can be productively modeled mathematically. Students interested in careers in this rapidly growing area should consider courses in biology as a complement to a mathematics major.

## Core Education Requirements

Besides satisfying the departmental requirements in the major as summarized above (and discussed in detail in the Mathematics section of the Catalog), students must satisfy the university’s Core Education Requirements. These requirements are discussed in detail in the Catalog and in the university’s Student Handbook.

• The Areas of Inquiry Requirements (formerly called Group Requirements) are that students take at least 15 credits in each of three areas (Arts and Letters; Social Science; and Science). Not all courses in these areas satisfy these requirements and the list of courses which do is in the Course Catalog (under General Education Courses). This provides an opportunity to concentrate on a field that is related to mathematics, and also provides an opportunity to learn about areas completely unrelated. The chance to study humanities, the arts, and social science should not be passed up, as a student may never have the opportunity for formal study of these subjects after leaving college.
• For students beginning at UO in Fall 2019 or later, the Multicultural Requirement is a requirement for one course in each of two areas: “Global Perspectives” and “US: Difference, Inequality, Agency”. For students who began at UO earlier, the requirement is to complete one course in two out of three categories (so two courses total): American Cultures; Identity, Pluralism, and Tolerance; International Cultures. Again, the courses which satisfy this requirement are listed in the Course Catalog.
• The Writing Requirement, WR 121 and either WR 122 or WR 123.
• The Mathematics Requirement for the BS will be filled automatically by any math major, and if a student wishes to get a BA instead, there is a foreign language requirement.

Upper-division credit requirement

In addition to the general education requirements, there are various credit requirements for graduation. Students need to be aware of the requirement for at least 62 credits of upper-division work (courses at the 300-level and above).

• Standard and Pure-track math majors who take MATH 307 will get 36 upper-division credits from the major, and so will need 26 more. Usually this means seven more upper-division, 4-credit courses.
• Standard and Pure-track math majors who take MATH 231-232 will get 32 upper-division credits from the major, and so will need 30 more. Usually this means eight more upper-division, 4-credit courses.
• Majors in the Secondary Teaching Track get 40 or 36 upper-division credits from the major (depending on whether they take MATH 307 or MATH 231-232). So students who take MATH 307 will need six more upper-division, 4-credit courses and students who take MATH 231-232 will need seven.

Also, students who are attempting to finish their degrees while non-resident need to be aware of the requirement that at least 45 credits of work AFTER the first 120 credits be done in residence at the university.