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This page contains some supplementary information about the course offerings for the mathematics major. There is no information here about courses below the 200 level or about the science group requirements for non-math majors. For that, and for the precise requirements for the various majors and minors offered in mathematics, please see the mathematics section of the University of Oregon catalog. The catalog also contains a complete list of all mathematics courses.

Warning: the information contained on this page is no substitute for consulting an official advisor in the department of mathematics!

Overview of Courses

Calculus is a core area of mathematics, and is a prerequisite for many courses required by the major. The major can be thought of as requiring a year of calculus at the outset (material prior to calculus must be made up first if it was not taken before entering the university). There are several calculus options open to potential math majors.

Our standard sequence is Math 251-253 which emphasizes mathematical and physical applications of calculus. Math 246-247-253 emphasizes applications in the life sciences and is equivalent to 251-253 for purposes of math majors. Our honors calculus sequence (Math 261-263) covers the same material as 251-253 and in addition covers the theoretical grounding of calculus (why things work the way they do rather than just how things work). Because of this, students who take Math 261-263 are exempt from the requirement for Math 315. (Note that Math 241-243 is our calculus for business majors and is not appropriate for potential mathematics majors).

Math 231-233 is another sequence of courses covering topics outside of calculus at a serious but elementary level. This sequence covers discrete mathematics where calculus is concerned with continuous mathematics. Math 231-233 is essential for students with a major in computer science (or mathematics and computer science). Although not required for the math major, it is a valuable course for any student to take.

Most mathematics majors will take courses in differential equations and vector calculus in the year after taking calculus. Typically this will be Math 256 and Math 281-282. Most majors will also take two terms of linear algebra (Math 341-342), which is a non-calculus based course in multivariable mathematics, and all majors must take Math 315 (Introduction to Analysis, which covers the proofs omitted from Math 251 and 253) unless they have taken Math 261-263. This group of six courses is typically taken more or less during the year following calculus.

After this, there are few standard courses taken by all students. Students not in the secondary education option often build their program around a selection of 400-level course. These include year long sequence of graduate preparation courses in algebra, analysis and topology/geometry, applied courses in numerical analysis and differential equations, courses in statistics, combinatorics, dynamical systems and complex analysis. The specific courses chosen depend on the specialization and interests of the student.

Majors in the secondary education program will take a different set of courses. These majors should take (after a year of calculus) Math 315, Math 341, number theory (Math 346), abstract algebra (Math 391-393), advanced geometry (Math 394-395), introduction to statistics (Math 461) and CIS 122, or a comparable computer programming course to be approved by an advisor.

Families of Courses

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, Functions of a Complex variable, Differential Equations, Fourier series, and Numerical Analysis. 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 391-393 and Math 444-446); and number theory (Math 346). Statistics Besides Math 243 and Math 425-426 (which are aimed at mathematically unsophisticated students and thus unsuitable for majors), the department offers Math 461-463 on regression and analysis of variance, and Math 464-466 on mathematical statistics.
  • Topology, Geometry and others.
    The department offers two terms of topology Math 431-432 and 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, mathematical modeling, dynamical systems (including some chaos theory) and occasional special courses. Students planning on graduate work are encourage 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.

General 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 general education requirements. These requirements are discussed in detail in the catalog and in the university's Student Handbook.

  • The group requirements are 16 credits in each of three areas (Arts and Letters; Social Sciences; and Science). Not all courses in these areas satisfy these requirements and the list of courses which do is in the Student Handbook. There are additional restrictions which are detailed in the catalog and student handbook. 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.
  • The multicultural requirement is a requirement for one course in each of two out of three categories (American Cultures; Identity, Pluralism, and Tolerance; International Cultures). Again, the courses which satisfy this requirement are listed in the Student Handbook.
  • 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. Besides these there are various credit requirements for graduation. Transfer students need to be aware of the requirement for at least 62 credits of upper-division work (courses at the 300-level and above), and similarly, 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.

Honors degrees

Students wishing to graduate with "honors in mathematics" are required to complete two theoretical sequences in mathematics (usually chosen from Math 413-415, Math 431-433, Math 444-446 and Math 464-466) with an average grade of "B" or higher and to write a thesis indicating mastery of an advanced topic studied independently. Any student wishing to do this should notify the head mathematics advisor and seek out an advisor to supervise their independent project by the beginning of the first term of their senior year. A degree with honors indicates ability to do extra work independently and to communicate mathematics in clear English, so it can be helpful in obtaining a good job or graduate fellowship.