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Mathematics

Department Overview

C138 Padelford

Mathematics is both a science and an art. Like any great art, mathematics has an intrinsic beauty and coherence that has attracted practitioners for centuries. Yet, unlike other arts, mathematics is a surprisingly effective tool for describing the natural world. Indeed, mathematics has come to serve as the foundation of modern science, through its language and results. Some mathematical results were initially developed in order to solve internally generated mathematical problems and only later found application in other disciplines; other mathematical results were inspired by the needs of these other disciplines. The two facets of mathematics -- tool of science and subject of inquiry for its own sake -- have come to be interwoven into a complex fabric.

Undergraduate Program

Adviser
C36 Padelford, Box 354350
(206) 543-6830
advising@math.washington.edu

The Department of Mathematics offers the following programs of study:

  • The Bachelor of Arts degree with a major in mathematics -- standard program
  • The Bachelor of Arts degree with a major in mathematics -- philosophy option
  • The Bachelor of Arts degree with a major in mathematics, with an option designed specifically for students who plan to pursue secondary teaching careers
  • The Bachelor of Science degree with a major in mathematics -- standard program
  • The Bachelor of Science degree with a major in mathematics -- comprehensive option
  • The Bachelor of Science degree with a major in applied and computational mathematical sciences (ACMS). The Department of Mathematics cooperates with the departments of Applied Mathematics, Computer Science and Engineering, and Statistics in offering this major. (See ACMS for requirements.)
  • A minor in mathematics

Bachelor of Arts

Department Admission Requirements

Admission Requirements for Standard Option and Philosophy Option:

A minimum 2.0 grade in the following courses: MATH 124, MATH 125, MATH 126 (or MATH 134, MATH 135, and MATH 136); a minimum 2.20 cumulative GPA in these courses

Admission Requirements for Teacher Preparation Option:

A minimum 2.0 grade in MATH 124, MATH 125, MATH 126 (or MATH 134, MATH 135, and MATH 136); a minimum 2.50 cumulative GPA in these courses.

Major Requirements

Standard Option (51 credits):

  1. MATH 124, MATH 125, MATH 126, MATH 307, MATH 308 (or MATH 134, MATH 135, and MATH 136); MATH 300; MATH 324; and 8 courses numbered 301 or higher from an approved list of electives. See adviser for approved list.
  2. A minimum 2.0 grade in all courses presented to satisfy the mathematics major requirements. A minimum 2.00 cumulative GPA or higher in all mathematics courses at the University, including course repeats.
  3. At least 18 credits of graded mathematics courses numbered 300 or higher must be taken in residence at the University.

Philosophy Option (58 credits):

  1. MATH 124, MATH 125, MATH 126, MATH 308 (or MATH 134, MATH 135, and MATH 136); MATH 300; MATH 327; MATH 328; five additional mathematics courses at the 300 or 400 level, including at least one two-quarter sequence at the 400 level other than MATH 407, MATH 408, MATH 409, or MATH 421, MATH 422
  2. PHIL 120 or an upper-level course in logic; PHIL 100, PHIL 160, or PHIL 240; one philosophy course at the 300 level; one philosophy course at the 400 level
  3. A minimum 2.0 grade in all courses presented to satisfy the mathematics major requirements. A minimum 2.00 cumulative GPA or higher in all mathematics courses at the University, including course repeats.
  4. At least 18 credits of graded mathematics courses numbered 300 or higher taken in residence at the University.

Teacher Preparation Option (52-59 credits):

  1. MATH 124, MATH 125, MATH 126, MATH 307, MATH 308 (or MATH 134, MATH 135, and MATH 136); MATH 300; MATH 394, MATH 411, MATH 412, MATH 444, MATH 445; either STAT 311, MATH 390/STAT 390; or Q SCI 381; 15 credits of approved electives at the 300 level in MATH, AMATH, or STAT, or PHYS 407, PHYS 408, and PHYS 409. At least 6 credits of electives must be from the Mathematics Department.
  2. A minimum 2.0 grade in all courses presented to satisfy the mathematics major requirements. A minimum 2.50 cumulative GPA or higher in all mathematics courses at the University, including course repeats.
  3. At least 18 credits of graded mathematics courses numbered 300 or higher taken in residence at the University

Bachelor of Science

Department Admission Requirements

Standard option: A minimum 2.0 grade in the following courses: MATH 124, MATH 125, MATH 126 (or MATH 134, MATH 135, and MATH 136); a minimum 2.20 cumulative GPA in these courses.

Comprehensive option: A minimum 2.0 grade in the following courses: MATH 124, MATH 125, MATH 126 (or MATH 134, MATH 135, and MATH 136); a minimum 2.50 cumulative GPA in these courses.

Major Requirements

Standard Option (66 credits):

  1. Elementary Mathematics Core (21 credits): MATH 124, MATH 125, MATH 126); MATH 300; MATH 324. (MATH 134, MATH 135, MATH 136 may be substituted for MATH 124, MATH 125, MATH 126, MATH 307, and MATH 308.)
  2. Intermediate Mathematics Core (9 credits): MATH 308; MATH 327, MATH 328. (MATH 334, MATH 335, MATH 336 may be substituted for MATH 300, MATH 309, MATH 324, MATH 327, and MATH 328.)
  3. Advanced Mathematics Core (21 credits): At least seven courses from the following, from at least three different areas, and including at least two two-quarter sequences:
    • Algebra: MATH 402, MATH 403, MATH 404.
    • Analysis: MATH 424, MATH 425, MATH 426.
    • Geometry: MATH 441, MATH 442, MATH 443.
    • Other Analysis: MATH 307, MATH 309; MATH 427, MATH 428.
    • Probability: MATH 394, MATH 395, MATH 396; MATH 491, MATH 492.
    • Other Mathematics: MATH 381; MATH 407, MATH 408, MATH 409; MATH 461, MATH 462; MATH 464, MATH 465, MATH 466.
  4. Electives (15 credits): Five additional mathematics courses, including a two-quarter sequence at the 300- or 400-level (teacher-preparation courses not allowed). With approval, two of the five courses may be chosen from appropriate courses offered by the departments of Applied Mathematics, Statistics, and Computer Science, or from certain other departments. Courses from the additional mathematics core sequences not used to fulfill core requirements can be used to fulfill the elective requirement.
  5. A minimum 2.0 grade in all courses presented to satisfy the mathematics major requirements. A minimum 2.00 cumulative GPA or higher in all mathematics courses at the University, including course repeats.
  6. At least 18 credits of graded mathematics courses numbered 300 or higher taken in residence at the University.

Comprehensive Option (69 credits):

Emphasizes the fundamental subjects of algebra, analysis, and geometry and is designed to provide a deep understanding of these basic areas of modern mathematics. Lays a good foundation for more advanced study. For this option, the grade, elementary core, and elective requirements remain unchanged, with the same substitutions permitted from the accelerated/Honors sequences. (Items 1, 2, 3, and 6 shown for the standard option, above.)

  1. Elementary Mathematics Core (21 credits): MATH 124, MATH 125, MATH 126; MATH 300; MATH 324. (MATH 134, MATH 135, MATH 136 may be substituted for MATH 124, MATH 125, MATH 126, MATH 307, and MATH 308.)
  2. Intermediate Mathematics Core (9 credits): MATH 308; MATH 327, MATH 328. (MATH 334, MATH 335, MATH 336 may be substituted for MATH 300, MATH 309, MATH 324, MATH 327, and MATH 328.)
  3. Advanced Mathematics Core (24 credits): At least eight courses from the following, including at least two in each of the first three areas. If only six courses are chosen from the first three areas, then the two courses chosen from the fourth area must form a two-quarter sequence:
    • Algebra: MATH 402, MATH 403, MATH 404.
    • Analysis: MATH 424, MATH 425, MATH 426.
    • Geometry: MATH 441, MATH 442, MATH 443.
    • Other Analysis: MATH 307, MATH 309; MATH 427, MATH 428.
  4. Electives (15 credits): Five additional mathematics courses, including a two-quarter sequence at the 300- or 400-level (teacher-preparation courses not allowed). With approval, two of the five courses may be chosen from appropriate courses offered by the departments of Applied Mathematics, Statistics, and Computer Science, or from certain other departments. Courses from the additional mathematics core sequences not used to fulfill core requirements can be used to fulfill the elective requirement.
  5. A minimum 2.0 grade in all courses presented to satisfy the mathematics major requirements. A minimum 2.50 cumulative GPA or higher in all mathematics courses at the University, including course repeats.
  6. At least 18 credits of graded mathematics courses numbered 300 or higher taken in residence at the University.

Continuation Policy

All students must make satisfactory academic progress in the major. Failure to do so results in probation, which can lead to dismissal from the major. For the complete continuation policy, contact the departmental adviser or refer to the department website.

Minor

Minor requirements (minimum 30 credits):

  1. Core (24-25 credits): MATH 124, MATH 125, MATH 126, MATH 307, MATH 308, and MATH 309; or MATH 134, MATH 135, and MATH 136 (25 credits, including 10 advanced-placement credits)
  2. Electives (6 credits): mathematics courses numbered 301 or higher
  3. At least 9 credits of courses numbered 301 or higher taken in residence at the University. Minimum 2.0 grade required for each course offered as part of the minor.

Student Outcomes and Opportunities

  • Learning Objectives and Expected Outcomes: The study of mathematics emphasizes exposure to the core foundational areas of analysis, modern algebra, and geometry. A mathematician's skill set includes the technical tools specific to each area as well as the development of critical thinking skills necessary for logical reasoning. Graduates have pursued careers in teaching, finance, science, engineering, and professional fields such as law and medicine.
  • Instructional and Research Facilities: Mathematical Research Library and Math Sciences Computing Center
  • Honors Options Available: With College Honors (Completion of Honors core curriculum and Departmental Honors); With Honors (Completion of Departmental Honors requirements in the major). See adviser for requirements.
  • Research, Internships, and Service Learning: When available, internship opportunities are passed on to students.
  • Department Scholarships: None offered.
  • Student Organizations/Associations: MAA Student Chapter, Actuarial Club, Math Club.

Graduate Program

Graduate Program Coordinator
C36 Padelford, Box 354350
(206) 543-6830
grads@math.washington.edu

The degrees of Master of Arts, Master of Science, and Doctor of Philosophy are offered. Opportunities are available within the department for study of abstract and applied mathematics for each of these degree programs. The Master of Arts degree is appropriate for students who need a broad background in advanced mathematics and who expect to continue working with mathematics of approximately the same level in their careers. The Master of Science degree is appropriate for students who expect to be working with more specialized mathematics of increasing order of complexity in their careers. The Doctor of Philosophy degree is the highest professional degree in mathematics. It is appropriate for students who plan on a career of research and/or teaching of mathematics at the highest levels.

Of the master's degrees, the MS non-thesis program has the most demanding course requirements and most closely matches the early stages of the PhD program. Most students who enroll in the department begin their studies with the PhD or MS non-thesis program in mind. The MS programs with options in numerical analysis or optimization provide more focused training in these directions, which can be useful for students seeking employment in certain industries; however, students intending to do research in these areas would normally follow the requirements of the PhD program. Note that the department does not offer a master's degree in mathematics education.

Master of Arts

Admission Requirements

Bachelor of Arts degree with major in mathematics or equivalent background (minimum of 45 quarter credits or 30 semester credits of mathematics beyond college algebra)

Degree Requirements

Master of Arts, Non-Thesis: Minimum twelve approved one-quarter courses at the 400 or 500 level, including two courses each in algebra, analysis, and one other field. The course total must include six courses chosen from the designated core graduate courses or, with prior approval of the Graduate Program Coordinator, from other 500-level sequences. The six courses at the 500 level should be distributed over no more than three sequences.

Written examination in an area agreed upon by the student and the chair of the examining committee. Oral examination may be substituted with prior approval of the Graduate Program Coordinator.

Master of Science

Admission Requirements

Bachelor of Science degree with major in mathematics, Bachelor of Arts degree with strong major in mathematics or equivalent background. In particular, at least one senior-level course in abstract algebra or real analysis is expected.

Degree Requirements

  1. Master of Science, Thesis: A total of twelve numerically graded one-quarter courses from MATH 402, MATH 403, MATH 404; MATH 424, MATH 425, MATH 426; MATH 427, MATH 428, MATH 429; MATH 441, MATH 442, MATH 443; any 500-level mathematics course; AMATH 507; AMATH 584, AMATH 585, AMATH 586; plus 9 thesis credits (MATH 700). Other courses may be included in the total with prior approval of the Graduate Program Coordinator. Courses to include at least two quarters from each of two designated core graduate courses and one other 500-level sequence. Transfer credits are not accepted at the 400 level; other transfer credits and substitutions are at the discretion of the Graduate Program Coordinator.

    The thesis, which is defended in an oral examination, should demonstrate the ability to do independent research.

  2. Master of Science, Non-Thesis: A total of fifteen numerically graded one-quarter courses from MATH 402, MATH 403, MATH 404; MATH 424, MATH 425, MATH 426; MATH 427, MATH 428, MATH 429; MATH 441, MATH 442, MATH 443; any 500-level mathematics course; AMATH 507; AMATH 584, AMATH 585, AMATH 586. Other courses may be included in the total with prior approval of the Graduate Program Coordinator. Courses to include at least two quarters from each of three designated core graduate courses, and in addition one three-quarter sequence of 500-level mathematics courses in an area of specialization approved by the Graduate Program Coordinator and the chair of the student's examining committee.

    Oral examination in the area of specialization on a topic agreed upon by the student and the chair of the examining committee, or the general examination for the PhD degree.

  3. Master of Science, Numerical Analysis and Optimization Options, Non-thesis: A total of fifteen one-quarter courses, at least six of which are at the 500 level, chosen from MATH 424, MATH 425, MATH 426; MATH 427, MATH 428, MATH 429; MATH 438, MATH 439; MATH 441, MATH 442, MATH 443; MATH 461, MATH 462; MATH 491, MATH 492; any 500-level mathematics course; AMATH 507; AMATH 584, AMATH 585, AMATH 586. Other courses may be included in the total with prior approval of the Graduate Program Coordinator. Courses to include four from AMATH 584, AMATH 585, AMATH 586 and MATH 594, MATH 595, and MATH 596.

    Oral examination in a special topic agreed upon by the student and the chair of the student's examining committee.

Doctor of Philosophy

Admission Requirements

Mathematical training equivalent to a bachelor's degree with strong major in mathematics, including rigorous coursework in real analysis and abstract algebra.

Degree Requirements

90 credits minimum, as follows:

  1. Courses: Six three-quarter sequences numbered 500 or above or equivalent, including three sequences from the department's list of core graduate courses. The list of core courses includes MATH 504, MATH 505, MATH 506; MATH 524, MATH 525, MATH 526; MATH 534, MATH 535, MATH 536; MATH 544, MATH 545, MATH 546; MATH 554, MATH 555, MATH 556. At least two sequences from this list must be satisfactorily completed during year one, and the third must be satisfactorily completed by the end of year two. A student may substitute a passing performance in a preliminary examination for satisfactory completion of the corresponding designated core course.
  2. Preliminary Examinations: Pass three preliminary examinations by September of the beginning of the third year.
  3. Foreign Language/Computer Requirement: Pass either two foreign language examinations or one foreign language examination and a computer programming examination. A PhD student is expected to pass one language or computer examination by the end of summer quarter after the second year, and the second by the end of summer quarter after the third year.
  4. General Examination: An oral examination on a special area of intended research, given by a committee after the student has passed the preliminary examinations and the language examinations. This examination can be given only after two years of graduate study. Normally, it should be taken by the middle of the student's fourth year. Thesis: An original contribution to knowledge. 27 credits of MATH 800 required.
  5. Final Examination: An oral exam given by a committee headed by the thesis supervisor.

Financial Support

Most graduate students in mathematics are supported by fellowships, research assistantships, and teaching assistantships. The workload of teaching assistants allows ample time for graduate courses and thesis work.