Concentration in Mathematics

Five bachelor's degrees are available in the Department of Mathematics:

It is possible to earn any of these degrees with Honors. In addition, there is a joint Bachelor's/Master's program in mathematics. Course programs qualifying students for the degree of Bachelor of Arts provide more elective freedom, while programs qualifying students for the degrees of Bachelor of Science require more emphasis in the physical sciences.

General Education Requirements. All degree programs, whether qualifying students for a degree in mathematics or in applied mathematics, require fulfillment of the College's general education requirements. The general education sequence in the physical sciences must be selected from either first-year basic chemistry or first-year basic physics. The courses that make up the concentration program include at least nine courses in mathematics (detailed descriptions follow for each degree), plus at least five courses within the Physical Sciences Collegiate Division (PSCD) but outside mathematics, one of which completes a three-quarter sequence in basic chemistry or basic physics, and at least two others which should form a sequence of courses from a single department. These latter courses must be chosen from astronomy, chemistry, computer science, physics (12000s or above), geophysical sciences, or statistics (22000 or above). We particularly call attention to two degree programs that are described in more detail in the following paragraphs: (1) the Bachelor of Science in mathematics with specialization in computer science, and (2) the Bachelor of Science in mathematics with specialization in economics.

Note: Mathematics students may use AP credit for chemistry or physics to meet their general education physical sciences requirement or the physical sciences component of the concentration. However, no credit designated simply as "physical science," from AP examinations or from the College's physical sciences placement examination, may be used in their general education requirement or in the concentration.

Students are required to complete both a 10000-level sequence in calculus (or to demonstrate equivalent competence on the calculus placement test) and a three-quarter sequence in analysis (Mathematics 20300-20400-20500 or 20700-20800-20900), and two quarters of a sequence in algebra (Mathematics 25400-25500 or 25700-25800). The normal procedure is to take calculus in the first year and analysis in the second.

Concentrators in mathematics or applied mathematics may take any 20000-level mathematics courses elected beyond concentration requirements for a grade of P. However, a grade of C- or better must be earned in each calculus, analysis, or algebra course, and an overall grade average of C or better must be earned in the remaining mathematics courses that a student uses to meet concentration requirements. Courses in the Physical Sciences Collegiate Division that are used to meet concentration requirements in mathematics must be taken for quality grades.

Students taking a bachelor's degree in mathematics or in applied mathematics should note that by judicious employment of courses from another field for extradepartmental requirements or for electives, a minor field can be developed that is often in itself a sufficient base for graduate or professional work in their field. A notable example is furnished by the field of statistics: the core programs are Statistics 24200 and 25100 for probability theory and Statistics 24400 and 24500 for statistical theory. For an emphasis on statistical methods, students would add Statistics 22200, 22400, or 22600; while for an emphasis on probability they would add Statistics 31200 or perhaps Statistics 38100-38200.

What is noted here for statistics can also be applied to computer science (consult following section), chemistry, geophysical sciences, physics, biophysics, theoretical biology, economics, and education.

While these remarks apply to all bachelor's degree programs in the Department of Mathematics, their force is particularly evident in programs looking to bachelor's degrees in applied mathematics, where minor fields are strongly urged.

Degree Programs in Mathematics. Candidates for the B.A. and B.S. in mathematics all take a sequence in basic algebra. Candidates for the B.S. degree must take the three-quarter sequence (Mathematics 25400-25500-25600 or Mathematics 25700-25800-25900), whereas B.A. candidates may opt for a two-quarter sequence (Mathematics 25400-25500 or Mathematics 25700-25800). The remaining mathematics courses needed in the concentration programs (three for the B.A., two for the B.S.) must be selected, with due regard for prerequisites, from the following list: Mathematics 17500, 21100, 24100, 24200, 26100, 26200, 26300, 27000, 27200, 27300, 27400, 27500, 27700, 27800, 27900, 28000, 28100, 28400, 29200, 29700 (as approved), 30000, 30100, 30200, 30300, 30900, 31000, 31200, 31300, 31400, 31700, 31800, 31900, 32500, 32600, 32700, and Statistics 25100. B.A. candidates may include Mathematics 25600 or 25900.

B.S. candidates are further required to select a minor field, which consists of an additional three-course sequence, which is outside the Department of Mathematics but within the Physical Sciences Collegiate Division, chosen in consultation with the departmental counselor.

Summary of Requirements:

General Education

  • CHEM 11100-11200 or higher†, or PHYS 12100-12200 or higher†
  • MATH 13100-13200, 15100-15200, or 16100-16200†

Concentration

  • 1 CHEM 11300 or higher†, or PHYS 12300 or higher†
  • 1 MATH 13300, 15300, or 16300†
  • 3 MATH 20300-20400-20500 or 20700-20800-20900
  • 2 courses in mathematics chosen from an approved list
  • 4 courses within the PSCD but outside of mathematics, at least two of which should form a sequence in a single department

plus the following requirements:

B.A.

  • 2 MATH 25400-25500 or 25700-25800
  • 1 MATH 25600, 25900, or an approved alternative

14

B.S.

  • 3 MATH 25400-25500-25600 or 25700-25800-25900
  • 3 three-quarter sequence in a minor field outside mathematics

17

† Credit may be granted by examination.

Degree Program in Applied Mathematics. Candidates for the B.S. in applied mathematics all take prescribed courses in numerical analysis, algebra, complex variables, ordinary differential equations, and partial differential equations. In addition, candidates are required to select, in consultation with the departmental counselor, a minor field, which consists of a three-course sequence that is outside the Department of Mathematics but within the Physical Sciences Collegiate Division.

Summary of Requirements:

Applied Mathematics

General Education

  • CHEM 11100-11200 or higher†, or PHYS 12100-12200 or higher†
  • MATH 13100-13200, 15100-15200, or 16100-16200†

Concentration

  • 1 CHEM 11300 or higher†, or PHYS 12300 or higher†
  • 1 MATH 13300, 15300, or 16300†
  • 3 MATH 20300-20400-20500 or 20700-20800-20900
  • 1 MATH 21100
  • 2 MATH 25400-25500 or 25700-25800
  • 3 MATH 27000-27300-27500
  • 6 courses within the PSCD but outside of mathematics, at least three of which should form a sequence from a single department

17

† Credit may be granted by examination.

Degree Program in Mathematics with Specialization in Computer Science. The concentration program leading to a B.S. in mathematics with a specialization in computer science is a version of the B.S. in mathematics. The degree is in mathematics with the designation "with specialization in computer science" included on the final transcript. Candidates are required to complete a yearlong sequence in calculus (Mathematics 15100-15200-15300 or 16100-16200-16300 strongly recommended), in analysis (Mathematics 20300-20400-20500 or 20700-20800-20900), and in abstract algebra (Mathematics 25400-25500-25600 or 25700-25800-25900), and earn a grade of at least C- in each course. The remaining two mathematics courses may be chosen from the list of approved courses in the section Degree Programs in Mathematics except for Mathematics 17500 and Statistics 25100; students are urged to take at least one of Mathematics 24200, 26200, 27700, or 28400. A C average or better must be earned in these two courses.

Besides the third quarter of basic chemistry or basic physics, the seven courses required outside the Department of Mathematics must all be in the computer science department. A two-quarter sequence in programming is required; Computer Science 11500-11600 is recommended. (Students may substitute Computer Science 10500-10600, although this is not encouraged.) Five additional courses must be selected from among computer science courses numbered 20000 or higher, except 27400. Students who take Computer Science 10500-10600 are encouraged to include Computer Science 22100 here. Students must earn a grade of C or better in each course taken in computer science to be eligible for this degree. For more information, consult the Computer Science section of this catalog.

Summary of Requirements:

Mathematics with Specialization in Computer Science

General Education

  • CHEM 11100-11200 or higher†, or PHYS 12100-12200 or higher†
  • MATH 13100-13200, 15100-15200, or 16100-16200†

Concentration

  • 1 CHEM 11300 or higher†, or PHYS 12300 or higher†
  • 1 MATH 13300, 15300, or 16300†
  • 3 MATH 20300-20400-20500 or 20700-20800-20900
  • 3 MATH 25400-25500-25600 or 25700-25800-25900
  • 2 CMSC 11500-11600
  • 2 approved courses in mathematics
  • approved courses in computer science

17

† Credit may be granted by examination.

Degree Program in Mathematics with Specialization in Economics. This concentration program is a version of the B.S. in mathematics. The B.S. degree is in mathematics with the designation "with specialization in economics" included on the final transcript. Candidates are required to complete a yearlong sequence in calculus, in analysis (Mathematics 20300-20400-20500 or 20700-20800-20900), and two quarters of abstract algebra (Mathematics 25400-25500 or 25700-25800), and earn a grade of at least C- in each course. Students must also take Statistics 25100 (Probability). The remaining two mathematics courses must include Mathematics 27000 (Complex Variables) and either Mathematics 27200 (Functional Analysis) for those interested in Econometrics or Mathematics 27300 (Ordinary Differential Equations) for those interested in economic theory. A C average or better must be earned in these two courses.

Besides the third quarter of basic chemistry or basic physics, the eight courses required outside the Department of Mathematics must include Statistics 22000 or 24400. The remaining seven courses should be in the economics department and must include Economics 20000-20100-20200-20300 and Economics 20900 or 21000 (Econometrics). The remaining two courses may be chosen from any undergraduate economics course numbered higher than Economics 20300. Students must earn a grade of C or better in each course taken in economics to be eligible for this degree.

It is recommended that students considering graduate work in economics use some of their electives to include at least one programming course (Computer Science 11500 is strongly recommended), and an additional course in statistics (Statistics 24400-24500 is an appropriate two-quarter sequence). Students planning to apply to graduate economics programs are strongly encouraged to meet with one of the economics undergraduate program directors before the beginning of their third year.

Summary of Requirements:

Mathematics with Specialization in Economics

General Education

  • CHEM 11100-11200 or higher†, or PHYS 12100-12200 or higher†
  • MATH 13100-13200, 15100-15200, or 16100-16200†

Concentration

  • 1 CHEM 11300 or higher†, or PHYS 12300 or higher†
  • 1 MATH 13300, 15300, or 16300†
  • 3 MATH 20300-20400-20500 or 20700-20800-20900
  • 2 MATH 25400-25500 or 25700-25800
  • 1 MATH 27000
  • 1 MATH 27200 or 27300
  • 1 STAT 25100
  • 1 STAT 22000 or 24400
  • 4 ECON 20000-20100-20200-20300
  • 1 ECON 20900 or 21000
  • 2 courses in economics numbered higher than 20300

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† Credit may be granted by examination.

Grading. Subject to College and concentration requirements and with the consent of the instructor, all students, except concentrators in mathematics or applied mathematics, may register for regular letter grades, P/N grades, or P/F grades in any course beyond the second quarter of calculus. A Pass grade is given only for work of C- or better.

Concentrators in mathematics or applied mathematics may take any 20000-level mathematics courses elected beyond concentration requirements for a grade of P. However, a grade of C- or better must be earned in each calculus, analysis, or algebra course, and an overall grade average of C or better must be earned in the remaining mathematics courses that a student uses to meet concentration requirements. PSCD courses taken to meet concentration requirements in mathematics must be taken for quality grades.

Incompletes are given in the Department of Mathematics only to those students who have done some work of passing quality and who are unable to complete all the course work by the end of the quarter. Arrangements are made between the instructor and the student.

Honors. The B.A. or B.S. with honors is awarded to students who meet the following requirements: (1) a grade point average of 3.25 or better in concentration courses and a 3.0 or better overall; (2) completion of one honors sequence (either Mathematics 20700-20800-20900 or Mathematics 25700-25800-25900) with grades of B- or better in each quarter; and (3) completion with a grade of B- or better of at least five additional mathematics courses chosen from the list that follows so that at least one course comes from each group (algebra, analysis, and topology).

Algebra courses: Mathematics 24100, 24200, 25700, 25800, 25900, 27700, 27800, 28400, 32500, 32600, 32700

Analysis courses: Mathematics 20700, 20800, 20900, 27000, 27200, 27300, 27400, 27500, 31200, 31300, 31400, 32100, 32200, 32300

Topology courses: Mathematics 26200, 26300, 31700, 31800, 31900

As approved, Mathematics 29700 (Proseminar in Mathematics) may be chosen so that it falls in any of the three groups. Students interested in the honors degree should consult with the departmental counselor no later than the third quarter of their third year.

Joint Degree Program

B.A. (B.S.)/M.S. in Mathematics. Qualified College students may receive both a bachelor's and a master's degree in mathematics concurrently at the end of their years in the College. Qualification consists of satisfying all the requirements of each degree in mathematics. With the help of placement tests and honors sequences, able students can be engaged in 30000-level Mathematics as early as their third year and, through an appropriate use of free electives, can complete the master's requirements by the end of their fourth year. Interested students should apply to the departmental counselor as soon as possible and in any event no later than the winter quarter of the third year.