# Lawrence Course Catalog

**Please note:** The information displayed here is current as of Sunday, June 17, 2018, but the official Course Catalog should be used for all official planning.

Period: 2017-2018 • 2016-2017 • 2015-2016 • 2014-2015 • 2013-2014 •

This catalog was created on Sunday, June 17, 2018.

## Mathematics

Professors: | K. Krebsbach (on leave term(s) III), A. Parks, B. Pourciau (on leave term(s) III) |
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Associate professors: | S. Corry (chair), J. Gregg, R. Sanerib |

Assistant professor: | J. Rana |

Visiting assistant professor: | B. Rocks |

Pattern and form surround us—from the branching angles of our blood vessels and the complexity of computer algorithms to inventory scheduling and the four-dimensional geometry of our universe. As the pure expression of pattern and form, mathematics provides the language for science. In the past 100 years, many disciplines have been virtually transformed by the infusion of mathematics, so that alongside the traditional field of mathematical physics, one now finds new disciplines such as mathematical biology, mathematical ecology, mathematical economics, mathematical linguistics and mathematical psychology.

But mathematics is so much more than its applications. As the study of formal structures, mathematics offers a supreme beauty, an abstract forest of pattern and form, at once deep, intricate, logical, and surprising, a forest holding wonders both known and unknown. The search for these wonders is no game, for mathematics bears on eternal truth: Primes—such as 2, 3, 5, 7, 11, 13, ...—cannot be written as the product of two smaller integers. How many primes are there? Infinitely many. This is a well-known wonder proved by Euclid. Twin primes—such as 3 and 5, 5 and 7, 11 and 13, 17 and 19, ...—are “consecutive” primes. How many twin primes are there? No one knows. Mathematicians have unleashed their most sophisticated weapons on this problem, but the question remains unanswered. It is an unknown wonder. Will you be the first to find the answer? Whatever the answer, it is an eternal and universal truth: true for all time, in all places, to every intellect.

To reflect the diversity of modern mathematics and its applications, the department, alone or in conjunction with the economics department, offers three separate majors:

- Mathematics
- Mathematics-computer science
- Mathematics-economics

Our core sophomore sequence provides majors with a firm foundation in the two pillars of mathematics (Abstract Algebra and Real Analysis), paving the way for exploration of diverse elective offerings at the junior and senior level. We offer courses in many areas of pure and applied mathematics, elementary and advanced statistics, and computer science. Majors engage in a one-term independent study during their senior year, working on a topic of their choice under the guidance of a faculty member. This transforming experience demonstrates a student’s ability to learn mathematics with little supervision and to clearly and cogently express this knowledge both verbally and in writing.

The department offers a number of elementary- and intermediate-level courses designed to meet the needs of students who wish to continue the study of mathematics or to complete required work in another major.

Lawrentians majoring in mathematics and/or computer science prepare themselves for a wide variety of interesting careers, but wherever life takes them, they have one thing in common—the logical and precise, yet intuitive and creative, habit of mind instilled by the serious study of abstract mathematics.

For a full description of Lawrence’s computer facilities and for descriptions of the computer science courses visit the Computer Science Website.

### Required for the mathematics major

- Complete or place out of the calculus sequence: MATH 140, 150, and 160
- One of the following:
- MATH 210
- MATH 220
- MATH 240

- One computer science course numbered 110 or above (excluding 170)
- MATH 300 and 310
- 24 additional units in mathematics courses numbered 400 or above
- Completion of a 6-unit independent study project in at least one term of the senior year.
- A C average in the major.

#### Course suggestions

In choosing courses beyond the core sequence, students should note that certain advanced courses may be particularly relevant to majors with specific interests or career goals. These lists offer suggestions; students are not expected to take all the courses in a given list.

- Pure mathematics: 410, 525, 530, 535, 540, 545, 550, 560, 565, and 600
- Computer science: 420, 435, 525, 540, and 565
- Operations research: 410, 420, 435, 440, 445, 525, and 550
- Applied mathematics: 410, 420, 435, 440, 445, 535, and 550
- Statistics and actuarial science: 410, 420, 435, 440, 445, and 550
- Engineering: 410, 420, 435, 440, 535, and 550
- Secondary teaching: 410, 495, 525, 530, 535, 545, 550, and 600

### Required for the mathematics minor

- Calculus through MATH 160
- One of the following:
- MATH 210
- MATH 220
- MATH 240

- MATH 300 and MATH 310
- 6 units in any one upper-level mathematics course numbered from 400 to 600, except MATH 495
- C average in the minor.

### Required for the interdisciplinary mathematics-computer science major

- The core sequence: MATH 140, 150, 160 and CMSC 150, 250, 270
- MATH 220 and 300
- CMSC 460, 510, 515
- 6 additional units in mathematics courses selected from:
- MATH 310
- MATH 420
- MATH 525
- MATH 540

- 6 additional units in a computer science course numbered 400 or above
- 6 additional units in a computer science course numbered 400 or above or selected from among MATH 310, 420, 525, and 540
- Completion of an independent study project prior to the Spring Term of the senior year
- CMSC 600 in the senior year

### Required for the interdisciplinary mathematics-economics major

- The mathematics component of the major is:
- MATH 140, 150, 160, 240, 300, 310
- Either MATH 435 or 445
- 6 additional units in a mathematics course numbered 400 or above, with 435, 440, 445, or 560 recommended

- The economics component of the major is:
- ECON 100
- ECON 300, 320, and 380 (majors must take all three courses prior to completion of the junior year. The Economics department must approve any exception.)
- Any three six-unit courses numbered between 400 and 580

- The interdisciplinary component of the major is:
- Completion of an independent study project that has been approved by both departments.
- A major must have an advisor in each department.

### Tutorials

The department views tutorials as opportunities to enhance its usual course offerings, not duplicate them. In order to reserve tutorials for this purpose, no tutorials are given for courses routinely offered, and the department does not normally permit a tutorial to be used to satisfy any requirement for the major.

### First-year courses

The department offers two calculus sequences: MATH 140, 150, 160 (*Calculus I, II, III*) and MATH 120, 130 (*Applied Calculus I, II*). Students intending to major in mathematics, mathematics-computer science, mathematics-economics, physics, or chemistry, or any student intending to take advanced mathematics courses, must complete the Calculus I, II, III sequence. Properly prepared students should enter this calculus sequence their freshman year. Proper preparation means strong high school mathematics, including a pre-calculus or elementary functions course. Strong scores in a standard college preparatory exam offer good evidence, as well. Students who lack this preparation yet need the three-course sequence should consult their advisor and the mathematics department as soon as possible.

The *Applied Calculus I, II* sequence is designed to introduce students to the mathematics used in the social and life sciences. This sequence demands less technical proficiency than does the *Calculus I, II, III* sequence. Good performance in high school mathematics through the junior year should be adequate preparation.

### Advanced Placement

Advanced placement in the *Calculus I, II, III* sequence and up to 12 Lawrence units may be obtained by presenting a score of 4 or 5 on the AB or BC calculus exams administered by the College Board or by performing well on an exemption-credit exam given by the department during Welcome Week. Consult the department for details. Students intending to enter *Calculus I* should not take the department's exemption-credit exam.

Advanced placement and six Lawrence units (for CMSC 150) may be obtained by scoring 4 or 5 on the A or AB College Board computer science exam. Consult the department for proper placement.

Six Lawrence units (for MATH 107) may be obtained by scoring 4 or 5 on the College Board statistics exam. Consult the department for proper placement.

### Off-campus and cooperative programs

Students wishing to combine a liberal arts degree with engineering should consider the 3-2 program in engineering.

The department encourages students to apply to the many Research Experiences for Undergraduates (REU) programs funded by the National Science Foundation; in these summer programs, students are paid to participate in research teams at various campuses throughout the country. Students may also be interested in the Budapest Semester in Mathematics or in one of several other off-campus study options. Department faculty members can provide details.

### Course numbering

Typically, course numbered below 400 are offered each year, while courses numbered 400 or higher are offered every other year.

### Senior Experience in Mathematics

The mathematics department's *Senior Experience* consists of a 6-unit (typically one-term) independent study project completed in the senior year. The project must demonstrate the capacity to learn mathematics (or statistics) independently or to utilize mathematics or mathematical technique as an innovative or substantive part of a larger project.

Interdisciplinary mathematics-economics majors must demonstrate the ability to combine topics in both disciplines—bringing appropriate techniques of mathematics or statistics to bear on the study of economics, or learning mathematics or statistics suggested by economic models

Interdisciplinary mathematics-computer science majors must complete their independent study project in two parts: an independent study in the Fall or Winter Term of the senior year (usually 3 units), followed by a presentation of their results in the Winter Term Computer Science Senior Seminar (3 units).

For mathematics and mathematics-computer science majors, the project must be approved and supervised by a faculty member in the mathematics department. For mathematics-economics majors, the project must be approved by a faculty member of each department and supervised by a member of one of the departments. Students should consult with departmental members in the spring before their senior year, in order to plan appropriately for their *Senior Experience*.