20192020 Academic Catalog [ARCHIVED CATALOG]
Mathematics Major


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Mathematics Overview
In keeping with liberalarts traditions, Clark’s mathematics major provides a solid education in mathematical principles for students who wish to apply mathematics in other fields and students who wish to pursue mathematics in graduate school. Clark mathematics majors have gone on to graduate school in pure mathematics, applied mathematics and computer science at such universities as Brown, Cornell, NYU (Courant Institute), and Stonybrook. Graduates are employed in the public and private sectors as statisticians, mathematical modellers and actuaries, as well as mathematics teachers at all levels.
The department supports undergraduate majors and minors in mathematics and computer science. The computer science program is described in the computerscience portion of this catalog. The department also offers courses that play an important role in other disciplines.
For more information, please visit the Mathematics Department’s website.
Mathematics Placement Test
All students who intend to enroll in an introductory mathematics course (with the exception of students with advancedplacement credit in calculus) must take the mathematics placement test given during preregistration. Based on placement test scores, students are placed into Precalculus, Calculus, or Honors Calculus. Students may challenge their placement by taking a backup placement test once.
Calculus
Calculus is an essential tool for every serious student of mathematics, natural sciences, computer science and economics. The Department of Mathematics recommends that students with quantitative skills take Calculus in their first year.
Two Calculus tracks are open to students with appropriate scores on the Mathematics Placement Test: the regular track MATH 120 MATH 121 , and the Honors track MATH 124 MATH 125 . Both tracks start in the Fall. Students who do not place into Calculus, but place into Precalculus (MATH 119 ), can start with MATH 119 to prepare for Calculus and continue with MATH 120 the following year.
Regular Calculus, MATH 120 MATH 121 , is geared toward students interested in the natural and social sciences who do not plan to take any mathematics courses at a higher level.
Honors Calculus (MATH 124 MATH 125 ) is the more theoretical track and prepares students for intermediate and upper level mathematics classes. It is therefore recommended that students with a strong mathematics background, who intend to take higherlevel mathematics classes in the future, start with MATH 124 MATH 125. We encourage students to take the honors calculus sequence to develop deep mathematical thinking skills and rigorous proofwriting techniques.
Students with a sufficiently high score on the AP (AB) Calculus test receive credit for MATH 120. This credit fulfills the prerequisite for MATH 121, but not for MATH 125. It is recommended that those students start with MATH 124 and continue into MATH 125 if they are interested in taking higherlevel mathematics classes in the future.
Students with a sufficiently high score on the AP (AB/BC) Calculus test receive credit for MATH 121 and may continue with MATH 130. In exceptional circumstances, firstyear students without credit for MATH 121 may enroll in MATH 130 with permission of the instructor.
Major Requirements
Entering students interested in mathematics, but enrolled in a firstyear intensive course in one of the programs outside mathematics or the natural sciences are encouraged to make a prompt choice of a second advisor from the mathematics faculty.
The mathematics major, built around a core of fundamental courses, is best started early with the Honors Calculus sequence MATH 124 MATH 125 in the first year. Advanced electives provide flexibility and allow students to tailor the major to their interests.
A total of 10 courses beyond two semesters of Honors Calculus are needed to complete the mathematics major: 4 core courses (MATH 130 MATH 131 , MATH 172 and MATH 225 ) and 6 elective courses. At least 4 elective courses must be on the 200level. Note that MATH 110 /Math 111 (Diving into Research) cannot be used to substitute a requirement for the major.
Students who later decide to become mathematics majors, can substitute the Honors Calculus sequence (MATH 124 MATH 125 ) with the regular Calculus sequence (MATH 120 MATH 121 ), but are required to takeMATH 114 (preferably together with MATH 121) as one of their elective courses. The same holds for students who were initially placed in the regular Calculus sequence.
Directed study (reading) courses on special topics may be arranged with the permission of a member of the departmental faculty who will serve as a supervisor. Departmental policy requires that reading courses may not be substituted for 200level courses to fulfill departmental major or minor requirements except under special approval of the department chair or associate chair in consultation with the student advisor.
Suggested Specializations in Mathematics
Many students are originally attracted to mathematics because of its powerful applications, but a taste for pure mathematics often develops after studying the subject. Students planning to study mathematics in graduate school should consider programs in either pure or applied mathematics.
Pure mathematics is the study of mathematics as an end in itself. Suggested courses: MATH 214 Modern Analysis; MATH 216  Functions of a Complex Variable; MATH 226  Modern Algebra II; MATH 228 Topology; and MATH 230  Differential Geometry.
Applied mathematics is the study of mathematics as applied to the natural or social sciences. The heart of the field is modelling  translating aspects of natural or social phenomena into mathematical objects that can be studied with such mathematical tools as differential equations, linear systems and stochastic processes. Suggested courses: CSCI 212  Numerical Analysis; MATH 214  Modern Analysis; MATH 216  Functions of a Complex Variable; MATH 217 Math 218  Probability and Statistics and Topics in Statistics; MATH 220  Introduction to Stochastic Modeling and MATH 244  Differential Equations; MBB 120  Mathematical Modeling of Biological Systems.
Actuarial science is the study of finance and insurance. Study in this field requires a grounding in mathematics and statistics and an understanding of economics and business management. Courses are offered which prepare students for passing actuarial professional exams which are a gateway to internships and becoming a working actuary. The department offers several courses which meet educational requirements marked by this country’s actuarial societies. Clark is listed as one of the American universities having an actuarial program by the Society of Actuaries. See www.soa.org and speak to our faculty for more information. Suggested courses: MATH 210  Introduction to Quantitative Finance; CSCI 212  Numerical Analysis; MATH 217  MATH 218  Probability and Statistics and Topics in Statistics; MATH 220  Introduction to Stochastic Modeling; MATH 244  Differential Equations; and appropriate courses in economics or business management.
Secondary Education Certificate in Mathematics Education
Certificate requirements include courses in education and in mathematics. Consult the Education Department for information on required courses in education and the most recent state guidelines.
Mathematics Capstone Requirement
Students majoring in Mathematics are required to fulfill a capstone credit in their senior year. The capstone serves one or more of the following purposes: solidifying a deeper understanding of a topic of interest, pursuing an integrative largescale project in mathematics or a related field, acquiring a proficiency at presenting mathematical concepts effectively, team collaboration with fellow students, and applying knowledge to realworld problems across a variety of domains.
Fulfillment of the capstone requirement is established via
one of the following:
1) Completing an Honors or Senior project;
2) Completing a capstone project as part of a 200level Mathematics elective course;
3) Directed Study with a faculty member;
4) Research experience at Clark or another institution;
5) Participation in the Putnam Competition or another Mathematics Competition;
6) Interdisciplinary projects containing a substantial mathematical component;
7) Internship related to Mathematics or Mathematics Education;
8) Community service related to Mathematics or Mathematics Education;
After choosing among these options, students must contact a faculty supervisor who will direct their capstone experience. Any request by a student to fulfill the requirement via different means must be approved by the department.
It is the student’s responsibility to coordinate all capstone processes necessary outside departmental requirements, such as university required forms.
Honors
A major who maintains at least a 3.2 average (4.0 scale) in courses required for the major may apply for the departmental honors program. A student’s application in writing must be directed to a prospective honors advisor or the department chair by the end of the student’s junior year. Honors may be achieved in one of two ways:
1. A unified fourcourse sequence as a senior (some parts of which may consist of reading courses), followed by a comprehensive examination.
2. An honors project to be presented at an oral defense or at a department seminar. This project may be an independent or joint research thesis, or it may be a programming project. Supporting course work may be required. Students interested in pursuing the honors program should consult their department advisor and register to receive course credit for an honors thesis.
NOTE: Upon satisfactory completion of the program, the department may recommend graduation with honors, high honors or highest honors.
Mathematics Faculty
Program
Amir Aazami, Ph.D.
Jacqueline Dresch, Ph.D.
Frederic Green, Ph.D.
Li Han, Ph.D., Chair
Gideon Maschler, Ph.D., Associate Chair
Robert Ream, Ph.D.
Michael Satz, M.S.
Natalia Sternberg, Ph.D.
Emeriti
David Joyce, Ph.D
John Kennison, Ph.D.
Lawrence Morris, Ph.D
Lee Rudolph, Ph.D.
Mathematics Courses
Courses offered recently:

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