Mathematics Overview
In keeping with liberal-arts 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.
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 advanced-placement 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.
See: https://canvas.clarku.edu/courses/165
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, but sometimes a Spring MATH 120 - Calculus I course is offered. 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, or in the Spring, if Math 120 is offered.
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 higher-level 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 proof-writing 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 higher-level 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 - Linear Algebra . In exceptional circumstances, first-year students without credit for MATH 121 may enroll in MATH 130 - Linear Algebra with permission of the instructor.
Major Requirements
Entering students interested in mathematics, but enrolled in a first-year 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 or the Calculus sequence MATH 120 -MATH 121 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), one additional course in Analysis, to be chosen by the student from among the following:
1. MATH 216 (Functions of a Complex Variable)
2. MATH 240 (Functional Analysis)
3. MATH 242 (Measure Theory)
4. MATH 245 (Intro to Partial Differential Equations)
The remaining 5 courses are electives. At least 3 of these elective courses must be on the 200-level.
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 200-level courses to fulfill departmental major or minor requirements except under special approval of the department 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 to itself, and as a foundational discipline. The subject matters vary, consisting of more general and abstract concepts, proven rigorously. Calculations still exist, but theorems play a more dominant role. Pure mathematics also provide a solid foundation for mathematics used in other sciences, especially Physics. Suggested pure courses are MATH 216 - Functions of a Complex Variable; - MATH 225 - Moden Algebra I; MATH 228 - Topology; MATH 230 - Differential Geometry; MATH 240 - Functional Analysis; MATH 242 - Measure Theory. Some other courses, such as differential equations and partial differential equations can be considered as both pure and applied mathematics.
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: MATH 210 - Introduction to Quantitative Finance ; MATH 212 - Numerical Analys; MATH 217 - MATH 218 - Probability and Statistics and Topics in Statistics; MATH 219 - Linear Models , MATH 220 - Markov Chains: Theory, Application and Algorithms; MATH 244 - Differential Equations; MATH 245 - Introduction to Partial Diffential Equations.
Actuarial science minor 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; MATH 212 - Numerical Analysis; MATH 217 -MATH 218 - Probability and Statistics and Topics in Statistics; MATH 219 - Linear Models; MATH 220 - Markov Chains: Theory, Application and Algorithms; MATH 244 - Differential Equations; and appropriate courses in economics or business management.
Mathematics Capstone Requirement
Students majoring in Mathematics are required to fulfill a capstone credit in their senior year. This offers an opportunity to delve into advanced mathematics, building on the foundations laid by the major. There are three ways to meet capstone requirement in Mathematics:
A. Doing an Honors Thesis.
B. Taking one of the following eight advanced 200-level electives, classified here by
topic and to be chosen by the student after consultation with their advisor:
Fulfilling the capstone via Probability Theory:
• MATH 218 (Topics in Statistics)
• MATH 220 (Markov Chains: Theory, Applications, and Algorithms)
Fulfilling the capstone via Topology & Geometry:
• MATH 228 (Topology)
• MATH 230 (Differential Geometry)
Fulfilling the capstone via Analysis:
• MATH 216 (Functions of a Complex Variable)
• MATH 240 (Functional Analysis)
• MATH 242 (Measure Theory)
• MATH 245 (Intro to Partial Differential Equations)
The capstone in Analysis cannot also double-count toward the Analysis requirement
above; i.e., it cannot be used to simultaneously fulfill the Analysis requirement. Thus, if a
student chooses to satisfy their Analysis requirement in their senior year by taking, e.g.,
MATH 216, and if they wish to also fulfill their Capstone via Analysis, then they must
choose either MATH 240, 242, or 245 to do so.
C. Doing a Directed Study. Under exceptional circumstances, for students who are
unable to meet the capstone requirements through (A) or (B), special arrangements
can be made for individually directed research work.
Students must submit the capstone declaration form with the instructor’s signature to
the Mathematics Department when enrolling in a course that they have designated as their Capstone.
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