Description of
the Mathematics
Curriculum and Major
Grinnell College
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Description of
the Mathematics
Curriculum and Major |
Grinnell College
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Mathematics is an important discipline in the liberal arts education, not only as an independent discipline, but also in how it interracts with other communities, providing a common language and set of tools for many disciplines in the natural and social sciences. As a field with a long history, mathematics has many subdisciplines and strands of thought.
At Grinnell, the mathematics curriculum provides appropriate background for students with a wide range of interests. For example, a very large percentage of Grinnell students take statistics, calculus, linear algebra, combinatorics, and/or differential equations as part of their liberal-arts education and because these subjects are vital for their interests in the social sciences and sciences. Mathematics majors and others with strong interests in mathematics take further courses to deepen their understanding and increase the breadth of their knowledge.
Students may enter the study of mathematics at different points, depending upon their background and interests. Those with good preparation normally start in 131, Calculus I; while those with less preparation may start in 123, Functions and Differential Calculus; and those with advanced standing in 133, Calculus II, or 215, Linear Algebra. Thereafter, the student's intellectual curiosity, interests, and abilities and the needs of various disciplines determine the particular mathematics courses selected. Several courses make use of the department's network of PC/Linux workstations for graphics, computation, data analysis, and numeric experimentation.
Mathematics majors pursue many interests. All are encouraged to study in depth at least one field, such as physics or economics, in which mathematics is applied extensively. Some enjoy working on challenging problems, such as those presented in the Putnam Examination or the Mathematical Contest in Modeling, both of which are national mathematics competitions. Many present talks to the Math Journal Club. Films and visiting lecturers extend the curriculum beyond the classroom, as do opportunities for students to do summer research in mathematics.
The mathematics curriculum starts with a two-semester introduction to calculus, Math 131-133. Following this sequence, the Department offers several choices, which students consider in consultation with their advisor. These choices are intended both for prospective majors in mathematics or computer science and for students who may only take an occasional course in mathematics or computer science.
The department's offerings reflect the fascinating breadth of the mathematics. The following list of course topics, discussed later in this document, indicate something of the variety and broad applicability of fields included in Grinnell's mathematics curriculum.
| linear algebra | differential equations | combinatorics |
| modeling | problem-solving | applied mathematics |
| analysis | topology | probability and statistics |
| abstract algebra | theory of computation | geometry |
In addition to these formal courses, students may be involved in a wide range of extra-curricular activities. As discussed in the notes that follow, these activities range from some that are quite mathematical to others that are just for fun.
| independent projects | summer research | internships |
| Math/CS Journal Club | contests/competitions | social events |
Math 215 Linear Algebra stresses linear systems of equations and linear transformations. In this context, the central topics of linear algebra are studied. Applications of these topics are clearly seen in such areas as fitting lines and curve to data, Markov processes, and linear differential equations. Overall, the course combines the techniques and concepts of linear algebra with major areas of applications.
At Grinnell, the study of differential equations begins with systematic and modern investigation of several types of equations, making solid use of linear algebra, computer experimentation, and applications from various disciplines.
Math 218 Combinatorics introduces this field, studying the basic objects, numbers, and techniques of combinatorics. The course stresses problem-solving and considers a rather different kind of reasoning and viewpoint than one finds in other mathematics courses. Some topics discussed in this class also are of considerable importance in the areas of statistics and computer science.
Beyond a sophisticated knowledge of the real numbers, many fields of science and engineering require a thorough understanding of functions of complex variables. Math 338 Complex Analysis considers this subject, beginning with a preliminary study of the complex number system, and including topics of analysis (e.g., differentiation and integration). Several important physical applications, such as fluid flow around barriers, are often included.
Math 115 Introduction to Statistics offers a one semester introduction to statistics, assuming only a background of high school algebra. The course is data-oriented with real-world examples drawn from the social and life sciences, and the computer is used for data analysis and to illustrate probability and statistical concepts. (Note that this course may not be counted toward either the mathematics or the computer science major.)
Math 209 Applied Statistics builds upon the calculus background from Math 131 and 133 to provide a one-semester introduction to statistics. The course covers the application of basic statistical methods such as univariate graphics and summary statistics, basic statistical inference for one and two samples, linear regression, one- and two-way analysis of variation, and categorical data analysis. As with Math 115, students use statistical software to analyze data and conduct simulations.
Math 335--336 Probability and Statistics I and II provide a full year introduction to probability and statistics, including some of the mathematical framework for these subjects. The first semester focuses on probability, while the second uses probability theory to study mathematical statistics, including principles of estimation and testing, regression, sampling distributions, analysis of variance, and non-parametric inferences. The course emphasizes applications of statistics to real-world data.
Math 324 Number Theory applies the basic algebraic structures to explore basic properties, such as congruences, quadratic reciprocity, and unique factorization.
Math 326 Field Theory extends the study of formal algebraic structures, begun in Math 321, by integrating group theory with field theory and the theory of equations. Fundamental topics of algebra include vector spaces and canonical forms, algebraic extensions, finite and cyclotomic fields, geometric constructions, and Galois Theory.
Altogether, this seminar provides a capstone experience, affording students the chance to work with an advanced topic in mathematics and preparing them for graduate work or any further experiences in mathematics. Students play an active in class sessions, by developing material on a day-to-day basis and by presenting special topics they have researched.
Our faculty enjoys working with students on many topics and welcomes the opportunity to explore options for independent study, based on particular student interests.
In addition to student presentations, both faculty and outside speakers talk about current topics in mathematics. Some speakers also highlight opportunities for further study at the graduate level or for careers using mathematics in business.
The Iowa Mathematics Competition is held every spring, but in this one teams of 3 students work together on the problems. (A Grinnell team has won this competition each of the last four years.)
Different yet is the Mathematical Contest in Modeling, held early every second semester over a long weekend. Teams of 3 work together on a single applied problem that usually has no best answer. The quality of the team's written report determines their success. (Twice a Grinnell team has achieved the highest rating, "Outstanding," and once Grinnell's team was flown out to Boston to present their solution at a national meeting.)
This document is available on the World Wide Web as
http://www.math.grinnell.edu/~walker/dept/math-curriculum.html
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created January 26, 1998 last revised September 27, 2001
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| For more information, please contact Henry M. Walker at (walker@math.grinnell.edu) |