| User's Guide to the Mathematics and Mathematics Teaching Majors | |
Extracurricular Activities
This User's Guide has been prepared for the use of mathematics and mathematics majors and minors at Edgewood College. It contains suggestions for planning a viable major or minor and for starting a career, as well as information about the mathematics program and extracurricular opportunities that will be of interest to students. However, no booklet is a substitute for individual advising. The Department strongly encourages students to seek out faculty members on an individual basis to discuss careers and plans. These discussions need not and should not be limited to your advisor; all members of the Department will be happy to discuss the program, as well as career options in mathematics, with anyone who cares to inquire. One of the reasons for coming to Edgewood is the personal attention available from faculty members; students are encouraged to take advantage of this opportunity.
The authors of this User's Guide to the Math Major would like to acknowledge that portions of this guide are modeled after other guides from other institutions, including Carleton College, Oberlin College, St. Olaf College, and University of Wisconsin-Madison.
The following section, What is Mathematics, is taken from the Oberlin College math handbook with only slight modifications.
Mathematics is the study of structure and the way it can be applied to solving specific problems. The mathematics one sees in high school and up through the calculus sequence in college -- techniques for solving equations, trigonometry, analytic geometry and calculus -- represent only a small corner of the discipline. Some of the structures discussed in more advanced courses include algebraic systems such as groups and vector spaces, geometric notions such as surfaces, manifolds and topological spaces, and spaces of differentiable or integrable functions. Such structures are used to construct mathematical models that may explain and predict events in a wide variety of disciplines. Mathematics has been with us since antiquity and is a pervasive force in our society; it is a diverse field encompassing many subjects that are, unfortunately, largely unknown outside mathematics. The major branches of mathematics and a few of their applications are briefly described below.
Pure mathematics has as its main purpose the search for a deeper understanding of mathematics itself. As a result pure mathematics seems at first far removed from everyday life. However, many important applications have been the results of advances in pure mathematics. The subject is traditionally divided into four main areas: algebra, analysis, geometry and logic. However, some of the most exciting developments throughout the history of mathematics have resulted from the interaction between different areas.
Algebra is the study of abstract mathematical systems. These systems, such as groups, rings, and fields, generalize properties of familiar structures such as integers, polynomials, and matrices. The general, abstract approach of algebra has been fruitful in solving many problems in both mathematics and other disciplines. For example, using algebraic techniques, one can show that it is impossible to trisect an angle using only a straight-edge and compass. Group theory has been employed liberally in quantum mechanical physics and physical chemistry. Other recent applications of algebra include cryptography and coding theory.
Analysis is the study of infinite processes. As such, it concerns itself with phenomena that are continuous as opposed to discrete. Starting with the fundamental notions of function and limit, it builds differential and integral calculus, which is the mathematics of continuous change. Analysis in turn gives rise to a deeper and more general study of functions of both real and complex variables. The area is pervasive, and it finds rich and varied applications in almost every field of pure and applied mathematics.
Geometry is the study of curves, surfaces, their higher-dimensional analogues, and the properties they possess under various types of transformations. Geometry and topology frequently make use of techniques and notions from algebra and analysis. Geometry is an important subject for our understanding of nature and structure of spatial relations.
Logic is at the very foundation of mathematics. In this field one studies the formulation of mathematical statements, the meanings and nature of mathematical truth and proof, and what can possibly be proved in a mathematical system. For example, there is a famous theorem by Kurt G(del that says that in any logical system rich enough to contain arithmetic there are true statements that can neither be proved or disproved. Logic has found many important applications in the study of computability in computer science.
Applied mathematics is the development and use of mathematical concepts and techniques to solve problems in many other disciplines. Unlike pure mathematics, the areas of applied mathematics fall under no simple classification. Nonetheless, the following topics cover many of the important applications.
Applied analysis involves the study of techniques for analyzing continuous processes and phenomena. For example, many methods from real and complex analysis are utilized when looking at problems of a physical or computational nature. Differential equations and numerical analysis are two examples of subjects that come under this heading.
Combinatorics, the study and enumeration of patterns and configurations, is one technique for analyzing phenomena that do not behave in a smooth or continuous fashion. Techniques from algebra and other areas are applied to study a wide variety of problems in such areas as arrangements, graph theory, scheduling, and game theory. There are also many important applications of combinatorics to computer science.
Probability and statistics are among the most fundamental tools for mathematical modeling. The importance of probability lies in its formulation of chance (or stochastic) processes and its application to the analysis of data and with the making of decisions in the face of uncertainty. It is frequently used in the social sciences as well as in all of experimental science.
Operations research involves applications of mathematical models and the scientific method to help organizations or individuals to make complex decisions. Traditionally, it has focused on mathematical optimization theory. Typical problems in operations research include the development of optimal flight schedules for airlines and finding the best inventory policy for a bookstore.
Actuarial mathematics is one of the early examples of mathematical modeling. This field uses the methods of probability and statistics, along with a study of economic factors, to estimate the financial risk of future events.
In light of the above descriptions concerning the breadth of the mathematical sciences, the mathematics major has been set up to provide a solid foundation in mathematics, balancing the number of options available to the student and the relative size of the program. Edgewood College offers the following set of advanced courses.
Algebra |
Analysis |
Geometry |
Logic |
Applied Analysis |
Probability and Statistics |
While the main motivation to choose math as a major should stem from a combination of keen interest and high ability in math, students are naturally concerned about the opportunities available to a mathematics major or a mathematics teaching major after graduation. At this time, the math major appears to be in a better position than many other majors for employment in business, industry, government agencies, and teaching. The prospects are also good for well-qualified students to obtain support for graduate studies in either mathematics or mathematics education. Also a major in mathematics is excellent preparation for further study in many other fields.
In order to help you clarify your thoughts on what you want to get out of your collegiate experience as a math major, here are some questions to ask yourself:
If you are not interested in a career in teaching, then: are you interested in a career in business, industry, government, nonprofits, other alternatives?
The Student Resource Center assists students in exploring and deciding upon college majors and careers through individual career counseling, workshops and class presentations, and a one-credit Career Development and Decision-Making course. Assistance is given in locating internships, part-time, summer, and full-time employment upon graduation. Numerous resources about careers, employers, and graduate schools are available for student use, including a self-directed computerized guidance program. Keep in mind, it is never too early to start looking for next summer's employment, internships, or for a job upon graduation.
The following pamphlets contain useful information about careers for math majors. Copies are available for inspection in R13, Regina Hall.
There are also various web sites which provide information about careers in mathematics. Check the homepages of the various professional mathematics organizations: MAA, AMS, AWM, SIAM, NCTM. See Professional Mathematics Organizations for links to these various sites.
The prospects for opportunities for math majors in business, industry and government have been good over the years although there has been, of course, some variation depending on the general economic situation. In some cases employers, having found math majors generally bright and flexible, desire them for positions which may involve considerable training on the job but perhaps not much direct use of their mathematical knowledge. In other positions math majors may make considerable use of their backgrounds in math, computer science, statistics or science. The possibilities range from positions in management to jobs as programmers, actuaries, or information systems consultants. To make their college backgrounds most valuable, math majors headed for business, industry or government should combine their math programs with courses in some related fields such as economics, sociology, psychology, business, computer science, statistics, or the physical and biological sciences. Some companies and agencies especially look for background in computer science and/or statistics. The Office of Career and Counseling Services provides students with career and job information, assists students in planning the job search.
There is always a demand for high school and middle school math teachers. And in coming years, the demand is expected to increase.
As preparation the qualified student should be admitted to the Teacher Education Program and complete a math teaching major and a secondary education minor either at the middle/secondary or secondary level. The requirements of this major and minor option are outlined in Section 3 of this Guidebook. Upon successful completion of math teaching major and secondary education minor the student is recommended for either secondary or middle/secondary teacher certification in mathematics in the State of Wisconsin. Certification in other states is subject to that particular state's regulations. However, it is generally agreed upon that Wisconsin's requirements are more stringent than most other states and certification out-of-state should be fairly easy.
It is possible to complete the requirements for secondary school teacher certification in mathematics after already earning a bachelors as a post-bac. Post-bac's need only complete the math teaching major and secondary education minor requirements and not the other requirements of a bachelors such as the general education requirements or the Human Issues requirement.
The services of the Education Department are available to those seeking teaching positions at all levels in the U.S. and abroad.
This program is dedicated to teaching in under-funded urban and rural schools and is especially interested in recruiting math majors. Teacher certification is not required. Information is available at the Office of Career and Counseling Services and a pamphlet for the program is on file in the departmental office.
There are usually opportunities to teach mathematics at various levels through the Peace Corps. Often teaching credentials are not required. Information is available at the Office of Career and Counseling Services.
Normally the student should apply in the fall of the senior year for admission the following fall. Most math departments with graduate programs offer support for graduate study on a competitive basis in the form of teaching assistantships, research assistantships or fellowships. Students should apply to departments of varying quality to better their chances of admission and/or support. Usually letters of recommendation and results of the GRE (Graduate Record Examination) are required. Some, if not all, of these letters should be from math faculty who know the student's work in advanced courses. Normally, students should plan to take the GRE General Test and the GRE Mathematics Subject test in the fall of the senior year. The fall dates are usually in October and December. In some cases it is important to take the October test to be sure the results arrive in time for the student to get full consideration for admission and/or support. Information and application booklets for the GRE are available in the Office of Career and Counseling Services. A copy of an information booklet about the GRE Mathematics Subject Test is available for inspection in R13, Regina Hall.
Students considering graduate work in mathematics should feel free to ask faculty members about various math departments and graduate programs. The list of information sources below about graduate programs also should be useful.
An undergraduate math major is often good background for graduate work in other fields which use mathematics, such as computer science, statistics, medicine, economics, industrial engineering, operations research, genetics, forestry, educational psychology, meteorology, law, physics, and various other fields in the social, biological and physical sciences. Of course, preparation for graduate work in one of these fields may also require a substantial number of courses more directly related to the field; however, some of these graduate programs accept math majors who have limited background in the area of study.
There are opportunities for well-qualified students to obtain support for graduate studies in mathematics. The academic job market for Math Ph.D.'s has been very poor in the recent past. There is some hope that this will improve with a large number of retirements among math faculty, but that is uncertain. Some Math Ph.D.'s have obtained non-academic jobs doing consulting or research.
At this point, most of the majors graduating from this department with a degree in mathematics have been mathematics teaching majors. Therefore, a large percentage of the majors went on directly into teaching either at the middle or secondary level in and around the State of Wisconsin. Recent mathematics major and minors have found employment in both buisness and research and development firms in Madison and the surrounding communities.
On to Programs
Copyright © 2001 Ken Jewell & Edgewood College All rights reserved.
Revised: January 17, 2006For more information please contact: jewell@edgewood.edu