The department offers majors and minors in mathematics and mathematical finance. The purpose of this page is not to discuss the specific requirements for each of these programs. For a detailed list of requirements, click here. Instead, this page will fill in some of the details surrounding these requirements.
The Department of Mathematics offers majors which produce students who can think and reason logically, who can communicate in the language of the discipline of mathematics, and who are prepared to continue their study of mathematics after graduation in both academic and non-academic spheres. They should finish the program with the joy that derives from the intellectual mastery of a subject.
With its curriculum designed to synthesize the traditional and the innovative, the program provides all students with the background historically expected by the displine of mathematics, as well as exposure to modern topics and cutting edge technology. For students who want to experience the intellectual challenge of mathematical research, the department ofers that opportunity in the form of independent studies and honors projects which compare favorably with the best work done by undergraduates at any institution in the country.
The mathematics majors and minors are designed to provide students with flexibility in how the complete their requirements. However, there are some time constraints that students need to consider.
Introductory courses. Technically, majors and minors in the mathematics department begin with Calculus II (Math 152). However, Calculus I (Math 151) is a prerequisite for Calculus II (Math 152) and is usually offered only during Fall and Winter term each year. Students who would like to major in a mathematics-related field and have not completed this course or equivalent courses outside of Knox should anticipate taking Math 151 during Fall or Winter during their first year at Knox. Additionally, students who need to review precalculus are strongly encouraged to enroll in Functions and Calculus I Math 140 during the Fall Term of their first year here.
Sophomore-level courses. Math 300 (Mathematical Structures) is a prerequisite for almost all 300-level courses. This course is only offered during the Spring Term of each year, and mathematics majors are strongly encouraged to complete this course during their sophomore year. Since at least one of Linear Algebra (Math 210) or Differential Equations (Math 230) is a requirement for Math 300, students interested in majoring in mathematics should also anticipate taking these courses some time during their first or second year at Knox. Since Math 210 is usually offered only during Winter Term and Math 230 is likewise usually only offered during Spring Term, students should keep these limitations in mind when planning their schedules.
Senior Research. Majors in the mathematics department require students to complete an individual research project which leads to a public presentation of their work. While students have the option of completing a year-long Honors Project or a special topics Math 399 course, most students have opted to complete an independent study (Math 350 or Math 360-361) during their senior year and present a colloquium for the department highlighting their work. These projects are carried out with the assistance of a mathematics faculty member and usually build on work done in another course. Students should leave room in their schedule during their senior year to complete this requirement and should begin speaking to a faculty member about possible research projects no later than Fall Term of their senior year.
In the last 40 years a new discipline has arisen that combines elements of mathematics and of economics. This is the area of finance, which is concerned with the properties of basic commodities in investment markets such as common stocks and bonds, and newer investment opportunities that are derivatives of these basic commodities such as futures and options. Finance has become a valid area of academic pursuit in that it attempts to abstract out the essential properties of investment objects and the risk management behavior of individuals and firms, and to pursue the implications of those properties to explaining the behavior of markets. The tools and concepts that the study of finance requires are at base mathematical, and are similar to those needed by other applications of mathematics, but they have a character of their own that depends on the underlying economics of the situation. For instance, many arguments used to derive fair prices of derivatives hinge on economic assumptions that earning riskless profits (called arbitrage) cannot be done by tinkering with portfolios of assets.
The driving ideas and questions of the mathematical finance minor are: What are the dynamics of investment markets? Are prices of objects predictable, or enforcable, and why? How does one characterize risk, and tolerance for risk? What is the implication of randomness, differing investor risk tolerances, etc. on market prices? How do investors balance their assets in a way that is personally optimal? How do firms balance equity and debt? How do prices of derivatives depend on the asset upon which they are constructed?
Many students come to Knox College with the idea of pursuing a career in business. Finance is currently a hot employment area, and graduate programs in finance are also growing. Students with an interest in the Mathematical Finance Minor should speak to Professor Hastings.
Education does not stop at the classroom door, and the Knox educational program has encapsulated this fact in it's Experiential Learning requirement. Consequently, students interested in mathematics should count on furthering their education through the other opportunitites that are available to them. Some avenues to explore:
Students play an important role assisting the department with its educational mission. Advanced mathematics students work as graders for introductory courses and at the evening help sessions that available to students in introductory courses. Contact Professor Armon or Professor Schneider if you are interested in filling one of these positions.
Additionally, advanced mathematics students are also employed as peer tutors in mathematics by the Center for Teaching and Learning. Please visit their office for an application. Note that a complete application for a peer tutoring position requires recommendations from two professors.
The National Science Foundation (NSF) funds a wide variety of research programs across the country for undergraduates every summer. For a detailed list of programs, see the REU Sites on the National Science Foundation Division of Mathematical Sciences web site. (Note that the links from this page are related to last summer's programs.)
Additionally, the college also has opportunities for students to work on summer research projects with faculty members. For instance, Professor Leahy and Professor Schneider received a grant from the National Science Foundation to develop two new courses in computational mathematics and employed student assistants for several summers. The college also has positions available through the Ford Fellowship Program and other programs. See Dean Bailey's office for information.
Internships are also available for mathematics students. These summer jobs can sometimes carry the possibility of permanent employment after graduation. Please contact the Center for Career and Pre-Professional Development for more information.
Students in their senior year at Knox (especially those interested in pursuing a graduate degree) may elect to complete an Honors Project. An honors project is a year-long independent research project students complete working under the direction of a faculty advisor.
An application, including a form listing the members of the committee that will evaluate the project and a brief introduction to the project must be submitted to the Associate Dean of the College no later than the second week of the term in which the project begins (usually the Fall Term of the student's senior year). The project will require a paper bringing together the results of the project and an oral defense of the project in which the student must demonstrate his/her mastery of the material covered in the project.The Budapest Semester provides mathematics and computer science students from across the country with an opportunity to spend a term or a year abroad in Budapest, Hugary, during their Junior or Senior year while pursuing their interest in mathematics or computer science. Courses are taught in English to students from all over North America by Hungarian mathematicians familiar with the American educational system. Course credits are transferable. Knox veterans of the program have reported that their time on the Budapest Semester was an exciting and rewarding educational experience.
For information, speak to a member of the mathematics department or visit the Budapest Semester web page.
Knox mathematics majors have continued on to successful careers in numerous professional fields, ranging from mathematical finance to college and secondary education. Some possibilities to consider:
Knox College has been approved by the Illinois State Board of Education (ISBE) to provide a professional education program for secondary school (grades 6-12) mathematics teachers. The Illinois State Board of Education uses a certification process which focuses on content-area standards. These standards are available at this link at the ISBE web site.
Students considering secondary mathematics education should begin taking mathematics courses as soon as possible, and discuss their intentions with a member of the mathematics department early on in their academic career. Since there are many courses necessary to acquire all of the competencies outlined in the ISBE standards, students should also discuss their intentions with a member of the education department before the beginning of their sophomore year.
Students interested in graduate school should also consider:
Courses such as the Theory of Numbers (Math 217), Vector Calculus (Math 215), and Discrete Mathematics (Math 175) may also be beneficial. The successful completion of an Honors Project in mathematics will greatly enhance a student's chance for success in graduate school.
Some fields in which statisticians have found employment are: actuarial science, agriculture, marketing, engineering, economics, quality control, education, government, and medicine. Governmental bureaus in particular hire many graduates with statistics specialties.
To become qualified for a career in actuarial science, students are advised to take the following courses at Knox:
Other very helpful courses are
Students should also have strong basic computer literacy, including experience with spreadsheets, and somewhat less important, database management systems.
The Actuarial Exams. Progress in the actuarial field is marked by a succession of exams. After the first few which are common to all actuaries, there is a directional split according to whether the person pursues life or casualty interests. The exams that are most accessible while you are still an undergraduate are Exam 100 (Calculus and Linear Algebra) and Exam 110 (Probability and Statistics). They are both offered at Knox in November and May. See Professor Hastings by September and February respectively to sign up for the exams. There is a cost involved, but the department offers a partial subsidy to reduce the impact. Companies are happy to hire graduates who have passed just two of the exams, but there is other work you can do at Knox to help you prepare for other exams later: one of them is in Operations Research, another in Numerical Methods, and a third in Applied Statistics including regression and time series forecasting. These can be covered either by courses in the Knox catalog or by independent study courses. Salaries are strongly linked to number of exams passed, so it is important to think about taking Exam 100 by fall of junior year, preferably in the spring of the sophomore year, and Exam 110 as soon as possible after taking M321-322.
There are still good employment opportunities for students with undergraduate degrees in mathematics who have background in statistics, especially in the actuarial field. But most students receive the large part of their training in statistics in graduate school, as either masters or Ph.D. degree candidates. Almost all large universities either have departments or interdisciplinary programs in statistics. Some statistics programs are entirely contained within mathematics departments. Biostatistics, which includes such applications as clinical trials, epidemiology, and ecology, is currently a very hot area which at many institutions has its own department.
To prepare for graduate work in statistics, you should take core mathematics courses such as single and multivariable calculus and linear algebra. At the upper level, mathematical statistics is the most important course sequence to take, followed closely by advanced calculus, and such courses as numerical analysis and operations research provide good breadth. You should also be conversant with statistical software, and it is helpful to have some computer programming experience.
Application to graduate school is a process similar to application to mathematics graduate school, in fact in some cases you may be applying to a math department. Teaching and research assistantships are widely available, which generally carry full tuition plus a stipend of at least $10,000. It is wise to take both the general GRE exam and the mathematics subject test in order to be a good candidate for admission and financial aid in the form of assistantships.
Students who earn advanced degrees in statistics find themselves highly sought after, and enter careers that are both intellectually fulfilling and financially rewarding.