# Mathematics Advising Guide

Mathematics is a field that is rich in both theoretical analysis and practical application. It is also quite broad in scope, encompassing sub-fields such as applied mathematics, algebra, geometry, and the classical subjects of analysis. This diversity within mathematics makes most definitions of mathematics either too narrow or too general. However, one can say that mathematicians deal with objects (e.g. numbers, triangles, functions), and their patterns and relationships (e.g. prime numbers, isosceles triangles, calculus of functions). The search for patterns and relationships involves the process of abstraction, that is forming a generalization from a set of examples that reflects shared properties of these examples. Mathematicians use the skills of creative and analytical thinking to hypothesize the existence of patterns and use logical argument to show the validity of these postulates.

### Mathematics Major

This section lists the requirements of the Mathematics major. A grade of C- or higher is necessary in all 11 courses used to satisfy the requirements of the major. Additionally, you can use the Mathematics Major Form, This form will help you plan out your mathematics courses and requirements which are as follows:

**The Mathematics Core:**These five courses form the core of the major and should usually be taken during the freshman and sophomore years.**MCS-122**Calculus II or**MCS-132**Honors Calculus II**MCS-150**Discrete Mathematics**MCS-220**Theory of Calculus**MCS-221**Linear Algebra**MCS-222**Multivariate Calculu

**Breadth:**These two courses in cognate fields to mathematics serve to give breadth to the mathematics major.**MCS-142**Introduction to Statistics**MCS-177**Introduction to Computer Science I

**Immersive Experience:**A sequence of two 300 level courses**MCS-313**and**MCS-314**Modern Algebra**MCS-321**and**MCS-331**Analysis**MCS-353**and**MCS-357**Dynamical Systems

**Collaborative Experience:**A course which includes a significant component of collaborative work in groups.**MCS-270**Software Development**MCS-344**Advanced Topics in Mathematics (Approved by thedepartment)**MCS-355**Scientific Computing and Numerical Analysis**MCS-358**Mathematical Model Building**MCS-368**An approved internship or summer research opportunity

**Elective:**One additional course chosen from the following:**MCS-303**Geometry**MCS-313**Modern Algebra II**MCS-314**Modern Algebra II**MCS-321**Elementary Theory of Complex Variables**MCS-331**Real Analysis**MCS-344**Advanced Topics in Mathematics**MCS-350**Honorâ€™s Thesis**MCS-353**Continuous Dynamical Systems**MCS-355**Scientific Computing and Numerical Analysis**MCS-357**Discrete Dynamical Systems**MCS-391**Independent Study

### Mathematics Minor

As with the major in mathematics, a minimum grade of C- must be attained in all courses used to satisfy the minor. The necessary courses are

- A grade point average of at least 2.33 in these four courses.
**MCS-122**Calculus II or**MCS-132**Honors Calculus II**MCS-150**Discrete Mathematics**MCS-220**Theory of Calculus**MCS-221**Linear Algebra**MCS-222**Multivariate Calculus

- At least one course from the following:

**MCS-256**Discrete Calculus**MCS-265**Theory of Computation**MCS-303**Geometry**MCS-313**Modern Algebra I**MCS-314**Modern Algebra II**MCS-321**Elementary Theory of Complex Variables**MCS-331**Real Analysis**MCS-344**Topics in Advanced Math**MCS-355**Numerical Analysis**MCS-357**Discrete Dynamical Systems**MCS-358**Math Model Building

### Sample Student Plans

All students should ideally lay out a schedule of their own showing what courses they plan to take, and when they plan to take them. This schedule may not accurately forecast the future, but it is helpful none the less. The sample plans below are a useful starting point in developing such an individual plan. You can select the sample plan that comes closest to fitting your own situation and then tailor it as necessary. Note that these sample plans show only courses within the Mathematics, Computer Science, and Statistics Department. Also note that certain courses are offered on an every-other year basis; for example **MCS-314** (Modern Algebra II) is offered in the spring of odd years and **MCS-332** (Topology) is offered in the spring of even years. Courses offered every other year include MCS-313, MCS-314, MCS-331, MCS-344, MCS-355, MCS-357, MCS-358, MCS-385, and MCS-394. These courses are listed with an astrix in the sample plans below. Please keep these course alterations in mind when planning out your major. Check the college catalog for when the courses you are interested in will be scheduled.

#### Algebra

Students interested in algebra should take MCS-313 and MCS-314 for their **Immersive Experience** along with MCS-357 as their **Elective**.** **

#### Real Analysis

Students interested in analysis should take MCS-321 and MCS-331 for their **Immersive Experience** along with MCS-313 as their **Elective**.

#### Applied Mathematics

Students interested in applied mathematics should take MCS-353 and MCS-357 for their **Immersive Experience** and MCS-328 for their **Collaborative Experience**.** **

#### Traditional Graduate School Bound

Students considering graduate school in mathematics should take MCS-313, MCS-314, MCS-321, and MCS-331 for their **Immersive Experience** and their **Electives.**

### Applied Graduate School Bound

### Fall Junior Year Abroad

### Spring Junior Year Abroad

### Junior Year Abroad

### Honors Program

In order to graduate with honors in mathematics, a student must complete an application for admission to the honors program, showing that the student satisfies the admission requirements, and then must satisfy the requirements of the program.

### Admission to the Honors Program

The requirements for admission to the honors program are as follows:

- Attainment of a GPA greater than 3.14 in courses used to satisfy the requirements of the major. If a student has taken more courses than the major requires, that student may designate for consideration any collection of courses satisfying the requirements of the major.
- Approval by the Mathematics Honors Committee of an Honors thesis. The thesis should conform in general outline to the previously approved proposal (or an approved substitute proposal), should include approximately 160 hours of work, and should result in an approved written document. Students completing this requirement will receive credit for the course
**MCS-350,**whether or not they graduate with Honors. (See the Mathematics Advising Guide for the thesis guidelines.) -
Oral presentation of the thesis in a public forum, such as the departmental seminar. This presentation will not be evaluated as a criterion for thesis approval, but is required.

### Requirements for Graduation with Honors

The requirements of the honors program, after admission to the program, are as follows:

- Attainment of a quality point average greater than pi in courses used to satisfy the requirements of the major. If a student has taken more courses than the major requires, that student may designate for consideration any collection of courses satisfying the requirements of the major.
- Approval by the Mathematics Honors Committee of an honors thesis. The thesis should conform in general outline to the approved proposal (or an approved substitute proposal), should include approximately 160 hours of work, and should result in an approved written document. Students completing this requirement will receive credit for the course MC96 (Honors Thesis), whether or not they graduate with honors. (See the Mathematics Honors Thesis Guidelines, below.)
- Oral presentation of the thesis in a public forum, such as the departmental seminar. This presentation will not be evaluated as a criterion for thesis approval, but is required.

### Honors Thesis Guidelines

Mathematics honors thesis proposals should be written in consultation with the faculty member who will be supervising the work. The proposal and thesis must each be approved by the Mathematics Honors Committee. These guidelines are intended to help students, faculty supervisors, and the committee judge what merits approval.

The thesis should include creative work, and should not reproduce well-known results; however, it need not be entirely novel. It is unreasonable for an undergraduate with limited time and library resources to do a thorough search of the literature, such as would be necessary to ensure complete novelty. Moreover, it would be rare for any topic to be simultaneously novel, easy enough to think of, and easy enough to do.

The thesis should include use of primary-source reference material. As stated above, an exhaustive search of the research literature is impractical. None the less, the resources of inter-library loan, the faculty supervisor's private holdings, etc. must be tapped if the thesis work is to go beyond standard classroom/textbook work.

The written thesis should sufficiently explain the project undertaken and results achieved that someone generally knowledgeable about mathematics, but not about the specific topic, can understand it. The quality of writing and care in citing sources should be adequate for external distribution without embarrassment.

The thesis must contain a substantial mathematical component, though it can include other disciplines as well. If a single thesis simultaneously satisfies the requirements of this program and some other discipline's honors program, it can be used for both (subject to the other program's restrictions). However, course credit will not be awarded for work which is otherwise receiving course credit.

The Mathematics Honors Committee will maintain a file of past proposals and theses, which may be valuable in further clarifying what constitutes a suitable thesis. In order to provide some guidance of the sort before the program gets under way, here are some possible topics that appear on the surface to be suitable:

- A student could study the history surrounding Fermat's last theorem, and discuss and explain past failed attempts and the recent successful attempt to prove this theorem.
- A student could research the topic of knot theory and discuss the implications of this theory to the study of DNA and other biological materials.
- A student could study the use of wavelets in signal analysis, and the general usefulness of orthonormal families of functions in signal analysis.

### Senior Oral Exam

As described above, every math major must either take an additional upper level math course from a specified list or alternatively submit to oral examination during the Spring semester of their final year.

A student who chooses to take the oral examination selects, in consultation with a faculty member, a topic to research. They then present a 20-minute talk on that topic to an examining committee of three faculty members. At the conclusion of the talk, the faculty question the student about the talk, and also about fundamental topics from the student's full four years' of courses. The goal is not to require recollection of details, but rather to make sure that the student is leaving with the essentials intact.

The examination committee confers privately immediately after the examination and delivers the results to the student at the conclusion of their deliberations. The outcome is either that the student is deemed to have satisfied the requirement or alternatively that the student is requested to retry the examination at a later date. In the latter case, specific suggestions for areas of improvement are provided by the faculty committee.

More information about the oral examination procedures and schedule are provided routinely to those fourth-year majors who will likely choose to take the examination.