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 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:

  1. These four courses form the core of the major and should usually be taken during the freshman and sophomore years.  A grade point average of at least 2.333 in these four courses is required.
    1. MCS-122 Calculus II or MCS-132 Honors Calculus II
    2. MCS-221 Linear Algebra
    3. MCS-228 Proofs in Mathematics and Computer Science
    4. MCS-222 Multivariate Calculus
  2. These two courses in cognate fields to mathematics serve to give breadth to the math major.
    1. MCS-142 Introduction to Statistics
    2. MCS-177 Introduction to Computer Science I
  3. At least four courses chosen from MCS-253, MCS-256, MCS-265, MCS-303, MCS-313, MCS-314, MCS-321, MCS-331, MCS-332, MCS-344, MCS-357, MCS-355, and MCS-358, subject to the following constraints:
    1. At least one sequence chosen from
      1. MCS-313 & MCS-314 Modern Algebra
      2. MCS-331 & MCS-321 Real and Complex Analysis
      3. MCS-331 & MCS-332 Analysis and Topology
      4. MCS-253 & MCS-357 Differential Equations and Discrete Dynamical Systems.
    2. Completion of at least one course from the classical core of mathematics listed below.  This course can count toward 3a.
      1. MCS-313 Modern Algebra
      2. MCS-313 Elementary Theory of Complex Variables
      3. MCS-331 Real Analysis
    3. Completion of at least one applied mathematics courses listed below.  This course can count toward 3a.
      1. MCS-253 Differential Equation
      2. MCS-256 Discrete Calculus and Probability
      3. MCS-355 Scientific Computing and Numerical Analysis
      4. MCS-357 Dynamical Systems
      5. MCS-358 Mathematical Model Building
  4. Complete one of the following listed below.  Courses from this list may not be used to satisfy requirement 3a.  
    1. MCS-314 Modern Algebra II
    2. MCS-332 Topology
    3. MCS-344 Topics in Advanced Mathematics
    4. MCS-350 Honors Thesis
    5. MCS-357 Dynamical Systems
    6. MCS-358 Mathematical Model Building
    7. Pass a  Senior Oral Exam.    

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

  1. A grade point average of at least 2.33 in these four courses. 
    1. MCS-122 Calculus II or MCS-132 Honors Calculus II
    2. MCS-228 Proofs in Mathematics and Computer Science
    3. MCS-221 Linear Algebra
    4. MCS-222 Multivariate Calculus
  2. At least two courses from the following:
    1. MCS-303 Geometry
    2. MCS-265 Theory of Computation
    3. MCS-256 Discrete Calculus
    4. MCS-321 Complex
    5. MCS-358 Math Model Building
    6. MCS-313 Abstract Algebra
    7. MCS-314 Abstract Algebra II
    8. MCS-357 Discrete Dynamical Systems
    9. MCS-355 Numerical Analysis
    10. MCS-331 Real Analysis
    11. MCS-332 Topology
    12. MCS-344 Topics Adv Math

Sample Student Plans

All students should ideally lay out a schedules of their own showing what courses they plan to take when. 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, but in some cases exceed the requirements of the major. 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-332, 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.

Traditional: Algebra

  Fall Spring
1st year MCS-121 MCS-122
MCS-177
2nd year MCS-228 
MCS-142
MCS-221
3rd year MCS-222
*MCS-313 or *MCS-357
MCS-321
*MCS-314
4th year *MCS-313 or *MCS-357

*MCS-314

Traditional: Real Analysis

  Fall Spring
1st year MCS-121
MCS-177
MCS-122
2nd year MCS-228 MCS-221
MCS-222
3rd year MCS-142
*MCS-313 or *MCS-331
MCS-256
*MCS-332
4th year *MCS-313 or *MCS-331 *MCS-332

Traditional: Graduate School Bound

  Fall Spring
1st year MCS-121
MCS-177
MCS-122
2nd year MCS-228 
MCS-142
MCS-221
MCS- 222
3rd year *MCS-313 or *MCS-331 *MCS-314 or *MCS-332
MCS-321
4th year *MCS-313 or *MCS-331 *MCS-314 or *MCS-332

 Traditional Applied Mathematics

  Fall J Term Spring
1st year MCS-121   MCS-122
MCS-177
2nd year MCS-228 
MCS-142
  MCS-221
3rd year MCS-222
*MCS-357
*MCS-358

MCS-253
*MCS- 355

4th year *MCS-357  *MCS-358 *MCS-355
MCS- 321

Applied: Graduate School Bound

  Fall J Term Spring
1st year MCS-121
MCS-177
  MCS-122
2nd year MCS-228 
MCS-142
  MCS-221
MCS-222
3rd year *MCS-313 or *MCS-357 *MCS-358

*MCS-355
MCS-321

4th year *MCS-313 or *MCS-357

 *MCS-358 *MCS-355

Start with Pre-Calculus

  Fall Spring
1st year MCS-118 MCS-119
MCS- 177
2nd year MCS-122
MCS-142
MCS-228 
MCS-221
3rd year MCS-222
*MCS-313 or *MCS-331
MCS-321
*MCS-314 or *MCS-332
4th year

*MCS-313 or *MCS-331

MCS-256
*MCS-314 or *MCS-332

Fall Junior Year Abroad

  Fall Spring
1st year MCS-121 MCS-122
MCS-177
2nd year MCS-228
MCS-142
MCS-221
3rd year abroad MCS-222
MCS-256
4th year MCS-321
*MCS-313 or *MCS-331

*MCS-314 or *MCS-332

Spring Junior Year Abroad

  Fall Spring
1st year MCS-121 MCS-122 
MCS-177
2nd year MCS-228 
MCS-142
MCS-221
3rd year MCS-222
MCS-313 or *MCS-331
abroad 

4th year MCS-321 
*MCS-313 or *MCS-331
MCS-256
*MCS-314 or *MCS-332

Junior Year Abroad

  Fall Spring
1st year MCS-121
MCS-177
MCS-122
2nd year MCS-228 
MCS-142
MCS-221
MCS-222
3rd year abroad abroad
4th year *MCS-313 or *MCS-331

*MCS-314 or *MCS-321
MCS-256

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:

  1. 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.
  2. 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.)
  3. 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:

  1. 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.
  2. 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.)
  3. 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.