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 subfields 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:
 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.
 MCS122 Calculus II or MCS132 Honors Calculus II
 MCS221 Linear Algebra
 MCS228 Proofs in Mathematics and Computer Science
 MCS222 Multivariate Calculus
 These two courses in cognate fields to mathematics serve to give breadth to the math major.
 MCS142 Introduction to Statistics
 MCS177 Introduction to Computer Science I
 At least four courses chosen from MCS253, MCS256, MCS265, MCS303, MCS313, MCS314, MCS321, MCS331, MCS332, MCS344, MCS357, MCS355, and MCS358, subject to the following constraints:
 At least one sequence chosen from
 MCS313 & MCS314 Modern Algebra
 MCS331 & MCS321 Real and Complex Analysis
 MCS331 & MCS332 Analysis and Topology
 MCS253 & MCS357 Differential Equations and Discrete Dynamical Systems.
 Completion of at least one course from the classical core of mathematics listed below. This course can count toward 3a.
 MCS313 Modern Algebra
 MCS313 Elementary Theory of Complex Variables
 MCS331 Real Analysis
 Completion of at least one applied mathematics courses listed below. This course can count toward 3a.
 MCS253 Differential Equation
 MCS256 Discrete Calculus and Probability
 MCS355 Scientific Computing and Numerical Analysis
 MCS357 Dynamical Systems
 MCS358 Mathematical Model Building
 At least one sequence chosen from
 Complete one of the following listed below. Courses from this list may not be used to satisfy requirement 3a.
 MCS314 Modern Algebra II
 MCS332 Topology
 MCS344 Topics in Advanced Mathematics
 MCS350 Honors Thesis
 MCS357 Dynamical Systems
 MCS358 Mathematical Model Building
 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
 A grade point average of at least 2.33 in these four courses.
 MCS122 Calculus II or MCS132 Honors Calculus II
 MCS228 Proofs in Mathematics and Computer Science
 MCS221 Linear Algebra
 MCS222 Multivariate Calculus
 At least two courses from the following:
 MCS303 Geometry
 MCS265 Theory of Computation
 MCS256 Discrete Calculus
 MCS321 Complex
 MCS358 Math Model Building
 MCS313 Abstract Algebra
 MCS314 Abstract Algebra II
 MCS357 Discrete Dynamical Systems
 MCS355 Numerical Analysis
 MCS331 Real Analysis
 MCS332 Topology
 MCS344 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 everyother year basis; for example MCS314 (Modern Algebra II) is offered in the spring of odd years and MCS332 (Topology) is offered in the spring of even years. Courses offered every other year include MCS313, MCS314, MCS331, MCS332, MCS344, MCS355, MCS357, MCS358, MCS385, and MCS394. 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  MCS121  MCS122 MCS177 
2nd year  MCS228 MCS142 
MCS221 
3rd year  MCS222 *MCS313 or *MCS357 
MCS321 *MCS314 
4th year  *MCS313 or *MCS357 
*MCS314 
Traditional: Real Analysis
Fall  Spring  

1st year  MCS121 MCS177 
MCS122 
2nd year  MCS228  MCS221 MCS222 
3rd year  MCS142 *MCS313 or *MCS331 
MCS256 *MCS332 
4th year  *MCS313 or *MCS331  *MCS332 
Traditional: Graduate School Bound
Fall  Spring  

1st year  MCS121 MCS177 
MCS122 
2nd year  MCS228 MCS142 
MCS221 MCS 222 
3rd year  *MCS313 or *MCS331  *MCS314 or *MCS332 MCS321 
4th year  *MCS313 or *MCS331  *MCS314 or *MCS332 
Traditional Applied Mathematics
Fall  J Term  Spring  

1st year  MCS121  MCS122 MCS177 

2nd year  MCS228 MCS142 
MCS221  
3rd year  MCS222 *MCS357 
*MCS358 
MCS253 
4th year  *MCS357  *MCS358  *MCS355 MCS 321 
Applied: Graduate School Bound
Fall  J Term  Spring  

1st year  MCS121 MCS177 
MCS122  
2nd year  MCS228 MCS142 
MCS221 MCS222 

3rd year  *MCS313 or *MCS357  *MCS358 
*MCS355 
4th year  *MCS313 or *MCS357 
*MCS358  *MCS355 
Start with PreCalculus
Fall  Spring  

1st year  MCS118  MCS119 MCS 177 
2nd year  MCS122 MCS142 
MCS228 MCS221 
3rd year  MCS222 *MCS313 or *MCS331 
MCS321 *MCS314 or *MCS332 
4th year 
*MCS313 or *MCS331 
MCS256 *MCS314 or *MCS332 
Fall Junior Year Abroad
Fall  Spring  

1st year  MCS121  MCS122 MCS177 
2nd year  MCS228 MCS142 
MCS221 
3rd year  abroad  MCS222 MCS256 
4th year  MCS321 *MCS313 or *MCS331 
*MCS314 or *MCS332 
Spring Junior Year Abroad
Fall  Spring  

1st year  MCS121  MCS122 MCS177 
2nd year  MCS228 MCS142 
MCS221 
3rd year  MCS222 MCS313 or *MCS331 
abroad 
4th year  MCS321 *MCS313 or *MCS331 
MCS256 *MCS314 or *MCS332 
Junior Year Abroad
Fall  Spring  

1st year  MCS121 MCS177 
MCS122 
2nd year  MCS228 MCS142 
MCS221 MCS222 
3rd year  abroad  abroad 
4th year  *MCS313 or *MCS331 
*MCS314 or *MCS321 MCS256 
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 MCS350, 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 wellknown 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 primarysource reference material. As stated above, an exhaustive search of the research literature is impractical. None the less, the resources of interlibrary 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 20minute 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 fourthyear majors who will likely choose to take the examination.