The Mathematics Major's Handbook

The Mathematics Major’s Handbook

(updated Spring 2016)

Mathematics Faculty and Their Areas of Expertise

Jennifer Bowen Abstract Algebra, Nonassociative Rings and Algebras,

Jordan Algebras

James Hartman Linear Algebra, Magic Matrices, Involutions,

(on leave) Statistics, Operator Theory

Robert Kelvey Combinatorial and Geometric Group Theory

Matthew Moynihan Abstract Algebra, Combinatorics, Permutation Enumeration

R. Drew Pasteur Diﬀerential Equations, Mathematics in Biology/Medicine,

Sports Data Analysis

Pamela Pierce Real Analysis, Functions of Generalized Bounded Variation,

Convergence of Fourier Series, Undergraduate Mathematics

Education, Preparation of Pre-service Teachers

John Ramsay Topology, Algebraic Topology, Operations Research

Ondˇrej Zindulka Real Analysis, Fractal geometry, Geometric Measure Theory, Set Theory

Contents

1 Mission Statement and Learning Goals 5

1.1 Mathematics Department Mission Statement . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2 Learning Goals for the Mathematics Major . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Curriculum 8

3 Requirements for the Major 9

3.1 Recommended Timeline for the Mathematics Major . . . . . . . . . . . . . . . . . . . . . . 10

3.2 Requirements for the Double Major . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.3 Requirements for Teaching Licensure in Mathematics . . . . . . . . . . . . . . . . . . . . . 11

3.4 Requirements for the Minor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4 Oﬀ-Campus Study in Mathematics 12

5 Senior Independent Study 13

5.1 Mathematics I.S. Student/Advisor Guidelines . . . . . . . . . . . . . . . . . . . . . . . . . . 13

5.2 Project Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

5.3 Project Submissions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

5.3.1 Project Proposal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

5.3.2 Project Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

5.3.3 Annotated Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

5.3.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5.3.5 Completed Chapters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5.3.6 Digitial I.S. Document . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5.3.7 Poster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5.3.8 Document Submission and oral presentation schedule . . . . . . . . . . . . . . . . 15

6 Independent Study Assessment Guide 21

7 Further Learning Opportunities 23

7.1 At Wooster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

7.2 Beyond Wooster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

8 Departmental Honors and Prizes 25

9 Mathematics After Wooster 25

List of Figures

1 Map of Department Learning Outcomes to Courses . . . . . . . . . . . . . . . . . . . . . . 6

2 Map of Department Learning Outcomes to Graduate Qualities . . . . . . . . . . . . . . . . 7

List of Tables

1 Recommended classes for double majors or minors in other ﬁelds . . . . . . . . . . . . . . 9

2 Recommended classes for majors preparing for graduate school . . . . . . . . . . . . . . . 10

3 Recommended Timeline for the Mathematics Major . . . . . . . . . . . . . . . . . . . . . . 10

1 Mission Statement and Learning Goals

1.1 Mathematics Department Mission Statement

The Mathematics Department’s mission is to provide quality academic programs in mathematics that

will allow students to prepare for graduate work and for employment in mathematics-related

positions. Students will develop their analytical and problem solving skills while learning about the

beauty of mathematics. In addition to providing speciﬁc content knowledge in mathematics, the

mathematics program will develop the strong communication skills that are necessary in today’s

society. We will also strive to provide courses that will serve the needs of other departments and

programs within the college.

1.2 Learning Goals for the Mathematics Major

The following ﬁve goals are what the department expects majors to achieve by the end of their course

of studies.

1. Communication

(a) Students should be able to read and understand mathematical statements.

(b) Students should be able to express mathematical ideas with precision and clarity orally.

2. Content

(a) Students should know the fundamental concepts, deﬁnitions, theorems and techniques of

calculus.

(b) Students should know the fundamental concepts, deﬁnitions, theorems and techniques of

linear algebra.

(d) Students should demonstrate competence in several speciﬁc areas of applied mathematics.

3. Problem Solving/Reasoning

(a) Students should be able to reason mathematically using graphical, numerical, and symbolic

points of view.

(b) Students should be able to write sound proofs.

4. Connection

(a) Students should be able to synthesize material from multiple perspectives.

(b) Students should be able to make connections between diﬀerent areas of mathematics.

5. Independent and Collaborative Learning

(a) Students should demonstrate skills in approaching and solving problems independently.

(b) Students should demonstrate skills in working together in teams to solve complex

problems.

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2 Curriculum

Core Courses

• 111. Calculus and Analytic Geometry I (or 108. Calculus with Algebra B)

• 112. Calculus and Analytic Geometry II

• 211. Linear Algebra

• 212. Multivariate Calculus

• 215. Transition to Advanced Mathematics [(W) Writing Intensive]

200-Level Courses

• 221. Diﬀerential Equations

• 223. Combinatorics and Graph Theory

• 225. Mathematical Modeling

• 227. Operations Research

• 229. Probability and Statistics I

• 299. Special Topics

Problem Solving

• 279. Fall Problem Seminar preparation for the Putnam Competition

• 279. Spring Problem Seminar Exploratory Mathematics or preparation for the Modeling contest

300-Level Courses

• 327. Numerical Analysis

• 329. Probability and Statistics II

• 330. Topology

• 332. Real Analysis I

• 333. Real Analysis II

• 334. Abstract Algebra I

• 335. Abstract Algebra II

• 336. Functions of a Complex Variable

• 399. Special Topics

Senior Independent Study

• 451. Senior Independent Study (I.S.) Semester One

• 452. Senior Independent Study (I.S.) Semester Two

3 Requirements for the Major

A major in mathematics requires completion of the following thirteen courses, with grades of C- or

better in each course:

• One of MATH 111 or 108

• MATH 112

• MATH 211

• MATH 212

• MATH 215

• CSCI 100 (Scientiﬁc Computing)

• Two 200-level math courses: MATH 221, 223, 225, 227, 229, or 299

• Two 300-level math courses: MATH 327, 329, 330, 332, 333, 334, 335, 336, or 399

• One elective full-credit Mathematics course numbered above 215

• MATH 451: Senior Independent Study

• MATH 452: Senior Independent Study

The mathematics program does not include a Junior Independent Study (401) course. The College

requirement for a third unit of Independent Study is satisﬁed through the independent work done as

part of the courses numbered above 200, which are taken to fulﬁll the requirements of the major.

At most, two courses of advanced placement may be counted toward a major or minor.

Majors are encouraged to pursue a minor and/or second major in related ﬁelds, such as the

natural sciences, computer science, economics, or education. Double majors write a multidisciplinary

I.S. thesis, typically using mathematics as a tool to better understand a problem in the other ﬁeld.

Tables 1 and 2 highlight recommended courses for students interested in double majors, minors,

and/or graduate school. Students considering a mathematics major should discuss their plans with a

member of the department, ideally during their ﬁrst year as a student.

Major or Minor Recommended Classes

Biology, BCMB, Environmental 221, 225, 229

Science, Neuroscience, Geology

Chemistry 221, 225

Computer Science 223, 229, 327

Economics 221, 227, 229, 329

Education (minor) 225 or 227 (required), 229 (required), 334 (required)

Physics, Pre-Engineering 221, 225, 327

Political Science 227, 229, 329

Table 1: Recommended classes for double majors or minors in other ﬁelds

Field Recommended Classes

Pure mathematics 221, 229, 215, 330, 332, 334, 336

Applied mathematics 221, 225 or 227, 229, 327, 332, also consider 329

Computational mathematics 221, 223, 225, 327, 332, also consider CSCI 200 and CSCI 220

Financial mathematics 221, 227, 229, 329, 332, also consider ECON 210 and ECON 224

Statistics 229, 329, also consider 221 and 227

Table 2: Recommended classes for majors preparing for graduate school

First Year: First Year:

Calculus I Calculus II

Calculus II Multivariate Calculus

CSCI 100: Scientiﬁc Computing CSCI 100: Scientiﬁc Computing

Sophomore Year: Sophomore Year:

Linear Algebra Linear Algebra

Multivariate Calculus Transition to Advanced Mathematics

Transition to Advanced Mathematics 200-level course

Junior Year: Junior Year:

200-level course 200-level course

200-level course 300-level course

300-level course 300-level course

Senior Year: Senior Year:

300-level course Senior IS Semester One

Senior IS Semester One Senior IS Semester Two

Senior IS Semester Two

Table 3: Recommended Timeline for the Mathematics Major

3.1 Recommended Timeline for the Mathematics Major

The courses in the department are systematically related; skills and knowledge developed in some

courses are presupposed and/or integrated into other courses. Thus, there is a timeline or schedule

that helps students most eﬀectively progress through the major. In general, we expect students to

follow one of the schedules in Table 3.

This sequence will help eﬀectively develop your mathematical skills and knowledge. Since Linear

Algebra, Multivariate Calculus, and Transition to Advanced Mathematics provide important background

for other courses, they should be completed by the end of your sophomore year. It is strongly

recommended that Transition to Advanced Mathematics an informative precursor to any 300-level

course. Additionally, students are urged to take courses that are relevant to their Senior I.S. before

their senior year.

However, we recognize that the program of study for each student may vary according to

individual circumstances and needs. For example, students who study oﬀ-campus for a semester will

need to carefully adjust their schedule, and double majors will need to be attentive to scheduling

conﬂicts that can arise between required courses, such as Junior I.S. It is important to follow one of

these proposed schedules when possible and to discuss possible variations with your advisor.

3.2 Requirements for the Double Major

We encourage students to consider a double major. There is a synergy between the study of

mathematics and of the basic concepts and principles of another discipline: each can enhance ones

understanding of the other.

Students who have a strong interest in two ﬁelds should begin by discussing their interests with

faculty in each department. This will help in identifying questions that can be eﬀectively explored

using the methodologies of diﬀerent disciplines. To oﬃcially declare a double major you need to

obtain the “Double Major Proposal” from the Dean of Curriculum’s website. To complete the form

you must meet with the Chair of each department to discuss potential topics for Senior I.S.

Requirements for each major in a double major are the same as those for a single major with the

exception that, subject to the approval of both departments/programs, a joint Senior I.S. project may be

done on a topic that incorporates materials, methodologies, and approaches from both disciplines.

Students who declare a double major must complete a separate Junior I.S. course (401)one in the

other major department. Students who have been approved for a double major must register for the

Senior Independent Study Thesis in one major during the fall semester and in the second major during

the spring semester. An individualized piece of work for two departments requires some additional

planning, and double major students are strongly advised to consult with both departments in

mid-April of their junior year. Your mathematics advisor should help you to build a preliminary

conceptual thesis that dovetails with your work in the other major.

As a double major student, your Senior I.S. thesis must satisfy the requirements of both

departments. For example, most of the social and natural sciences will expect you to complete

empirical research using the appropriate methods. Likewise, in the humanities, you will be expected

to employ the critical methodology of the other discipline, such as literary criticism. Thus, you will

learn how each discipline can inform the work of the other. In this way, one can write a joint Senior I.S.

that satisﬁes the criteria for both departments and yet that has the integrity of a uniﬁed piece of work.

In addition, the Dean of Curriculum requires a “Double Major IS Agreement” to be completed by the

student in conjunction with their advisors before the end of the fourth week of the fall semester. This

form is available at the College’s website.

3.3 Requirements for Teaching Licensure in Mathematics

Students who are planning to receive licensure in early childhood education are required to take

Education 260 Curriculum: Math/Science/Social Studies in the Early Childhood Years. No mathematics

beyond this course is required to fulﬁll the State requirement; however, MATH 100 would be an

excellent choice to help meet Woosters Learning Across the Disciplines requirements. Any student

wishing to pursue licensure in early childhood education should plan a program carefully with the

Department of Education.

For Ohio licensure in middle school or adolescent to young adult/secondary teaching of

mathematics, State requirements call for at least a minor in mathematics. Because speciﬁc courses in

education and mathematics are required for licensure, mathematics majors seeking licensure for

teaching middle school or adolescent to young adult/secondary mathematics should plan their

program early, in consultation with the Department of Education. These students may choose to write

a Senior I.S. thesis on a topic related to the teaching of middle school or adolescent to young

adult/secondary mathematics.

3.4 Requirements for the Minor

A minor in mathematics consists of six courses for credit, three of which must be Calculus I (111 or

108), Calculus II (112), and Linear Algebra (211). The remaining three mathematics courses must be

full credit and numbered above 211. To determine which math courses would be most applicable to

another discipline, students should contact a member of the department. A maximum of three courses

may be transferred in to count toward a minor.

To oﬃcially declare a minor you need to obtain the “Declaration/Change of Minor” from the Dean

of Curriculum’s website.

4 Oﬀ-Campus Study in Mathematics

• Budapest Semesters in Mathematics:

The College has direct connections with the overseas program Budapest Semesters in

Mathematics (http://www.budapestsemesters.com/ ). This program is designed for American

and Canadian undergraduate mathematics students interested in an overseas study experience

that does not hinder their progress toward a degree. Junior mathematics students with a very

strong mathematics background may spend one semester in Budapest, Hungary. All courses are

taught in English by Hungarians, most of which have spent some time teaching in the U.S. or

Canada. Most ﬁnancial aid is applicable to the program, but students with ﬁnancial aid should

consult directly with the Director of Financial Aid. Courses taken in Budapest appear on the

student’s transcript, but grades do not count toward the student’s grade point average. Only

courses receiving a grade of C or above will receive Wooster credit.

• Math in Moscow: http://www.mccme.ru/mathinmoscow/

• MASS program at Penn State: (advanced courses in Fall semester; also has summer research

opportunities) http://www.math.psu.edu/mass/

5 Senior Independent Study

5.1 Mathematics I.S. Student/Advisor Guidelines

To meet the graduation requirements of The College of Wooster, the major in mathematics requires a

two-course Independent Study Project, which culminates in an Independent Study thesis along with

an oral presentation describing the thesis. The additional college requirement of one course in

Independent Study is satisﬁed by work in courses above 212 taken to fulﬁll the major. This guide is

intended to complement the general regulations governing Independent Study (I.S.) as articulated in

the College’s Handbook for Independent Study and to assist students in the planning, organization,

and completion of the I.S. thesis. This guide also provides a description of what the I.S. advisor

expects from the student.

I.S. is of central importance in the mathematics major and in the entire academic experience of the

student. I.S. is the student’s opportunity to do a signiﬁcant piece of work in an area of personal interest

and to expand his or her understanding of mathematics. The ability to engage in independent study is

one of the primary goals of the major, and the successful completion of the I.S. thesis represents the

culmination of the student’s academic program. To this end we recommend that the student give

serious thought to the I.S. requirement and become thoroughly familiar with the Handbook for I.S.

and this guide. We reserve the right to make changes in future editions of this guide.

5.2 Project Topics

The range of topics in mathematics is very broad. Theoretical, applied, pedagogical (for those

intending to be certiﬁed to teach), and perhaps historical I.S. topics are possible. The crucial question

the student must ask when evaluating a possible topic is: ”Will there be a signiﬁcant increase in my

knowledge of some area of mathematics or in mathematics education?” The previously mentioned

conversations with faculty members will be helpful in answering this question. Since I.S. constitutes

two courses in the major, it is expected that about two courses worth of work in mathematics beyond

that in previous courses will be done.

The topic should be chosen on the basis of the student’s total academic experience and personal

interests. Students are encouraged to develop projects that grow out of previous course work and

related reading. Often topics, which can be only surveyed brieﬂy in a formal course, can be expanded

into an appropriate I.S. thesis. Some practical considerations that should be taken into account when

choosing a topic:

1. Personal background and ability

Be sure that the topic chosen is within the range of your abilities as determined by your previous

course work and reading. For instance, a student would be unwise to choose a topic in the area

of Topology or probability if no formal courses have been taken in these areas. This holds true

especially in application-oriented topics from speciﬁc subject matter areas. For example, a

student should not choose a mathematical modeling project in biology without demonstrable

background in biology as well as the formal course in mathematical modeling.

2. Manageability and available resources

Be sure that the project is narrow enough in scope to complete within the time allotted for the I.S.

thesis. A student should be certain that there exists a suﬃcient bibliography to support the

project. Necessary materials that are not among the holdings of the Andrews Library can usually

be acquired through other Library services, although a considerable time lag might be involved.

Therefore, students should use existing resources available on campus as much as possible.

3. Limitations.

• The project must expand the student’s knowledge and demonstrate a synthesis of

information on a topic from many sources.

• There must be resources available, or which can be readily acquired, for the project.

• The student must have the appropriate mathematical background for the project.

• A faculty member must agree to supervise the project.

• Working selected problems from a single textbook on any topic will not constitute an

acceptable I.S. project.

• The history of an area of mathematics is not acceptable in and of itself unless it encompasses

the learning of a signiﬁcant body of mathematics.

• Although the faculty advisor must approve all topics, the student is free to pursue virtually

any area of mathematics that is of interest. Some suggested topics include Abstract Algebra,

Number Theory, Partition Theory, Combinatorics, Graph Theory, Matrix Theory, Operations

Research (Deterministic and Stochastic), Mathematical Programming (Linear, Nonlinear,

Integer, Dynamic), Management Science, Topology, and Algebraic Topology.

5.3 Project Submissions

5.3.1 Project Proposal

The project abstract is a formal document, not a slip of paper with a few vague ideas on it about what

the student thinks would be interesting to do. In order to receive approval for a project, the student

will present a proposal outlining the following:

• The project’s focus (e.g., examine the Riemann Hypothesis, study Queuing Theory, examine the

Axiom of Choice).

• The project’s objectives in terms of the topics that the I.S. thesis will cover and the learning that

will result from accomplishing the project;

• The eﬀorts that will contribute to the project: programming, interviews, special library research,

trips, and needed materials (books, software, documentation, etc.).

• Potential problems in the project that might become trouble spots. Identify the challenges the

student might encounter in accomplishing the project. The student should investigate whether

these trouble spots could make the rest of the project impossible if they can’t be surmounted.

• A suggested timetable specifying the points throughout the two semesters at which the various

phases of the project will be complete.

• A minimum of ﬁve references (journal articles, technical reports, books) on your proposed topic.

Online references are not, generally, acceptable.

5.3.2 Project Research

The project should begin with a substantial amount of library research. The description of this

research should involve a clear exposition of the problem or research area, an annotated bibliography,

and an outline for conducting the research.

5.3.3 Annotated Bibliography

An annotated bibliography is a bibliography in which each entry includes a description of the entry’s

content and the role it might take in the research. This description is not a copy of the entry’s abstract.

For example:

Taalman, Laura. “Taking Sudoku Seriously.” Math Horizons. September 2007, 5-7.

The author gives an overview to the Sudoku puzzle, including the rules and counting the number of

possible Sudoku boards. It is an introductory article complete with concise terminology to use, mention of results

about Sudoku and remaining open questions are included. Many of the primary resources in the article should be

investigated and evaluated.

5.3.4 Thesis Outline

This will include a proposed table of contents (or outline) for the thesis. The table of contents should

include a title and a speciﬁcation of chapters and sub-sections.

5.3.5 Completed Chapters

In mid-October, the student will reach an agreement with his/her advisor about a comprehensive

narrative to be completed as a prerequisite to satisfactory completion of the ﬁrst semester of Senior I.S.

This comprehensive narrative must be submitted by the date given on the timeline later in this

document. The comprehensive narrative is not an outline or a draft, but a signiﬁcant written portion

of the I.S. that has been through at least one review by the advisor.

A full ﬁnal draft will be submitted to the advisor in the second semester of the Senior I.S. project.

5.3.6 Digitial I.S. Document

It is required that students submit online to the Registrar a digital copy of your Senior I.S. project for

the Digital I.S. Repository.

5.3.7 Poster

This document represents the I.S. in poster form and will be presented during the Senior I.S.

celebration day in April. It can be a traditional or digital in nature and students should consult their

advisor about the format of their poster.

5.3.8 Document Submission and oral presentation schedule

The student will meet with the advisor once a week to discuss ideas relating to the project, review

progress, and map out work to be done. In December, all Mathematics I.S. students will meet as a

group to give a brief presentation of their work and progress to that point (dates are below).

With the exception of the oral defense, the student will submit a typed document for each item by

4:00 PM on the indicated day. The student will submit the ﬁnal thesis to the Registrar’s oﬃce on the

indicated day; all other documents will go to the advisor. Advisors will not discuss assignments with

students on the day they are due or the day before. The schedule of submission follows here.

Junior Year, Second Semester

• Tuesday of Final Exams Week - IS Preliminary Proposal

Proposal form needs to be submitted to the Department Chair.

Senior Year, First Semester

• Friday of 3rd week - Topic and Annotated bibliography

An annotated bibliography is a list of citations to books, articles, and documents. Each citation is

followed by a brief (usually about 150 words) descriptive and evaluative paragraph, the

annotation. The purpose of the annotation is to inform the reader of the relevance, accuracy, and

quality of the sources cited. Below is an example of one such citation that would appear:

Taalman, Laura. “Taking Sudoku Seriously.” Math Horizons. September 2007, 5-7.

The author gives an overview to the Sudoku puzzle, including the rules and counting the number of

possible Sudoku boards. It is an introductory article complete with concise terminology to use, mention of

results about Sudoku and remaining open questions are included. Many of the primary resources in the

article should be investigated and evaluated.

• Friday of 6th week - Project Proposal - Description/Goals

This is a one-page description of what your project will be about.

• Friday of 12th week - A Comprehensive Narrative

This could be a background exposition, a history chapter describing the general area of research,

a literature review, or it may be a later chapter of the thesis. In any case, it should be a substantial

written portion of the thesis.

• Friday after Thanksgiving Break - Outline

This should be a detailed outline of the thesis.

• Tuesday of last week of classes - Oral presentation

This should be a ﬁve-seven minute presentation on your project and progress in the ﬁrst

semester. Your presentation should make use of some form of presentation software.

Grading, Fall Semester:

Below are the components that will determine your IS grade for MATH 451 (usually completed in

the fall semester of the Senior year). The due dates given earlier are suggestions and you will

determine and record the actual due dates in consultation with your advisor. Each component is

worth approximately 20% of your overall grade for MATH 451. Your grade on each component will

reﬂect your promptness, clarity of presentation, thoroughness, and consistency with documents

already submitted. To obtain a satisfactory progress (SP) grade in MATH 451, the student must

complete all indicated submissions and receive at least an 81%. The table below suggests a 100-point

scale but it is within the purview of the advisor to determine how they will measure successful

progress and to communicate this to the student.

Project Proposal and Outline 20 points

Oral Presentation 20 points

Subject and Annotated Bibliography 20 points

Comprehensive Narrative 20 points

Attendance 20 points

Grade for ﬁrst semester: SP (81-100 points); NC (0-80 points).

Senior Year, Second Semester

• Tuesday of 1st week - IS Student meeting

A meeting to remind students of formatting requirements and to answer any questions they may

have.

• Friday of 1st week - Table of Contents and Second chapter

A Table of Contents that should be close to the ﬁnal product and another substantial written

portion of the IS.

• Friday of 7th week - First complete draft

Changes beyond this copy should only be editorial and only a minimum of new material should

be written. See the IS Guidelines for formatting information.

• First Monday after Spring Break - Final thesis

• Oral

TBD

Grading, Spring Semester:

The spring semester grade (H, G, S, NC) will largely represent an evaluation of the ﬁnal thesis, the

oral presentation, and the organization of the project eﬀort. The following criteria determine the ﬁnal

grade. You should also look at the attached evaluation rubrics for the IS thesis and oral presentation.

• CONTENT:

The content of the independent study document must meet the requirements agreed upon by the

IS advisor and advisee. These requirements will diﬀer for each project.

• FORM:

The ﬁnal independent study document is evaluated for mechanical and grammatical errors. The

text must be well organized, grammatically correct, and complete - including a table of contents,

an introductory and conclusion chapter, a bibliography, and a user manual if necessary.

– Formatting:

∗ Overall Document

· Left margin 1.5 in

· Right margin 1.25 in

· Top margin 1 in

· Bottom margin 1 in

· Pages should also be numbered

· Double-sided and Spiral bound

· Chapters start on a new page

· Theorems, lemmas, examples, corollaries, deﬁnitions, propositions, remarks,

notation, terminology, ﬁgures, and tables numbered within Chapters.

∗ Title page (no page number - everything centered except Advisors which are on left

margin)

Title

Independent Study Thesis

Presented in Partial Fulﬁllment of

the Requirements for the Degree Bachelor of Arts in

the Department of Mathematics and Computer Science

at the College of Wooster by

Author

The College of Wooster

Year

Advised by:

Advisors

∗ Frontmatter (Page numbers at bottom of pages)

· Blank page hidden page number

· Copyright page (optional and hidden page number)

· Abstract (roman page number (ii or iii based on copyright or not))

· Dedication (optional)

· Acknowledgments (optional)

· Table of Contents

· List of Figures (only needed if there are ﬁgures)

· List of Tables (only needed if there are tables)

· List of Listings (only needed if there are code listings)

· Preface (optional) (A chapter which is not numbered or lettered)

∗ Mainmatter

· Numbered Sections (Page numbers in arabic, ﬁrst page number of chapter centered

at bottom, remaining page numbers in upper right and running header on upper

left (Chapter number Chapter title))

· Introduction (Chapter 1)

· Body (Chapters 2-?)

∗ Backmatter

· Lettered Sections (Page numbers in arabic, ﬁrst page number of appendix centered

at bottom, remaining page numbers in upper right and running header on upper

left (Appendix letter Appendix title))

· Appendices

∗ Sections not lettered or numbered

· Afterword (optional)

· References

· Index (optional) (two column alphabetized)

· Colophon (optional)

· Blank page (hidden page number)

An example of a completed thesis can be seen in the LaTeX IS Guide found at:

https://wiki.wooster.edu/display/latex/Downloads and a template will be circulated

in fall semester for all seniors.

• METHODOLOGY:

The essential factor here is the degree to which the student has approached the project in an

organized and eﬃcient manner and has applied eﬀort consistently throughout the entire year.

The quality and promptness of intermediate submissions is highly important. A major item is

the promptness and quality of the rough draft submission since it measures the ability of the

student to eﬀectively coordinate the research eﬀort in an eﬃcient manner. Attendance and

presentation issues from the ﬁrst semester will carry a heavy weight for this criterion.

• ORAL PRESENTATION:

Grading of the oral presentation evaluates the organization, spontaneity, ﬂow, continuity, and

comprehensibility of the presentation. It also evaluates the student’s ability to respond to

reasonable questions and explain points of confusion. The student should use visual aids as a

means of guiding the presentation, but should avoid reading material to the audience. The

presentation should last approximately thirty-ﬁve minutes to permit approximately ﬁfteen

minutes for questions and extended discussion. A major challenge of the presentation is to

identify the key points to cover in giving a good description of the project in a relatively short

time period.

6 Independent Study Assessment Guide

Math 452 Evaluation Rubric (revised fall 2012)

This rubric serves as a starting point for discussion among the mathematics faculty about Math 452 grades. Not

all questions apply equally well to every project, and some are only appropriate for the first reader. Roughly

speaking, a score of 4 in an area corresponds to Honors-level achievement, 3 to Good, and 2 to Satisfactory, with

1 and 0 indicating substandard performance. However, the way in which these elements are weighted is topic-

dependent, and a particular set of scores does not guarantee a certain 452 grade. For double majors, the

evaluation of the project from the perspective of the other discipline is also significant in determining the grade.

1. Extent of Material Covered – Based on the material covered in the final written document and (for first

readers only) your weekly meetings with the student, which statement best describes the extent of the

student’s investigation? (Use 1a for all projects, and also 1b if it applies.)

1a. Extent of Investigation – Which statement best describes the extent of the student’s investigation?

 (4 - Exceptional) The student did a thorough investigation into a focused topic, providing examples and going well beyond the

minimum extent required of a two-semester project.

 (3 - Strong) The student did a comprehensive summary of a focused topic, providing examples and personalizing the material.

 (2 - Adequate) The student did a good summary of material pertaining to a defined topic, and the extent is sufficient for a two-

semester investigation.

 (1 - Marginal) The student covered some portions well, but failed to go far enough with others, and/or lacked a topical focus.

 (0 - Unsatisfactory) The student provided a brief summary of the material, but the extent was insufficient for a two-semester

investigation and/or the content was so widely scattered as to make the central topic unclear.

1b. Extent of Application – If applicable, which statement best describes the student’s mathematical modeling?

 (4 - Exceptional) The student has a thorough understanding of the application area, which is reflected with originality in an

innovative model.

 (3 - Strong) The student has a thorough understanding of the application area, and all key aspects are reflected in the model.

 (2 - Adequate) The student has an understanding of the application area, with some key aspects reflected in the model.

 (1 - Marginal) The student has a weak understanding of the application area, resulting in a deficient model.

 (0 - Unsatisfactory) The student has a clear lack of understanding of the application area, resulting in a poorly-designed model.

2. Appropriate Use of Resources (Use one or both parts, based on their applicability to the student’s project.)

2a. Use of Prior Literature – Allowing for differences based on mathematical subfields and the topic of the

student’s investigation, which statement best describes the use of related prior literature in the thesis?

 (4 - Exceptional) The student used appropriate resources, integrated them into one coherent narrative, and understands the

place of their own work in the context of the wider subfield of mathematics.

 (3 - Strong) The student successfully used appropriate resources, and some integration is apparent in the thesis.

 (2 - Adequate) The student successfully used appropriate resources.

 (1 - Marginal) The student’s use of resources is somewhat inadequate.

 (0 - Unsatisfactory) The student’s use of resources is substantially inadequate, significantly impacting the quality of the thesis.

2b. Use of Computational Tools – Which statement best describes the student’s use and justification of

computational methods used in this investigation?

 (4 - Exceptional) The student successfully used appropriate computational tools, and fully justified them (through literature

review and/or preliminary investigation).

 (3 - Strong) The student successfully used appropriate computational tools, and mostly justified their use.

 (2 - Adequate) The student successfully used appropriate computational tools, but the justification is weak.

 (1 - Marginal) The student used inappropriate computational tools, did not justify their selection, and/or was only partially

successful in using them.

 (0 - Unsatisfactory) The student was unsuccessful in using computational tools.

3. Writing Quality – Which statement best describes the quality of the student’s writing in the thesis, including

organization, readability, mathematical precision, form (grammar, spelling, typesetting), and style?

 (4 - Exceptional) The I.S. is written in a clear, precise well-organized manner, with excellent form. Moreover, it is written in the

student’s unique style and directed toward an audience of peers.

 (3 - Strong) The I.S. is well-organized and very readable, with only minimal errors in any of these areas.

 (2 - Adequate) The I.S. is well-organized and readable, despite some lack of precision and/or errors in form.

 (1 - Marginal) The I.S. is somewhat difficult to read, because of weak organization and/or significant issues in form or precision.

 (0 - Unsatisfactory) The I.S. is quite difficult to read, because of disorganization and/or pervasive issues in one or more of these

areas.

4. Presentation – Which statement best describes the quality of the student’s final oral presentation,

considering organization, knowledge of content, audience awareness, and professionalism? (For double majors

whose oral exam begins from a poster, rather than an oral presentation, consider the poster instead.)

 (4 - Exceptional) The presentation was excellent overall, and strong in each of these aspects.

 (3 - Strong) The presentation was solid, with only minimal problems in any of these aspects.

 (2 - Adequate) The presentation was acceptable, despite some weakness in one or more aspects.

 (1 - Marginal) The presentation was substantially hampered by a pronounced weakness in at least one aspect.

 (0 - Unsatisfactory) The presentation was unacceptable, with pronounced weaknesses in multiple aspects.

5. Independence of Learning (for first readers only) – Based on the weekly meetings with your I.S. student,

which statement best describes the student’s initiative and independence throughout the process?

 (4 - Exceptional) The student demonstrated strong initiative and independence, requiring only a minimal amount of guidance.

 (3 - Strong) The student demonstrated good initiative and worked mostly independently, requiring an appropriate amount of

guidance.

 (2 - Adequate) The student was self-directed for some of the thesis, but required lots of guidance on other parts.

 (1 - Marginal) The student was unable to work without strict deadlines and lots of guidance regarding the direction of the

thesis.

 (0 - Unsatisfactory) Despite deadlines and guidance from the advisor, the student failed to complete work in a timely manner.

6. Student Understanding and Mastery of the Subject – Based on the written thesis, the oral examination, and

(for first readers only) weekly meetings, which statement best describes this student’s understanding of the

content in the I.S.?

 (4 - Exceptional) The student has a thorough understanding of the material and was able to answer nearly all probing

questions.

 (3 - Strong) The student has a good understanding of the material was able to answer questions in all areas of content,

including some probing questions.

 (2 - Adequate) The student has a good understanding of most of the material, but had difficulty answering probing questions.

 (1 - Marginal) The student lacks understanding of significant portions of the material, and had difficulty answering most

questions.

 (0 - Unsatisfactory) The student lacks a basic understanding of the material and was unable to answer basic questions.

7 Further Learning Opportunities

7.1 At Wooster

• Mathematics Colloquia

Throughout the year, mathematicians are invited to campus to give talks. These are valuable

opportunities to be exposed to diﬀerent mathematical ideas and to engage mathematicians

outside of Wooster faculty.

• Math Table

Roundtable is held every week, usually in Lowry dining hall. All majors, faculty, and friends are

invited to attend.

• Student Mathematical Association of America Chapter (SMAAC)

Students are encouraged to join Math Club. The organization plans social activities and an

annual high school mathematics competition. Each year, ‘Taylor Bowl’ pits the Mathematics and

Physics departments against one another in bowling at Scot Lanes.

• Putnam Exam

The William Lowell Putnam Mathematical Competition, often abbreviated to the Putnam Exam,

is an annual mathematics competition for undergraduate college students of the United States

and Canada, awarding scholarships and cash prizes ranging from 250to2,500 for the top students

and 5, 000to25,000 for the top schools. Elizabeth Lowell Putnam founded the competition in 1927

in memory of her husband William Lowell Putnam, who was an advocate of intercollegiate

intellectual competition. The exam has been oﬀered annually since 1938 and is administered by

the Mathematical Association of America.

• COMAP Mathematical Contest in Modeling (MCM)

Mathematical Contest in Modeling (MCM), challenges teams of students to clarify, analyze, and

propose solutions to open-ended problems. The contest attracts diverse students and faculty

advisors from over 500 institutions around the world each February.

• Teaching Apprenticeships

The department oﬀers students the opportunity to serve as a teaching apprentice for some

courses. The goal of this course is to help students reﬂect upon the nature and process of

teaching and education and to also gain a deeper understanding of the courses subject matter. If

there is an area of mathematics in which you are especially interested and you would like to

assist in the teaching process, please approach the professor as early as possible.

• The Math Center Tutoring and Grading

The Math Center staﬀ assists students with understanding of concepts, examples, and

homework problems. Each semester there are tutor openings for students and availability for

students to grade homework assignments for faculty.

• Sophomore Research

Faculty are engaged in research projects, and the department itself sometimes has research

needs. If you are interested in participating in the Sophomore Research Program, please ask

members of the department. Information about the Colleges support for undergraduate research

is available on the College website.

• Applied Mathematical Research Experience (AMRE)

The Applied Mathematical Research Experience (AMRE) is a program initiated by the

Department of Mathematics and Computer Science designed to give students from The College

of Wooster experience in the practical applications of mathematics and computer science that the

classroom cannot provide. For eight weeks of the summer, student teams and faculty advisors

from the College of Wooster are joined with a (usually local) business, industry, or agency

(client).

The structure of the program is based upon several research teams that work independently on

separate projects, but also come together for discussion of progress. These teams are comprised

of students (usually three) and a faculty advisor. The faculty advisor involvement is heavy

initially as the student team becomes familiar with the project deﬁnition. After approximately

two weeks, involvement becomes primarily advisory as the students work directly with client

representatives and others. Student teams give weekly progress reports in the form of oral

presentations, in addition to periodic presentations to their respective clients. Each team also

gives a ﬁnal oral presentation and written report to the client upon completion of the project.

In addition to work done on the project, a number of lectures are a part of the AMRE program.

These lectures are intended to teach the students skills or tools necessary to complete their

assigned projects. Colloquia are also given on a variety of topics including group dynamics and

oral presentation. These presentations are given by individuals from academia, local

corporations and professional consultants.

Applications are accepted each February and positions are open to all College of Wooster

students.

7.2 Beyond Wooster

• Summer Programs in Mathematics

Program Website

REU (Research Experiences for Undergraduates) www.nsf.gov/crssprgm/reu/

Further Undergraduate Opportunities www.ams.org/employment/undergrad.html

www.maa.org/students/undergrad/

SIAM www.siam.org/students/resources/fellowship.php

Miami University of Ohio SUMSRI www.units.muohio.edu/sumsri/

SMI at Cornell University www.math.cornell.edu/

smi/

Wabash College www.wabash.edu/academics/math/wsim

• Summer Programs that do not require US citizenship

Program Website

Williams College SMALL http://math.williams.edu/small/

Park City Math Institute http://pcmi.ias.edu/program-ugss

RIPS and UCLA www.ipam.ucla.edu/programs

MBI at Ohio State http://mbi.osu.edu

• Summer Internships

Summer Experience Website

Math-related Jobs in Industry www.ams.org/employment/internships.html

Math internships database www.jyi.org/SCC/internships.php

Statistics internships www.amstat.org/education/internships.cfm

• Summer Teaching

Program Website

PROMYS at Boston University www.promys.org/

CTY at Johns Hopkins University www.cty.jhu.edu

Other similar programs www.ams.org/employment/mathcamps.html

8 Departmental Honors and Prizes

• The Foster Prize in Mathematics was established in 2001 with gifts from Walter D. Foster and

Richard S. Foster 71. Income from the fund is awarded annually to the senior mathematics major

who has demonstrated the most improvement in mathematics during his or her college years, as

judged by the Mathematics Department faculty.

• The Lyman C. Knight, Sr. Prize in Physical Education and Mathematics was established in

1978 and honors Professor Knights thirty years of service from 1910 to 1940 as a member of the

Department of Mathematics. It is awarded to a sophomore who has demonstrated both

outstanding promise in high school and ﬁrst-year mathematics and has superior physical skills.

• The Elizabeth Sidwell Wagner Prize in Mathematics, established in 1966 by Dr. and Mrs. Cary

R. Wagner, is awarded annually at the beginning of the senior year to that student who showed

the greatest aptitude during the junior year and, in the opinion of a jury, seems most likely to

succeed in mathematics.

• The William H. Wilson Prize in Mathematics was established in 1926 in memory of William H.

Wilson, of the class of 1889, professor of mathematics in the College from 1900 to 1907. The prize

is awarded annually to that member of the senior class who has shown the greatest proﬁciency

in mathematics.

9 Mathematics After Wooster

Selected Mathematical Careers

Organization Website

American Mathematical Society (AMS) www.ams.org

Mathematical Association of America (MAA) www.maa.org

Society for Industrial and Applied Mathematics (SIAM) www.siam.org

National Security Agency (NSA) www.nsa.gov

Society of Actuaries (SOA) www.soa.org

US Bureau of Labor Statistics (BLS) www.bls.gov

The Society for Mathematical Biology (SMB) www.smb.org

Mathematical Sciences Research Institute (MSRI) www.msri.org

The College of Wooster also has a Career Services oﬃce in APEX. The mission of Career Services

oﬃce is to help students bridge their liberal arts education with their career journey. They oﬀer a

comprehensive range of services, including individual career advising and group programs, assisting

students in understanding their skills, interests, and values while connecting this knowledge with

various career options.