Math 498
**SENIOR
SEMINAR** Fall
2016

4:00- 4:55 Tuesday COHH 3121 Section 501: 3 hours

**Course Description: **Math 498 is a required
course for seniors completing a bachelorŐs degree in mathematics. The course is used to assess the
studentŐs independent thinking skills and ability to write and present formal
mathematics. The course has a director
who oversees the course, but each student will work individually with a faculty
member on a project.

**Director: ** Dr. Tom
Richmond
COHH 3106 745-6219

Tom.Richmond@wku.edu

http://people.wku.edu/tom.richmond/

**Office Hours: 9:00**-10:00 MWF, 1:15-1:45 MWF, and by appointment

**Learning
Outcomes: **Students will
communicate mathematics orally and in writing and will conduct a capstone
research project synthesizing or extending material from earlier coursework.

**Requirements:
**

1. Maintain regular contact with your supervising faculty member and make regular progress on your project according to a timetable set by your supervising faculty member.

2. Give 3
colloquium talks. The first is to
be approximately 10 minutes in length and given within the first 6 weeks of the
semester. The second is to be 15 to
20 minutes in length and given during the 7^{th} to 12^{th}
weeks of the semester. The final
presentation is to be approximately 25 minutes long and must be given by the
end of the semester.

**Note 1:** If the presentation requirement is not
completely fulfilled then the student must withdraw from the course or receive
an incomplete.

**Note 2:** The final presentation may be given at a
conference instead of in the departmental colloquium, as long as there are an
adequate number of faculty members present to grade the presentation, as
outlined below.

3. Attend other 498 talks. A student will be scored on a scale of 0 (unacceptable) to 4 (excellent) for attending all of the fellow studentsŐ talks, up to a maximum of 10 such talks. Other talks may be substituted with the permission of the director.

4. Submit, on schedule, a 7-11 page paper (single spaced) on your project. The paper will be read by the supervising faculty member and two other faculty members. The student will be allowed to make revisions suggested by the readers before the final version is graded by the readers according to the departmental rubric.

5. A copy of the final version of your paper must be submitted to the course director. This copy must include the name of the supervising faculty member and the names of the other graders.

6. You must complete the exit-interview Senior Survey to assist the department in assessment and evaluation of our program. Submissions are anonymous.

**Method of Evaluation:**

The studentŐs written paper and final oral presentation will be evaluated by a committee of three mathematics faculty members, including the studentŐs supervisor. The committee shall use the departmental rubrics for grading the presentation and paper, available online.

http://people.wku.edu/tom.richmond/498PaperRubric.pdf

http://people.wku.edu/tom.richmond/498PresentationRubric.pdf

The grades are determined by the averages of
the committeeŐs scores. Grading for
the paper and presentation will adhere to the guidelines:

0 – unacceptable 0.5 – very poor 1 – poor 1.5 – below
average 2
– fair 2.5 – above
average 3
– good 3.5 – very good 4 –
excellent

The course grade will be determined by the
average of the paper and presentation scores according to the following scale:

F – [0, 1) D
– [1, 2) C
– [2, 3) B
– [3.0, 3.5) A
– [3.5, 4.0]

_________________________________________________________________________________________________

**Evaluating the Paper:**

The paper will be graded on (i) its organization, (ii) presentation of mathematical
material, (iii) demonstration of mathematical reasoning and problem solving, (iv) readability, grammar, and style, and (v) level of
difficulty. The faculty members will grade each of these parts on a scale of 0
(unacceptable) to 4 (excellent). The final grade on the paper will be the
average of all scores on all parts. Evaluation of the paper will be based on
the following set of expectations:

**Organization**

a. The paper includes a title
page and a bibliography in the standard scientific format.

b. The main body of the paper is from
seven to eleven (single-spaced) pages and is typeset with an appropriate word
processor and equation editor. (Exceptions in length can be made if the
supervising faculty member feels that it is necessary.)

c. The paper begins with an
introduction that describes the material to be presented, clearly states the
objectives of the paper, and explains any special techniques to be used by the
author.

d. Following the introduction,
the paper has an identifiable body that focuses on the main points with logical
and clear transitions between them.

e. Bibliographic and
equation number references are cited throughout the paper as appropriate.

f. The paper contains a
conclusion that, as appropriate, describes specific applications, related
problems, or directions for future development.

**Presentation of
Mathematical Material**

a. The paper includes all
necessary definitions as well as a description of all terms or background
results that are cited.

b. The paper includes appropriate examples that illustrate the key
concepts.

c. Results and exposition flow in
a logical order.

d. All results, statements,
definitions, theorems, and proofs are accurate.

**Mathematical Reasoning and Problem Solving**

a. Student demonstrates a clear
understanding of the material/problem being presented.

b. Student draws upon his/her
accumulated knowledge of a variety of mathematical ideas to explain/solve

their topic/problem.

c. Student demonstrates the
ability to work independently.

d. Student is able to relate the
topic/problem to other mathematical ideas they have encountered in their

course work.

**Readability,
Grammar, and Style**

a. The paper should be readable
by a fellow mathematics major who has completed the
foundation core MATH 136, 137, 237, 307, 310, 317, and some other 400-level
mathematics course.

b. There should be distinction
between concepts and results that should be known to readers versus those that
require review or some introduction and development.

c. Spelling, punctuation, and
grammar must be correct.

d. Equations, figures, and tables
should be properly inset and numbered for reference.

**Level of
Difficulty**

The material should be appropriately
challenging given the studentŐs mathematical background and coursework. _______________________________________________________________________

**Evaluating
the Presentation:**

The presentation will be graded on (i) its structure, (ii) engagement of the audience, (iii)
demonstration of mathematical comprehension and problem-solving ability, (iv) style, and (v) level of difficulty. The faculty members
will grade each of these parts on a scale of 0 (unacceptable) to 4 (excellent).
The final grade on the presentation will be the average of all scores on all
parts. Evaluation of the oral presentation will be based on the following set
of expectations:

**
Structure**

a. The presentation should begin
with an introduction that describes the material to be presented, clearly
states the objectives of the presentation, and states any special techniques to
be used by the speaker.

b. Following the introduction,
the presentation should have an identifiable body that focuses on the main
points with logical transitions between the key ideas.

c. As appropriate, the speaker identifies specific applications, related questions, or directions for future
development.

d. The presentation should be
from 20 to 25 minutes in length followed by a question and answer period.

**Engagement of
Audience**

a. The presentation should be
delivered in such a way as to assure its understanding by the audience.

b. The speaker should assume that
the listeners have solid mathematical reasoning skills and have been exposed to
the ideas of calculus and the fundamentals of logic, sets, and proofs. The
presenter should not assume that members of the audience have any specific
detailed background on the subject matter.

c. The speaker should provide
appropriate review or development of any specific background necessary for
understanding the material in the presentation.

d. The speaker may use note
cards, overhead transparencies, and other forms of support as appropriate, but
should speak to members of the audience as opposed to reading the paper.

e. The speaker should maintain
eye contact during the presentation and should make an effort to include
everyone in the audience.

f. The speaker should invite
questions and comments, specifically at the conclusion of the presentation, and
the speaker should treat all questions and questioners with respect.

**Demonstration
of Mathematical Comprehension and Problem-Solving Ability**

a. If the presentation is to communicate an
overview of the entire topic through a selection of definitions and theorems,
then the speaker should explain the central concepts and results formally and
accurately, and should provide appropriate examples to illustrate them.

b. If the presentation is to communicate an
overview of the whole topic, but the mathematical treatment is more informal,
then the speaker should introduce central concepts and results through examples
and informal statements designed to stimulate intuitive understanding.

c. If a formal proof is part of
the presentation, then the speaker should demonstrate a clear understanding of
the way that definitions and prior results are applied in the course of the
proof.

d. The speaker should respond
appropriately and correctly (within the scope of the studentŐs research) to
questions during the question and answer period.

e. The
speaker should identify, in the course of the presentation, the key issues of
their topic/problem and the steps they took to resolve those issues.

**Style**

a. The speaker should speak clearly and loudly enough for all audience members to hear.

b. The presentation should be
delivered with sufficient clarity and professionalism so that the main points can be understood by most audience members.

c. The presenter should use
adequate technology in the presentation. PowerPoint presentations with
elaborations on the blackboard are encouraged.

**Level of Difficulty**

The material should be appropriately challenging given the studentŐs mathematical background and coursework.