Request for New Course
EASTERN MICHIGAN UNIVERSITY
DIVISION OF ACADEMIC AFFAIRS
REQUEST FOR NEW COURSE
DEPARTMENT/SCHOOL: ________MATHEMATICS_______COLLEGE:
ARTS & SCIENCES
CONTACT PERSON: ________C. GARDINER________________________________________________________________
CONTACT PHONE:
7-1444
CONTACT EMAIL:
cgardiner@emich.edu
REQUESTED START DATE: TERM___WINTER___YEAR___2015___
A. Rationale/Justification for the Course
This new course, MATH 520 Real Analysis I, will be the graduate credit equivalent of MATH 420 Introduction to
Real Analysis. This course, along with MATH 411 Abstract Algebra and MATH 416 Linear Algebra are the
“foundation” courses of our M.A. in Mathematics. All students are required to take these three courses if they have not
previously had them. Currently, they take them for graduate credit.
The title will be Real Analysis I because we already have a follow-up course MATH 526 Real analysis, for which
MATH 420 is a prerequisite. We will change the name of MATH 526 to Real Analysis II.
Rather than list specific courses as prerequisites, we include the assumed prior knowledge in the catalog description.
We do this with all of our graduate courses.
B. Course Information
1. Subject Code and Course Number:
2. Course Title:
Real Analysis I
3. Credit Hours:
3
4. Repeatable for Credit? Yes_______
MATH 520
No___X___
If “Yes”, how many total credits may be earned?_______
5. Catalog Description (Limit to approximately 50 words.):
A rigorous introduction to the foundations of calculus: real numbers, elementary topology of the real line, sequences
and series, limits, continuity, uniform continuity, differentiation, Riemann integration. Completion of two semesters of
calculus and experience in writing proofs is assumed.
6. Method of Delivery (Check all that apply.)
a. Standard (lecture/lab) X
On Campus
X
Off Campus
b. Fully Online
c. Hybrid/ Web Enhanced
7. Grading Mode:
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Sept. 09
Normal (A-E)
X
Credit/No Credit
New Course Form
8. Prerequisites: Courses that MUST be completed before a student can take this course. (List by Subject Code, Number and Title.)
9. Concurrent Prerequisites:
Code, Number and Title.)
Courses listed in #5 that MAY also be taken at the same time as a student is taking this course. (List by Subject
10. Corequisites: Courses that MUST be taken at the same time as a student in taking this course.
(List by Subject Code, Number and
Title.)
11. Equivalent Courses. A student may not earn credit for both a course and its equivalent. A course will count as a repeat if an equivalent
course has already been taken. (List by Subject Code, Number and Title)
MATH 420 Introduction to Real Analysis
12. Course Restrictions:
a. Restriction by College. Is admission to a specific College Required?
College of Business
Yes
No
X
College of Education
Yes
No
X
b. Restriction by Major/Program. Will only students in certain majors/programs be allowed to take this course?
Yes
No
X
If “Yes”, list the majors/programs
c. Restriction by Class Level Check all those who will be allowed to take the course:
Undergraduate
Graduate
All undergraduates_______
All graduate students__X__
Freshperson
Certificate
Sophomore
Masters
Junior
Specialist
Senior
Doctoral
Second Bachelor________
UG Degree Pending_____
Post-Bac. Tchr. Cert._____
Low GPA Admit_______
Note: If this is a 400-level course to be offered for graduate credit, attach Approval Form for 400-level Course for Graduate
Credit. Only “Approved for Graduate Credit” undergraduate courses may be included on graduate programs of study.
Note: Only 500-level graduate courses can be taken by undergraduate students. Undergraduate students may not register for
600-level courses
d. Restriction by Permission. Will Departmental Permission be required?
Yes
No
(Note: Department permission requires the department to enter authorization for every student registering.)
13. Will the course be offered as part of the General Education Program?
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Yes
No
X
X
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New Course Form
If “Yes”, attach Request for Inclusion of a Course in the General Education Program: Education for Participation in the Global Community
form. Note: All new courses proposed for inclusion in this program will be reviewed by the General Education Advisory Committee. If this
course is NOT approved for inclusion in the General Education program, will it still be offered? Yes
No
C. Relationship to Existing Courses
Within the Department:
14. Will this course will be a requirement or restricted elective in any existing program(s)? Yes X
No
If “Yes”, list the programs and attach a copy of the programs that clearly shows the place the new course will have in the curriculum.
Program
M.A. in Mathematics
Required X
Restricted Elective
Program
M.A. in Applied Statistics
Required
Restricted Elective X
15. Will this course replace an existing course? Yes X
No
16. (Complete only if the answer to #15 is “Yes.”)
a. Subject Code, Number and Title of course to be replaced:
This course will replace MATH 420 Introduction to Real Analysis in both the programs mentioned above.
b. Will the course to be replaced be deleted?
Yes
No
X
17. (Complete only if the answer #16b is “Yes.”) If the replaced course is to be deleted, it is not necessary to submit a Request for
Graduate and Undergraduate Course Deletion.
a. When is the last time it will be offered?
Term
Year
b. Is the course to be deleted required by programs in other departments?
Contact the Course and Program Development Office if necessary.
Yes
No
c. If “Yes”, do the affected departments support this change?
Yes
No
If “Yes”, attach letters of support. If “No”, attach letters from the affected department explaining the lack of support, if available.
Outside the Department: The following information must be provided. Contact the Course and Program Development office for
assistance if necessary.
18. Are there similar courses offered in other University Departments?
If “Yes”, list courses by Subject Code, Number and Title
Yes
No
X
19. If similar courses exist, do the departments in which they are offered support the proposed course?
Yes
No
If “Yes”, attach letters of support from the affected departments. If “No”, attach letters from the affected department explaining the lack of
support, if available.
D. Course Requirements
20. Attach a detailed Sample Course Syllabus including:
a.
b.
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Course goals, objectives and/or student learning outcomes
Outline of the content to be covered
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New Course Form
c.
d.
e.
f.
g.
h.
Student assignments including presentations, research papers, exams, etc.
Method of evaluation
Grading scale (if a graduate course, include graduate grading scale)
Special requirements
Bibliography, supplemental reading list
Other pertinent information.
NOTE: COURSES BEING PROPOSED FOR INCLUSION IN THE EDUCATION FOR PARTICIPATION IN THE GLOBAL
COMMUNITY PROGRAM MUST USE THE SYLLABUS TEMPLATE PROVIDED BY THE GENERAL EDUCATION
ADVISORY COMMITTEE. THE TEMPLATE IS ATTACHED TO THE REQUEST FOR INCLUSION OF A COURSE IN THE
GENERAL EDUCATION PROGRAM: EDUCATION FOR PARTICIPATION IN THE GLOBAL COMMUNITY FORM.
E. Cost Analysis (Complete only if the course will require additional University resources.
Fill in Estimated Resources for the
sponsoring department(s). Attach separate estimates for other affected departments.)
Estimated Resources:
Year One
Year Two
Year Three
Faculty / Staff
$_________
$_________
$_________
SS&M
$_________
$_________
$_________
Equipment
$_________
$_________
$_________
Total
$_________
$_________
$_________
F. Action of the Department/School and College
1. Department/School
Vote of faculty: For ___17______
Against ___0_____
Abstentions ___0_____
(Enter the number of votes cast in each category.)
Department Head/School Director Signature
Date
2. College/Graduate School
A. College
College Dean Signature
Date
B. Graduate School (if Graduate Course)
Graduate Dean Signature
Date
G. Approval
Associate Vice-President for Academic Programming Signature
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Date
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New Course Form
Sample Syllabus for MATH 520 Real Analysis I
a. The goal of this course is for students to gain a deep understanding of the foundations of single-variable calculus.
b. Topics to be covered are:
Axioms for the real numbers
The Heine-Borel Theorem
Limits
Continuity
Uniform continuity
The derivative
The Mean-Value Theorem
The Riemann integral
Properties of the integral
The Fundamental Theorem of Calculus
Taylor polynomials
Infinite sequences
Monotone and Cauchy sequences
Infinite series and convergence tests
Absolute and conditional convergence
Sequences of functions
Series of functions
c. Assessment will consist of regular homework assignments, 2 or 3 tests, and a final. The final will be cumulative.
d. A typical grading scheme would be:
homework assignments
40%
2 midterms
40%
final exam
20%
e. Grading scale:
90% and above
80% to 89.9%
70% to 79.9%
below 70%
A- or A
B-, B or B+
C-, C or C+
F
f. This class will run concurrently with MATH 420 Introduction to Real Analysis. Each assignment will include
problems which are required for graduate students (in MATH 520) and optional/extra credit for undergraduate students
(in MATH 420). These extra problems will generally be of greater difficulty, or will probe a topic in greater depth.
Graduate students are graded on a different grading scale from undergraduate students.
g. Bibliography (including possible texts)
Foundations of Analysis by David Belding & Kevin Mitchell, Dover Publications, 2nd edition (2008).
Introduction to Real Analysis by Robert Bartle and Donald Sherbert, Wiley, 4th edition (2011).
Real Analysis by Halsey Royden and Patrick Fitzpatrick, Pearson, 4th edition (2010).
All the Mathematics You Missed: But Need to Know for Graduate School by Thomas Garrity and Lori
Pedersen, Cambridge, 2001.
Advanced Calculus: An Introduction to Analysis, by Watson Fulks, Wiley, 3rd edition (1978)
An Introduction to Analysis by James Kirkwood, Waveland Press, 2nd edition (2002)
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New Course Form
Master of Arts in Mathematics (MTH)
Objectives
• To develop competence in mathematics and related areas beyond the undergraduate level.
• To improve the teaching of mathematics.
• To prepare for study beyond the master’s level in mathematics or mathematics education.
• To strengthen the mathematical background of professionals needing analytical and quantitative skills.
• To meet the needs of teachers continuing their education.
• To provide opportunities for research in mathematics and mathematics education.
Admission Requirements
Applicants must:
• Meet the Graduate School’s degree admission requirements; and
• Possess a strong undergraduate major in mathematics (approximately 30 hours with a GPA of 2.75 in
mathematics courses). Students without such a major may be admitted to the program after meeting
requirements specified by the department.
Degree Requirements
The master of arts degree in mathematics requires at least 30 graduate hours beyond the bachelor’s degree,
distributed with the approval of the department according to the course requirements below. Approval by the
student’s advisor of each semester’s courses prior to registration is recommended. Final approval for the degree
by the coordinator of advising is required.
Research Requirement
Students must select one of the following options:
Option I: Four hours of thesis research. Additional thesis hours may be taken, but will not replace the
requirements listed below under required courses, restricted electives, electives and cognates. Before starting
thesis research, students must submit to the department head a request to form a thesis committee to be made up
of three faculty members in the department. The chair, who will direct the research, is usually selected by the
student and requires the approval of the department head. The chair, in consultation with the student, will then
recommend for department-head approval the other two committee members. At the conclusion of their
research, students must submit to the department head the original thesis plus three copies written in a manner
suitable for publication and approved by the thesis committee. A presentation, based on the thesis, will be made
to at least three departmental faculty members.
Option II: At least two hours in research study. Students who elect this option will, with the approval of the
coordinator of advising, select a supervisor to direct the research study. A copy of the study, written in good and
acceptable form, must be filed with the department.
Advisor Information:
Bingwu Wang Ph.D.
515 Pray-Harrold
(734) 487-1444
bwang@emich.edu
Course Requirements:
The M.A. in Mathematics requires the completion of 30 hours of course work to be distributed among required courses,
restricted elective courses, research courses, elective courses in mathematics and cognate courses as follows:
Required Courses: 0-9 hours
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New Course Form
* MATH 512 - Abstract Algebra 3 hrs
* MATH 516 - Linear Algebra I 3 hrs
* MATH 520 - Real Analysis I 3 hrs
Restricted Elective Courses: 5-6 hours
One course from two of the following three groups:
Algebra
MATH 514 - Theory of Fields 3 hrs
MATH 517 - Linear Algebra II 3 hrs
MATH 518 - Theory of Groups 3 hrs
Analysis
MATH 522 - Fourier Analysis 3 hrs
MATH 524 - Complex Analysis 3 hrs
MATH 526 - Real Analysis II 3 hrs
Probability and Statistics
MATH 568 - Biostatistics 3 hrs
MATH 571 - Mathematical Statistics I: Probability Theory 3 hrs
MATH 573 - Statistical Data Analysis 2 hrs
MATH 671 - Mathematical Statistics II: Statistical Inference 3 hrs
Research Courses: 2-4 hours
MATH 691/692 Research Study (2/3 hrs) for either two or three hours in research study or four hours of thesis
research
Elective Courses in Mathematics: 5-23 hours
Usually no more than six hours in mathematics education courses. Thesis or research study hours in
mathematics education do not count as part of this six-hour limitation.
Cognate Course: 0-6 hours
May be taken, in consultation with the graduate advisor, outside the Department of Mathematics, but in an area
related to mathematics. The number of such hours permitted in the program will be based on the student’s
background and needs. Current or prospective teachers of mathematics may take, instead of cognates, up to six
additional hours in mathematics education beyond those permitted as electives above.
Program Total: 30 hours
* Students with undergraduate credit equivalent to any or all of these courses (MATH 512, MATH 516 or MATH 520)
will substitute approved mathematics electives for these hours.
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New Course Form
Master of Arts in Applied Statistics
Objectives
• To develop competence in mathematics and statistics beyond the undergraduate level.
• To improve the teaching of both mathematics and statistics.
• To prepare for study beyond the master’s level in mathematics and/or statistics.
• To strengthen the mathematical background of professionals needing analytical and quantitative skills related to
mathematics and statistics.
• To provide opportunities for research in mathematics and/or statistics.
Admission Requirements
Applicants must:
• Meet all Graduate School degree admission requirements; and
• Have completed a course in multivariable calculus, a course in calculus-based probability and statistics and a
mathematics “proof” course, although a major in either mathematics or statistics is preferred. A GPA of at least
2.75 is required in both mathematics and statistics course work. Students without such a background may be
admitted to the program after meeting requirements specified by the department.
Degree Requirements
This program requires a minimum of 34 graduate hours beyond the bachelor’s degree, distributed with the
approval of the department according to the course requirements below. Approval by the student’s advisor of
each semester’s courses prior to registration is recommended. Final approval for the degree by the coordinator
of advising is required.
Advisor Information:
Bingwu Wang Ph.D.
515 Pray-Harrold
(734) 487-1444
bwang@emich.edu
Course Requirements:
The M.A. in Applied Statistics requires the completion of 31-34 hours of course work in mathematics and statistics to
be distributed among required courses, restricted elective courses, elective courses and research courses in mathematics
and statistics courses as follows, in such a way that the mathematics and statistics courses total 29-30 credits:
Mathematics Courses: 6-9 hours
Required Course: 3 hours
MATH 516 - Linear Algebra I 3 hrs
Restricted Elective Courses: 3-6 hours
MATH 519 - Stochastic Mathematical Modeling 3 hrs
MATH 536 - Numerical Analysis 3 hrs
MATH 560 - Introduction to Optimization Theory 3 hrs
either
MATH 520 - Real Analysis I 3 hrs
or
MATH 526 - Real Analysis II 3 hrs
Statistics Courses: 20-24 hours
Required Courses: 12 hours
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New Course Form
MATH 571 - Mathematical Statistics I: Probability Theory 3 hrs
MATH 572 - Design and Analysis of Experiments 3 hrs
MATH 575 - Linear Regression Analysis 3 hrs
MATH 671 - Mathematical Statistics II: Statistical Inference 3 hrs
Restricted Elective Courses: 8-12 hours
MATH 568 - Biostatistics 3 hrs
MATH 569 - Categorical Data Analysis 3 hrs
MATH 570 - Statistical Concepts and Methods for Bioinformatics 3 hrs
MATH 573 - Statistical Data Analysis 2 hrs
MATH 574 - Applied Statistics 3 hrs
MATH 576 - Applied Survey Sampling 3 hrs
MATH 577 - Applied Multivariate Statistics 3 hrs
MATH 578 - Nonparametric Statistics 3 hrs
Research Course: 2-4 hours
At least two hours of thesis or research study in either mathematics or statistics are required. Students will, with
the approval of the coordinator of advising, select a supervisor to direct the thesis or research study. See the
description of the research requirement for the M.A. in Mathematics.
Program Total: 31-34 hours
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