Motion: That ARCC recommend to the Arts and Science Executive the addition of new course, MATH4036: Introduction to Measure Theory.
Respectfully Submitted,
Alexandre Karassev, Ph.D.
Associate Professor and Chair
Department of Computer Science and Mathematics
Nipissing University
NIPISSING UNIVERSITY
Department of Computer Science and Mathematics
New Course Proposal
Submitted to ARCC
MATH4036: Introduction to Measure Theory
Introduction
It is proposed that new undergraduate course MATH4036: Introduction to Measure Theory is added to the undergraduate course offerings in the Department of Computer Science and Mathematics.
Rationale
The proposed course will facilitate to:
· increase enrollment in graduate courses;
· in the framework of common degree structure, create more 4000-level options for honors specialization in mathematics (currently, the only two 4000-level courses are MATH 4496: Senior Research Project I and MATH 4497: Senior Research Project II; both are directed study courses);
· reduce the number students enrolled in directed studies courses.
Within the current undergraduate course offering model in the Department of Computer Science and Mathematics, “Introduction to Measure Theory” course will be placed in new group - Group IV: Advanced Courses, together with the existing courses – MATH 4496 and MATH 4497. The proposed course is of fundamental nature for pure mathematics and is offered for both graduate and undergraduate students in many Ontario universities..
Course Delivery and Teaching and Learning Methods and Materials
It is expected that this course will be taught in the same classroom, the same time, and by the same instructor as MATH 5036 – Measure Theory. Two courses will share teaching and learning methods and materials. The difference between the courses will be in the evaluation components.
Evaluation Components
The difference between MATH 5036 – Measure Theory and MATH 4036 – Introduction to Measure Theory will be in the evaluation of students’ performance. MATH 4126 will have different set of home assignment, as well as different midterm and final examinations.
Additional Required Resources
None, since the courses will be jointly taught with MATH 5036. MATH 5036 belongs to core group of courses in the M.Sc. in Mathematics program and is offered on the regular bais. In the years when MATH 5036 is not offered due to potential low enrollment in the graduate program, MATH4126 – Introduction to Measure Theory will be offered in place of MATH 3396 -Selected Topics I. Note that MATH 3396 will be removed from the course cycling.
A) Descriptive Data
Course title: / Introduction to Measure Theory
Short title:
(maximum 29 characters) / Intro to Measure Theory
If this course belongs to a major that has course groupings, please indicate which group the course belongs with: / Group IV – Advanced Mathematics Courses
Course Prerequisites: / MATH3137 or equivalent
Course Co-requisites:
Antirequisite:
Total Hours:
(Lecture / Lab / Seminar) / 36 hours
Breakdown of Hours
(e.g. Two hours of lecture and one hour of laboratory work per week for one term.) / 3 hours of lecture per week for term
Course Credits: / 3 credits
Course Description:
(as it will appear in the academic calendar) / Sigma-algebras and measures, Borel and Lebesgue measures on Euclidean spaces, measurable functions and integration, convergence theorems, signed measures and the Randon-Nikodym theorem, product measure and Fubini theorem. The course can be taught together with MATH 5036-Measure Theory with the undergraduate students being subject to different assignments and evaluation criteria than the graduate students
Program Implications: / The course is part of the course requirements for the Honours Specialization in Mathematics – general, pure, applied, and also a part of Group IV - Advanced Mathematics Courses.
Cross-listing or cross-coding
(please indicate if this course is approved for either cross-listing or cross-coding, and to which discipline)
B) Comparative Data
Brock
Carleton
Guelph
Lakehead / Math 5211/4211: Measure Theory
Laurentian
McMaster / MATH 4A03/6A03 - Real Analysis II
Ottawa / MAT4125 - Measure and Integration I
Queen’s
RMC
Ryerson
Toronto / MAT1000/457 - Real Analysis I
Trent / Math 4790H - Analysis III: Measure & integration
Waterloo / PMATH 451/AM 431 - Measure and Integration
Western / Math 4122/9022 - Lebesgue Integration and Fourier Series
Wilfrid Laurier / MATHEMATICS 450 – Measure and Integration
Windsor
York / MATH 6280 - Measure Theory
C) Statement of Need
Addition of this course will: help to increase enrollment in graduate courses; in the framework of common degree structure, create more 4000-level options for honors specialization in mathematics; help to reduce the number students enrolled in directed studies courses.
D) Statement of Resource Requirements
None, since the courses will be jointly taught with MATH 5036. MATH 5036 belongs to the core group of courses in the M.Sc. program in Mathematics and is offered on the regular. In the years when MATH 5036 is not offered due to potential low enrollment in the graduate program, MATH4036 – Introduction to Measure Theory will be offered in place of MATH 3396 -Selected Topics I. Note that MATH 3396 will be removed from the course cycling.
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December 1, 20011