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: Miller, New Course 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? Miller, New Course Sept. ‘09 Yes No X X Page 2 of 9 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. Miller, New Course Sept. ‘09 Course goals, objectives and/or student learning outcomes Outline of the content to be covered Page 3 of 9 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 Miller, New Course Sept. ‘09 Date Page 4 of 9 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) Miller, New Course Sept. ‘09 Page 5 of 9 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 Miller, New Course Sept. ‘09 Page 6 of 9 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. Miller, New Course Sept. ‘09 Page 7 of 9 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 Miller, New Course Sept. ‘09 Page 8 of 9 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 Miller, New Course Sept. ‘09 Page 9 of 9