Fri Mar 26 11:55:08 2010
Approvals Received: 



Approvals Pending:  College/Dean > Catalog  
Effective Status:  Active  
Effective Term:  1109  Fall 2010  
Course:  MATH 4603  
Institution: Campus: 
UMNTC  Twin Cities UMNTC  Twin Cities 

Career:  UGRD  
College:  TIOT  Institute of Technology  
Department:  11133  Mathematics, Sch of  
General  
Course Title Short:  Advanced Calculus I  
Course Title Long:  Advanced Calculus I  
MaxMin Credits for Course: 
4.0 to 4.0 credit(s)  
Catalog Description: 
Axioms for the real numbers. Techniques of proof for limits, continuity, uniform convergence. Rigorous treatment of differential/integral calculus for singlevariable functions.  
Print in Catalog?:  Yes  
CCE Catalog Description: 
<no text provided>  
Grading Basis:  Stdnt Opt  
Topics Course:  No  
Honors Course:  No  
Delivery Mode(s):  Classroom  
Instructor Contact Hours: 
3.0 hours per week  
Years most frequently offered: 
Every academic year  
Term(s) most frequently offered: 
Fall, Spring, Summer  
Component 1: 
LEC (with final exam) 

AutoEnroll Course: 
No  
Graded Component: 
LEC  
Academic Progress Units: 
Not allowed to bypass limits. 4.0 credit(s) 

Financial Aid Progress Units: 
Not allowed to bypass limits. 4.0 credit(s) 

Repetition of Course: 
Repetition not allowed.  
Course Prerequisites for Catalog: 
((2243 or 2373) and (2263 or 2374)) or 2574 or #  
Course Equivalency: 
01072  Math 4606/Math 5615/Math 5616  
Consent Requirement: 
No required consent  
Enforced Prerequisites: (coursebased or noncoursebased) 
No prerequisites  
Editor Comments:  <no text provided>  
Proposal Changes:  New course. The intention is to replace Math 4606 by Math 4603/4604. Some students will only take Math 4603, others will skip Math 4603 and instead enter Math 4604 after taking Math 5615.  
History Information:  <no text provided>  
Faculty Sponsor Name: 
Lawrence Gray (Director of Undergrad Studies)  
Faculty Sponsor Email Address: 
gray@math.umn.edu  
Student Learning Outcomes  
Student Learning Outcomes: 
* Student in the course:
 Can identify, define, and solve problems
Please explain briefly how this outcome will be addressed in the course. Give brief examples of class work related to the outcome. This course is an introduction to the foundations of calculus and techniques of rigorous proof. When a student is asked to prove something, he/she must identify exactly what part of the statement needs proof, what part consists of assumptions, and what is the background knowledge that can be used to create the proof. The student must learn and understanding precise mathematical definitions, and also make new definitions. Students are repeatedly asked to find proofs of mathematical facts. Creating and communicating such proofs is a very rich form of problemsolving. How will you assess the students' learning related to this outcome? Give brief examples of how class work related to the outcome will be evaluated. Students will be asked to write proofs in homework assignments and for exams. They may also be asked to present proofs at the blackboard. 

Liberal Education  
Requirement this course fulfills: 
None  
Other requirement this course fulfills: 
None  
Criteria for Core Courses: 
Describe how the course meets the specific bullet points for the proposed core
requirement. Give concrete and detailed examples for the course syllabus, detailed
outline, laboratory material, student projects, or other instructional materials or method.
Core courses must meet the following requirements:
<no text provided> 

Criteria for Theme Courses: 
Describe how the course meets the specific bullet points for the proposed theme
requirement. Give concrete and detailed examples for the course syllabus, detailed outline,
laboratory material, student projects, or other instructional materials or methods. Theme courses have the common goal of cultivating in students a number of habits of mind:
<no text provided> 

Writing Intensive  
Propose this course as Writing Intensive curriculum: 
No  
Question 1: 
What
types of writing (e.g., reading essay, formal lab reports, journaling)
are likely to be assigned? Include the page total for each writing
assignment. Indicate which assignment(s) students will be required to
revise and resubmit after feedback by the instructor or the graduate TA. <no text provided> 

Question 2: 
How does assigning a significant amount of writing serve the purpose
of this course? <no text provided> 

Question 3: 
What types of instruction will students receive on the writing aspect
of the assignments? <no text provided> 

Question 4: 
How will the students' grades depend on their writing performance?
What percentage of the overall grade will be dependent on the quality and level of the students'
writing compared with the course content? <no text provided> 

Question 5: 
If graduate students or peer tutors will be assisting in this course,
what role will they play in regard to teaching writing? <no text provided> 

Question 6: 
How will the assistants be trained and
supervised? <no text provided> 

Question 7: 
Write up a sample assignment handout here for a paper
that students will revise and resubmit after receiving feedback on the initial
draft. <no text provided> 

Readme link.
Course Syllabus requirement section begins below


Course Syllabus  
Course Syllabus: 
For new courses and courses in which changes in content and/or description and/or credits
are proposed, please provide a syllabus that includes the following information: course goals
and description; format;structure of the course (proposed number of instructor contact
hours per week, student workload effort per week, etc.); topics to be covered; scope and
nature of assigned readings (text, authors, frequency, amount per week); required course
assignments; nature of any student projects; and how students will be
evaluated. The University "Syllabi Policy" can be
found here
The University policy on credits is found under Section 4A of "Standards for Semester Conversion" found here. Course syllabus information will be retained in this system until new syllabus information is entered with the next major course modification. This course syllabus information may not correspond to the course as offered in a particular semester. (Please limit text to about 12 pages. Text copied and pasted from other sources will not retain formatting and special characters might not copy properly.) Syllabus for Mathematics 4603, Advanced Calculus I This is the first semester of a treatment of mathematical analysis based on definitions, theorems and complete proofsbut also with illustrative important examples. It is expected that students in Math 4603 will have already successfully completed courses in singleand multivariable calculus, as well as a course involving a significant about of linear algebra (such as a semester course treating both linear algebra and differential equations) In Math 4603, the major topics will be: mathematical induction; limits of both sequences and functions: continuity, differentiation, and integration in a singlevariable setting; infinite series of numbers and functions. Since this is a 4.0 credit course, students should normally expect to spend at least 12 hours per week on this course, including time in class. Approximate details for Fall 2010 The class will meet on MW from 12:202:15 with a 15minute break. Student grades will be determined by examinations (two 115minute midterm exams and a final examination), as well as regular homework assignments. Textbook: Introduction to Analysis (Revised Fifth Edition), by Edward D. Gaughan., Brooks/Cole, Pacific Grove, CA, 2009. Summary outline of the topics by week: Week 1: Relations, functions, and mathematical induction Week 2: The real numbers, convergence of sequences, and subsequences Week 3: Limits of monotone sequence, limits of functions Week 4: Algebra of limits, Enrichment and review based on first 3 chapters Week 5: Continued review and enrichment, First midterm Week 6: Continuous functions Week 7: Differentiation of functions Week 8: Singlevariable inverse function theorem, Riemann integral Week 9: Riemann integral, RiemannStieltjes integral (from class notes) Week 10: Enrichment and review based on weeks 610 Week 11: Second midterm, infinite series Week 12: Infinite series, Taylor's formula, sequences of functions Week 13: Sequences and series of functions Week 14: Enrichment and review based on weeks 1113 and review of entire course [Note: The teacher for Fall 2010 has found it useful to move quite quickly through chaptersand then in the week before a test to go back both for review and further teaching of some things that had been given too little time earlier. The above schedule reflects this, but other teachers could use different strategies that work for them. Additional standard components of syllabus, such as statements about students with disabilities, the university definitions of the grading system, statements about academic honesty, etc., are left out of this sample syllabus, even though they would be included in any actual syllabus used for the course.] 
