MATH 4603 -- New Course

Fri Mar 26 11:55:08 2010

Approvals Received:
on 03-24-10
by Lawrence Gray
Approvals Pending: College/Dean  > Catalog
Effective Status: Active
Effective Term: 1109 - Fall 2010
Course: MATH 4603
UMNTC - Twin Cities
UMNTC - Twin Cities
Career: UGRD
College: TIOT - Institute of Technology
Department: 11133 - Mathematics, Sch of
Course Title Short: Advanced Calculus I
Course Title Long: Advanced Calculus I
Max-Min Credits
for Course:
4.0 to 4.0 credit(s)
Axioms for the real numbers. Techniques of proof for limits, continuity, uniform convergence. Rigorous treatment of differential/integral calculus for single-variable functions.
Print in Catalog?: Yes
CCE Catalog
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Grading Basis: Stdnt Opt
Topics Course: No
Honors Course: No
Delivery Mode(s): Classroom
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)
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
Repetition not allowed.
for Catalog:
((2243 or 2373) and (2263 or 2374)) or 2574 or #
01072 - Math 4606/Math 5615/Math 5616
No required consent
(course-based or
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>
Sponsor Name:
Lawrence Gray (Director of Undergrad Studies)
Sponsor E-mail Address:
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 problem-solving.

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
this course fulfills:
Other requirement
this course fulfills:
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:

  • They explicitly help students understand what liberal education is, how the content and the substance of this course enhance a liberal education, and what this means for them as students and as citizens.
  • They employ teaching and learning strategies that engage students with doing the work of the field, not just reading about it.
  • They include small group experiences (such as discussion sections or labs) and use writing as appropriate to the discipline to help students learn and reflect on their learning.
  • They do not (except in rare and clearly justified cases) have prerequisites beyond the University's entrance requirements.
  • They are offered on a regular schedule.
  • They are taught by regular faculty or under exceptional circumstances by instructors on continuing appointments. Departments proposing instructors other than regular faculty must provide documentation of how such instructors will be trained and supervised to ensure consistency and continuity in courses.

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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:
  • thinking ethically about important challenges facing our society and world;
  • reflecting on the shared sense of responsibility required to build and maintain community;
  • connecting knowledge and practice;
  • fostering a stronger sense of our roles as historical agents.

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Writing Intensive
Propose this course
as Writing Intensive
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.

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Question 2: How does assigning a significant amount of writing serve the purpose of this course?

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Question 3: What types of instruction will students receive on the writing aspect of the assignments?

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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?

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Question 5: If graduate students or peer tutors will be assisting in this course, what role will they play in regard to teaching writing?

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Question 6: How will the assistants be trained and supervised?

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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.

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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 proofs---but also with illustrative important examples.  It is expected that students in Math 4603 will have already successfully completed courses in single-and multi-variable 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 single-variable 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 12:20-2:15 with a 15-minute break. Student grades will be determined by examinations (two 115-minute 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 mid-term
Week 6:   Continuous functions
Week 7:   Differentiation of functions
Week 8:   Single-variable inverse function theorem, Riemann integral
Week 9:   Riemann integral, Riemann-Stieltjes integral (from class notes)
Week 10:  Enrichment and review based on weeks 6-10
Week 11:  Second mid-term, 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 11-13
    and review of entire course

[Note: The teacher for Fall 2010 has found it useful to move quite quickly through chapters---and 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.]