MATH 4604 -- New Course

Mon Apr 19 09:52:33 2010

Approvals Received:
on 04-16-10
by Lawrence Gray
Approvals Pending: College/Dean  > Catalog > PeopleSoft Manual Entry
Effective Status: Active
Effective Term: 1113 - Spring 2011
Course: MATH 4604
UMNTC - Twin Cities
UMNTC - Twin Cities
Career: UGRD
College: TIOT - Institute of Technology
Department: 11133 - Mathematics, Sch of
Course Title Short: Advanced Calculus II
Course Title Long: Advanced Calculus II
Max-Min Credits
for Course:
4.0 to 4.0 credit(s)
Sequel to Math 4603.  Topology of n-dimensional Euclidean space.  Rigorous treatment of multi-variable differentiation and integration, including chain rule, Taylor's Theorem, implicit function theorem, Fubini's Theorem, change of variables, Stokes' Theorem.  
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:
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:
4603 or 5615 or #
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 take both 4603 and 4604, and still others will skip 4603 and enter 4604 after taking Math 5615. It is also possible for students who have taken Math 4606 to take Math 4604 (but not Math 4603).
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 the second semester of 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 and/or analyze proofs in homework assignments and for exams. They may also be asked to present and/or explain proofs at the blackboard and in class discussion.

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 4604, Advanced Calculus II

This is the second semester of a rigorous treatment of mathematical analysis, building on the first semester, Math 4603.  It is expected that students in Math 4604 will have already completed Math 4603 or Math 5615 or a similar course.

In Math 4604, differentiation and integration theorems for functions of several variables will be the central topic.  As time permits, additional topics may include convergence properties for sequences and series of functions of several variables.

This is is a 4.0 credit course, involving at least three hours of regular class lectures per week, as well as office hours with the lecturer.  Students should normally expect to spend at least 12 hours per week on this course, including time in class.

Student grades will be determined by examinations (two midterm exams and a final examination), as well as regular homework assignments.

Textbook:  Advanced Calculus of Several Variables, by C.H. Edwards, Jr., Dover Publications, New York, 1994.

Summary outline of the topics by week:

Week 1:  Review of n-dimensional vectors.  Vector algebra, inner products, linearity.
Week 2:  Basic topics in matrices and determinants.
Week 3:  Topology and convergence in n-space.
Week 4:  Curves, velocities and potentials.  General derivatives of functions on n-space.
Week 5:  The chain rule and its consequences.  Optimization and Lagrange multipliers.
Week 6:  Taylor's Formula, Newton's Method.
Week 7:  The Implicit  Mapping Theorem.
Week 8:  Area and Integration. Fubini's Theorem.
Week 9:  Fubini's Theorem, Change of Variable.
Week 10:  Arc-length, line integrals, notion of a linear differential form.
Week 11:  Multilinear Functions.  Surface area.
Week 12:  The classical versions of the Divergence Theorem and the Theorem of Stokes.
Week 13:  Multilinear differential forms.
Week 14:  The General Theorem of Stokes.

[Note:  Standard components of a syllabus, such as statements about the university definitions of grades, scholastic dishonesty, etc., have been omitted from this sample, even though they will be part of any actual syllabus used for the course.]