[

 

Approved by Faculty Senate.

University Studies Course Approval Proposal

Flag Requirements – Writing Flag

The Department of Mathematics and Statistics proposes the following course for inclusion in
University Studies as a course satisfying the requirements for a Writing Flag. This was approved
by the full department on Thursday, January 18, 2001.

Course: Advanced Calculus I (MATH 330), 4 s.h.

Catalog Description: A systematic approach to the theory of differential and integral calculus
for functions and transformations in several variables. This is a University Studies course
satisfying requirements for a Writing Flag. Prerequisite: MATH 210, and MATH 260.
This is an existing course, previously approved by A2C2.

Department Contact Person for this Course:

Name: Barry A. Peratt
Title: Assistant Professor of Mathematics and Statistics
Email: bperatt@winona.edu

General Discussion of University Studies – the Writing Flag in relation to MATH 330

University Studies: Writing Flag

Flagged courses will normally be in the student’s major or minor program. Departments will need
to demonstrate to the University Studies Subcommittee that the courses in question merit the
flags. All flagged courses must require the relevant basic skills course(s) as prerequisites (e.g., the
"College Reading and Writing" Basic Skill course is a prerequisite for Writing Flag courses),
although departments and programs may require additional prerequisites for flagged courses. The
University Studies Subcommittee recognizes that it cannot veto department designation of flagged
courses.

The purpose of the Writing Flag requirement is to reinforce the outcomes specified for the basic
skills area of writing. These courses are intended to provide contexts, opportunities, and
feedback for students writing with discipline-specific texts, tools, and strategies. These courses
should emphasize writing as essential to academic learning and intellectual development.

Courses can merit the Writing Flag by demonstrating that section enrollment will allow for clear
guidance, criteria, and feedback for the writing assignments; that the course will require a
significant amount of writing to be distributed throughout the semester; that writing will comprise
a significant portion of the student’s final course grade; and that students will have opportunities
to incorporate readers’ critiques of their writing.

These courses must include requirements and learning activities that promote students’ abilities
to:

 

a. practice the processes and procedures for creating and completing successful writing in
their fields;

This course is a rigorous introduction to higher level mathematical analysis. To successfully
complete the course, the student is required to demonstrate not only an understanding of the
mathematical concepts involved in analysis, but also an ability to convey those concepts in
concise written form. Mathematical proof represents a very precise writing style that has
developed over several hundred years. Proper use of this writing style requires a knowledge
of the relevant jargon and a facility with the grammar and sentence structure that is germane
to good expositional writing. The student receives feedback on their written presentation of
logical arguments throughout the semester.

b. understand the main features and uses of writing in their fields;

It is in rigorous courses such as analysis that the student’s conceptual understanding of
mathematics is expanded into a rigorous understanding of the logical underpinnings of
mathematical abstraction. This logical foundation, by its very nature, is inextricably
interwoven with the precise writing that is used to express it. It is here that the student gains
an awareness that proofs of mathematical theorems and propositions lie not in convincing
pictures or clever examples, but in very precise and carefully applied logical analysis. Such
analysis is only as clear as its exposition.

c. adapt their writing to the general expectations of readers in their fields;

Writing mathematical proof is a very different type of writing from most other exposition. In
this course, the successful student must learn to weave good sentence structure with
mathematical formulae and symbolism in a way that brings clarity to the subject of the
exposition. Particularly close attention must be paid to the implications of uni and bi-conditional
statements and the differences between theorems, conjectures, lemmas, and
definitions.

d. make use of the technologies commonly used for research and writing in their fields;
and

When attempting to uncover patterns in analysis, the student routinely make use of various
graphical and algebraic computer aids, such as graphing calculators or computer algebra
systems. Additionally, there are special scripting languages for typesetting mathematical
exposition, such as TeX and LaTeX. Either these or the equation editors in most popular
word processors may be used to render proofs in this class. However, the use of typesetting
tools is not a requirement of the course, but an option whose implementation is left to the
discretion of the instructor.

e. learn the conventions of evidence, format, usage, and documentation in their fields.

As discussed above, the student encounters heavy use of mathematical jargon, mathematical
reasoning, and the expositional strategies unique to the field of mathematical analysis as well as the
conventions for citing previously proven results, such as lemmas or theorems, in a mathematical
proof.

 

Winona State University
Department of Mathematics and Statistics
Course Outline—M330
1

Course Title: Advanced Calculus I

Number of Credits: 4 s.h.

Prerequisite: Discrete Mathematics and Foundations (M210) & Multivariable Calculus (M260).

Grading: Grade only for all majors, minors, options, concentrations and licensures within the
Department of Mathematics and Statistics. The P/NC option is available to others.

Course Description: A systematic approach to the theory of differential and integral calculus for
functions and transformations in one and several variables.

Statement of Major Focus and Objectives of the Course: The major focus of this course is to
introduce students to the logical underpinnings of mathematical analysis and to provide
students with the ability to demonstrate a rigorous understanding of analysis by writing
clear, accurate, and concise proofs.

Possible Texts:

Fundamental Ideas of Analysis by Reed.
Advanced Calculus by Buck.
Advanced Calculus by Fulks.
Advanced Calculus by Widder.
Advanced Calculus, a Friendly Approach by Kosmala.
An Introduction to Analysis, 2nd edition by Bartle and Sherbert.
Introduction to Real Analysis by Gaughan.
Introduction to Real Analysis by Schramm.
Principles of Mathematical Analysis by Rudin.

Methods of Instruction: Lecture, Discussion, Problem Sets (possibly cooperative).

Course Requirements: None other than the text.

Evaluation Process: Tests, Quizzes, Problems Sets.

University Studies: Writing Flag

Flagged courses will normally be in the student’s major or minor program. Departments
will need to demonstrate to the University Studies Subcommittee that the courses in
question merit the flags. All flagged courses must require the relevant basic skills course(s)
as prerequisites (e.g., the "College Reading and Writing" Basic Skill course is a
prerequisite for Writing Flag courses), although departments and programs may require
additional prerequisites for flagged courses. The University Studies Subcommittee
recognizes that it cannot veto department designation of flagged courses.
The purpose of the Writing Flag requirement is to reinforce the outcomes specified for the
basic skills area of writing. These courses are intended to provide contexts, opportunities,
and feedback for students writing with discipline-specific texts, tools, and strategies.
These courses should emphasize writing as essential to academic learning and intellectual
development.

1 Prepared by Barry A. Peratt on February 9, 2001.

Courses can merit the Writing Flag by demonstrating that section enrollment will allow for
clear guidance, criteria, and feedback for the writing assignments; that the course will
require a significant amount of writing to be distributed throughout the semester; that
writing will comprise a significant portion of the student’s final course grade; and that
students will have opportunities to incorporate readers’ critiques of their writing.

These courses must include requirements and learning activities that promote students’

abilities to:

a. practice the processes and procedures for creating and completing successful
writing in their fields;
b. understand the main features and uses of writing in their fields;
c. adapt their writing to the general expectations of readers in their fields;
d. make use of the technologies commonly used for research and writing in their
fields; and
e. learn the conventions of evidence, format, usage, and documentation in their fields.

Topics below which include such requirements and learning activities are indicated below using
lowercase, boldface letters a.-d. corresponding to these requirements.

Course Outline of the Major Topics and Subtopics:

The real number system and an introduction to proof. a., b., c., d., e.
Elementary Topology—open/closed sets, countability, boundedness, compactness. a., b.,
c., d., e.
Functions, Sequences, and Limits. a., b., c., d., e.
Continuity. a., b., c., d., e.
Differentiation. a., b., c., d., e.
Integration. a., b., c., d., e.
Vectors and Curves. a., b., c., d., e.
Infinite Series. a., b., c., d., e.

Additional Information about Writing Assignments: In accordance with criteria a., b., c., d.,
and e., this course provides the rigorous underpinnings of proof construction and writing
that are expected of students planning to attend graduate school in mathematics. The
proofs that students write in this course constitute the vast majority of their grade. Two
such proofs are given below as an example of the type of writing required in this course:

      

 

 

 

 

Approval/Disapproval Recommendations

Department Recommendation: Approved Disapproved Date

Chairperson Signature Date

Dean’s Recommendation: Approved Disapproved Date

Dean’s Signature Date

*In the case of a Dean’s recommendation to disapprove a proposal, a written rationale for the recommendation

to disapprove shall be provided to USS.

USS Recommendation: Approved Disapproved Date

University Studies Director’s Signature Date

A2C2 Recommendation: Approved Disapproved Date

A2C2 Chairperson Signature Date

Faculty Senate Recommendation: Approved Disapproved Date

FA President’s Signature Date

Academic VP’s Recommendation: Approved Disapproved Date

VP’s Signature Date

President’s Decision: Approved Disapproved Date

President’s Signature Date