*[*

Approved by Faculty Senate.

University Studies Course Approval Proposal

Flag Requirements – Writing Flag

**T**he 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

**f**eedback 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: D**iscrete 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