Upper-division Writing Requirement Review Form (2/14)
I. General Education Review – Upper-division Writing Requirement
Dept/Program
Mathematical
Course # (i.e. ANTY
Subject
Sciences
455) or sequence
Course(s) Title
History of Mathematics
Description of the requirement if it is not a single course.
II. Endorsement/Approvals
Complete the form and obtain signatures before submitting to Faculty Senate Office.
Please type / print name Signature
Instructor
Bharath Sriraman
Phone / Email
Program Chair
Dean
Math 429
Date
9/15/14
4062436714/
sriramanb@mso.umt.edu
Leonid Kalachev
Chris Comer
III. Type of request
New
Renew
X
Reason for new course, change or
deletion
One-time Only
Change
Remove
IV Overview of the Course Purpose/ Description
The goal of the course is to familiarize students with mathematics starting from the pre-Socratic times onto the
modern period. Attention is paid to particular time periods and individuals within those time periods whose work
has left a lasting impression on the field of mathematics.
Over the course of the semester, students will be required to demonstrate competence with
- historical techniques (methods for computing trigonometric functions, derivation of trigonometric
identities and series representations), algebra, analysis (approximating roots and irrational numbers
particularly logarithms), and Calculus (finite differences, and geometric techniques developed by
Archimedes, the Bernoullis, Fermat, Newton and Leibniz).
- Improving expository and scientific writing skills
- Reading some original sources in the history of mathematics
Develop a critical stance in
- assessing popular myths about mathematics (science) or competing histories of the origins and/or models
of the development of mathematics (science)
- assessing whether mathematics (science) is value-free; [consider gender, class, race, non-Western
approaches and contributions, etc.]
V Learning Outcomes: Provide examples of how the course will support students in achieving each learning
outcome.
Identify and pursue sophisticated
x Yes
questions for academic inquiry
If yes, how will student learning be supported?
Reading historical literature on the development of the same mathematical
techniques in different cultures/locations written in different pre-modern
notation, and being able to synthesize these ideas to explain the modern
mathematical concept that grew out of these techniques.
Explore the history and mathematics of map making in relation to the advent
of European colonization.
Examine the contributions of eminent female mathematicians and historical
forces of their time period to examine whether mathematics (science) is
value-free.
Find, evaluate, analyze, and
synthesize information effectively
and ethically from diverse sources
(see:
http://www.lib.umt.edu/libraryinformation-literacytables#Table2) Subject liaison
librarians are available to assist
you embed information literacy
into your course:
http://www.lib.umt.edu/node/115
#instructors
Manage multiple perspectives as
appropriate
Recognize the purposes and needs
of discipline-specific audiences
and adopt the academic voice
necessary for the chosen
discipline
Use multiple drafts, revision, and
editing in conducting inquiry and
preparing written work
Follow the conventions of
citation, documentation, and
 No
If no, course may not be eligible
x Yes
If yes, how will student learning be supported?
See Research Paper description in appended course syllabus. In particular
students are encouraged to find a research paper topic that involves some
controversy over precedence of a mathematical idea [e.g., the series
representation of trigonometric functions from India versus Newton’s
representations], with books kept on reserve at the Mansfield Library to help
them find diverse sources [see syllabus].
 No
If no, course may not be eligible
x Yes
If yes, how will student learning be supported?
Students are given a primer on reliable databases (Springerlink, JSTOR,
Academic Search Premier; Informa, and a list of scholarly journals and
books. Non-peer reviewed sources or information obtained from nonscholarly sources are not allowed.
 No
If no, course may not be eligible
x Yes
If yes, how will student learning be supported?
Reading examples of expository writing are provided from different journals.
Students are provided anonymous copies of exemplary papers from previous
semesters
 No
If no, course may not be eligible
X Yes
If yes, how will student learning be supported?
See appended course syllabus
 No
If no, course may not be eligible
x Yes
If yes, how will student learning be supported?
formal presentation appropriate to
that discipline
APA (6th edition or higher) is required of all the research papers. In addition
students have to use a compatible equation editor to use the appropriate
notation for the topic in question.
 No
If no, course may not be eligible
VI. Writing Course Requirements
Enrollment is capped at 25
students.
The course has sometimes had close to 30 students. This has been difficult for
If not, list maximum course
the instructor to manage because of the amount of time required to provide
enrollment. Explain how
feedback. However formative feedback provided consistently over the course
outcomes will be adequately met
of the semester alleviates the pressure to grade 30 papers simultaneously.
for this number of students.
Justify the request for variance.
Briefly explain how students are
Students are provided samples of historical papers from Historia
provided with tools and strategies Mathematica, Archive for the Exact Sciences, The Mathematics Enthusiast
for effective writing and editing
and Mathematical Intelligencer as examples of good expository (and
in the major.
technical) writing. Instructor provides feedback on drafts of research paper.
Which written assignment(s)
All papers include revision in response to the instructor’s feedback.
includes revision in response to
instructor’s feedback?
VII. Writing Assignments: Please describe course assignments. Students should be required to individually
compose at least 20 pages of writing for assessment. At least 50% of the course grade should be based on students’
performance on writing assignments. Quality of content and writing are integral parts of the grade on any writing
assignment.
Formal Graded Assignments
Two papers were 62.5% of the course grade (meeting the > 50% threshold
required for designated upper division writing courses)
The first paper was expected to be 10-15 pages (double spaced) in length and
the second 20-30 pages in length [with more focus based on the feedback
provided for paper 1]
The following parameters were applied to determine grades on the first and
second paper.
1. The paper must meet the following specifications
2. Paper should be typed in APA style
3. The bibliography/references must be appended as well as copies of pages
from books/articles that were referred to for the assignment.
4. The paper must contain a relative in depth exposition or narrative about
one or two aspects of the topic and the relevant mathematics. The second
paper will focus on only one particular
aspect.
5. The research must be archival in nature, with no primary or secondary
online references. This criteria was stringently applied to the papers.
6. The criteria of novelty: The second paper should not only extend the ideas
from the first paper, but also result in some new findings on the topic based
on your archival research.
7. The paper should not parse or include quotes more than 30 words in length.
Informal Ungraded Assignments
Paste or attach a sample writing assignment, including instructions for students.
For detailed instructions regarding the two required papers, see the syllabus.
VIII. Syllabus: Paste syllabus below or attach and send digital copy with form.
The syllabus must include the list of Writing Course learning outcomes above.
Math 429: History of Mathematics [Spring 2014]
Professor: Bharath Sriraman
MWF, 12.10- 1.00 [room 103]
Pre-requisite: Math 307 (or 305)
Office Hours: Wednesday 11-12 [Math 301] and by appointment
Required Textbook: George M. Phillips: Two Millennia of Mathematics: From Archimedes to Gauss,
Springer
Additional readings will be provided via e-mail
n
What is the closed form of
i
41
?
i 1
Name 5 female mathematicians before 1900
Can you decipher the “fundamental” anagram of Calculus?
6accdae13eff7i3l9n4o4qrr4s8t12ux
"The foundations of these operations is evident
enough, in fact; but because I cannot proceed with
the explanation of it now, I have preferred to
conceal it thus: 6accdae13eff7i3l9n4o4qrr4s8t12ux.
On this foundation I have also tried to simplify
the theories which concern the squaring of curves,
and I have arrived at certain general Theorems"- Newton
Course Purpose and Goals
The goal of the course is to familiarize students with mathematics starting from the pre-Socratic times onto
the modern period. Attention is paid to particular time periods and individuals within those time periods
whose work has left a lasting impression on the field of mathematics.
Over the course of the semester, students will be required to demonstrate competence with
- historical techniques (methods for computing trigonometric functions, derivation of trigonometric
identities and series representations), algebra, analysis (approximating roots and irrational
numbers particularly logarithms), and Calculus (finite differences, and geometric techniques
developed by Archimedes, the Bernoullis, Fermat, Newton and Leibniz).
-
Improving expository and scientific writing skills
-
Reading some original sources in the history of mathematics
Develop a critical stance in
-
assessing popular myths about mathematics (science) or competing histories of the origins and/or
models of the development of mathematics (science)
-
assessing whether mathematics (science) is value-free; [consider gender, class, race, non-Western
approaches and contributions, etc.]
Course Specifics/ Administrative Policies and Important Dates:
Important Dates:
February 4
Last Day to Add via CyberBear
February 14
Last Day to drop and/or change grading option. After this
date, a drop results in W on transcript and no refund is given.
February 17
President’s Day- No Classes, Offices Closed
March 31- April 4
Spring Break
April 7
Last Day to Drop by Paper Forms. After April 7 student is
only allowed to make changes by petition with instructor
signature and recommendation. The petition also requires the
Dean’s signature. This option ends on May 9.
May 9
Last Day of Regular Classes
May 12-16
Finals week
Academic misconduct is subject to an academic penalty by the course instructor and/or a disciplinary
sanction by the University. Academic misconduct is defined as all forms of academic dishonesty and the
Student Conduct Code. The Code is available for review online at
http://www.umt.edu/AS/APSA/index.cfm/page/1321
In particular, Student Conduct Code Section IV.a.5 identifies the following violations:
Submitting false information: Knowingly submitting false, altered, or invented information, data,
quotations, citations, or documentation in connection with an academic exercise
Students with disabilities may request reasonable modifications by contacting me. The University of
Montana assures equal access to instruction through collaboration between students with disabilities,
instructors, and Disability Services for Students (DSS). “Reasonable” means the University permits no
fundamental alterations of academic standards or retroactive modifications. For more information, please
consult http://www.umt.edu/disability
Grading Distribution:
Take Home Exam
Paper 1
Paper 2
150 points
100 points
150 points
Total
400 points
Grading Scale:
90-100 A ;
80-89.9
B;
70-79.9
C ;
60-69.9 D ;
Below 60
F
Endnotes:
Some interesting sources in reserve at the Library:
E. Robson and J. Stedhall (Eds). The Oxford Handbook of the History of Mathematics. Oxford University
Press
W. Dunham. Journey through Genius: The Great Theorems of Mathematics. Penguin Books.
W.W. Rouse Ball. A Short Account of the History of Mathematics. Dover Publications.
P.J. Davis. Ancient Loons: Stories that David Pingree Told Me. CRC Press
1. Take Home Exam
There will be homework assignments in the form of (a) problems in which you apply some mathematical
techniques, (b) summarize readings to share with your peers and (c) develop your writing skills. It is
important that you complete these assignments properly. I.e., spend time reading, writing and doing
mathematics based on the class lectures. In mid-March a take home exam will be administered to assess
your performance on these aforementioned aspects of the course.
2. Papers
Omnium rerum principia parva sunt - Cicero
[Everthing has a small beginning]
This is essentially the crux of this course. The only way to become proficient at expository scientific
writing is to write and write and write and… be open to critiques… a lot of them. Writing in the
mathematics community is a communicative activity. Since this course fulfills the upper division writing
requirement, there will be a lot of writing involved in the form of 2 papers. Over the course of the semester,
I hope to see your writing mutating favorably based on the ongoing readings and lectures.
Students will start by choosing one “episode” from the history of mathematics. What I mean by episode is
not something “BIG” but something small- such as the derivation of a result or a theorem. For example the
Mean Value Theorem, or Series Inversion theorem, or the Liouville number or Unique Factorization
Domains or a Particular statistical co-efficient or Solving the Quartic etc; Something specific that piques
your interest. The textbook has many excellent examples as well in the context of Logarithms and the
development of Calculus.
-researched and over-written topics [so
these are NOT allowed as the object of research in this class].
You will research events/people/places/correspondences/related mathematical ideas that led to the result.
Your first paper should present a coherent synthesis of this “episode” Formatting/researching guidelines
will be provided over the course of the semester. The second paper can be an extension of this “episode”,
i.e., it should contain more historical and mathematical details about the object of investigation. The final
paper will also be presented in class in the form a TED talk [15 minutes]. Note: The final paper should
substantially build and extend on the first and present more historical and mathematical details.
3.
Scoring Rubric and Consulting for Papers
I suggest you make an appointment with me about your paper topic at your earliest convenience, so I
can point you to some relevant sources. I cannot help if I do not know what you need help with!
A scoring rubric for the papers will be provided to you as well.
Scoring Rubric
Structure and Format [20%]
Does the paper/writing follow a consistent style of writing? Is the narrative in a consistent tense? Are
quotes, paraphrases and references properly acknowledged with the body of the text [in our case we are
using APA style of citing references]
Citations [13 1/3 %]
Does the paper reference primary sources? Are the sources credible? Is full citation information given in
APA style?
Exposition of History [33 1/3 %]
Does the paper provide the relevant background to the problem in terms of the time period, people and
places involved? Is the historical exposition accurate, i.e., do two or more credible sources say the same
thing? Are there discrepancies in the historical exposition in the literature, i.e., do two or more sources say
different things? If so why and what are the differences?
Exposition of the Mathematics [33 1/3%]
Does the paper provide mathematical examples or examples of problems using a historical technique? Is
more than one technique provided for the same type of problem? Is the mathematics clearly explained and
easy for the reader to follow?