MATH 410
History of Mathematics
Syllabus for Spring 2010
Tuesday, Thursday, 2:00PM – 3:20PM
325 Gildemeister Hall
Prerequisite: Passing grades in MATH160 and MATH210.
About This Course: This course is intended to provide the
student with an overview of the history of mathematics. We will emphasize the
contributions made by various cultures across the globe and will ask the
question: What is mathematics and who did it? We will also discuss the role of
mathematics in these cultures, the surrounding history at the time, and the
bias in historical accounts.
Expectations: Students who complete this course with a passing grade are
expected to be able to demonstrate the following skills: (i) Knowledge of the
historical development of mathematics, (ii) Understand the mathematics created
and used by various peoples throughout history, (iii) Analyze, scrutinize and
discuss possible mathematical writings, developments and arguments, (iv) Write
a paper and present on a researched biographical topic.
Texts: “Math
Through the Ages” by William P. Berlinghoff and Fernando Q. Gouvêa
“The Crest of the Peacock” by George Gheverghese Joseph (this book is out of
print, so photocopies are available for purchase in the WSU book store).
“Journey
Through Genius: The Great Theorems of Mathematics” by William Dunham
Course Website: http://course1.winona.edu/eerrthum/math410
Instructor: Dr. Eric Errthum Office: 124A Gildemeister Hall and 2B Lourdes Hall
Winona Email Username: eerrthum Office Phone: 474-5775
Office Hours: See schedule on my home page.
Grading: Reading
Quizzes 100
points---------- 10%
Class
Participation 180
points---------- 18%
Midterms (3 @ 80
points) 240
points---------- 24%
Presentations (3 @
50 points) 150
points---------- 15%
Biography Paper
and Presentation 200
points---------- 20%
Final 130
points---------- 13%
--------
1000
points total
Grades: A = 90% (900 pts), B = 80% (800 pts), C = 70% (700 pts), D = 60% (600 pts)
Reading Quizzes: Each class will start with a short quiz over the previously assigned readings. Completing the assigned readings is imperative for this class since lecture will only contain the main points and topics.
Class Participation: A significant portion of each class will involve discussion of the previously assigned readings and discussion questions. You will be graded each day on your level of participation in these discussions. If you are absent you will receive a zero for the day, no exceptions.
Exams: There will be three in-class exams and one final exam. The final exam will be in two parts. The first part being similar to the three midterms and only on material covered in the fourth part of the class (i.e. it’ll be the fourth midterm). The second part of the final will be a comprehensive essay section. Exam dates are tentative until officially announced in class. The final exam is tentatively scheduled for Tuesday, May 4, 1:00 – 3:00pm.
Presentations: During the class period after each exam, students will each give a presentation. Each student will have 7 minutes to present on a topic chosen from a list given by the instructor (or a topic Okayed by the instructor). Make sure you come prepared as time will be limited. Make sure you come prepared as running short will hurt your grade. Powerpoint, PDF, or other electronic format encouraged. Sign up for a topic by following the links below.
|
Presentation Topics |
||
|
Presentation I |
Presentation II |
Presentation III |
Biography: There will be a biography paper due near the end of the semester that you should be working on throughout (see schedule for due dates of various steps). The topic must be on a mathematician who was alive on December 7, 1941. Specifics of the paper:
1. 2500 words typed and well-written (i.e. correct spelling, complete sentences, good grammar, etc.)
2. Must use at least one approved book source (an autobiography or complete biography) and 2 other sources (1 online source maximum)
3. Must have information on at least the following aspects of their life:
a. Early Life
b. Mathematical Contributions (does not need to be overly technical)
c. Their view on what mathematics is/should be
d. Activities Outside of Mathematics
e. Effects of WWII and/or Nazi Germany on Their Life
Possible Mathematicians: Richard Courant*, Paul Erdös*, Kurt Gödel*, Alexander Grothendieck*, David Hilbert*, Srinivasa Ramanujan*, John von Neumann*, Andre Weil*, Nicolas Bourbaki* (* indicates the instructor knows a biography you may use as your book source). The breakdown of points is: (Proposal: 10 points; Outline: 10 points; Rough Draft: 20 points; Final Paper: 90 points) Sign up for a topic here.
Presentation: During the last week of classes you will have to give a 15 minute presentation on the same mathematician you wrote your biography paper on. The presentation will be worth 70 points.
Late/Missed Work: Late assignments or missed quizzes will result in a score of zero. There are no make-up quizzes. Make-up exams and presentations will be given at the discretion of the instructor. If you miss class, it is your responsibility to obtain notes and assignments from fellow students. If you have an unavoidable absence, please inform the instructor beforehand.
Desire2Learn: Some course materials can be found on D2L.
Academic Dishonesty: Any type of academic dishonesty (cheating, copying, plagiarism, etc.) will result in failure and will be reported to school authorities. If you are having trouble with an assignment, please see the instructor first. The instructor reserves the right to google any part of your written work to check for plagiarism.
Note: This syllabus is subject to change if deemed necessary by the instructor.
Tentative Schedule of Events – Math 410
(subject to change)
|
Week
Starting |
Tuesday |
Thursday |
|
1/11 |
Introductions What
is Mathematics? |
European
vs. Non-European Roots Ages:
Beginnings (pp 1 – 14) |
|
1/18 |
In
the Beginning… (Supplemental
Reading: Andean Calculators) |
Biography Proposal Due |
|
1/25 |
Presentation
I Topic Due |
Early
China and India All
Presentation I topics (see page numbers above) |
|
2/1 |
|
“Math
and the Maya” |
|
2/8 |
|
Beginning
of Greeks |
|
2/15 |
Pythagorean
Theorem |
Presentation
II Topic Due |
|
2/22 |
|
|
|
3/1 |
VIDEO |
(Total
# pages: 26) |
|
3/8 |
SPRING
BREAK |
|
|
3/15 |
Classical
China Ages:
Nothing Becomes a Number (pp 79 – 82) |
Biography Outline Due Ages:
Arabic (pp 28 – 32) |
|
3/22 |
Presentation
III Topic Due |
Algebra All
Presentation III topics (see page numbers above) |
|
3/29 |
|
|
|
4/5 |
|
Rough Draft of Biography Papers
Due |
|
4/12 |
Series |
Number
Theory II |
|
4/19 |
Current
Mathematics Ages:
A Marvelous Proof (pp 147 – 152) |
VIDEO or
maybe “Fermat’s Last
Theorem” Other
Students’ Biography Papers |
|
4/26 |
Biography Presentations |
Biography Presentations |
Final Exam (Exam IV and Essay Questions)
Tuesday, May 4
1:00 – 3:00pm
Welcome to college math!
If this is your first math class taken in college, there are some important things you need to know. College math classes are run very differently from high school math classes. On the surface it may seem they are similar as you listen to the lecture and take notes, but there are significant underlying differences. Knowing these ahead of time can help you make the most of this coming semester.
#1: College math classes generally stay on the schedule in the syllabus. If there is one day allotted to the topic that is probably all of the class time that will be spent on it, even if “most” of the students “don’t get it.”
#2: It is expected that you will read the text and do the problems in order to learn the material, even if no one checks up on you. The instructor might never collect the homework, but that doesn’t mean it doesn’t affect your grade.
#3: You will sometimes be responsible for material in the textbook that is not covered in class. If there is a text reading and/or homework problems covering a concept that was not discussed in class, you are still expected to learn it. If you don’t understand it, make an appointment with your instructor for help.
#4: Some material is covered only in class, is not in the textbook, and may not have any homework problems on it. If you miss class, you may miss content that you are responsible to know. If you have an unavoidable absence, be sure to get the notes and any announcements from a classmate.
#5: There will be test questions that don’t look “just like the homework.” In college, you are expected to focus on learning the concepts, not just memorizing how to do certain types of problems. These concepts can – and will – appear in very different forms on tests and quizzes.
#6: At times you will be expected to be able to explain why a problem is done a certain way in addition to being expected to do the problem. As you work on problems in class and on homework, don’t be satisfied with getting the correct answer; ask yourself why that method is logical, and how you could explain that logic to someone else.
#7: Most importantly, you are responsible for your own learning. If you attend class faithfully, get the notes and announcements if you have an unavoidable absence, read the text, do the homework and question yourself (as in #6), and still don’t understand something, it is up to you to get the extra help you need. Visit the instructor during office hours or make a special appointment to ask questions, form a study group, etc. There are many resources and people willing and happy to help, but you need to take the initiative and seek out the help you need.
Welcome to college history!
If this is your first history class taken in college, there are some important things you need to know. College history classes are run very differently from high school history classes. On the surface it may seem they are similar as you listen to the lecture and take notes, but there are significant underlying differences. Knowing these ahead of time can help you make the most of this coming semester.
#1: Do not put off the readings. As much as possible, do the readings on the day they are assigned. Set aside plenty of time to complete the readings. Trying to make up hundreds or thousands of pages at the last minute will not work.
#2: Always read contextually. Ask yourself how each chapter and each source relates to one another, and to points discussed in class. As you read, outline the material. This will make it much easier for you to study for the exams.
#3: Always keep the main ideas in minds. When reading a chapter, ask yourself what the important points are. This may require you to wade through lots of historical details.
#4: In high school history classes, you probably had to do lots of memorization. This doesn't go away in college history, but there's much more to it. In college history, you'll be asked to understand the significance of historical events and people, and how these events and people relate to each other and to current events. Keep this in mind as you take notes, do the readings, and study for exams. It's important to keep in mind the significance of what you study. When studying an event, don't just memorize dates and names. Be able to explain why this event was important then and remains important today.
Good luck on a happy and successful semester!
Commitment
to Inclusive Excellence: WSU recognizes that
our individual differences can deepen our understanding of one another and the
world around us, rather than divide us. In this class, people of all
ethnicities, genders, religions, ages, sexual orientations, disabilities,
socioeconomic backgrounds, regions, and nationalities are strongly encouraged
to share their rich array of perspectives and experiences. If you feel your differences may in some way
isolate you from WSU’s community or if you have a need of any specific
accommodations, please speak with the instructor early in the semester about
your concerns and what we can do together to help you become an active and
engaged member of our class and community.
Campus
Resources (Short version):
- Student Support
Services, Howell Hall 133, 457-5465 (http://www.winona.edu/studentsupportservices/)
- Inclusion and
Diversity Office, Kryzsko Commons Room 122, 457-5595 (http://www.winona.edu/culturaldiversity/)
- Disability
Resource Center, Howell Hall 136, 457-2391 (http://www.winona.edu/disabilityservices/)
- Counseling
Center, Gildemeister Hall 132, 457-5330 (http://www.winona.edu/counselingcenter/)
- Writing Center, Minné Hall 348, 457-5505
(http://www.winona.edu/writingcenter/) - GLBTA Advocate,
Gildemeister Hall 132, 457-5330 (http://www.winona.edu/counselingcenter/)
- Advising and
Retention, Phelps 129, 457-5600 (http://www.winona.edu/advising/)
Campus
Resources (Long version):
- Two good places
to help you find resources of all kinds on campus are Student Support
Services and the Inclusion and Diversity Office. Both offices are dedicated to helping
students of all races, ethnicities, economic backgrounds, nationalities,
and sexual orientations. They can
facilitate tutoring and point you to a wide range of resources. Student Support Services is in Howell
Hall 133, and they can be reached at 457-5465. The Inclusion and Diversity Office is in
Kryzsko Commons Room 122, and they can be reached at 457-5595.
- If you have a
disability, the Disability Resource Center can document it for your
professors and facilitate accommodation. Their office is in Howell Hall
136, and they can be reached at 457-2391.
If you have a documented disability that requires accommodation,
please let me know as soon as possible. If you suspect you may have a
disability, you are encouraged to visit the DRC as soon as possible.
- College can be
very stressful. The Counseling
Center is there to help you with a wide range of difficulties, ranging
from sexual assault, depression, and grief after the loss of a loved one
to stress management, anxiety, general adjustment to college, and many
others. Their office is located in
Gildemeister Hall 132, and they can be reached at 457-5330.
- For help with
writing and the development of papers, the English department has a
Writing Center available to students and staffed by trained graduate
students pursuing their Master’s degree in English. The Writing Center is located in Minné
Hall 348. You can make an
appointment on the sign-up sheet on the door or call 457-5505.
- The GLBTA
Advocate is responsible for documenting homophobic incidents on campus and
working with the appropriate channels to get these incidents resolved. In
addition, the advocate can direct people to GLBT resources on campus and
in Winona. Contact the Counseling
Center for the name and number of the current GLBTA Advocate. (Gildemeister Hall 132, 457-5330)
The
Standard Disclaimer applies.