University of Colorado Denver College of Liberal Arts and Sciences Math 4010/5010: The History of Mathematics

Semester: Fall 2011 Professor: Dr. Diana White Course Times: TR 3:30-4:45 Office: CU 624 Course Location: King 212 Phone: 303-556-8482 (please use e-mail) Office Hours: TR 4:45-5:30 pm Email: [email protected] (and by appointment)

Prerequisites: 1. Math 1401 (Calculus I) or permission of instructor 2. Academic maturity to handle a senior-level course

Required Texts: The History of Mathematics, by David M. Burton (Addison-Wesley, Seventh Edition) and Journey Through Genius, by William Dunham

Recommended Texts: You will need other books and sources throughout the semester, depending on your choices of topics and projects. These can be checked out of a library, or purchased online or from a local bookstore. If our library does not have a book you want, you can request it from inter-library loan. The library staff can help you do this.

Catalogue Description: A history of the development of mathematical techniques and ideas from early civilization to the present, including the inter-relationships of mathematics and sciences.

Instructor Description: We will center our course on four main mathematical problems:

1. How did the concept of number develop, and how did societies develop methods of computation? 2. How did societies find the area of a given shape? 3. How did societies solve equations? 4. How did rigor develop in mathematics?

While the course will center on the development of these historical topics, this is not a math class in the traditional sense. Nor is it a traditional history course. Mathematical ideas did not simply “always exist”. They developed based on societal needs. Hopefully this course will develop an appreciation of this fact.

In addition to specific content goals, this class is designed to develop other transferable skills – such as working with others, being a critical consumer of information, articulating and communicating mathematics in written and oral form, and the ability to learn mathematics independently. Specifically, here are the goals and objectives.

1 Course Goals/Objectives:

1. Increase understanding of the complex interplay between mathematics and the social milieu in which it is developed 2. Increase understanding of the historical interconnections between various areas of mathematics 3. Increase knowledge of mathematical development in non-Western societies 4. Increase mathematical content knowledge 5. Develop skill at critical analysis of historical sources 6. Expand and refine the ability to find information on mathematical and historical topics 7. Improve the ability to explain technical material in written and oral form 8. Increase ability to understand and learn mathematics independently of the instructor 9. Increase ability to work with others to understand mathematics 10. Develop ability to provide meaningful feedback on the oral and written work of others, and to accept such feedback for yourself

Course Methodology: This course will use several main pedagogical techniques, in order from most to least common 1. Students working/discussing in groups combined with full-class discussion 2. Students giving short presentations to small groups of fellow students 3. Student work days on group projects 4. Expert lectures

Assignments/Time commitment: Expect approximately 5-6 hours outside of class per week. Graduate students should expect to spend an average of an extra 2 hours per week over the course of the semester.

Attendance: We will often be working in groups or having group discussions during class. For this to work effectively, it is essential that everyone be present as much as possible. You are permitted three (3) absences from this class with no penalty (and you need not notify me in advance unless you have an assigned task that day). After that, each missed day will result in a 3% penalty in your final grade. The only exception to this is a documented/sustained absence for health, family, or military reasons. Such exceptions will be dealt with on an individual basis, but will require make-up work. I strongly urge you not to “skip” class, and to save your absences for real-life situations that arise. If you miss more than 10 minutes of class it will count as half an absence, and if you miss more than 25 minutes of class it will count as a full absence. If you repeatedly arrive late, then I reserve the right to count this as an absence.

Homework: Homework will be a combination of short, problem-based assignments and more substantial problems.

Homework can be done in groups unless announced otherwise, but your individual write-up must be your own. On these problems you generally must explain your work using full sentences with an intro and conclusion and use appropriate grammar and syntax (including capital letters and punctuation). You must write neatly and submit a final draft (not a first draft) of you work. Leave generous margins and space to allow for comments. Staple your work in order, unless otherwise instructed. I will not have a stapler with me in class. (You can purchase a little one for a few dollars at any office supply store, or at most grocery and drug stores.)

2 Presentations: Periodically throughout the semester you will be expected to present your solution to a problem at the board. You will also be asked to present your biography and final assignments to small group of peers. There may be other occasional presentations to small groups of classmates or to the entire class.

Participation: This portion of your grade will be based on your contributions to the classroom during class time, and is separate from the attendance requirements. It reflects your engagement with the material and with contributions and citizenship within your group. It is not measured by quantity, but by quality, attitude, and effort.

Exams/Final: There will not be written exams or a written final. Expect to meet during the final exam period for a final class or final presentations.

Estimated Grading Summary: SALG/feedback 5% Participation/Citizenship/In-class quizzes/reflections 15% Presentations 10% Written Homework 20% Biography 10% Other assignments – may include: 20% Galois Assignment Blackwell Assignment Website Assignment Original Source Assignment(s) Topical Project ______20% Total: 100%

Note that I reserve the right to adjust the percentages by up to 10% based on which we actually emphasize more as the class progresses.

Your final grade range will be determined as follows. A: 90-100%, B: 80-89.99%, C: 70-79.99%, D: 60%-69.99%, F: Below 60%. I will uses plusses and minuses when assigning final grades, but these scales will not be determined in advance. While there is a chance these cut-offs will be lowered, there is no chance they will be raised.

Generic Grading Rubric: I generally grade according to a rubric on a scale of 0-5, with the most common scores being 4, 3, 2.5, and 2. Here is the generic rubric upon which others will be based.

Rubric Score Description Percentage equivalent 5 All features of 4.5, but truly above and beyond in some 125 important ways 4.5 Exceeds expectations, excellent work, no errors, could serve 100 as key or model to other students 4 Meets expectations, excellent work, fully correct or at most 95 an extremely minor error 3 Meets most expectations, good, solid work, major progress, 85 minor errors only 2.5 Meets some to most expectations, significant progress, 70 worthy of passing grade, but contains significant shortcomings

3 2 Meets some expectations, weaker work, some valid progress, 50 major errors 1.5 Minimal progress, but some evidence of related knowledge 30 1 Minimal progress, meets few to none of the expectations 10 0 Not submitted, left blank or almost blank, no progress 0

Incomplete Grades (I): Incomplete grades (I) are not granted for low academic performance. To be eligible for an Incomplete grade, students must (1) successfully complete 75 percent of the course, (2) have special circumstances (verification may be required) that preclude the student from attending class and completing graded assignments, and (3) make arrangements to complete missing assignments with the original instructor. A CLAS Course Completion agreement is required. The student will have one year to make up the missed course work or the (I) will be replaced with an F as a course grade.

Course Communication: In addition to announcements made and written handouts distributed in class, I may need to contact you between classes, which I'll do through individual and group email messages. One of the requirements for this course is that you maintain a UCD email address, check it regularly for messages, and be sure it is working. You are responsible for any messages, including assignments and schedule changes, I send you via email. You also may contact me via email, in addition to seeing me during office hours.

4 Fall 2011 CLAS Academic Policies The following policies pertain to all degree students in the College of Liberal Arts and Sciences (CLAS).  Schedule verification: It is each student’s responsibility to verify online that his/her official registration is correct: verify before classes begin and prior to the drop/add deadline. Failure to verify schedule accuracy is not sufficient reason to justify a late add or drop.  E-mail: Students must activate and regularly check their official student e-mail account for CU Denver business: http://www.ucdenver.edu/student- services/Pages/WebMail.aspx. Those who forward email to a private account are still responsible for checking their official student e-mail account for messages not automatically forwarded.  Waitlists:  Students are not automatically notified if they are added to a class from a waitlist. Students are not automatically dropped from a class if they never attended, stopped attending, or do not make tuition payments.  Waitlists are purged after the 1st week of classes, after which a paper Schedule Adjustment Form (drop/add form) is required. It is the student's responsibility to get the form (online or at the Advising Office, NC 4002), have it signed, deliver it to the Registrar (Annex 100) or the Student Services Center (NC 1003), and verify her/his schedule online.  Late adds (after 7 September) will be approved only when circumstances surrounding the late add are beyond the student’s control. This will require a written petition and verifiable documentation. Petition forms are available in NC 4002. The signature of a faculty member on a Schedule Adjustment Form does not guarantee that a late add petition will be approved.  Late drops (after 14 November) will be approved only when circumstances surrounding the late drop have arisen after the published drop deadline and are beyond the student’s control. This will require a written petition and verifiable documentation. The signature of a faculty member does not guarantee that a late drop petition will be approved.  Tuition: Students are responsible for completing arrangements with financial aid, family, scholarships, etc. (depending on tuition plan selected) to pay their tuition prior to Census Date (7 September). Students who drop after that date are (1) financially responsible for tuition and fees, (2) academically responsible and will receive a "W" grade, and (3) are ineligible for a refund of COF hours or tuition.  Graduation:  Undergraduate students wishing to graduate in fall 2011 must complete the online Intent to Graduate Form and meet with their academic advisor to obtain a graduation application. This application must be submitted by Census Date (7 September). You can obtain an application only after meeting with your advisor. There are no exceptions to this policy.  Graduate students wishing to graduate in fall semester 2011 must complete the online Intent to Graduate form and have a Request for Admissions to

5 Candidacy on file with the CU Denver Graduate School (Lawrence Street Center) no later than 5 PM, September 7, 2011.

Important Dates and Deadlines  August 22, 2011: First day of classes.  August 28, 2011: Last day to add a class or be added to a waitlist using the UCD Access student portal. After this date, you must use a Schedule Adjustment Form to change, add, or drop.  August 29, 2011: LAST DAY TO DROP WITHOUT DROP CHARGE – THIS INCLUDES SECTION CHANGES.  August 29, 2011: Waitlists are dropped. Any student not added to a course automatically from the waitlist by this date MUST complete a Schedule Adjustment Form to be added. Students are NOT automatically added to the class from the waitlist after this date and time. If your name is not on the official student roster, you are not registered for the course.  August 30-September 7, 2011: Students are responsible for verifying an accurate fall 2011 course schedule via the UCDAccess student portal. Students are NOT notified of their waitlist status by the University. All students must check their schedule prior to 9/7 for accuracy.  August 30, 2011: First day instructor may approve request to add a student to a course with a Schedule Adjustment Form.  September 7, 2011: Census date.  9/7/11, 5 PM: Last day to add structured courses without a written petition for a late add. This is an absolute deadline and is treated as such. This deadline does not apply to independent studies, internships, project hours, thesis hours, dissertation hours, and late-starting modular courses.  9/7/11, 5 PM: Last day to drop a fall 2011 course or completely withdraw from all fall 2011 courses using a Schedule Adjustment Form and still receive a tuition refund, minus the drop fee. After this date, tuition is forfeited and a "W" will appear on the transcript. This includes section changes. This is an absolute deadline and is treated as such.  9/7/11, 5 PM: Last day to request pass/fail or no-credit option for a course.  9/7/11, 5 PM: Last day for a graduate student to register for a Candidate for Degree.  9/7/11, 5 PM: Last day for a Ph.D. student to petition for a reduction in hours.  9/7/11, 5 PM: Last day to apply for fall 2011 graduation. You must make an appointment and see your academic advisor before this date to apply for graduation if you are an undergraduate; you must complete the Intent to Graduate and Candidate for Degree forms if you are a graduate student.  September 19-28, 2011: Faculty can use the Early Alert system.  October 31, 2011, 5 PM: Last day for non-CLAS students to drop or withdraw without a petition and special approval from the academic dean. After this date, a

6 dean’s signature is required.  November 14, 2011, 5 PM: Last day for CLAS students to drop or withdraw with signatures from the faculty and dean but without a full petition. After this date, all schedule changes require a full petition. Petitions are available in NC 4002 for undergraduates and in the CU Denver Graduate School offices for graduate students.  November 21-27, 2011: Fall break (no classes; campus closed). Be thankful.  December 12-17, 2011: Finals Week. No schedule changes will be granted once finals week has started. There are NO exceptions to this policy.  December 27, 2011: Fall final grades available on UCD Access (tentative).

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