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Perspectives in Mathematics: Long Synthesis Assignments, Fall 2013

There will be three synthesis take-home assignments, consisting largely of conceptual questions for which you will have to provide essay-like responses. You will be given a week to complete such assignments. The deadlines for turning these assignments in will be October 9th, November 27th, and December 11th, all by 9AM. Feel encouraged to turn in the assignments in class a day early.

    First Long Synthesis Assignment: The pdf file with all the guidelines for the assignment can be found here. Please note that you are allowed to rely on the material from your textbook, posted readings, your earlier worksheets and your lecture notes. However, you are required to complete all the work by yourself.
    Second Long Synthesis Assignment: The pdf file with explicit prompts/guidelines can be found here. Please report any typos and such to Iva. Reminder: you are allowed to rely on the material from your textbook, your earlier worksheets and your lecture notes. However, you are required to complete all the work by yourself.
    Third Long Synthesis Assignment: The pdf file with guidelines can be found here.
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Perspectives in Mathematics: Reading List for Fall 2013

The following is the tentative list of readings which you will be expected to complete by the indicated date. Note that class feedback may prompt changes to this list.

  • Week 1

      Thursday, September 5th: Chapters 1 and 2 from the textbook.
  • Week 2

      Thursday, September 12th: Chapter 13 from the textbook.
  • Week 3

      Tuesday, September 17th: Chapter 3 from the textbook.
      Thursday, September 19th: Chapter 9 from the textbook, up to and including Exercise 9.3.
  • Week 4

      Tuesday, September 24th: entire Chapter 9 from the textbook.
      Thursday, September 26th: Chapter 10 from the textbook; Exercises 10.1 and 10.2 will be done in class.
  • Week 5

      Tuesday, October 1st: For the pdf of the reading please click here.
      Thursday, October 3rd: For the pdf of the reading on curvature please click here.
  • Week 6

      Tuesday, October 8th: None.
  • Week 7

      Tuesday, October 15th: Chapter 14 with the exception of the material on projective three-space, and the entire Chapter 15.
      Thursday, October 17th: Reading on historical and philosophical underpinnings of geometry.
  • Week 8

      Tuesday, October 22nd: Chapter 4, ending with Exercise 4.10.
      Thursday, October 24th: complete Chapter 4.
  • Week 9

      Tuesday, October 29th: Chapter 5, ending with Exercise 5.6.
      Thursday, October 31st: complete Chapter 5.
  • Week 10

      Tuesday, November 5th: Chapter 12, focusing on material having to do with the Euler characteristic.
      Thursday, November 7th: Watch videos (part I, part II) on Platonic solids.
  • Week 11

      Tuesday, November 12th: Chapter 12, focusing on material having to do with the Gauss-Bonnet Theorem.
      Thursday, November 14th: NONE – review/synthesis day.
  • Week 12

      Tuesday, November 19th: Chapter 11.
      Thursday, November 21st: Chapter 6, focusing on two dimensional examples.
  • Week 13

      Tuesday, November 26th: Chapter 6, focusing on three- dimensional examples.
  • Week 14

      Tuesday, December 3rd: Chapter 19
      Thursday, December 5th: Read and research popular articles to get a sense of the statement and the significance of the Poincaré Conjecture. Links to these articles can be found on the website maintained by Prof. Christina Sormani of CUNY’s Lehman College. Warning: this is going to be a somewhat lengthy reading.
  • Week 15

      Tuesday, December 10th: complete the readings on the Poincaré Conjecture.
  • Perspectives in Mathematics: Syllabus for Fall 2013

    Textbook
    “The Shape Of Space” by Jeffrey R. Weeks. We will rely on its second edition. Do note that some of the course content and/or activities will not be directly based on the textbook material. At times, you will be expected to rely on your lecture notes.

    Readings
    Most lectures will assume that you have done your daily reading. The list of readings can be found under the Reading List below.

    Short in-class assignments
    Most lectures will be accompanied by a short assignment, which will largely depend on your daily reading. Ideally you will be able to finish this assignment in class. To accommodate people who might need extra time, a more private space, or an office hour or Math Skills Center visit to complete the assignment, all assignments will be due by 9AM the following morning. There will be an envelope for your assignments by my office door.

    Synthesis take-home assignments
    There will be three synthesis take-home assignments, consisting largely of conceptual questions for which you will have to provide essay-like responses. You will be given a week to complete such assignments. The deadlines for turning these assignments in will be October 9th, November 27th, and December 11th, all by 9AM. Feel encouraged to turn in the assignments in class a day early.

    Late or missed assignments
    I understand that you might find yourself in a situation where you cannot complete an assignment on time. You will nevertheless be expected to turn in what you have by the due date and immediately inform me about your situation. Assuming you are making a good faith effort to stay current in the class, you will be given an opportunity to make up an incomplete assignment.

    Grading scheme
    Course grades will be based on the short and the synthesis assignments you turn in. Specifically, for each rubric under Educational Goals you will receive a letter grade determined by your performance on the corresponding assignments. The final course grade will be a weighted average of the above. Borderline situations will be resolved by looking at class participation (e.g discussion on the day of the final exam). For the description of letter grades please refer to our College Catalog.

    Perspectives in Mathematics, Fall 2013: Educational Goals

    Math 103: Perspectives in Mathematics is a course which satisfies Science and Quantitative Reasoning Category B requirement. Thus, the educational goals of this course are largely centered around symbolic reasoning.

  • Goal 1:
    To further students’ ability to think and work with abstract objects by means of their symbolic (at times algebraic) forms. Working towards this goal gives you an opportunity to liberate yourself from thinking solely in terms of concrete tangibles. In this class you will have an opportunity to use concrete examples to develop an inductive understanding of abstract objects, relationships and ideas which are usually inaccessible to mathematically untrained minds. Specifically, in this course the students will:

      Work with abstract shapes represented in symbolic form; the corresponding assessment will be based on student performance on assignments from weeks 1, 8, 9 and 10.
      Work with higher dimensional objects in symbolic/algebraic form; the corresponding assessment will be based on student performance on assignments from weeks 2, 7 and 12.
      Execute arguments based on algebraic manipulations; the corresponding assessment will be based on student performance on assignments from weeks 3, 10 and 11.
      Analyze functional relationships between geometric quantities; the corresponding assessment will be based on student performance on assignments from weeks 4 and 5.
  • Goal 2:
    To further students’ ability to recognize the abstract concepts discussed above as they manifest themselves in our physical world. The extent to which this goal is achieved will be determined based on assignments which explore the concept of curvature and possible geometries of our universe (e.g weeks 5, 6 and 15).
  • Goal 3:
    To develop a basic understanding of what modern practice of mathematics is about. The extent to which this goal is achieved will be determined based on assignments which explore the distinction and interaction between geometry and topology (e.g weeks 3 and 13).
  • Goal 4:
    To situate the practice and communication of mathematics within its larger intellectual and social context. Specifically, this course presents an opportunity to learn about a currently active area of mathematics research, as well as its historical and philosophical underpinnings. The extent to which this goal is achieved will be determined based on assignments having to do with developments which lead to the discovery of hyperbolic geometry and the proof of the Poincaré conjecture (e.g weeks 7 and 15).