451_homework_2016

Homework Assignments

12/10
  1. Exercises 10.2: 6, 7, 8; Exercises 10.3: 4, 11, 12.
  2. Complete your paper. Due 12/12.
  3. Here is a list of study topics and practice problems for the final exam.
12/05
  1. Read Sections 10.2 and 10.3 of Venema for discussion on Tuesday. You can read Section 10.2 lightly, concentrating on understanding the statements of the theorems—don’t worry about details of the proofs. (Venema’s presentation and proofs work in neutral geometry, but we will concentrate on the Euclidean case when we discuss it in class.)
  2. Exercises 10.1: 1, 3, 4.
  3. Work on your paper.
12/03
  1. Read Section 10.1 of Venema for discussion on Thursday.
  2. Exercises 6.5: 1, 2.
  3. Work on your paper.
11/26
  1. Have a good break!
11/21
  1. Read Section 6.5 of Venema, for discussion on Tuesday. As with Section 6.4, concentrate first on understanding the statements of the theorems, and making sense of what is happening.
  2. Exercises 6.5: 1, 2, 4.
  3. Work on your paper.
11/19
  1. Read Section 6.4 of Venema, for discussion on Thursday. Several of the proofs in this section (and Section 6.5) are quite technical, and you can ignore the details on a first reading. Concentrate on understanding the statements of the theorems, and making sense of what is happening. (Draw lots of pictures of the Poincaré disc!) We will use Theorems 6.4.4 (Endpoint Independence), 6.4.5 (Existence and Uniqueness of Limiting Parallels), and 6.5.4 (Angle-Side Congruence Condition) in the next section, so concentrate particularly on those three results.
  2. Exercises 6.4: 1, 2.
  3. Work on your paper.
11/14
  1. Read Section 6.3 of Venema for discussion on Tuesday. You do not have to send me a question this time, but feel free to do so if anything is not clear.
  2. Hand in Exercises 4.8: 8; Exercises 6.2: 2. Due 11/21.
11/12
  1. Read Section 6.2 of Venema.
  2. Exercises 6.2: 1, 2 and 3.
11/07
  1. Continue reading Section 6.1 of Venema for discussion in class on Tuesday. (Send me questions as you read.) We will be using properties of Lambert and Saccheri quadrilaterals from Section 4.8 extensively for the rest of this chapter, so you might want to review that section also.
  2. Exercises 6.1: 1, 4, 5.
  3. Hand in Exercises 6.1: 5. Due 11/14.
11/05
  1. Read as much of you can of Section 6.1 of Venema (this is a long section) for discussion in class on Thursday. Send me questions (at least one!) as you read. Due 11/06.
10/31
  1. Read Sections 5.5 and 5.6 of Venema for discussion on Tuesday. Note that Section 5.6 is really about “exploring” the geometry of triangles. If you don’t have dynamic geonetry software on your own computer, you can use the online GeoGebra calculator to do the suggested explorations. (There is a link to the website on the “Links” page.)
  2. Decide on a topic for your paper, and hand in a 1-paragraph proposal next Thursday. Here are some guidelines for the paper.
  3. Exercises 5.5: 1, 2 and 3.
  4. Hand in Exercises 5.3: 2; Exercises 5.4: 3; Exercises 5.5: 2; your paper proposal. Due 11/07.
10/29
  1. Read Sections 5.3 and 5.4 of Venema for discussion on Thursday.
  2. Exercises 5.3: 1, 2 and 3; Exercises 5.4: 3, 4.
10/24
  1. (Re)read Section 5.3 in Venema for discussion on Tuesday, and send me a question by Monday evening. Due 10/28.
  2. (Optional) Rewrite any questions from Exam 1 that you wish to have regraded. You can earn back up to 50% of any points lost on any rewritten question. You may work with your classmates, or ask me about anything that is not clear, as you work on the rewrite. Hand in your original exam together with your rewritten questions with this week’s homework. Due 10/31.
  3. Hand in Exercises 5.1: 2, 5; and (optional) your exam rewrite. Due 10/31.
10/22
  1. Read Section 5.2 of Venema, and as much of Section 5.3 as you can, for discussion on Thursday. Send me a question, on this reading or the previous one, by Wednesday evening.
    Due 10/23.
10/17
  1. We will discuss the final sections of Chapter 4 on Tuesday, so you might wish to reread some or all of those sections (and maybe Section 5.1) to refresh your memory of them.
10/10
  1. Finish reading Chapter 4 of Venema, and read Section 5.1 (which is largely a summary of results from the later sections of Chapter 4), for discussion on Tuesday. Send me any final questions on Chapter 4 by Monday evening. Due 10/14.
  2. Exercises 4.8: 1, 2, 3, 5, 8; Exercises 5.1: 2, 3, 5, 7, 8. (Note that the context changes between these two sets of exercises: in the first set (Chapter 4), you are still working in neutral geometry; in the second set (Chapter 5), you are working in the special case of Euclidean geometry.)
10/08
  1. Read Sections 4.6 and 4.8 of Venema, through the proof of Theorem 4.8.4, for discussion on Tuesday. We will discuss this theorem and its proof on Thursday. Send me a question by Wednesday evening. Due 10/09.
  2. Begin your preparation for Exam 1, which will be given in class next week: Thursday, October 17.
  3. Exercises 4.6: Problems 1, 2, 3, 4 and 8.
  4. Update Here is a list of study topics and practice problems for the midterm exam.
10/03
  1. Read Section 4.7 of Venema for discussion on Tuesday. Concentrate on making sense of the list of equivalent statements; don’t worry too much about all the details of all the proofs (unless you are feeling particularly virtuous). Exceptions: you should read the proofs of Theorems 4.7.1 and 4.7.4. (The latter will require you to read the proof of Lemma 4.7.5 also.) You do not have to send me a question, but feel free to do so if anything is unclear.
  2. We may also discuss Section 4.6 on Tuesday, and it will be part of the reading for next Thursday, so you may read that section now also if you want to read ahead over the weekend, but concentrate on Section 4.7.
  3. Exercises 4.7: 2, 4, 6 (and any of 1, 3, and 5 you would like to do for practice).
  4. Hand in Exercises 4.5: Problems 1 and 2. Due 10/10.
10/01
  1. Read Section 4.5 of Venema for discussion on Thursday.
  2. Exercises 4.5: Problems 1 and 2.
09/26
  1. In class today, work in small groups to solove (or compare your solutions to) Exercises 4.2: Problems 2, 3, 5; and Exercises 4.3: Problems 2, 3, 4. (Exercise 4.3: 2 is the Triangle Inequality, and it is Euclid’s Proposition 20 from his Book 1. One approach to this exercise is to see how Euclid proves this proposition, and then try to justify every step carefully from our postulates and previous theorems.)
  2. If you have time, working on any of Exercises 4.4: Problems 1, 2, 3.
  3. Hand in Exercises 4.4: 1, 2. Due 10/03.
09/24
  1. Read Section 4.4 of Venema for discussion next Tuesday.
    You do not have to send me a question, but feel free to do so if anything is unclear.
    (You may also wish to re-read Sections 4.2 and 4.3 in light of today’s discussion.)
  2. Exercises 4.4: Problems 1, 2, and 3.
  3. Homework update: Since I will not in town this Thursday, the homework originally due on 09/26 is now Due 10/01.
09/19
  1. Read Sections 4.2 and 4.3 of Venema for discussion on Tuesday.
    Send me a question by Monday evening.
    Due 09/23.
  2. Exercises 4.2: Problems 2, 3, 4 and 5; Exercises 4.3: Problems 1, 2, 3, 5, 6, 8 and 9.
  3. Hand in Exercises 4.2: Problems 3 and 4; Exercises 4.3: Problems 2 and 3.
    Due 09/26.
09/17
  1. Read Sections 3.7 and 4.1 of Venema for discussion on Thursday.
    Send me a question by Wednesday evening.
    Due 09/18.
  2. Exercises 3.7: Problems 1 and 2; Exercises 4.1: Problems 1 and 2.
09/12
  1. Read (or re-read) the following sections of Venema, for discussion on Tuesday: Section 3.4, Section 3.5 through to the end of page 60, Section 3.6. Make sure you understand the statements of the postulates, and of any major theorems (hint: any theorem with a name is likely to be a major theorem), but don’t worry about the details of the proofs. Try to convince yourself of the “big picture” goal of this chapter: that we have identified a set of axioms that will enable us to prove rigorously the theorems of plane geometry, with no need for additional, unstated, assumptions.
    Send me a question on the reading by Monday evening.
    Due 09/16.
  2. Exercises 3.4: Problem 2; Exercises 3.5: Problems 2, 3; Exercises 3.6: Problem 2.
  3. Hand in Exercises 3.3: Problem 5; Exercises 3.4: Problem 2.
    Due 09/19.
09/10
  1. Read Section 3.3 of Venema, and as much of Section 3.4 as you can,
    for discussion on Thursday. You do not have to send me a question on
    this reading, but feel free to do so if you wish (or if there is something you
    particularly want to go over in class).
  2. Exercises 3.2: Problems 17 and 18; Exercises 3.3: Problems 1, 2, 4, and 5.
09/05
  1. Finish reading Section 3.2 of Venema, for discussion on Tuesday.
    (You may also wish to re-read the first part of the section in light of today’s
    discussion.) Send me a question on the reading by Monday evening.
    Due 09/09.
  2. Exercises 3.2: Problems 7, 9, 11.
  3. Hand in Exercises 3.2: Problems 3, 7, 9. Due 09/12.
09/03
  1. Read Sections 3.1 and 3.2 of Venema, through the statement of Theorem 3.2.16
    (The Ruler Placement Postulate), for discussion on Thursday.
    Send me a question on the reading by tomorrow evening. Due 09/04.
  2. Exercises 3.2: Problems 1, 3, 5, 6. (You do not have to hand these problems in
    this Thursday, but some of them might appear in the assignment that will be due
    next Thursday.)
08/31
  1. Purchase the textbook—Gerard A. Venema, Foundations of Geometry (2nd edition)—and read
    Chapter 1 before the first class meeting. This is only 10 pages, and largely historical rather than
    mathematical (though you may find Section 1.4 to be more challenging). We will discuss this
    chapter during that first class, so try to be prepared. If you have not managed to obtain
    a copy of the textbook in time, let me know and we can work something out.
  2. Send me a question on the reading by noon on Tuesday, so that I can read it before class. Due 09/03.

Kevin Mcleod

08/31/2019