| Date |
Sections
covered |
Suggested
assignment |
Comments |
| Jan 5 |
Introd. to Chapter 1 |
Review vectors from any Calculus
III textbook |
|
| Jan 7 |
Review of vectors see sections 12.2, 12.3 of Anton's Calculus, 8th edition |
Do as many exercises from these
sections to feel confortable with the concepts. In particular, do 29-40, 51-58 from 12.2; 4-10, 13, 14, 22-28, 39-44 from 12.3. |
I am teaching Calculus
III, TR 12:30-2:10pm, GC 287B. If you want to refresh on vectors by sitting in my Calc. III class, feel free to do so. |
| Jan. 12 |
Review vectors 12.4, 12.5, 12.6 of Anton's Calculus |
12.4 - #10, 11, 15, 17, 21, 25,
26, 31-34, 41, 42 12.5 - #11, 15, 25, 27, 37, 45, 52 12.6 - #13, 17, 23, 25, 27, 35, 36, 50 |
Homewok 1 due Tuesday, Jan. 19 |
| Jan. 14 |
Chapter 1 |
Pbs 1, 2, 3 Chp. 1 textbook |
|
| Jan. 19 |
Chapter 1 |
see Homework 2 |
Homework 2 due Tuesday, Jan. 26 |
| Jan. 21 |
2.1.1 Incidence Theorem 2.1.3 Thales in 3-d |
Prove Thales thm. for two
intersecting lines in the plane, cut by three parallel lines. Do (preferably using vectors) Pb. 23, page 94. |
Section 3.1 in the textbook
contains some material on affine maps and the associated linear maps. A different definition for an affine map is used; it is a good exercise to understand why this is equivalent to the definition used in class. |
| Jan. 26 |
2.1.2 Pappus Thm. 2.1.4.Desargues Thm Newton's complete quadrilateral Thm. |
Prove Pappus Thm. in the case
that the two initial lines are parallel. Prove Desargues Thm. in the case that the three initial lines are parallel. |
A good complementary book for
the course is "Geometry: A Comprehensive Course" by Dan Pedoe. Right now, you can find the book on www.barnesandnoble.com for less than 4 dollars. I also put a copy of this book on reserve in the library. |
| Jan. 28 |
2.2.3 Congruence and similarity
of triangles |
Try Pbs. 2, 3, 9, page 89-91 Come up with a criterion of congruency for quadrilaterals. Would an SSSS criterion work? Prove remaining parts of Theorem 14 and prove Theorem 16 from Chapter 2 |
Look on and know proofs for Theorems 7, 8, 9, 10, 11, 12 from Chapter 2 textbook (it's ok to have proofs different than the the textbook). |
| Feb. 2 |
2.2.6 Important lines and points
in a triangle |
Additional
suggested problems -- Set 1 (these are not for turning in) |
Homework 3 due Tuesday, Feb. 9 |
| Feb. 4 |
2.2.7 Euler line |
Fill in
the details of the proof for the Euler line Theorem Try Pbs. 11, 12, 13 from Chapter 2, textbook. (for 11&12 use the Law of Sines and some trig. identities) |
I
have to reverse the decision about the room for our class. DM 409A is too small for 30 students. Thus, we'll still meet in our regular room CP102 (they fixed the screen). |
| Feb. 9 |
2.2.4 Menelaus & Ceva |
Prove the implication left
exercise of Ceva's Theorem. Try Pbs. 6, 15 page 90-92 textbook (try to use Ceva for #15 imitating the proof in the textbook of Theorem 19 ). Problems 4.1-4.5 are also very good problems for this section. |
Exam1
will be on Thursday, Feb. 18 (final date) |
| Feb. 11 |
2.2.8 & 2.2.9 Area formulae; Isoperimetric inequality |
Prove Theorem 28 and Corollary 4
(p. 44-45 textbook) Additional suggested problems -- Set 2 |
Here is a
link to Peter Lax's proof of isoperimetric inequality. Now you can enjoy it for yourself . I will not ask you this for the exam! |
| Feb. 16 |
Review for Exam 1 |
For Exam 1 any problem in the
suggested or assigned homework is a
possible exam question. You also have to know all the important
definitions and theorems covered, with their proofs (parts of the proofs could also be on the exam). |
|
| Feb. 18 |
Exam
1 |
This is a copy of Exam 1. Choose
two
problems from 4(b), 5(b), 6, 7. that you did not do well in class, do them home, and turn them in on Thursday, Feb. 25. You'll receive half the points above what you scored in class. The offer is valid for a maximum of 12 bonus points. |
|
| Feb. 23 |
2.3.2 Inscribed angles and more |
Suggested
Problems |
|
| Feb. 25 |
Cyclic (chordal) quadrilaterals Theorem 38 (page 56) 2.3.3 The nine-point circle |
Suggested
Problems |
|
| Mar. 2 |
2.3.3 The nine-point circle |
Homework 4 due Tuesday, Mar. 9 |
|
| Mar. 4 |
2.3.4 Simson line, Steiner (first) line 2.3.5 Tangent quadrilaterals |
Try Pbs. 19, 21, 22 page 93
textbook. More suggested Problems |
|
| Mar. 9 |
2.3.1 Power of a point w.r.t. a circle (Thms 31, 32) Apollonius' Circle |
Suggested
Problems |
Nice pictures and further
problems about Apollonius circles you can find on Jim Wilson's page at University of Georgia |
| Mar. 11 |
Geometric extremum problems (Heron and Fagnano Problems) |
Homework 5 due Thursday, Mar. 25 |
|
| Mar. 16 |
Spring Break |
||
| Mar. 18 |
Spring Break |
||
| Mar. 23 |
2.3.6 Inversion
(Reflection) in a circle |
Try Pbs.24, 25 page94 textbook Some more suggested problems on circle inversion. |
Since
many of you have Adv. Calculus midterm on Mar. 25, the Exam 2 for College Geometry is postponed one week. Thus, it will be on April 1 (no joke!). It covers material done between Feb. 23-Mar.25. All suggested and homework problems are potential exam questions. |
| Mar. 25 |
2.3.6
More inversion |
Just
one more suggested problem |
Since I'll not be here later
today (and will be gone the entire weekend), you can return Hwk. 5 on Tue. Mar. 30. |
| Mar. 30 |
Review for exam |
||
| Apr. 1 |
Exam
2 |
This is a copy of Exam 2 Choose any parts of problems 2, 3, 4 that you did not do well in class, do them home, and turn them in on Thursday, Apr. 8. You'll receive half the points above what you scored in class. The offer is valid for a maximum of 15 bonus points. |
|
| Apr. 6 |
2.3.6 Linear Fractional
Transformations |
Suggested
problems for LFT More suggested problems for LFT |
|
| Apr. 8 |
2.3.6. Cross-Ratio |
Homework 6 due Thursday, April 15
|
|
| Apr. 13 |
4.2 Poincare model of H^2 |
||
| Apr. 15 |
Review for Final |
Look at all suggested and
Homework problems. Look also at Pbs. 24, 25 page 94 textbook. |
Review session: Saturday, April
17, 12:00noon-1:30pm in DM 409A I will also be in my office on Monday, April 19 roughly from 10:00am to 1:00pm |
| Apr.20 |
Final
exam 9:45 -11:45 regular room |
Here are
your scores on the final (out of 150) and the grade for the class. |
Enjoy
your Summer! |