MATH 119 B1

Announcements

• August 22: Welcome to the class!

• August 31: Some problems on HW1 has been moved to HW2. Please also see the suggestions for HW1.

• September 7: New office hours: Thursday 1-1:50 (ends sharply), and 3:30-4:30 (can be extended when needed).
  Extra appointment generally not available on Thursday, but very available on Tuesday.

• November 9: Homework 10 is adjusted. See homework section below.

• November 13: Office hours for THIS week: TUE 1~2 and 3:30~4:30. THU: None. (or by appointment)

• December 4: Office hours for THIS week: TUE 1~2 and 3:30~4:30. THU: 1~3 pm (can be extended). HW 12 is now due together
  with your Exam IV (see below).

• December 5: Update to homerok 12: see below.

Class Logs

• August 22: Syllabus introduction. Class orientation.

• August 24: Introuction to mathematical proof.

• August 26: 1.1-Introduction to set theory.

• August 29: 1.1-Finish set theory. 1.2-Introduction on tessellations.

• August 31: 1.2-Finish tessellations.

• September 2: 1.3-Fix notations for gemetrical proofs. Congruence of triangles. "Proof" of Pythagorean Theorem.

• September 5: Labor day holiday! (Salute to your laborious instructor!!)

• September 7: Finish up 1-3. Scaling (applications to infinite sums). Area of triangle.

• September 9: Demonstrate the invalidity of "Proof by pictures".

• September 12: Compass and straightedge constructions: reproduction of lines, angels, and triangles.

• September 14: Perpedicular bisectors.

• September 16: Angle bisectors, circumcenter of a triangle.

• September 19: Incenter of a triangle.

• September 21: Centroid of triangles, concurrency of perpendicular bisectors.

• September 23: Constructions of special angles. Trickier constructions.

• September 26: Constructions of triangles given particular sides and angles.

• September 28: Q&A session.

• September 30:Midterm exam 1.

• September 30:Midterm exam 1.

• October 3: Discuss Midterm exam 1.

• October 5: Introduction of origami construction.

• October 7: Origami constructions on perpendicular and parallel lines.

• October 10: Origami constructions on angle trisections.

• October 12: Similar triangles.

• October 14: Similar triangles and introduction to coordinate constructions.

• October 17: Finish up on coordinate constructions about lines. Algebraic and geometric correspondences.

• October 19: Q&A session for exam II.

• October 21: Midterm Exam II.

• October 24: Introduce equation of circles and their intersection with lines. Angle Bisectors. Return Exam II.

• October 26: Parabolas: sketching, completeing the squares, and definitions of focus and directrix.

• October 28: Constructions of numbers: addition, multiplications, and divisions.

• October 30: Constructions of square root and its proof. Constructibility of numbers.

• November 2: Classifications of real numbers. Identify constructible numbers.

• November 5: Solving (estimating the roots of-) cubic polynomials using origami and coordinate.

• November 7: Proof of origami/coordinate constructions of cubic roots. Introduction to city geometry.

• November 9: Circles in city geometry.

• November 11: Midset and parabolas in City geometry.

• November 14: Q&A session for Exam 3.

• November 16: Exam3.

Homework Assignments

• HW1 Due Friday, September 2
  Problems from the course reader:
  Section 1.1: 8,10,12,18,22,23
  Section 1.2: 8,11
  suggestions for problem 11
  Section 1.3: 2,5
  *Justifications with mathematical proofs are required for each problem.*
  Solutions

• HW2 Due Friday, September 9
  Section 1.3: 2,5,14,18,19,21,31,32
  *Justifications with mathematical proofs are required for each problem.*
  Solutions

• HW3 Due Friday, September 16
  Section 1.3: 27,28
  Section 2.1: 6,10,12,15 *Justifications with mathematical proofs are required for each problem.*
  Solutions

• HW4 Due Friday, September 23
  Section 2.2: 4,5,6,7,14,16,18,19 *Proofs are not required, but steps in your constructions must be clearly listed.*
  Solutions: see class notes.

• HW5 Due Friday, September 30
  Section 2.3: 2,5,6,16,19,23 *Proofs are not required, but steps in your constructions must be clearly listed.*
  Solutions

• HW6 Due Friday, October 14
  Section 3.1: 4,6,9,11,12(and prove why you trisected the angle),16. *Proofs are not required except for 12, but steps in your constructions must be clearly listed.*
  Solutions

• HW7 Due Friday, October 21
  Section 3.3: 3,5bc,7b,11 Section 4.1: 11,14 and an extra problem: Start with any triangle. Use origami to construct similar triangles whose ratios of corresponding sides are 1/2, 2, and 3.5. Solutions

• HW8,9 Due Friday, November 5
  This homework consists of two parts: individual part and group work. Individual: Section 4.2: 7fg, 9, 11ab, 19, 22.
  Section 4.3: 8,14,22,25,26.
  Work in group of 3 or 4:
  Verity the two formulae at the beginning of p.83. Why are they focus and dirextric to the parabola with equation
  at the end of p.82?

  Solutions

• HW10 Due Wednesday, Novermber 16
  Section 4.4: 10bc.
  Section 5.1: 1,7,8.
  Section 5.2: 2,4,7,12.
  Solutions

• HW11 Due Wednesday, Novermber 30
  Section 6.1: 15, 36, 38, 40 Solutions

• HW12 Due Monday, December 12 at My Desk at 6pm
  Section 6.1: 16,21,31.
  Section 6.2: 9,11,14,20.
  The extra problem: Find the reflection of the point (0,2) about the line y=2x+1
  Solutions

Exams

Handouts