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L01-Mon-5-Sep-2016-No-Class-University-Closed-Labor-Day

L02-Wed-7-Sep-2016-Sec-A-2-Geometry-HW02-Moodle-Q01 • Introduction: I am a visiting professor from the department of

Curriculum and Instruction in CEHD.

• Brief description of the course: This course is specifically designed to prepare you for Precalculus II, which will prepare you for calculus. This course satisfies the Mathematical Thinking graduation requirement.

• Role as lecturer I will be introducing important ideas and concepts and working out examples that are similar to your assigned homework and exam problems. At the start of each lecture I will ask you to work out the solution to a problem that covers the content of the previous lecture. Also, during lecture I will ask you to work some problems. You are welcome to ask questions during the lectures but be sure to speak loudly so everyone can hear you. I may defer answering some questions until after class if time is short or if I think the question would not be of interest to most of the other students.

• The course has three parts:

MWF Lectures: The primary source of new material will be the textbook and the Monday-Wednesday-Friday lectures. Attending the lectures is very important—students who skip the lectures tend to fail the course.

Tuesday DIS (Discussion) Sessions: Each Tuesday, you will attend a discussion session that usually is led by a mathematics graduate teaching assistant (GTA) or sometimes by a teaching

specialist who will do some sample problems that I think are important and answer any questions you have on the material or the homework. Your GTA will also collect most of your homework and return your graded homework and exams.

The GTAs are math graduate students working on a Ph.D. in math. Some may not be native speakers of English but they all have passed English qualifying exams. If you cannot understand what they are saying you should feel comfortable asking them to repeat it or write it out. I doubt this will be necessary.

Thursday PAL Sessions: Each Thursday, you will attend a Peer Assisted Learning (PAL) session. These are small classes where you will work with a PAL facilitator (who is an undergraduate student) and your fellow students to actively solve problems using a structured approach. This is not a homework question and answer session but a guided work session.

• Be sure you read the syllabus.

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• Calculator policy. On the exams, you may use a scientific calculator but no other type (graphing, cell phone, iPad, etc.).

• Textbook: You are expected to read the textbook sections before lecture. The answers to homework problems are at the back of the book and worked-out solutions can be found in the Student Solutions Manual that comes bundled with the book.

You do not have to bring the textbook to lecture. Your DIS and PAL instructors will tell you if you should bring it to their sessions.

• Check my web site for course materials.

Homework will be done according to the schedule at the end of the syllabus. It will be collected on most DIS days and exam days. It will be returned in your DIS session.

Homework is where the majority of your learning will take place because you will be practicing what you have learned from lecture and the textbook.

Homework papers are meant to communicate your understanding to the grader. We are interested in your solutions, not merely your answers. So, be sure to show your work clearly and in detail. Do not try to save paper by cramming as much as you can on a single page. Rather, spread out your work, write clearly, and include enough detail that the grader can see how you arrived at the final answer. This will be good practice for the exams also—the exams are graded primarily for procedure and an unsupported correct answer will not receive any points.

To hand in a homework assignment, put the papers in order and staple them in the upper left corner. Write your HWID, name, and the homework number in the upper right corner of the first page of the packet of papers.

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Help from tutors is available from the several different sources listed in the syllabus. Free tutors are available at lots of different times and locations and you can also get help from GTAs and me during office hours, as well as your classmates. Doing homework with someone else is a great way to learn the material as long as each person in the group participates and learns what is going on mathematically so they can perform well on the exams.

I will be asking you to answer some questions during each lecture. At the end of the lecture you will place your work in the folder for your section. This classwork will count as 5% of your final course grade. You cannot makeup the classwork.

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Ok, now let’s do some math.

We will discuss models like this to make predictions of things we want to know (distance) from things we know or can measure (time).

Math models can be quite complicated and even divinely inspired: Here is a quote from Genesis:

This model was developed by James Clerk Maxwell in 1865 to describe the propagation of light in a vacuum. For a discussion of God and Mathematics, check out Mario Livio. http://www.mariolivio.com/

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Pythagorean Theorem: The theorem is named after the Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof, although knowledge of the theorem almost certainly predates him. He lived from about 580 BC to 500 BC.

2 230 60

450067.08

12867100 1

67 .9667 1

c

feetinft

ftft inft inch

Find the hypotenuse of a right triangle with legs 30 ft and 60 ft and measure that from one corner to the other. That will guarantee a right angle.

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What do we mean by "How far could he see?"

Use Pythagoras to find x:

2 2 2

2 2 2

3955 1250 20 3955

5225 39553414

x

xx

He could see all the way across the US to the Pacific Ocean?!! No. We must convert feet to miles before continuing.

So, KK could see 43.45 miles.

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L02-Wed-7-Sep-2016-Sec-A-2-Geometry-HW02-Moodle-Q01, page 8

Get r in terms of h. Since the triangles have the same angles, they are similar. So, we can write

4 16

41

4

6

hh r

h

r

r

Now we can write

2

2

3

2

1313

163

48

4

1

h

h

h

r

h

V

h

h

Here is the graph of Volume versus height: