1.
3 3
Step 1: Recognize that the numerator is a
difference of cubes.
Step 2: Recall that a difference of cubes can be
factored as such: a3 b3 = (a b)(a2 + ab + b2)
Step 3: Factor the numerator into the following:
m3
n3 = (m n)(m2 + mn + n2)
Step 4: Rec

KEITH DEVLIN: Introduction to Mathematical Thinking (Fall 2015)
ASSIGNMENT 10.2
1. Let A = cfw_r Q | r > 0 r2 > 3. Show that A has a lower bound in Q but no greatest lower bound
in Q. Give all details of the proof along the lines of the proof given in the

KEITH DEVLIN: Introduction to Mathematical Thinking (Fall 2015)
ASSIGNMENT 10.1
1. Prove that the intersection of two intervals is again an interval. Is the same true for unions?
2. Taking R as the universal set, express the following as simply as possibl

KEITH DEVLIN: Introduction to Mathematical Thinking (Fall 2015)
ASSIGNMENT 5
1. Express the following as existence assertions. (Feel free to use a mix of symbols and words.)
(a) The equation x3 = 27 has a natural number solution.
(b) 1,000,000 is not the

KEITH DEVLIN: Introduction to Mathematical Thinking (Fall 2015)
ASSIGNMENT 6
1. Show that [xA(x)] is equivalent to x[A(x)].
2. Prove that the following statement is false:
There is an even prime bigger than 2
3. Translate the following sentences into symb

KEITH DEVLIN: Introduction to Mathematical Thinking (Fall 2015)
ASSIGNMENT 1
1. Find two unambiguous (but natural sounding) sentences equivalent to the sentence The man saw
the woman with a telescope, the rst where the man has the telescope, the second wh

KEITH DEVLIN: Introduction to Mathematical Thinking (Fall 2015)
ASSIGNMENT 3
Remember, the intention is that you work with other students on the assignments. In particular, share
your attempts with others and get their feedback. It will take you much long

KEITH DEVLIN: Introduction to Mathematical Thinking (Fall 2015)
ASSIGNMENT 2
1. Simplify the following symbolic statements as much as you can, leaving your answer in the standard
symbolic form. (In case you are not familiar with the notation, Ill answer t

Math 140
In-Class Work
College of the Canyons
Chapters 13: Experiments
1. What are the 4 principles of experiment design? Include a description of each.
2. Researchers plan to investigate a new medication that may reduce blood pressure for individuals
wit

1. Two containers are filled with gases at the same temperature. In the container on the left
is a gas of molar mass 2M, volume 2V, and number of moles 2n. In the container on the
right is a gas of molar mass M, volume V, and moles n. Which is most nearly

1. What is the formula for zinc fluoride? B. ZnF2
2. What is the formula for the compound formed by lead(II) ions and chromate ions? A. PbCrO4
3. Name the compound Ni(ClO3)2? 1. Nickel(II) chlorate
4. Name the compound CF4? C. Carbon tetrafluoride
5. What

Daniela Torres
Geometry
February 3
Over the course of this module I learned many new things and my knowledge about
geometry expanded. I found many things challenging but the most difficult thing for me to
understand was the how to find a ratio of line. Th