Math 111: Mathematics as a Liberal Art

MA 111: Mathematics as a Liberal Art

Reading Assignments
See the homework schedule.

RA W2-4

Read the following pages:
Gardner, "Ambidextrous Universe" ("AU", henceforth): Chapters 1 and 2
Weyl, "Symmetry": Preface and pp 3 - 18.

Answer the following questions briefly. You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Friday, Feb. 6.

1. In Chapter 1, Gardner claims that your reflection in two perpendicular mirrors is exactly how others see you. Do you agree with his claim? Explain your agreement or disagreement.
2. In Chapter 1, Gardner gives multiple examples of mirrors and mirror images in literature. What are two of them?
3. Do exercise 1 on page 12 of "Ambidextrous Universe".
4. Gardner uses the term "superposable". What does it mean for a figure to be superposable on its mirror image?

The remaining questions concern the reading from "Symmetry".

5. Explain informally what is meant by "symmetric with respect to a given plane".
6. Explain what is meant by a "mapping" and give two example related to the notion of "symmetry".
7. Weyl gives a number of examples of bilateral symmetry or near bilateral symmetry in art. List three of them.
8. What does Weyl say about the "scientific mind" in relation to the difference between "right" and "left"?
9. Explain, in your own words, the concepts of "congruence" and "automorphism".

RA F2-6

Read the following pages:
Gardner, "AU": Chapter 3 (carefully) and Chapter 4 (quickly)
Gardner, "Left or Right" in the Course Reader.
Weyl, "Symmetry": pp 19 - 28. (Stop before the discussion of crystals)

Answer the following questions briefly. You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Monday, Feb. 9.

1. According to Gardner, what is the difference between symmetric and asymmetric objects? (Recall that Gardner has a more restrictive notion of what it means to be symmetric than we do in class.)
2. What is an enantiomorph?
3. Answer Exercise 3 on page 17 of AU.
4. What is the essence of Gardner's explanation of why a mirror reverses left/right but not up/down?
5. What is meant by saying that modern dice are "left-handed"?
6. List 5 examples of symmetry given by Gardner in "Left or Right".
7. Gardner gives an answer to the "mirror question" (see 4. above). In the Addendum to "Left or Right", Tschirgi and Taylor give a psychological answer. Do the two answers contradict or reinforce each other? Which of them do you find most convincing? Why?

The remaining questions concern the reading from "Symmetry".

8. Summarize and explain "Mach's shock". Why doesn't this violate parity?
9. Summarize Weyl's summary of the disagreements between Newton, Leibniz, and Kant concerning left/right.
10. Summarize Weyl's comments concerning the presence or absence of symmetry between past/future and positive/negative charge (electricity).
11. According to Weyl, why is symmetry so common in biological organisms?

RA M2-9

Read the following pages:
Gardner, "AU": Chapter 5. (You may skim the discussion of palindromic numbers.)
Weyl, "Symmetry": pp 28 - 38.

Answer the following questions briefly. You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Wednesday, Feb. 11.

1. Gardner points out a contrast between the treatment of symmetry in Western art and in Japanese art. What is it?
2. Why are vertical axes of symmetry so common in nature?
3. What are some examples of symmetry in music or poetry?

The remaining questions concern the reading from "Symmetry".

4. What is meant by "laevo" and "dextro"-forms of a substance?
5. What achievement of Pasteur's is described by Weyl?
6. On page 32, Weyl refers to "a real difficulty". What is this real difficulty? State it in your own words. What are some solutions posited by Weyl and/or Pascual Jordan?
7. Is it the case that how a fertilized egg initially divides determines what becomes left and right in a bilaterally symmetric creature?
8. What is inversive regeneration?

RA W2-11

Read the following pages:
Gardner, "AU": Chapters 6 - 9.
Weyl, "Symmetry": pp 41 - 46 (stop before the first full paragraph on page 46).

Answer the following questions briefly. You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Friday, Feb. 13.

(Questions regarding AU)
1. What are ways that our galaxy is symmetric?
2. What are ways that our galaxy is asymmetric?
3. What is the relationship between ``spinning'' and ``handedness''?
4. What is the Coriolis force?
5. Why does Gardner find the honeysuckle to be an interesting plant?
6. List several types of symmetry found in plants and animals.
7. Give an evolutionary explanation for the bilateral symmetry found in land mammals.
8. List three instances of spirals or helices in animals.
9. What makes the sex life of the anablep asymmetrical?
You can read more about anableps (and see photos) here. 10. Without looking answer the following question and then check your answer: On a penny, does Lincoln face left or right?
11. Enjoy Chapter 9, but realize that all of the studies quoted are significantly out-dated.
The remaining questions concern the reading from "Symmetry".

12. If S and T are symmetries, what are two ways of writing the inverse of their combination ST?
13. Weyl introduces a number of new terms, most of which we won't use. One distinction worth making, though is his distinction between a proper congruence (or automorphism) and an improper congruence (or automorphism). What is the distinction here between ``proper'' and ``improper''?
14. The most important part of the reading occurs at the top of page 45. For a spatial configuration F, what is the mathematical description of the symmetries of F? (See the sentence in italics.)
15. How many symmetries does the pentagram have?
In the terminology of this course, here is an explanation of what Weyl is discussing.

If we have a shape F in the plane and a congruent shape F' somewhere else in the plane, the act of moving F to F' creates an automorphism of the plane. Weyl calls this a congruent transformation. That is, a ``congruent transformation'' is a transformation of the plane made by moving some shape F to some congruent shape F'. When we discuss congruent transformations, we should always have specific shapes F and F' in mind. Every congruent transformation is also an automorphism of the plane. Thus the congruent transformations (of F and F') are a subgroup of the group of automorphisms of the plane. A congruence is proper if it takes a circle with a clockwise-pointing arrow on it to a circle with a clockwise-pointing arrow on it. (Weyl discusses this in terms of screws, rather than circles with arrows.)

When Weyl discusses a ``similarity'' he means a transformation of the plane which might stretch or shrink the plane. The similarities of the plane also form a group. The automorphisms of the plane are a subgroup of this group.

One other aspect worth noting in this discussion is that Weyl considers reflections to be improper rotations.

RA F2-13

Read the following pages:
Gardner, "AU": Chapter 10.
Gardner, "Rotations and Reflection" in the Reader.
Weyl, "Symmetry": pp 46 - 50 (stop before the first full paragraph on page 50).

Answer the following questions briefly. You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Monday, Feb. 16.

(Questions regarding AU)
1. Gardner provides multiple examples of situations where a left-handed person is at a disadvantage. List two that are no longer relevant due to changes in technology or culture.
2. List two examples of current situations where left-handers are at a disadvantage or are inconvenienced that would not have existed in the 1960s when this chapter was first written.
3. List two examples of situations where left-handed people have a (perhaps marginal) advantage. (You may list examples given by Gardner.)
4. On page 88, Gardner suggests experimenting with writing a mirror image of your name. Try this and report on the results.
(Questions regarding "Rotations and Reflections")
5. Who was Gustav Verbeek?
6. What is your reaction to the "severed head" party game?

The remaining questions concern the reading from "Symmetry".

7. If a plane figure has a symmetry which changes the scale then the figure must extend to infinity. (Imagine for example a sequence of nested circles, centered at the orign with radii that increase towards infinity and decrease towards zero.) Weyl gives an argument that this must be the case. Summarize the crux of his argument.
8. If a translation t moves all points on a line by a distance of a, how far does the translation t^{n move the points? (The notation tⁿ means the translation t repeated n times.)

9. Describe (in words) the two types of symmetry possible for a 1-dimensional pattern or ornament.

RA M2-16
Read the following pages:

Gardner, "AU": Chapters 11 and 12.

Weyl, "Symmetry": pp 50-64.

Answer the following questions briefly. You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Wednesday, Feb. 18.

(Questions regarding AU)

1. What are the three types of elementary particles?

2. Read about the Large Hadron Collider (LHC) at the LHC's website. What is the LHC and why was it built?

3. What is a lattice?

4. On page 97, Gardner discusses the rotational symmetries of a cube. What are the different kinds of rotational symmetry. Explain in your own words.

5. What does Gardner mean by the phrase ``nonperformable operation''?

6. What is a ``platonic solid'' and what are the five platonic solids?

7. How can the asymmetry of certain crystals affect a beam of light?

8. What were Biot and Pasteur's contributions to the study of crystals?

9. What is Pasteur's ``well-marked line of demarcation that can at present be drawn between the chemistry of dead matter and the chemistry of living matter''? (p 106)

10. Summarize what is meant by ``right-handed'' and ``left-handed'' substances (like tartaric acid).

(If you like mysteries and are intrigued by the consequences of chemicals having a ``handedness'' you might enjoy The Documents in the Case by Dorothy L. Sayers.)

The remaining questions concern the reading from "Symmetry".

11. Describe the symmetries of the scolopendrid.

12. Name some composers whose works can be studied using group theory.

13. Describe how a band ornament can be used to decorate a cylindrical object.

14. What type of cyclic symmetry is most common in flowers?

15. Name two authors who refer to the symmetry of snowflakes.

RA W2-18
Read the following pages:

Gardner, "AU": Chapter 13

Weyl, pp 65-67.

Answer the following questions briefly. You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Friday, February 20.

(Questions regarding AU)

1. What is an isomer? and what is stereoisomerism?

2. What does racemic mean?

3. Why is grape sugar called dextrose and what is the difference between in and fructose?

4. It may interest you to know that the L-sugar referred to on page 119 is now called Naturlose and is in clinical trials.

5. What is the alpha helix?

6. What causes the difference in smell between oranges and lemons?

7. Would the enantiomorph of milk taste the same as milk? Why or why not?

The remaining questions concern the reading from "Symmetry".

8. What did Leonardo da Vinci do and what is its relation to group theory?

9. What are some examples of cyclic, but not dihedral, symmetry in nature?

RA F2-20
Read the following pages:

Gardner, "AU": Chapters 14 and 15

Weyl, pp 68-70.

Answer the following questions briefly. You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Monday, February 23.

(Questions regarding AU)

1. What makes the ``mosaic disease'' virus asymmetric? (Your answer should involve the words amino acid.

2. Gardner spends some time discussing the ambiguity of the term ``life''. How do you define the term? In your answer, be sure to react and respond to Gardner's discussion.

3. What would happen to a person who suddenly became their own entantiomorph? What would make survival difficult?

4. On pages 135-136, Gardner challenges certain religious believers who reject an evolutionary account of the origin of life. Summarize and critique Gardner's argument. How would a religious believer of the sort Gardner refers to respond to Gardner's statements? The purpose of this question is not, necessarily, to have you disagree with Gardner, but rather to think carefully about what he is saying. You may, of course, choose to agree or disagree with him.

5. What is the theory of panspermia?

6. What did Pasteur prove with regard to spontaneous generation?

7. According to Japp, what does asymmetry have to say about the origin of life?

8. Summarize Gardner's rebuttal of Japp's arguments (p 143).

The remaining questions concern the reading from "Symmetry".

9. How is a logarithmic spiral like a straight line and circle?

10. What are two examples of logarithmic spirals in nature?

RA M2-23
Read the following pages:

Gardner, "AU": Chapters 16 and 17

Answer the following questions briefly. You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Wednesday, February 25.

(Questions regarding AU)

1. What were two possibilities considered by Pasteur for the origin of asymmetry in life?

2. What are two other possibilities for the origin of asymmetry in life?

3. What is Leibniz's view of space?

4. What is the Newtonian view of space?

5. What was Kant's thought experiment which argued for a Newtonian view of space? What is its error?

6. What is Kant's ultimate synthesis of Newton's and Leibniz's views?

7. What are two examples of science fiction stories which use a fourth dimension to turn something into its entantiomorph?

8. What did Zollner require Slade do in order to demonstrate command of a fourth dimension?

9. You do not need to understand Gardner's explanation of non-orientable surfaces. It is tangential to his main point and it is regrettable that he relies on the swastika for his example.

RA W2-25
Read the following pages:

Gardner, "AU": Chapters 18 and 19

Answer the following questions briefly. You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Friday, February 27.

(Questions regarding AU)

1. What is Project Ozma?

2. Summarize the Ozma Problem.

3. Why should the (magnetic) north pole of the earth really be called the south pole?

4. What is the Bohr model of the atom?

5. What is used to help guide a spaceship?

6. What is the Barkhausen effect?

7. What is a monopole?

8. What is the solution to Mach's shock?

RA F2-27
Read the following pages:

Gardner, "AU": Chapter 20

Gardner, ``Group Theory and Braids'' in the Reader

Answer the following questions briefly. You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Monday, March 2.

(Questions regarding AU)

1. Do exercise 14 on page 189.

2. What is meant by a system of ``even parity'' (p 190)?

3. What does Gardner mean when he says that ``nature is apparently completely ambidextrous'' ?

4. Does Gardner's science fiction story sound like it would be an enjoyable read?

(Questions regarding ``Group Theory and Braids'')

5. How can the permutation groups (or symmetric group as we called it in class) be used to decide who pays for drinks?

6. Gardner describes how braids form a group. What is the inverse of a braid?

7. Is the braid group on n strands the same as the symmetric group of n dots? Why or why not?

8. Summarize how Piet Hein's braid game is played.

Piet Hein is most well-known for his poems called ``Grooks''. You may read some of them here.

RA M3-2
Read the following pages:

Gardner, "AU": Chapter 21

Gardner, ``The Monster and Other Sporadic Groups'' in the Reader

Answer the following questions briefly. You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Wednesday, March 4.

(Questions regarding AU)

1. What is as "grotesque as a stamp collection"?

2. What is the J-psi?

3. What was James Clerk Maxwell's big achievement and how is it related to something Einstein did?

4. What differentiates a particle from an antiparticle?

5. What is antimatter?

6. A lot of the hypothesizes uses for antimatter are militaristic. What would be two civilian uses? Name one given by Gardner, and come up with one yourself.

7. Does the existence of antimatter violate parity? Why or why not?

(Questions regarding ``The Monster'')

8. What is the cyclic 4-group?

9. What is the Klein 4-group?

10. What is a Lie group?

11. What is Gardner definition of ``geometry''?

12. When were the first five sporadic simple groups discovered?

13. According to Gardner, when was the classification of finite simple groups completed? (The actual history, however, is much more complicated.)

RA W3-4
Read the following pages:

Gardner, "AU": Chapter 22

Weyl, ``Symmetry'': pages 71-73 (stop after the discussion of phyllotaxis.)

Answer the following questions briefly. You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Friday, March 6.

(Questions regarding AU)

1. What is the strong force?

2. Why do physicists believe in the weak force?

3. Who asked whether or not parity could be violated on on whose behalf was it asked?

4. Who devised experiments to determine if parity was conserved in weak interactions?

5. Who performed an experiment?

6. What did the experiment involve?

7. How does the experiment solve the Ozma problem?

8. Do Exercise 16 on page 217

9. What does Gardner mean when he describes science as a "continual, perhaps neverending, discovery of new lumps?"

(Questions regarding ``Symmetry'')

10. What is phyllotaxis?

11. What kind of symmetry to the scales on a fir-cone demonstrate?

RA F3-6
Read the following pages:

Weyl, ``Symmetry'': pages 73-79

Answer the following questions briefly. You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Monday, March 9.

(Questions regarding ``Symmetry'')

1. What are the five Platonic Solids?

2. What use did Etruscans make of the dodecahedron?

3. Why did Kepler care about the Platonic solids?

4. What does Weyl think of Kepler's search for mathematical harmony?

5. What is an Umklappungen?

6. Do each of the 5 Platonic solids produce a different group of symmetries? Explain.

RA M3-9
Read the following pages:

Weyl, ``Symmetry'': pages 83-93

Answer the following questions briefly. You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Wednesday, March 11.

(Questions regarding ``Symmetry'')

1. What is a ``minimal surface''?

2. Name two occurences of a froth of 2-dimensional bubbles.

3. Why is it impossible to (smoothly) cover a sphere with a hexagonal net?

4. Why are bees such good geometers?

5. What is special about the tetrakaidekahedron?

RA M3-16
Read the following pages:

Weyl, ``Symmetry'': pages 103-104 (start with the first full paragraph on p 103), 109-115

Answer the following questions briefly. You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Wednesday, 3-18.

(Questions regarding ``Symmetry'')

1. How many possibilities are there for a symmetry group of a two dimensional repeating pattern?

2. Who were the ``greatest masters'' of the geometric art of ornament?

3. In Figures 64-66 some basic ornamental patterns are pictured. Which is your favorite?

RA M3-30
Read the following pages:

Flatland Dedication and pp 3-22 (sections I.1 through I.5)

Also read Euclid's Elements Book I, Proposition 1.

Answer the following questions briefly. You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Wednesday, April 1.

1. Why does A Square write Flatland? (See the dedication to the book.)

2. Describe what a Flatlander sees.

3. How does a Flatlander determine where North is?

4. What happens to a Flatlander who inquires into the nature of light?

5. Describe the physical difference between a male Flatlander and a female Flatlander. What is Abbott conveying by this distinction?

6. Who are the priests?

7. What is the Law of Nature concerning the number of sides of a Flatland male?

8. What is the Law of Compensation?

9. Name 4 rules governing the conduct of Flatland females?

10. Name 2 methods used by Flatlander's to recognize each other?

11. How does feeling work?

12. What happened to Square's great-great-great-great grandfather?

13. What happens to the Criminal and Vagabond classes?

14. What is the purpose of proposition 1 from book I of Euclid's Elements? Have you ever done something similar in a math class?

15. What is one objection to the proof of this proposition?

RA W4-1
Read the following pages:

Flatland Sections 6 - 12

Answer the following questions briefly. You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Friday, April 3.

1. Describe the role of fog in using sight to recognize a fellow Flatlander.

2. Do all Flatlanders practice sight recognition? If not, who does?

3. What happens to those who do not pass the sight recognition exam at University?

4. Describe the effect of admitting irregular shapes into society on society.

5. Are irregular shapes criminal by nature or because they were brought up that way?

6. Who was Chromatistes?

7. What similarities between women and priests are mentioned?

8. Name two effects that colour had on Flatland society.

9. Name two effects that colouring women and priests would have on society.

10. What made the women turn against the colour bill?

11. Who was Pantocyclus?

12. How is the colour revolution overcome?

13. When Square is writing, where can colour be found?

14. How many sides (according to popular agreement) does the Chief Circle have?

15. How can a polygon's child leap ahead many generations in terms of the number of sides?

16. What, according to Square, is the merit of the Circles?

17. What are the disadvantages, according to Square, of forbidding females education?

RA F4-3
Read the following pages:

Flatland Sections 13 - 16

Answer the following questions briefly. You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Monday, April 6.

1. Describe the inhabitants of Lineland.

2. How are marriages in Lineland consummated?

3. Who (in your opinion) leads the duller life -- Square or the King of Lineland?

4. How does Square respond to his grandson's questions about cubing the number 3?

5. How is it that Sphere can see the insides of Square?

6. How does Square describe the geometric properties of women? Reflect on this in relation to previous descriptions of women.

7. Describe two ways in which Sphere attempts to convince Square of the existence of the 3rd dimension.

8. How many vertices would a 4-dimensional square have? (Reason by analogy to lower dimensions.)

9. How many sides would a 4-dimensional square have?

RA M4-6
Read the following pages:

Flatland Sections 17- 22

Answer the following questions briefly. You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Wednesday, April 8.

1. Name two actions taken by Sphere to convince Square.

2. What is omnividence?

3. Why is Square unconcerned by the Assembly's proclamation?

4. What was the ``Climax, the Paradise,'' of Squares visit to Spaceland?

5. What does Square come to believe that Sphere is no longer the Perfection of All Beauty?

6. How are the Monarch of Pointland's psychology and physical being related?

7. What happens when Square tries to explain his experiences?

8. React to Square's ultimate fate.

RA W4-8
Read the following pages:

Jann's article: Abbott's Flatland: Scientific Imagination and ``Natural Chrisitianity'' in the Course Reader

You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Friday April 10.

1. Summarize the main points of Jann's article in one paragraph.

2. Ask one question about Jann's article. I will try to address some of these questions in class.

RA F4-10
Read the following pages:

Smith, Berkove, and Baker article: ``A grammar of dissent'' in the Course Reader

You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Monday, April 13.

1. Summarize the main points of the in one paragraph.

2. Ask one question about the article. I will try to address some of these questions in class.

RA M4-13
Read the following pages:

pp 209 - 226 Plato's Republic in the Course Reader.

Gardner's story ``The Church of the 4th Dimension'' in the Course Reader

You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Wednesday, April 15.

1. List 3 parallels between Square's life and experiences and that of the released prisoner in the ``Allegory of the Cave''.

2. According to Socrates (the main speaker in the Republic), what is the cause of ``all things right and good''?

3. Why should a general master arithmetic and calculation? (p 219)

4. What is the real purpose of Geometry? (p 221)

5. What is the relationship between the allegory of the cave and the course of studies proposed by Socrates? (p 226)

6. Who was Henry Slade?

7. Name a spiritualist interested in the concept of the 4th dimension.

RA W4-15
Read the following pages:

Banchoff's introduction to Flatland (p. xv to xxxvi)

Gardner's essay ``Flatlands'' in the Reader

Gardner's essay ``The wonders of the planiverse'' in the Reader.

You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Monday, April 20.

1. List two facts (mentioned by Banchoff) about Abbott that you found interesting (mentioned by Banchoff)

2. What is one way in which ideas of higher dimensions are used today?

3. Who was C.H. Hinton?

4. What makes Astria different from Flatland?

5. How did Dewdney's Planiverse begin?

6. Why don't planiverse 2-legged creatures fall over as often as 3-dimensional 2-legged creatures?

7. What is pinch?

RA W4-22
Read the following pages: p v - 47 of Devlin's The Unfinished Game

You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Monday, April 27.

1. When did the correspondence between Pascal and Fermat occur?

2. Aristotle taught that there were 3 kinds of events. What are they?

3. What is the problem of the points? Give a thorough description of the problem.

4. What is frequentist probability?

5. What is subjective probability?

6. Who was Girolamo Cardano?

7. How did Galileo's approach to probability differ from Cardano's?

8. What is the method for creating Pascal's triangle?

9. What was Fermat's profession?

10. What instigated the correspondence between Pascal and Fermat?

11. If Blaise and Pierre are to play a game by flipping a coin 5 times and if after three tosses Blaise is ahead 2 to 1, how should the pot of money be divided if the game is interrupted? Explain your answer carefully.

12. What were Pacioli's contributions to probability theory?

13. How does Cardano define ``the probability of an event''?

RA M4-27
Read the following pages: p 49-84 of Devlin's The Unfinished Game. Chapter 6 is rather technical. You need not dwell too much on the details.

You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Wednesday, April 29.

1. Describe the person Blaise Pascal.

2. What religious sect influenced Pascal?

3. What killed Pascal?

4. What was Fermat's main area of mathematical research?

5. What is Pascal's method for trying to understand Fermat's approach?

6. What number theory mistake did Fermat make?

RA F5-1
Read the following pages: p 85 - 143 of Devlin's book.

You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Monday, May 4.

1. What was John Graunt's major contribution to the history of thought?

2. How did Graunt come to believe that rickets was a new disease?

3. What was Huygen's main contribution to probability theory?

4. Summarize Pascal's wager (his argument concerning belief in the existence of God).

5. What is the difference, according to Jakob Bernoulli, between a priori and a posteriori probabilities?

6. Summarize the St. Petersburg Paradox.

7. What is ``utility''?

8. On page 129, there is a summary of when the bell curve shows up. This is worth emphasizing, so repeat the summary here.
9. What is the main idea behind Bayes' method?
10. What is the prosecutor's fallacy?

RA M5-4
Read the following pages: p 145- 169 of Devlin's book.

Read this article from Wired Magazine.

You should copy and paste these questions and your answers into an email message to either MA111A (at) colby.edu or MA111B (at) colby.edu . The subject line of your email should contain the title of this assignment only. Your responses are due by 6 AM on Wednesday, May 6.

1. What is SiteProfiler?

2. Devlin gives the example of his brother Peter who tells you that he has two children, at least one of whom is a girl. What is the probability that the other child is a boy?

3. What is the significance of the birthday paradox for DNA profiles?

4. What is the point of the Black-Scholes equation?

5. What was the point of Li's copula function?

6. What is a credit default swap?

6. What went wrong (according to Wired)?}