Connecting STE to M. Robert Rogers SUNY Fredonia. JMM January 11, 2015
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1 Connecting STE to M Robert Rogers SUNY Fredonia JMM Januar 11, 2015
2 MAED 310 Reading/Writing Mathematics
3 MAED 310 Reading/Writing Mathematics Created b the department to partiall satisf the 6 hour literac requirement for all pre-service teachers in NYS
4 MAED 310 Reading/Writing Mathematics Created b the department to partiall satisf the 6 hour literac requirement for all pre-service teachers in NYS Required of all Mathematics/Middle Childhood Education Mathematics and Mathematics/Adolescence Education majors and Elementar Education Middle Childhood Mathematics Etension majors.
5 MAED 310 Reading/Writing Mathematics Created b the department to partiall satisf the 6 hour literac requirement for all pre-service teachers in NYS Required of all Mathematics/Middle Childhood Education Mathematics and Mathematics/Adolescence Education majors and Elementar Education Middle Childhood Mathematics Etension majors. I use this course to promote STEM education and help answer the question Does anone actuall use this stuff?
6 Richard E. Smalle, Robert F. Curl, Sir Harold Kroto
7 Richard E. Smalle, Robert F. Curl, Sir Harold Kroto are:
8 Richard E. Smalle, Robert F. Curl, Sir Harold Kroto are: a. members of the 1965 Manchester United Championship Soccer Team.
9 Richard E. Smalle, Robert F. Curl, Sir Harold Kroto are: a. members of the 1965 Manchester United Championship Soccer Team. b. members of the UK Olmpic Committee that helped institute soccer as an Olmpic sport in 1988.
10 Richard E. Smalle, Robert F. Curl, Sir Harold Kroto are: a. members of the 1965 Manchester United Championship Soccer Team. b. members of the UK Olmpic Committee that helped institute soccer as an Olmpic sport in c. award winning architects who worked with Richard Buckminster Fuller on the geodesic domed US pavilion at the 1967 World Fair in Montreal.
11 Richard E. Smalle, Robert F. Curl, Sir Harold Kroto are: a. members of the 1965 Manchester United Championship Soccer Team. b. members of the UK Olmpic Committee that helped institute soccer as an Olmpic sport in c. award winning architects who worked with Richard Buckminster Fuller on the geodesic domed US pavilion at the 1967 World Fair in Montreal. d. winners of the 1996 Nobel prize in chemistr.
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13 Richard E. Smalle, Robert F. Curl, Sir Harold Kroto are: a. members of the 1965 Manchester United Championship Soccer Team. b. members of the UK Olmpic Committee that helped institute soccer as an Olmpic sport in c. award winning architects who worked with Richard Buckminster Fuller on the geodesic domed US pavilion at the 1967 World Fair in Montreal. d. winners of the 1996 Nobel prize in chemistr.
14 Richard E. Smalle, Robert F. Curl, Sir Harold Kroto are: a. members of the 1965 Manchester United Championship Soccer Team. b. members of the UK Olmpic Committee that helped institute soccer as an Olmpic sport in c. award winning architects who worked with Richard Buckminster Fuller on the geodesic domed US pavilion at the 1967 World Fair in Montreal. d. winners of the 1996 Nobel prize in chemistr.
15 The Nobel Prize in Chemistr 1996 Robert F. Curl Jr. Sir Harold W. Kroto Richard E. Smalle 1/3 of the prize 1/3 of the prize 1/3 of the prize USA United Kingdom USA Rice Universit Houston, TX, USA Universit of Susse Brighton, United Kingdom Rice Universit Houston, TX, USA b b b d. 2005
16 Before 1985, scientists knew of onl two forms of pure carbon. Diamond Graphite
17 In 1985, Curl, Kroto, and Smalle discovered a new pure carbon molecule. C 60
18 The called it a Buckminsterfullerene, in honor of the architect Richard Buckminster Fuller. C 60
19 Fuller pioneered the design of geodesic domes. U. S. Pavilion, Epo 67 Montreal
20 1. Who are Robert F. Curl, Jr., Richard E. Smalle, and Sir Harold W. Kroto, what is a Buckminsterfullerene, and what does this have to do with polhedra? Briefl describe how a Buckball is produced from graphite and it makes sense (molecularl) that graphite would be used. Name three uses/potential uses for a Buckball. 2. Briefl describe how a Fullerene nanotube is made from a Buckball. What is the length of the longest nanotube to date? Suppose a ¼ inch diameter straw had the same length to diameter ratio as the longest nanotube to date. How man miles long would it be? Name three uses/potential uses for a nanotube. 3. Use Euler s formula for a planar graph to prove the Euler- Descartes Formula for a hollow polhedron. Euler-Descartes Formula: Given a hollow polhedron with v vertices, f faces, and e edges v + f e = 2
21 Some Uses of a Buckball : Medicine: BUCKY DRUG. Model of a fullerene-based HIV protease inhibitor recentl designed b Simon Friedman. Scientists also want to use buckballs as a passke to inject drugs into cancer cells.
22 How man pentagons are in this Dodecahedron
23 How man pentagons are in a soccer ball?
24 How man pentagons are in this Callawa HX Hot Plus golf ball?
25 How man pentagons are in this C 540 carbon molecule?
26 4. Show that a hollow polhedron whose faces consist of either pentagons or heagons must have eactl 12 pentagons. (One can show that such a polhedron must have three edges emanating from each verte, but ou can just assume this.) 5. In light of Problem #4, both a soccer ball and a Callawa HX Hot golf ball contain 12 pentagons. How man heagons does each contain?
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28 This machine is:
29 This machine is: a. an industrial baker dough mier.
30 This machine is: a. an industrial baker dough mier. b. a device for treating kidne stones.
31 This machine is: a. an industrial baker dough mier. b. a device for treating kidne stones. c. a forensic spectral analzer.
32 This machine is: a. an industrial baker dough mier. b. a device for treating kidne stones. c. a forensic spectral analzer. d. a device for testing the effects of vibrations on small airplane components.
33 Dornier HM-1 lithotripter (1980)
34 This machine is: a. an industrial baker dough mier. b. a device for treating kidne stones. c. a forensic spectral analzer. d. a device for testing the effects of vibrations on small airplane components.
35 This machine is: a. an industrial baker dough mier. b. a device for treating kidne stones. c. a forensic spectral analzer. d. a device for testing the effects of vibrations on small airplane components.
36 Dornier HM-1 lithotripter (1980) [Etra-corporeal shock wave lithotrips (ESWL)]
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39 Question from NYS June 2007 Math B Eam 30 A landscape architect is working on the plans for a new horse farm. He is laing out the eercise ring and racetrack on the accompaning graph. The location of the circular eercise ring, with point R as its center, has alread been plotted. Write an equation that represents the outside edge of the eercise ring. The equation of the outside edge of the racetrack is = Sketch the outside edge of the racetrack on the graph.
40 There is a histor of asking sill contetual math questions.
41 There is a histor of asking sill contetual math questions. Liber abbaci (1228) Leonardo of Pisa (Fibonacci) There is a lion at the bottom of a pit 50 feet deep. The lion climbs up 1/7 of a foot each da and then falls back 1/9 of a foot each night. How long will it take the lion to climb out of the pit?
42 There is a histor of asking sill contetual math questions. Liber abbaci (1228) Leonardo of Pisa (Fibonacci) There is a lion at the bottom of a pit 50 feet deep. The lion climbs up 1/7 of a foot each da and then falls back 1/9 of a foot each night. How long will it take the lion to climb out of the pit? Leonardo gives the incorrect answer of 1575 das. (Actual answer is 1573 das.)
43 IBM Quantum Mirage Project
44 IBM researchers have placed 36 cobalt atoms in an elliptical ring on a copper substrate in their efforts to design nanoprocessors for nanobots. An equation for such an ellipse is given b = 1 Plot the graph of this ellipse on the accompaning aes (units are in nanometers) and give IBM the Quantum lengths Mirage of the Project major and minor aes of this ellipse.
45 1. Consider the ellipse whose equation is given b 2 2 = 1, where a > b. Find the coordinates of the foci and show how ou obtained them. + 2 a 2 b 2. Who coined the term quantum mirage and when did he/she do this? What was his/her occupation at the time? What is the length and width of the smallest quantum corral to date? Briefl describe how IBM intends to use quantum corrals? 3. When did Dornier build the first commercial lithotripter and what was the model number. Briefl describe how it uses ellipses to break up kidne stones.
46 4. Consider the following ellipse. Show that the equation of This ellipse is given b a 2 a a 1 = 1 Solve this for 2 and take the limit of this as a approaches infinit to show that a parabola can be thought of as an ellipse, one of whose foci is at infinit. Eplain how this gives us the reflective propert of the parabola. 5. What is the diameter of each of the primar mirrors in the Giant Magellan Telescope and who casts these? Wh do the use spin casting? Where will the Giant Magellan Telescope be located and when is it scheduled for completion.
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50 2. What do the various digits in a ten-digit International Standard Book Number (ISBN) represent? Who developed the ISBN-10 sstem and when? When was this finall converted to the ISBN-13 sstem and wh was this done? What does this have to do with an EAN and how does one convert an ISBN-10 number to an ISBN-13 number? 3. Referring to the old ISBN-10 sstem, I saw in a book that the number d 1 d 2 d 10 is a valid ISBN provided 11 (1 d d d d 10 ) I saw in another book that it is a valid ISBN provided 11 (10 d d d d 10 ) Which book is correct? Eplain.
51 4. The Universal Product Code (UPC) is a 12-digit code number on each product manufactured. The first digit represents the kind of product. The net five digits represent the manufacturer. The net five digits represent the product. The last digit is a check digit. The number d 1 d 2 d 3 d 12 is a valid UPC number provided 10 (3 d 1 + d d 3 + d d d 11 + d 12 ) Show that this scheme will detect all single-digit errors and will detect approimatel 88.89% of errors where two consecutive digits are switched.
52 1.a. Who are the R, S, and A in the RSA public ke encrption scheme and when did the develop RSA encrption? What were their occupations at the time? What is the original name of the compan the formed? Who owns the compan now, when did the acquire it, and how much did the pa for it? b. What is the RSA factor challenge? When and wh was it formed? When and wh did it end? What was the largest cash prize ever offered and what was the largest prize ever paid out? 2. Find the largest prime number known to date. When was it discovered and how man digits long is it?
53 The rest of the homework deals with the mathematics behind public ke encrption. 3. Prove the following lemma. Lemma. Let p be a prime number and let k be an integer with 0 < k < p. Then where C p, k = p! k! p k!. p C(p, k) Show that this is not necessaril true if p is not prime.
54 4. Use the above lemma to prove the following theorem due to Pierre de Fermat (1640). Fermat's Little Theorem. Let p be a prime number and let N be an integer. Then p (N p N) In particular, if p does not divide N then p (N p 1 1). 5. Let p and q be distinct prime numbers. Let a = p q and b = p 1 (q 1). Then a (N 1+bf N) for an positive integers N and f.
55 Nikolai Egorovich Joukowski ( )
56 Nikolai Egorovich Joukowski was:
57 Nikolai Egorovich Joukowski was: a. Minister of Defense under Stalin.
58 Nikolai Egorovich Joukowski was: a. Minister of Defense under Stalin. b. Minister of Science under Czar Nicholas II.
59 Nikolai Egorovich Joukowski was: a. Minister of Defense under Stalin. b. Minister of Science under Czar Nicholas II. c. the father of Russian Aviation.
60 Nikolai Egorovich Joukowski was: a. Minister of Defense under Stalin. b. Minister of Science under Czar Nicholas II. c. the father of Russian Aviation. d. the head of the Moscow Conservator of Music,
61 Write the following comple number in the form + i i
62 Write the following comple number in the form + i i Solution: i = i 2 i 2 i = 2 i 5 = i
63 Im z z i i i i i z i z
64 Im z z i i i i i z i z
65 Im z z i i i i i z i z
66 Im z z i i i i i z i z
67 Plot Im z 1 z 2 2 c for various constants c
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71 What happened?
72 z = + i, = 1 f z = i = 2
73 Im( w) c
74 The function f is called the Joukowski Transformation Im( w) c
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77 Nikolai Egorovich Joukowski was: a. Minister of Defense under Stalin. b. Minister of Science under Czar Nicholas II. c. the father of Russian Aviation. d. the head of the Moscow Conservator of Music,
78 Nikolai Egorovich Joukowski was: a. Minister of Defense under Stalin. b. Minister of Science under Czar Nicholas II. c. the father of Russian Aviation. d. the head of the Moscow Conservator of Music,
79 STEM can be infused passivel into the curriculum (internet searches for etra credit, etc.) and often can be motivated b a picture or a question. It won t necessaril make everone a scientist, but it ma turn on a few and at least provides a reason for studing mathematics.
80 STEM can be infused passivel into the curriculum (internet searches for etra credit, etc.) and often can be motivated b a picture or a question. It won t necessaril make everone a scientist, but it ma turn on a few and at least provides a reason for studing mathematics. Eample A tease for net time: What was the first movie to use fractals to computer generate its special effects?
81 Thank ou!
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