Thursday, July 30, 2015

Teaching NCC SII M111: PreCalculus UNIT05 Vectors, Series and Conic Sections! 07/27/15 - 07/30/15

Teaching NCC SII M111:
PreCalculus UNIT05
Vectors, Series and Conic Sections!
07/27/15 - 07/30/15

WEEK05 ScreenCasts:
CH12 was about Vectors. CH13 is about Series. CH14 covered Conics! That's it for this semester. Have a great Summer Break!

WEEK05 GROWING PAINS:
All the topics this week were what I  would call "Capstone Topics!" What I mean by that is that they build on all the concepts we've being working on all Summer long! So, this unit was by far the most challemging for the students.

Not a FILK. Why units mater!

Walking from North Lot to Cluster E
After Cluster F you're at the Libe
Now you are in front of Building T
Near Builing T again
Walking to South Parking Lot
You can see the Nassau Colosseum
Walking back to Building T
Walking around Cluster A
Walking back to Cluster B by East Lot

Teaching NCC SII M111:
PreCalculus UNIT04
Polynomial vs. Rational Functions!
07/20/15 - 07/23/15

WEEK04 ScreenCasts:
CH09 was about CIS(theta) and Trig Identities. CH10 covered Compostition of Functions and Inverse Functions. CH11 discussed Polynomial Functions and Rational Functions.

WEEK04 GROWING PAINS:
Chapters 9-12 talk about solving equations using all the tools we've developed so far this semester. The main point is: we can use inverse functions to simplify equations and make said equations easier to solve. For example, to solve sin(theta)=0.8 we used the Inverse Sine function to find theta. Also, to solve ln(x)=12, we need to raise both sides of the equation as powers of e thereby using exponential functions to solve logarithmic equations.

BTW, CIS(theta) makes products, quotients and powers (even radicals) of Complex Numbers very easy. We even introduced Euler's Identity: e^(i*theta)=CIS(theta) in radian mode. Since CIS(theta) is short hand for cos(theta)+i*sin(theta) we were able to derive DeMoivre's Theorem. Further, we found that e^(i*pi)=cos(pi)+i*sin(pi)=-1. In other words, e^(i*pi)=-1 or e^(i*pi)+1=0. This is quite possibly the most profound, yet useless, statement in all of arithmetic as it involves 5 of the most important constants we use whenever we solve equations! This is not to say that Euler's Identity and DeMoivre's Theorem are not very useful, especially in Calculus I, II, III and IV!

This week we finished off our Astronomy YouTubes with Carl Sagan's Pale Blue Dot on Monday and Morgan Freeman's Powers of 10 on Tuesday. Then, on Wednesday, we introduced The Queen of Software, Gracey herself! Why did we have a bunch of Astronomers as Guest Speakers? Because, Astro-Physicists use preCalculus and Calculus all day every day to plot planet orbits and figure out if asteroids are on a collision course with Earth! Also, Astronomers talk about really, really big and really, really small numbers which is the heart of the branch of mathematics that we are studying called Analysis. Calculus and preCalculus are a part of Analysis!

Carl Sagan:
Powers of 10:
Look on CBSrewind for 60 Minutes Interview!

WEEK04 VISITING PROFESSOR's WALK ABOUT: (coming soon)
Eastern Parking Lot:
Life Sciences by East Lot:
North Lot Charging Station:
North Lot view of Tower:
North Lot Security Gate:
BookStore by North Lot:
Mitchel Field Hanger (WWI Pilot Training) by Quad:
Office Buildings by Quad (WWI Air Force Barracks):
Libe by Cluster F and Tower:

Teaching NCC SII M111:
PreCalculus UNIT03
Transformational Geometry and Trig!
07/13/15 - 07/16/15

WEEK03 ScreenCasts:
CH06 was about Translations, Reflections and Dilations of Functions. CH07 applied these Transforms specifically to Trigonometric Functions in degree mode. CH08 was about modeling with Trig Functions and Polar Mode using radians.

WEEK03 GROWING PAINS:
I we have our routine down to a science. Each class is a bout 3 hours. The 1st hour is usually some sort of review. The first week, Monday started with what I call Administrativa. This entails going over the syllabus, filling out some biographical information and seating assignments. Most of the time since then, hour 1 consists of homework review from the previous night. On Thursdays we usually go over a preTest I give out on Mondays as part of the homework. Hour 2 each day is usually new material. Hour 3 is usually practice previewing that night's homework.

Guest Speakers from the field of Astronomy.
Phil Plait:
Neil deGrasse-Tyson:
Bill Nye The Science Guy:

I had some business in the Administrative Tower, Building T, in South Campus. So, here's my trek starting at the water fountain by the North Faculty Parking Lot.
Bench just South of fountain:
Cluster C Ramp:
Cluster C Ramp:
Inside Cluster C 2nd Floor:
2nd Floor Hallway to Cluster B:
Cluster B:
View from window going upstairs:
Cluster B 3rd Floor Adjunct Office:
Western view from end of 3rd Floor Hallway:
Eastern view from end of 3rd Floor Hallway:
More construction below Building T:
1st floor outside Cluster A:
1st floor outside Cluster A:
1st floor outside Cluster A:
Building T:
Inside Building T:

Teaching NCC SII M111:
PreCalculus UNIT02
Exponential and Logarithmic Functions!
07/06/15 - 07/09/15

WEEK02 ScreenCasts:
I think this week went well! We covered CH04 Exponential Functions and CH05 Logarithmic Functions as well as solving related equations.

WEEK02 GROWING PAINS:
I hope that the students are getting acclimated to the expectations of the Harvard Curriculum. Said curriculum was one of the first to embrace the use of Graphing Calculators and the Rule of Four in the early 1990s.

The Rule of Four, simply stated, is about how to attack a problem. You need to be able to GNAW at every problem. If you are not sure how to approach a given situation, you may look at it Graphically or Numerically or Algebraically or Wordily (aka Verbally but GNAV is not too catchy), or any combination of the above modalities.

So, students are not expected to do a lot of "drill and kill" exercises where they memorize a set of steps to solve model problems. We expect the students to apply what they learn in class to new and different situations. This text is great for that as it has tons of word problems based on real world data and applications.

Tom Lehrer's New Math (Common Core?):
Tom Lehrer's Lobachevsky:
Tom is imitating Danny in Lobachevsky

Water fountain by North Faculty Parking Lot:
View of fountain looking toward Cluster D:
View from fountain toward Life Sciences:
View from fountain toward Cluster B:
View from fountain toward Cluster E:
View from fountain toward Cluster B:
View from fountain toward the Book Store:
View from fountain toward North Lot:
Video sound scape:

Teaching NCC SII M111:
PreCalculus UNIT01
06/29/15 - 07/02/15

WEEK01 ScreenCasts:
We covered chapters 1-3 of the Harvard PreCalculus textbook edition 4. Chapter 1 was mostly about Linear Functions. Chapter 2 was about Compositions of Functions. Chapter 3 was about Quadratics.

WEEK01 GROWING PAINS:
We were given B123 on the first day. This room was a bit small and only had a projector. Since I use my Droid Tablet as a SmartBoard (even though I'm not ScreenCasting this Summer) I needed to lug around an old laptop and hook it up to the PC Projector everyday. So, I put in for a room change. Since my fave room B218 was taken (please see last summer's blog), I asked for B221. We've now been in the new room for 2 days and things are running smoothly. All I did was copy my TeamViewerXournal and Wabbit folders to the desktop and away we go! I didn't need my USB Mic or Screencast-o-matic as I'm following ScreenCasts from just 2 Summers ago. I also tried to get SplashTop Streamer (as it's more efficient than TeamViewer) installed on the PC Desktop, but the tech guy was on vacation and I didn't have administrator rights. Now I see B218 is available....

Tom Lehrer's The Elements:
The Elements sung by Harry Potter:
The Elements sung by Sheldon:

Here's the view from the North Faculty Parking Lot this morning!

Getting out of car:
Security Gate:
New Life Sciences Building:
Nassau Transit Bus:
Garden and Flag Pole by Bus Stop:
Cluster E:
Water Fountain on my way to Cluster B:
Flag Pole in the Garden by the Bus Stop:

Well, that's all folks!

Sincerely,

A. Jorge Garcia
Applied Math, Physics and CS

Teaching with Technology,