## Wednesday, August 9, 2017

### LAC 2017: Power Series, DiffEqus & Euler's Identity!

LAC 2017:
Power Series, DiffEqus & Euler's Identity!

Welcome to Life After Calculus 2017 (LAC2017)! Yes, there is life after Calculus! If you don't believe it, take a look at this blog's sidebar for evidence. This year must be the 9th LAC I've recorded on YouTube and BlogSpot.

DAY01: 2017 AB2

The first 3 days were about solving the latest AP Calculus Part IIA Free Response Questions (FRQ) which are calculator active.

DAY02: 2017 AB2BC1

These FRQs are meant to be completed with a Graphing Calculator (GC). Now-a-days said GC would most likely be a TI84C or a TI nSpire CX CAS.

DAY03: 2017 BC2

However, our LAC final project was about using coding to solve these sorts of questions instead. So we used Python and the latest version of SAGE. SAGE is a Computer Algebra System (CAS) based on python with lots of other FLOSS math utilities built in to solve problems in Calculus and even higher order Mathematics. BTW, I use FLOSS every day, don't you? FLOSS stands for Free Linux Open Source Software.

DAY04: Arithmetic

So, on the fourth day I went back to basics and talked about the 7 arthimetic operators that Python is based on: addition, subtraction, multiplication, decimal division, integer division, integer remainders and exponentiation. Python also has conditional and looping syntax that's very easy to learn and use. In fact, if you are working with sequences and series, Python's List data structure is very useful!

DAY05A: Complex Powers

It soon became apparent to me that some of my students didn't really know how to exponentiate. My students were fine calculating powers as long as the exponents were real. For example, 2^2 aka real^real, (2i)^2 aka imaginary^real and (2+2i)^2 aka complex^real were all familiar operations we could do by hand sans technology! Then I showed my students powers with imaginary exponents and complex exponents on SAGE and asked how we could accomplish these calculations by hand?

DAY05B: DeMoivre's Theorem

On the fifth day we derived Euler's Identity using McLaurin Power Series and used said identity to compute each complex power mentioned above by hand! I was running out of school days so I didn't get to DeMoivre's Theorem (Day05B) which is a nice extension of Euler's Identity making powers and roots of complex bases very easy. That would have been our sixth day but I had to skip it. See the video above for completeness sake!

DAY06: DiffEqus & Power Series

On our sixth and final day in LAC 2017 we talked about solving Variable Separable Differential Equations (DiffEqus) without separating the variables and without Anti-Differentiation! In fact, all we did was differentiate known McLaurin Power Series! Then we found we could solve non-variable separable DiffEqus the same way. We even solved 2nd order DiffEqus!

DAY07: Vectors

This year we had a lot less time after the AP Exam since ETS moved our exam to the second week. Also, we had our annual Math Movie Marathon every Monday and Friday. I had planned for 12 Days Of Calculus after the exam using SAGE. So here's the rest of what I planned for your viewing pleasure. Maybe we'll try this version of our final project again next year.

DAY08: Matrices

Since we covered Calc I and Calc II this year, most of my students will take Calc III (Vector Calculus) next year. That's why I was planning to cover Vectors on Day07 and Matrices on Day08 using SAGE (should be 2 or more days each).

DAY09: Surveyor's Formula

Finally, the ninth day was going to be devoted to a cool application of Vector Cross Products in 3D, namely the Shoelace Algorithm aka the Surveyor's Formula aka Gauss's Method of Polygonal Areas. Please see the video above for my proof of this algorithm. Like I said, my proof is based on Vector Cross Products. I don't think I've seen this proof anywhere else!

UPDATE:
*********************************************
That reminds me, if you want to see the Free Fall Model with Air Resistance DiffEqu Solution, by hand without tech mind you, we did that in the Physics LAC listed in the side bar. I've never seen this solution anywhere else either! Don't forget my preCalc video on graphing Rotated Conic Sections in Polar Mode on a GC which isn't in any textbook I've used either. Aren't you lucky, getting all these original mathematics concepts here for free?
*********************************************

DAY10A: Encryption By Hand!

The tenth day was going to be devoted to a cool application of Matrices, namely Encryption! We were going to make our own version of the Enigma Device cracked by Alan Turing during World War II! This lesson was to have a non-tech half (Day10A) as well as a tech aka SAGE half (Day10B). I just recorded these two screencasts for the first time so you can see what I mean!

DAY10B: Encryption By SAGE!

Since I broke this up into 12 videos, I think of this as the 12 Days After Calculus! I hope to find 12 days to do this project justice next year as we only really completed 6 days. We did have fun with our Math Movie Marathon too including: Hidden Figures (Katherine Johnson, Dorothy Vaughan & Mary Jackson), The Imitation Game (Alan Turing), The Man Who Knew Infinity (Srinivasa Ramanujan), Proof (Fiction) as well as Stand And Deliver (Jaime Escalante). So we did justice to our Math Movie Marathon. Somehow we didn't get to A Beautiful Mind (John Nash), but there's always next year! Maybe we'll through in The Martian (Fiction) for fun!

Hope you enjoyed our final project!

Have a great rest of the Summer!!

Happy LAC2017!!!

Teaching With Technology,

Well, that's all folks,
A. Jorge Garcia

Applied Math, Physics and CS
2017 NYS Secondary Math PAEMST Nominee

TpT

## Tuesday, August 1, 2017

### 21st Century Multimedia: Extreme Video & Audio Edition?

21st Century Multimedia:
Extreme Video & Audio Edition?

What not to watch on TV In 2017:
Here's an update on my annual post regarding using apps, not TV, to watch the latest episodes of your fave genre TV shows! The pictures, links and videos in this post are not my own and are all related to the shows and apps that I recommend in the order that they are returning to the air.

A Note On Extreme Video & Audio:
BTW, this is not only my Extreme Video edition but also my Extreme Audio edition this year! Why? I've always wanted to add an Extreme Audio edition but the post would have been almost the same as the Extreme Video post since I tend to listen to many shows and sound tracks when I'm busy doing other stuff. Sometimes I'll download a favorite episode on my phone and listen to it on the drive or when I'm grading. I don't have to watch the show, say Star Trek or Babylon5, as I know the episode so well already! I'll also listen to Original Sound Tracks on YouTube or Pandora by composers I like from TV or movies. Don't forget all the great audio books too! Maybe you'd prefer to listen to a nice https://www.ted.com talk perhaps?

Dark Matter (SyFy)
Season 3 Starts Friday 6/9/17

A Note On DirecTV & Netflix:
I got rid of all my extra channels on my local cable bill and now just share a DirectTV and a Netflix account with my kids who are all "growed up!" I also have Amazon Prime and I subscribe to the PBS app. Watching shows on my Android Phone or Tablet or on Chromecast is a great experience now with all the streaming services, fast WiFi and HD hardware out there. Just ask my students about YouTube Wednesdays streaming HD videos from my tablet via Chromecast on my SmartBoard in the dark like a movie theater. All that's missing is the popcorn! As you will see below, there's also ton's of binge worthy new series on Netflix!

Game Of Thrones (HBO)
Season 7 Starts Sunday 7/16/17

A Note On Summer Seasons:
So, let's start with Summer Season! The Summer season has grown to include some great shows. Studios tended not to do much in the summer, but all that has changed in recent years. A lot of series don't run Fall/Spring schedules with 24 some odd episodes anymore. Most shows run Fall or Spring with only 10 or 12 episodes. Some series will run Winter or Summer only. Producers used to experiment in the summer with such shows as Speilberg's Terranova (FOX) which failed or BBC's Merlin (NBC then BBCA) which thrived. Don't even get me started on Legends (TNT), Dominion (SyFy), Forever (ABC), Exorcist (FOX), Lucifer (FOX) or Damien (A&E).

The Last Ship (TNT)
Season 4 Starts Sunday 8/20/17

A Note On Summer Season 2015:
Summer 2015 saw the end of 2 mainstays: Falling Skies (TNT) and Defiance (SyFy). Falling Skies, by Noah Wyle, was always top notch. I'm gonna miss it! Sorry, Wyle's Librarians just ain't gonna cut it. BTW, Falling Skies started the "After Show" tradition that Walking Dead is so famous for now. Will Wheaton hosted the Falling Skies After Show for 2 seasons and then it fizzled out. I like Chris Hardwick's After Show for Walking Dead, but I miss Will Wheaton! Also, Defiance started putting Comic Book stories on TV way before Walking Dead did.

Nova (PBS: minimum \$5/month donation)
Season 44 Ends Monday 8/21/17
Great American Eclipse Day!

A Note On Summer Season 2016:
When Summer 2016 rolled around, I was wondering if it was gonna be a flop. Well, enter The Last Ship (TNT) and Dark Matter (SyFy). Both of these series started in prior Summers but escaped my notice. So, it was time for a bit of binge watching to catch up. All I have to say is: SyFy finally has some real SciFi back on the air!

Outlander (Starz)
Season 3 Starts Sunday 9/10/17

A Note On Wyle & Dane:
Oh, The Last Ship isn't quite a genre show (SciFi-Fantasy-Horror) but it's top notch! Eric Dane is great as the commander of the Nathan James and he's a great Producer too. He, like Noah Wyle, also started out on a prime time medical soap opera. Noah started out on ER and Eric started out on Grey's Anatomy. Both are fine shows and both are fine actors, producers, writers and directors!

The Orville (FOX)
Season 1 Starts Sunday 9/10/17

A Note On Summer Season 2017:
Summer 2017 is a great smash! Dark Mater was back in June. The long awaited Season 7 of Game Of Thrones started in July. Last, but not least, The Last Ship is coming back in August!

The Big Bang Theory (CBS)
Season 11 Starts Monday 9/25/17

A Note On Mini Retirement Practicum:
Ahh ... the pursuits of Summer! Finally, it's time for some R&R. I know, perish the thought, but its time for some non Math related activities! In fact, I'm off the whole Summer for the only the second time in 33 years of teaching! Can you believe it? I'm still pinching myself. I guess this is a practice run at retirement?

Supernatural (CW)
Season 13 Starts Thursday 5/18/17

A Note On Other Pursuits:
Now I finally have plenty of time to devote to walking, biking, swimming and eating right! For me, the Summer is a spiritual time to regroup and fortify myself mind, body and soul for next school year. I like to focus on outdoor activities for exercise and a good diet.

Season 8 Starts Sunday 10/22/17

A Note On More Fun:
It's also time for more soulful activities of Wood and Stone such as playing chess and classical guitar. I'm attending to some of my old hobbies such as gaming, reading and catching up on genre TV and film!

The Vikings (History)
Season 5 Starts Wednesday 11/29/17

A Note On CBS All Access:
CBS has been removing free content for some time. You can still get scenes of Sunday Morning and 60 Minutes on YouTube, but the CBS Rewind archival site is all gone. CBS Rewind is now part of CBS All Access too! So, if you want to watch the Morley Safer interview with Admiral Hopper from the 60 Minutes archives, for example, you better cough up your \$6/month! Note, that \$6/month comes with ads. If you don't want ads, you better make that \$8/month....

Doctor Who (BBCA)
Season 10 Continues Monday 12/25/17

A Note On Honorable Mentions:
There are several shows that I loved last year that have not announced their plans for a new season: Nature (PBS), Bill Nye Saves The World (Netflix), Marvel's Agents Of Shield (ABC), Medici: Masters Of Florence (Netflix), Sense8 (Netflix), Star Wars Rebels (Disney XD), Star Talk TV (National Geographic), The Last Kingdom (Netflix), Victoria (PBS). Last, but not least, we're sad to see Reign (CW) end rather abruptly. Of course we know what happens to the real Mary Queen Of Scots, but does the last episode really have to cover 20 years of her life in one swell foop? If you have a story arc in your series, kindly finish it in some satisfying way other than letting her rot in jail for 20 years and decapitating her! I know these endings were controversial, but Merlin and BattleStar sure got it right!

Nature (PBS: minimum \$5/month donation)

A Note On Last Year's Season:
I enjoyed most of last year's recommended shows which I continue to recommend this year. However, some shows turned out to be a flop: Timeless (CW), Aftermath (SyFy) and Frequency (CW). Unfortunately, Timeless was a bit too predicable. However, Aftermath got really insane near the end of the first season! Maybe they ran out of ideas based on End Of The World mythos? Trying to outdo Supernatural isn't gonna fly! Frequency started out OK, but it's just a long drawn-out version of the 2000 movie.

Bill Nye Saves The World (Netflix)

A Note On SyFy Channel:
I really miss good SciFi on SyFy ever since Babylon5 (originally on UPN), StarGate (originally on Showtime) and BattleStar Gallactica ended! It's such a shame that the SyFy Channel is no longer the SiFi Channel! Now we get to watch WWF on SyFy, ST: TNG on BBCA and FireFly on History Channel?

Marvel's Agents Of Shield (ABC)

A Note On Star Wars:
I discovered Star Wars Rebels and binged on it two Summers ago. It's very much like the original Star Wars movies. It has great characters and writers. I recommend it, even though it's animated. Maybe since it's animated, it has some great graphics! I wanted to catch up to this season, as one of my fave SciFi writers of all time, Timothy Zahn, is joining the writing team and contributing his Grand Admiral Thrawn character for good measure!

Medici: Masters Of Florence (Netflix)

A Note On Historicals:
BTW, Reign, Vikings, Downton, Victoria, Outlander and The Last Kingdom aren't really genre shows, but I highly recommend them if you are into historical fiction. In fact, get all the Bernard Cornwell novels you can, and read up on The Last Kingdom yourself! However, only Victoria is still currently in production. Downton and Victoria are on PBS as part of Masterpiece Theatre. Also, Outlander isn't really a historical but it is based on historical events.

Sense8 (Netflix)

A Note On Web Series:

Star Wars Rebels (Disney XD)

A Note On Streaming Apps For Your Tablet:

Star Talk TV (National Geographic)

A Note On Steve Jobs:
FYI: I refuse to get a tablet with 4G. Why pay extra for such hardware when WiFi Hot Spots are so prevalent now? Remember the early days of the iPhone and iPad? That's Steve Job's legacy. You had to get 2 devices each with it's own data plan. So, you pay Apple and a data provider twice as much as should be necessary: 2 devices and 2 data plans??? That was the business model that made Jobs rich!

The Last Kingdom (Netflix)

A Note On Axanar:
BTW, you may be wondering about the 2000 MegaTon Ape in the center of the room??? Yes, CBS nuked (via lawyers) the whole Axanar idea. Now fans cannot make their own full-length episodes of Star Trek anymore since Axanar raised over 1 Million Dollars in crowd sourced funds and decided to profit from their production.

Victoria/Masterpeice
(PBS: minimum \$5/month donation)

A Note On STDs:
Also, CBS is starting it's own new Star Trek Series on TV. Or is it on TV? Well it is and it isn't. The first episode of ST: Discovery, some call it STD, airs on CBS on Sunday 9/24/17. Guess who's boycotting it? Me, that's who! Why? Because all subsequent episodes will only be available on CBS All Access for \$6/month. I don't watch anything else on CBS (other than Sunday Morning, 60 Minutes and TBBT, but I watch those live) so why should I pay \$6/episode for the STD? I have never missed a first airing of any Star Trek episode of any series since the very first episode of ST: TOS on NBC at 8:30pm on a Thursday night 9/8/1966! BTW, if you like Star Trek TV, you can watch all series on Heros and Icons TV (sorry, no app). They show 26 hours of Trek every week! Sunday-Friday they have 5 hours of non-animated Trek (ST: TOS, ST: TNG, ST: DS9, ST: Voyager and ST: Enterprise). They also have 2 half-hour episodes of animated Trek on Sundays. No Trek on Saturdays, I'm afraid. Well, I guess you can't have it all, now can you? Anyway, I bet The Orville will be a better STD than STD!

Reign (CW)

A Few Notes On A Few More Helpful Apps:
In addition to all the great streaming apps listed above, here's a short rundown on some other apps to help you on your audio and video extreme multimedia adventures:

If you like Nature, Nova or Masterpeice Theatre, you're gonna love the PBS app. One drawback to this app, however, is that PBS requires a minimum \$5/month donation. However, in my estimation, said donation is well worth all the archives they make available to members.

Another useful app is NextEpisode. The free version allows you to input up to 20 of your favorite shows. This app will track for you when a new episode is coming up as well as a list of all previous episodes and other interesting data on the show.

go90 is a great app if you want free streaming video! Most of the stuff on there is junk if you ask me. However, it has two redeeming qualities that far outweigh all the reality TV, music videos and sports on go90 as far as us geeks are concerned. What are these redeeming qualities you ask? Number 1 is that you can watch every single Babylon5 episode for free. If that's not enough, number 2 is that you can stream anything on go90 data free if you are using your 4G data plan on Verizon on your cellphone! How's that for nifty?

The IMDB app is like Google for TV shows and Movies. You can look up your favorite shows and look up information about cast and crew. Actually, most of the time I use this app in tandem with the Pandora app. If I like the musical score of a particular TV show or movie, I'll look up the composer to add to my Pandora channels! You could always go to your fave composer's website if you like: Bear McCreary or Ramin Djawadi!

Last but not least, don't forget to listen to your favorite audio blog on your browser or on the PodCastAddict and TuneIn apps. I highly recommend Destinies: The Home Of Science Fiction, deFlipSide and Star Talk Radio! How about some nice classical music, http://sundaybaroque.org, or celtic music, http://thistleradio.com?

A Few Final Notes In Closing:
If ever there were a binge worthy series it's Game Of Thrones! If you even remotely like fantasy stories like Lord Of The Rings, run, don't walk, to your nearest binging device and watch HBO's GOT. Here's a plan, you can watch all 60 episodes of the first 6 seasons of GOT in 6 weeks. Each Season is only 10 episodes of 1 hour each. Season 7 is only 7 episodes, but each is a bit longer than usual. Season 8, the last season, will have only 6 episodes. Rumor has it that the last 6 episodes may each be a 2 hour movie. I just love George R. R. Martin's novels. He's worthy successor to J. R. R. Tolkein, that's for certain! Hence the name, I suppose? BTW, you just gotta love how Bran is some sort of Super Cosmic Uber Power Wizard and no one seems to know it! Anyway, I'm up to episode 705 and all I can say is (SPOILERS):
L+R=J!
There are more Targaryens.
Will there be more dragon riders too?

I'm not usually into horror, but The Walking Dead and Supernatural are two series that have consistently high quality production values: music, writing, acting and special effects! I highly recommend both series. Technically, these aren't really about horror, despite all the blood and gore! TWD is really about how ordinary people rise up to surmount extraordinary situations. Also, Supernatural has very unique story lines that invoke Norse and Greco-Roman Mythology as well as Judeo-Christian beliefs.

Sense8, Black Mirror and Medici come very highly recommended from my fellow geeks, thanx! I must admit to being behind in my binging on these Netflix shows. However, these series are supposed to be great, so I'm gonna get to them soon, somehow! Sense8 will have a 2 hour series finale coming up soon. Black Mirror is supposed to be very similar in style to the Original Twilight Zone (CBS) and the New Outer Limits (Showtime). Medici is a historical with some actors from GOT that looks fun!

Vikings (History) and The Last Kingdom (originally BBCA, now Netflix) are both very well researched historicals about the Viking era. Vikings' last few seasons have been about the sack of Paris and what happens to Ragnar Lothbrok and his family in the aftermath. The Last Kingdom is about King Alfred The Pious of Wessex and his dream of a united England. This series is based on a collectiom of ten novels by Bernard Cornwell about the life of one of his ancestors, a great warrior named Uthred, who was raised by Vikings but aids Alfred. Both these series are very well written and well acted. I recommend these shows very highly!

Wow, I can't believe The Big Bang Theory is back for it's 11 season! That's good and that's bad. I liked the early years when geekdom was not yet cool. But now being a geek is so mainstream that's it's no longer cool for me. I'm afraid TBBT is just perpetuating the nerd stereotype - no longer displaying our genre culture in a good light. Also, ever since season 9, the top three actors have been getting \$1000000 per half hour episode? You know what that means? We get tons more commercials per episode and lots less story to enjoy.

Last but not least, you just gotta love how active both Neil DeGrasse Tyson (AMNH) and Bill Nye (Planetary Society) are lately! They are both doing a great job getting the word out on the importance of Science education in schools and Science literacy in our electorate. Neil has Star Talk TV on National Geographic and Bill has a new show on Netflix called Bill Nye Saves The World. Star Talk has great guests and interviews with scientists and celebrities talking about issues of the day. Neil's show is very informative and entertaining, I highly recommend it! I did have an issue last year with Star Talk, however. I wanted to screen parts of Neil's interviews with Elon Musk and Andy Weir for my students. I didn't realize that the National Geographic app only kept each episode online for a couple of months. By the time I got around to showing these interviews for YouTube Wednesday, the episodes were no longer available. All I had access to was the audio version of these interviews from Star Talk Radio, but that wasn't quite what I had in mind. Bill's show is very entertaining and also addresses current events of the day complete with panel discussions with guest experts! Bill Nye Saves The World is a lot like Bill Nye The Science Guy but for adults!

Let's see if some of the new series are any good: The Good Doctor (ABC), Kevin (Probably) Saves The World (ABC) and Young Sheldon (CBS). The last 2 are comedies and Young Sheldon is a spin off from TBBT. The Good Doctor looks more promising - think a young Dr. House!

Well, that's all folks! Now, go enjoy some of your own Extreme Video Streaming adventures!

Generally Speaking,

Well, that's all folks,
A. Jorge Garcia

Applied Math, Physics and CS
2017 NYS Secondary Math PAEMST Nominee

TpT