Saturday, November 29, 2014

Alex's Extra Credit Linear Algebraic Proofs



Song:  Einsamer Hirte (The Lonely Shepard)

Artist:  Gheroghe Zamfir




Alex's UNR Linear Algebra professor had given his class the opportunity 
to earn some extra credit by writing proofs on certain problems.

It took Alex a total of 15 hours (spread out over a week) for him to complete it.

It involved two true/false problems...
each of which had 15 to 20 separate proofs needing to be written...
and another 18 problems needing only one proof each.

Alex typed out the whole assignment...
which totaled 60 pages.

Alex started learning how to write mathematical proofs over a year ago
through his Sunday math club sessions.

Alex said his math club practice has really helped him in this...
as well as in all of his other assignments
(these problems are similar to his competition math problems).

He also said that although he had to do some research 
on a few components of the problems by reading ahead in his text...
and by looking them up online...for the most part...
Alex knew most of the material already.

Alex loves doing extra credit in all of his classes.
They not only provide an academic buffer...
he learns so much by doing them.

I've included a sample of his typed proofs in the pictures below:










Alex was typing part of this up on the way home from our trip to 
Southern California.

He actually finished this assignment on Thanksgiving day.

Alex said that he really liked this assignment because he had to use everything 
he has learned in order to complete it.

He thought it was very good practice for writing mathematical proofs.

Alex has also been busy finishing up his AP Computer Science course...
and studying for his Biology final next week.

Alex's final in Linear Algebra is also coming up in a couple of weeks...
so he is very busy reviewing for each of his classes.

Just today...
as Alex completed a different assignment in his Linear Algebra class...
he looked up at me and said that he really enjoys this class.

Alex also said that he really loves learning at the University.

He is, at this moment...
looking at next semester's schedule.

He is on the waiting list for Calculus III
(he needs this course in order to take more advanced math).

Hopefully they will be adding more courses for Calculus III...
otherwise he will have to take some other math in the meantime.









Thursday, November 27, 2014

Alex's 2014 Thanksgiving



Song:  Divenire

Artist:  Ludovico Einaudi


Alex did a full day's studying...
worked out with his Thursday weight training...
showered...
and we then went out to eat at our favorite buffet at the Atlantis.



We are getting ready to pull into the parking lot here.

The street and the parking lot are lined with Christmas lights.


I love exterior elevators.


We are going into one of the entrances from the parking lot.


This is the outside entrance to the skyway.


This was at the top of the escalator.


The buffet is in the casino, so we have to walk to the end of the skyway...


and then down another escalator...


and into the casino.


This is the best buffet we have found in Reno.


A view of some of the casino as we waited in line to get in the buffet.


Alex started eating crab...


while momma got him another plate of different food to eat.


Alex then finished the meal with an assortment of desserts.


Momma had crab, prime rib, and a small assortment of other foods.


On our way back to the skyway, to our car, and then back to home.

As it is just we three in our family...
we usually do not celebrate holidays.

I know Thanksgiving is supposed to be a day of thanks...
however, with me...
I am so thankful everyday.

Everytime I see my son...
I am almost overwhelmed with gratefulness toward life.

Even at 14 years old...
Alex still has his pure heart and kind nature.
He is respectful and affectionate...
and always so driven toward his dreams.

Several times throughout the day...
while Alex is studying at his station...
or when he is just relaxing...
I just feel the urge to give him a big hug and a kiss...
and I do.

I am thankful for having a wife who is a great mother to Alex.
She has always sacrificed herself for him.

She is always researching educational opportunities for Alex's future.


I have been living the American dream.

It has been over 3 1/2 years since I fully retired.
I still feel giddy knowing that I have all the time in the world 
to spend with my son while he is still young.

I am thankful to myself.

I had thought long term.

Even though I had, long ago...
dreamt of what my life would be
when I had reached retirement...
never had I thought that I would have such a blessed life.

First and foremost...
to have such a son as is Alex...
I am just so grateful.

I do know how fortunate I am...
to have so much of what is our most valuable commodity...
that of time.

Unless I am taking Alex to the University...
or if we have something planned...
I wake up whenever I end up waking up.

I do as I please throughout the day or night
(although Alex no longer needs much academic guidance...
I still guide where it is needed...and I guide him in his other activities).

Even after 3.5 years since retiring...
every day still feels magical.

I had stayed the course in a career that, at first, I had thought of leaving.
Looking back...I not only have no regrets for having stayed...
I am so glad that I had.


I am so glad that at a relatively young age...
I had realized the concept of a positive spiral in life.

Each year of my life just keeps getting better because of my adherence to this concept.

I have so much to look forward to because of forethought.

Life is exciting...
life is so beautiful...
because I have planned it to be so.

I continue to plan...
and to act on those plans.

This is why life is so great...
and why it will just continually get better.


Explore...
Dream...
Plan...
Achieve...

and most of all...

Stay The Course...
Never Give Up.

Always nurture the...
Intellectual...
Emotional...
Physical.

Each facet builds and supports the others.

Continually plant future seeds...
you will then have a continuous supply of fruit.

This is living life on a Positive Spiral.


This is one of the most important concepts I have taught Alex
(and everything we do reinforces this concept).

Alex doesn't merely understand this...
Alex lives it
(mere understanding is nothing without the application of it in life).

By applying this concept...
Alex shall always know deep satisfaction and great happiness
throughout his life.

This is what I am most grateful and thankful for.








Tuesday, November 25, 2014

From Caltech To Reno: Hwy 395



Song:  The Grace Of Undomiel

From:  'The Lord Of The Rings:  The Return Of The King'





Hwy 395 - The Great Eastern Sierra Nevada Scenic Route

Although our drive home was 9 hours long...
I greatly enjoyed driving on Hwy 395
(We took hwy 210 from Caltech...
to hwy 10 to hwy 15...
and then connected with hwy 395
near the San Bernardino mountains).

All the way home
 (until it got too dark to see the views)...
I was treated to grand mountain views
from the front windshield and from the driver's side window.



Our first stop was at this small desert town...
where I filled up on gas...
we all used the restrooms...
and where we picked up some drinks and snacks.

I had picked up Alex a Scorpion Sucker.


Inside the candy is a real scorpion which had its venomous tail tip and glands removed.

It is just a novelty item for Alex.


At first...
the mountains were sort of generic looking.
They were a little too symetrical to make them interesting.



A short while later...
the knife ridges made their appearance...
along with the numerous and interestingly shaped peaks.

The farther northward we went...
the cooler the temperature...
and so, the more snow on the mountains.





Although there are nowhere near the number of RVs on the road as in the 1960s and 70s...
we had gone past some nice ones during our trip.





As this competition interrupted Alex's normal study routine...
Alex worked on his studies on his laptop as we drove home.



This particular style of RV is popular.

While on the road...
this is the type I most often see.


About half way home...
near Mammoth Mountain...
the mountains took on their familiar shapes and snow caps.

This is where the mountains become particularly beautiful.












As the sun was setting...
I decided to pull off the highway to allow us to take some photos...
and to stretch our legs.



Alex was playing knight here.

He loves to pick up sticks and pretend they are swords.

After the sun had set...
it had rapidly gotten dark...
and we still had a couple of more hours to go until we reached Reno.


We arrived at approximately 8 PM...
and we stopped in at our favorite neighborhood Chinese restaurant for supper.


Alex ordered pork chow mien, and pot stickers for an appetizer.


I had Prawns and Scallions.


Over our 3 day trip...
we had driven a little over 1,000 miles (1,600 KM)...
almost all of which were covered on day 1 and day 3 of our trip.

It was a very worthwhile and enjoyable trip.


For the remainder of Sunday night...
and all of Monday (after his UNR class)...
Alex reviewed for his Psychology final exam...
which he is to take in a few hours (Tuesday afternoon).

Over the Thanksgiving holiday...
Alex will be working on finishing up his AP Computer Science class.

Besides having finals in all of his remaining classes...
Alex has two major exams coming next month.

Alex is trying to finish his regular school work early
so he will have more time to dedicate to studying for these exams.


--------------


Sometime in the next few months (preferably after a heavy snow fall)...
Alex and I will be taking a scenic tour (round trip)
of the Sierra Nevadas by train (The California Zephyr).



It leaves out of Reno and crosses the Sierra Nevadas (Westward) to near Sacramento...
where we will then board an east bound snow train coming back to Reno.







It has a skyview railcar and dining facilities...
so we may view the snow covered mountains in depth and up close...
and in perfect peace and comfort.

We are very much looking forward to taking this train ride sometime soon.



















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