Number Sense Practice Tests // Update

First off, thanks to everyone that has made my Auto-Generated Number Sense Practice Tests (both for High School and Middle School) such a success!

In late July, A friend of mine added a better way to track the number of downloads of all the practice exams posted on my website. I’m very happy to report that there were just about 2,000 unique downloads in about a span of 9 weeks! Incredible! I’m very proud to say that I’ve played (albeit a small) part in fostering a love of math with so many students!

Just to give y’all a quick update of the status of the project:

  • There are about 11,000 question in the Middle School and about 8,000 questions in the High School databases. Collectively, that represents enough problems to total 225 exams!
  • Now that the databases are pretty robust, I’m going to concentrate on making column-specific drill sheets. Basically, they’ll be full 80-question tests that focus on just questions from Column 1, 2, 3, and 4 of the exam. That way, students can better stretch themselves practicing on questions that they are currently reaching within the time limit.
  • I’m also going to start making topic-specific drill sheets. This will pair nicely with the work I’ve already done with my Number Sense Manual as I’ll provide even more practice problems for each topic. For instance, if you want to learn how to multiply two numbers close to 100, I’ll have drill sheets specifically highlighting those types of questions.
  • I’ve decided against making videos of each individual topic for the time being. If you’re looking for better explanations of the tricks outside of my manual, I suggest going to Math Ninja’s Youtube Page as he has already made a ton of videos detailing how to do most of the tricks.

That’s about it! Good luck to all the students and teachers with their competitions during the 2017-2018 school year!

30 Day Challenge // Part 1

Was inspired by a recent TED talk I heard concerning challenging yourself to do something new every day for thirty consecutive days. Basically, it’s a behavioral modification technique that is rooted in the idea that in order to develop a new habit you need about a month’s time of doing it continuously. If you really wish that you could stop biting your fingernails — go a month with biting them and, odds are, the behavior will stick.

For my first set of thirty day challenges, I simply wanted to go without mindless surfing, so I axed out Facebook and Reddit completely from my life. Additionally, I also wanted to give either my dog or baby a walk around the neighborhood because it is something I love to do but oftentimes — whether through fatigue or scheduling — I hadn’t been able to do consistently.

Well, with August in the books I’m here to report that I almost completely kept to my two goals! I successfully didn’t check Facebook or Reddit for the whole month and I only missed three days of walking due to inclement weather — so I’ll chalk that up as a success as well. I definitely can see both of these new habits sticking and plan on brainstorming a complete set of challenges I want to do and start implementing them on a monthly basis, two-at-a-time.

Patent Issued // Customizable RF for Use in Particle Accelerator Applications

Patent 9,750,123

Received notification that my team’s US Patent concerning recent advancements to our linear accelerator officially got issued yesterday (August 29th). If you want to look it up, you can do a US Patent Search for Patent #9,750,123 or just click on the link here (note: might not work on mobile).

This was a pretty big milestone that was celebrated at our site and it gave me a chance to go through Boeing’s Invention Disclosure process for the first time. All-in-all it was relatively painless and I was very impressed by how quickly our patent attorney was able to pick up on the technical concepts despite being not too familiar with high energy physics. Probably the worst thing about the whole deal was the long wait — the patent was filed last August and it took a little over a year to go through the US Patent Office review process.

Regardless, it was worth the wait and I am very pleased with the outcome! Currently, I have two more invention disclosures in the works that are in various stages of development, so I hope that this is the first of several patent awards for myself and my team in the near-future!

Advice for College-Bound Students

Since the majority of the current traffic to my site is motivated, high achieving students (who else would be wanting to practice mental math over the summer?!), I thought I’d spend a short amount of time talking about my path to where I got to currently and share a few valuable things I’ve learned along the way.

For starters, I know personally how important where you go college means to you. If you were anything like me, that decision occupied the majority of your senior year of high school. Additionally, you can’t help but compare where you go with other people. I never in my wildest dreams thought I would go to Texas Tech — especially after I got into some other top tier universities. Nothing was more depressing as I sat on the award’s podium at TMSCA State sharing with the newsletter writer that I was going to Tech after hearing my fellow winners rattle off a seemingly top-ten list of prestigious universities (Harvard, Princeton, MIT, Cal Tech, etc…). At another time, I’ll talk a bit more about my decision making process of going, for free, to a state-school rather than accepting student loans to go to a more renowned university…

Anyways, one thing that I now learned, with the help of hindsight, that I didn’t particularly think much about back then is how college is a means to end rather than the end itself. No doubt, you are so wrapped-up in completing all your essays, applying for financial aid (whether it’s scholarships or FAFSAs), and prioritizing where you want to go with every admissions letter you receive that it’s tough to take some time and reflect on exactly what you want to use college for and how it can help you advance towards some of your over-arching life goals. I know, heady “adult” stuff for 17/18 year-olds to think about.

Nowadays more so than ever, what you study in college — especially for your Bachelor’s Degree — will not be applicable in 99% of things you will need to do for your future profession. So why do we go through this costly routine if it doesn’t matter? The simple answer is to show future employers (or reaffirm to yourself, if you are fortunate to have entrepreneurship tendencies) that you can do something hard and can challenge yourself further than you have ever challenged yourself before. Although we think of college as a quantitative judge of character (what was your degree, your GPA, your GRE score, etc…), in actuality it is a qualitative one. The most important things you can learn while at university are not Maxwell’s equations or the litany of Joyce’s obscure allusions in Ulysses, but rather stuff like proper time management, self motivation, goal setting (and achieving), and work-life balancing.

And these qualitative lessons are applicable wherever you decide to go. Even if you go to an non-elite university where the coursework is a breeze for you, there are always additionally opportunities that you can find to push yourself forward and help improve on your character . I tell yourself as someone who learned this lesson the hard way. I spent my first year at Tech mostly brooding about easy I had it and how unchallenged as was — wishing a lot for just something more. What I slowly realized is that if I wanted to challenge myself, I can’t relay on others to do this, I have to rely on myself. This idea, what some would call “grit,” was the number one thing I took from college, and needless to say, I didn’t learn it from a textbook. As a direct result of my sudden personality change, I approached professors to help with Putnam training, enrolled in graduate-level courses early on in my under-grad, wrote IEEE student papers, and the list goes on… These are all things I did mostly outside of my classes to become a better person — both from a technical as well as from an inner-human perspective. Even with these few activities I did during my undergrad, it started a chain reaction that led me to where I am today: it led to my getting considered and accepted into an all-expenses-paid dual-degree graduate program that I got to do in Denmark and Germany → my securing an awesome job at the height of the financial crisis when good jobs were hard to come by → my current career advancement and my successful completion of my MBA → and no doubt it will lead to where I want to be in the future, whatever that is.

So when you are choosing colleges and where to go to, please don’t lose sight of what exactly is the worth of college. To be honest, most universities teach the same material in their classes, but it’s what you decide to do to push yourself beyond the lessons that will lead you to the true value of that degree.

Middle School A+ / TMSCA Number Sense Auto-Generated Practice Tests

I’ve been very surprised (and pleased!) by the response of my Auto-Generated High School Number Sense practice exams — we’ve reached upwards of 3,000 total downloads since I began posting about them earlier this year!

As a result of their popularity, several individuals have asked me to produce something similar for the Middle School version of the exam. Since I recently reached my goal of 10,000 questions for my high school competition database, I decided to switch gears and focus on starting up a similar Middle School database. Over the past two weeks, I was able to generate 2,000 questions (sorted in the same way as the high school exam) and I’ve produced my first Auto-generated Exam and Answer Key (which you can download via the links).

I also created a Middle School repository where students can access all the number sense practice exams I generate for free. For the time being, I still intend to publish them on a weekly basis but will ultimately create a button where students can generate a practice test anytime they want a new one. I hope to have this implemented by the end of June — so stay tuned!

Boeing Frontiers Article

LMTF Article

Late last month, there was a nice write-up of Little Mountain Test Facility (where I work at) on the Boeing website. Originally, it was scheduled for a December release, however, it was delayed until late-March. As a result, we missed the window for a physical copy release in the Boeing Frontiers Magazine (they moved to online-only in January), but nevertheless it is always great getting exposure for our facility.

Anyways, for those curious at what exactly I do for a living, this article provides some insight. Pictured above is me (far right) doing a mock set-up of an experiment in front of our linear accelerator. As mentioned in a prior post, I’ll be presenting the results of that particular machine’s updated capabilities at this year’s Hardened Electronic and Radiation Technology (HEART) conference next week.

Buffalo Run 50-Miler // Race Recap

Buffalo Run 50 Miler

Name: Buffalo Run
Date: March 18, 2017
Distance: 50 Miles
Location: Antelope Island, Utah
Finishing Time: 9 hours 40 minutes (22 out of 85)

Now that it’s been a couple of weeks since the race and I’ve fully recovered, I thought I would share in a long-winded post a recap of my first 50-Miler:

Going into it, the two goals I wanted to achieve were (1) Finish the race within the cut-off time of 12 hours and 30 minutes, (2) Finish under 10 hours. Since I have never run this far before, I thought finishing would be quite the accomplishment, so I set that as my primary goal. After my two training runs on the island, I was able to determine a reasonable pace time which would put me into the finish at around the 10 hours mark, so I made that my stretch goal. So, obviously, I wasn’t trying to break any course records and go as fast as I could — I was more focused on survival!

The night before the race I packed up everything I ever thought I might need. In typical fashion I over-packed both my hydration vest that I wore the whole trip as well as my two drop bags. I tried to cover every contingency I could imagine (what if the aid stations really didn’t have sunscreen; what if I eat way more than I have scheduled; what if I want to change socks more frequently), but after the race I quickly came to the realization that I should have only carried a couple of chew bars, a bladder of water half-full, and a change of shirts and socks, mostly because the aid stations were so exceptionally prepared!

The start time was at 6:00am on the island which was about an hour drive from my house. I woke up at about 3:30am so that I could eat a light breakfast, get my first coat of sunscreen on, and pack everything up. I made it to the start line about 45 minutes early right around the time the first 100 Miler participants crossed the finishing line (in about 17 hours and 30 minutes). Needless to say, that gave me a shot of inspiration seeing them!

At the start, the weather was cool, so I was wearing a lightweight long-sleeved shirt, shorts, high socks, hat, and headlamp. The weather forecast showed that it was going to be heating up well into the 70s, so I had a couple of t-shirts and ankle socks in my drops bags at the 19 mile mark and the 28/38 mile mark (it was an aid station on an out and back). All the runners lined up — I estimated about 100 of them — and the race director (who was quite the hoot, by the way), drew a line in the sand and counted down the seconds until the start. 5 – 4 – 3 – 2 – 1 – and we’re off!

You can see from the elevation profile that the first 8 miles had most of the climbing for the whole race. I intentionally took it slow — which was hard to do when you have fresh legs and have all the excitement of the start of the race coursing through your body.  In hindsight, I attribute the “success” I had with the race mostly on this strategy. Looking at my Strava, you can tell that some of my slowest running miles within the first 2/3rds of the race came during those first few miles (note: anything over a 15 min/mile was a stop at an aid station). The sunrise was slated for around 7:30am, so I had a goal of at least completing the out-and-back to Elephant Head (mile marker 9 // 1 hr 33 min) — an elevated look-out point to the west-side of the Great Salt Lake — by then. Sure enough, I hit that goal, but it was still too dark to get rid of my headlamp as we made our way for a brief downhill section into a second climb marked by switchbacks. Again, being conservative and saving my legs, I decided on a run-a-switchback-walk-a-switchback strategy for the quick 700 feet ascent. After that, it was smooth sailing for the rest of the Split Rock Bay loop (mile marker 14 // 2 hr 25 min) and I began heading back to the start/finish line (mile marker 19 // 3 hr 11 min).

I had a drop bag at the start/finish line where I changed out of my high socks, switched to a short sleeve shirt, ate half a cliff bar, and dropped off my headlamp before heading out to do the trails on the east-side of the island. I was surprised how well my legs were feeling (from my training runs, fatigue started to creep in at around this point) and I was motivated for the next short section (up to mile marker 21.5 // 3 hr 41 min) as I had my family waiting for me there! Much to my surprise, it was quite the welcoming crew from my wife, baby daughter, and parents-in-law who brought some really creative signs and cheered me on as I came into the aid station. I spent a good 10 minutes there chatting with them about the race thus far and how relieved I was to make it through the elevation feeling relatively good. The conditions of the trail was exceptional — a little sandy at points, but otherwise very compact dirt — and the cool weather was holding up well up until that point due to the cloud cover. I was pretty confident I was going to be able to achieve my primary goal of finishing and my pace thus far was spot on for a sub-10 hour finish, but I didn’t want to get my hopes up because I figured anything could happen with such a long race. I bid my farewells and gave them a prospective time of when I would arrive at the next major aid station (mile marker 33) where I could see them.

From my training runs, I knew that the next stretch would be a grind: a 20 mile out-and-back on flat terrain hugging the east coast of the island. What makes it hard is that you can see for miles and miles, so it’s difficult to be encouraged by your progress as it might take you hours to reach a point behind a nubby peninsula that you spotted a while back. Additionally, this is the part where my legs started to get a little tired and, because the terrain wasn’t too varying, I wasn’t as distracted by the scenery so I started focusing on how tired I was getting. I had a drop bag at the Lower Fray section of the out-and-back (mile marker 27.5 // 4 hr 54 min) where I spent a few minutes to rest and refocus myself. I ate a quesadilla triangle with some bacon and drank some Coke and was feeling better about myself. Knowing that I was 5 miles away from seeing my family helped out a lot too. The temperatures were starting to climb and a little bit of a headwind started to creep in, but I powered through and made it to the Ranch House (mile marker 33 // 5 hr 59 min), somehow below my best-case-scenario time of 6 hours. Again, I spent a fair amount of time at the aid station visiting with family and three of my friends (one of which was volunteering at the station) and resting my legs. Typically, I don’t like sitting down during these long runs, but I was feeling close to my “race nadir” at that point and decided that a little break off my legs certainly couldn’t hurt anything. At this point in time I was 100% certain I would finish below cut-off (I could just walk the rest of the way and make it) and, after doing some mental calculations, knew that the 10 hour mark was well within my ability. This was a strong motivating fact for the remainder of the race.

Again, bidding my family and friends adieu, I told them I’d see them at the finish line — hopefully sometime around 3:30pm to 4:00pm. I collected myself and headed off. Within a few hundred yards of leaving I past a runner who was running the 100 Mile race in full fireman regalia (long yellow pants/shirt, hard hat, and oxygen tank). I learned that he was raising funds to help pay for one of his friend’s cancer treatment — a truly remarkable act of friendship. This served as a secondary motivating thought, knowing that if this guy had the strength in him to run 100 miles dressed like that, at the very least I can do half the distance outfitted in the latest-and-greatest gear.

Between the Ranch House and the end of the long out-and-back (mile marker 44 // 8 hr 25 min), a lot of it was a blur. My running was strong as I would consistently pass people along the way, but I spent relatively long periods of time at the aid stations, allowing those same people to catch up. We yo-yoed like this for a while up until we started the homestretch for the finish line. Again, my legs were in surprisingly good shape (although they got a little killed on the final hill at the 45 mile mark!) and could pretty much consistently “run” the last 5 miles. I reached the final aid station (mile mark 46 // 8 hr 52 min) in good time and I knew I was going to break 10 hours — I just didn’t know by how much.

This last stretch was a bit rocky, so I had to be careful not to land wrong on my foot or stub my toes. I took it more slowly than what I was probably able to as I didn’t want to jeopardize my 10 hour finish. After rounding the northwest corner on the Lakeside Trail, I could see the finish line. It was only here when I began to let my mind wonder and to start thinking about how I was actually going to finish. Like a race of any distance, the last section is always the hardest as you begin to come to grips how exhausted you are and you get a little antsy to finish. This race was no exception. Arguably, the hardest mile was the last one for me as I had the finish in my sights but knew it was still sometime away — I just couldn’t move so I walked probably a third of it. As I rounded the final corner, I gathered myself and pushed it as hard as I could to end on a high note. I caught my family and friends a little bit off-guard (I don’t think they were expecting me so soon!) and I kind-of lost it once I saw my wife and baby there right before the finish line. Crossing the line and hearing how I finished at 9 hours 40 minutes — an exceptionally long amount of time to be exercising — really made me realize how crazy this day was and how proud I was of my performance!

As a whole, I felt pretty good afterwards. I knew I was going to lose a couple of toenails and got a few inconvenient blisters, but as a whole I felt about as good as when I ran my 55km race in Iceland. This race was a bellwether for me to see if I wanted to continue to run 50 Mile races and whether or not I could see myself doing a 100 Miler. As a whole, I am optimistic! I think I will do another 50 Miler in the Fall and, depending on how that goes, sign up for a 100 Miler next year.

I can’t say enough about how well this race was managed and the kindness of all the volunteers who took a large chunk of their time out of the weekend to help — in any way possible — a bunch of people like myself complete in a crazy race. For anyone on the fence about running ultras, I would definitely recommend this race as there are a few distance options (25km, 50km, 50 Mile, 100 Mile) and terrain is very conducive to a good finish.

Here’s to hoping to hit the trails soon!

HEART Conference // Paper + Presentation

Just received some exciting news that I gained final approval and will be making a presentation at the 2017 Hardened Electronics and Radiation Technology (HEART) Conference in Denver, Colorado at the end of April. The topic I’ll be discussing (via the poster session) involves the characterization of our facility’s linear accelerator after some upgrades we recently implemented.

This is the first time in recent memory that someone from my work will be presenting at a conference, so everyone is pretty excited about the opportunity to showcase some of our site’s capabilities. My team worked very hard over a span of several weeks in order to accomplish all the appropriate testing so that I could compile the data and submit my paper to the conference. It was truly a joint effort and I am looking forward to presenting for the first time the results!

Number Sense Auto-Generated Practice Tests // Update

Without a doubt, the most trafficked part of this site is my auto-generated number sense practice tests, so I thought I’d give you an update on the project. Here is where we stand at the moment as well as some things I want to implement in the near- to mid-term:

  • The process is almost entirely automated now. The only human component is the transcribing from .pdf to LaTeX code. This should reduce the number of errors you see on practice tests as everything else — from segmenting out a test’s LaTeX code to adding the questions to the appropriate database to generating the practice test itself — is entirely automated and, hence, error free!
  • I have about 6,000 questions in my database. This equates to about 75 complete tests that have been translated in LaTeX code and are being used to generate the practice material.
  • I’m adding at a rate of about 500 questions per week. This means I should hit my goal of having a 10,000 question bank by the beginning of May.
  • As we approach the latter stages of the competition season, I will begin posting practice material more frequently on the repository page, so check back often.
  • I’m going to try to begin making a separate database of regional and state-level type of problems (harder difficulty, multiple steps in order to solve, etc…) in order to gear up for the more challenging exams. I should be able to begin posting that material by late-March.
  • I’m also going to start doing a series of youtube videos detailing step-by-step instructions on how to solve most types of questions asked on the exam. This should help out the more visual learners grasp the concepts.
  • Over the summer, I am going to revise my Number Sense Manual in order to update the LaTeX code, add more sections that are applicable to the current exams, and include much more practice material. Because the manual is sectioned off into types of problems (e.g. multiplying by 11, squaring tricks, roots of polynomials, etc…), students can focus more easily on a particular type of problem they are having difficulty with and do drills to really solidify their understanding.
  • Finally, beginning for the 2017-2018 school year, I’ll make it where students can generate their own practice exams through my website — thus eliminating their dependence on my posting on a weekly basis. You’ll be able to practice as much as you want, whenever you want!

Putnam and Beyond // Putnam Exam

Came across something cool today searching for some test writing material for math contests. As I’ve mentioned previously, I’m trying to get back into the swing of things with creating problems for middle/high-school aged competitions that are medium in difficulty (similar to AMC/AIME type of difficulty). Anyways, I stumbled across this preface to the book Putnam and Beyond, written by my former math instructor at Texas Tech University, Razvan Gelca.

One of my biggest regret after graduating college was how I did not push myself harder to try earnestly at the Putnam Exam. At the time, I overextended myself with my coursework (trying to pull off a Mathematics and Engineering dual-degree, all within four years time) while neglecting some of my extra-curricular activities. If only I knew then what I know now about how classes are, effectively, pretty useless when it comes to the “real-world,” I would have focused more on qualitative accomplishments (like discovering new ideas, the value of research to find answers, etc…) rather than trying to maintain a high GPA. Although I never truly embarrassed myself on the exam (I didn’t ever record the dreaded final score of “zero,” for example), I certainly should have focused my attention more and worked longer hours practicing.

The Putnam Exam is one of the few math contests I feel genuinely strive towards recognizing inventiveness rather than regurgitation of math concepts. This “flicking on of the light bulb” of new ways of approaching problems is really what I cherished most about my Putnam sessions with Dr. Gelca. Although, without much consistent practice since, the math has probably laid dormant in me for a while, I still try to approach problems I come across in my work from multiple perspectives in order to determine the best course of action. There is and will always be high value attached to thinking of things in novel ways.

Anyways, discovering that I was mentioned in the Acknowledgements Section of the book Dr. Gelca was working so hard to compile while I was with him in the mid-2000s made me feel exceptionally proud and provided me a window to reflect on all life lessons I learned during that time.

And if you are math competitor, I highly recommend the book as well (I just ordered a copy myself as I have only a marked-up manuscript in my possession)!