I love math and I cannot lie

I don’t think this blog post will give my love of math justice. Reader (channeling my inner Jane Eyre), I would need to sit you down and you would need to see for yourself. Then, you could see my face light up and my heart beat quicken. You could see me just stare in awe at the beautiful numbers (and letters in some case).  You could hear the tone of my voice change from normal to extraordinarily excited. Because we have the World Wide Web between us, you’ll have to settle for this mediocre blog post.

There’s something about math that makes it feel right. It’s different than other subjects. Everything else is up for interpretation. Even in science, you can view a certain experiment differently than someone else. But math…there’s always a right answer. It may not always come as a 1 or 2 or square or circle, but an answer can be found somehow. And if there isn’t an answer like . You can say the limit doesn’t exist. You can prove that there is no answer.

Not all subjects have that kind of certainty.

Nothing against English class (I’m an avid reader), but can I really prove that the author used an “ad hominem” argument in line five to make an appeal to his or her ethos? I can assume, but I cannot truly prove an author’s purpose or the effect it has on the reader. Maybe my neighbor feels the passage portrays nature as sad, while I think it portrays nature as indifferent.  Do I even care about how the author portrays nature at all?

I don’t feel that way towards math, though. Unlike other students, I rarely question when I will use the math in real life. I know I would. I see friends and family members solving differential equations or using trig for their jobs. Even if I didn’t see the practical applications, I wouldn’t care. I just love math so much.

There’s a beauty behind the numbers. There’s just so many cool things you can do with them. Using the numbers 1-9 you can make a number that simplifies to  to a couple decimal places. Very impressive if you ask me. You can see the video here.

Right now I am taking Calculus, and I can wholeheartedly say it is my favorite class. Every day, I discover something more amazing about the math. It also certainly does help that my teacher is so passionate about the subject. Her enthusiasm is contagious. Even if you hate math, you can’t help but get excited in her class.

I just did some homework about Riemann sums and there was a feeling of peace and satisfaction after I completed it. I didn’t feel like it was busywork, but rather enriching my life with wonderful mathematical knowledge.

So this ends my blog post on math. I apologize if it seems more of a babble and less of a blog post, but maybe that’s a way you can understand how much I love the subject. I get so excited about it I can’t formulate a coherent post.

 

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Scientist Spotlight: Maria Agnesi

How many people have a mathematical curve named after them? Let me rephrase that, how many women have a mathematical curve named after them? I don’t know but I do know that Maria Gaetana Agnesi is one of these people. And guess what? Today is her birthday!

Born in Italy on May 16, 1718, she was the oldest of 21 children (her father had three wives). Because her father was a wealthy man, he was able to provide his children with the best of tutors.

Maria was lucky that she lived in the birthplace of the Renaissance because in Italy women were admired for their academic ability and were never scorned for their intellect. This attitude allowed Maria to prosper and eventually become a great mathematician.

By the age of nine Maria fluently spoke French (which she mastered at age five!), Greek, Hebrew, Latin, and other modern languages. She was known as a child prodigy and referred to as the “oracle of the seven tongues.” Also at the age of nine, she wrote and published (with the help of her tutor) a Latin discourse on the higher education of women as it was not practiced at the time.

Maria was a quiet and reserved child, but participated in the seminars and meetings of intellectuals that her father hosted. There she discussed philosophical and mathematical ideas. At the age of twenty, however, after her mother’s death, Maria took over the household duties and maintained a private life.  At the same time, she published a set of essays on philosophy and natural science called “Propositiones Philosophicae.” Much of it was based on the meetings she attended with her father.

Her most important work, a two volume book entitled “Analytical Institutions”, focused on differential and integral calculus. It was meant to be a textbook for her brothers but ended up making big waves in the world of academia. The ten years it took Maria to write it paid off because it helped bring “calculus to general use” (John H. Lienhard) and “was one of the first and most complete works on finite and infinitesimal calculus” (Agnes Scott College).

witchofagnesi

Drawing the “Witch of Agnesi” curve

Most people don’t hear of Maria Agnesi, rather they hear of the “Witch of Agenis”, her famous curve. If you look at the curve, there is nothing sinister about it. It is a versed sine curve called a versiera for the Latin vetere which means “to turn.” However, versiera was also an abbreviation for the Italian word avversiera which means “wife of the devil.” When versiera was translated into English it got confused with “witch.” If you want to learn more about this curve check out http://mathworld.wolfram.com/WitchofAgnesi.html They can explain it better than I ever could wish.

May notable institutions recognized Maria Agnesi for her work. Maria was appointed as an honorary reader at the University of Bologna by Pope Benedict XIV. She was later sent a diploma and her named was added to the faculty list but there is controversy regarding if she accepted the position. Maria also became a member of the Bologna Academy of Science and the French Academy expressed their admiration but could not admit her because she was a woman.

Once Maria’s father died, she retired from mathematics to pursue charity work. Growing up she wanted to enter the covenant, but her father would not allow it. So, she spent his life making contributions to mathematics and then the rest of her life after his death taking care of the ill and dying. Some may argue that she only really worked with mathematics to please her father and that her real passion lied in charity.  In 1763, the University of Turn asked her for her opinion on recent articles on the calculus of variations she explained she was no longer interested in such topics. Maria was appointed the director of the Pio Instituto Trivulzo, a home for the ill, and served the needy until her death.

For more about Maria:

http://www.uh.edu/engines/epi217.htm

https://www.agnesscott.edu/lriddle/women/agnesi.htm

http://www.math.wichita.edu/history/women/agnesi.html

Career Corner: Actuaries

The first time I heard about actuaries I thought they were people who did some stuff with birds. Maybe I was confused with an aviary, a place where they keep birds? Nonetheless, I was wrong.

Actuaries deal with numbers, not birds. They may deal with birds, if they are calculating financial risk for an aviary.

And that, is primarily what actuaries do. They calculate, using mathematical models, financial risks for companies and help the companies minimize the cost of risks. They mathematically calculate the chance of future events occurring and then plan ways to prevent unwanted events. If these undesirables end up occurring, actuaries figure out to reduce their impact. I guess you could think of actuaries as financial superheroes, they predict the problems, try to stop the problems, and then if they can’t stop the problem, do everything in their power to alleviate the consequences of the problem. Actuaries do a lot of business with insurance agencies, though their expertise is also used in many other areas.

Actuaries need to be strong in business, statistics, and most importantly mathematics. I personally love math. Calculus is currently my favorite class of the ones I am taking. The fact that math is not up for debate, there is an answer or there is not, draws me to it. There is always a way to either find a solution or admit there is no solution.

Alas, this is not a math appreciation post but a post about actuaries. Time to get back to business (no pun intended). My calculus teacher recommended to my mom that I be an actuary, as did my dentist and a few others.

It takes a lot to become an actuary, however, but the rewards are fruitful. Actuaries are in high demand and always needed. They never have to worry about losing their job because companies always need someone to determine risk. Actuary science is also a very lucrative job. My dentist said his son’s friend entered with a starting salary of $80,000 with no internship experience under his belt.

All these benefits come at an initial price, though, because there are a lot of tests needed to become certified. Many people give up because the math gets too complicated or the stress becomes too high. It takes a special kind of person, but maybe that person is YOU.

Actuary science is often a forgotten career path, but one not to be understated. If you love math, it could be an option for you; I know I am looking at it as an option for me. Who knows, maybe one day we will be crunching numbers together (at an aviary, of course).

 

To learn more about actuaries:

http://www.actuary.org/

http://beanactuary.org/what/

http://www.math.purdue.edu/academic/actuary/what.php?p=what

http://www.bls.gov/ooh/Math/Actuaries.htm

Scientist Spotlight: Mileva Einstein-Maric

Anyone could tell you who Albert Einstein is. School children know his equation  without even knowing what the letters mean. Einstein has become synonymous with genius. I mean, there was even a TV show “Little Einsteins”! But contrary to what you may be thinking this post isn’t about Einstein, at least not Albert. This post is highlighting the less popular but equally important Einstein: Mileva Einstein-Maric. She was his first wife and had no blood relations to him, unlike his second wife who is justifiably pointed out to be his double-first cousin.

Mileva was born in 1875 in Austria-Hungary (present-day Serbia). Coming from a wealthy family, Mileva’s father got permission for Mileva to enter an all-boys school where she received the highest grades possible in physics and mathematics. After falling ill, Mileva decided to move to Switzerland where she attended the “Girls High School” in Zurich. Once she passed the Matura-Exam, Mileva began studying medicine at the University of Zurich. However, she soon transferred to the Zurich Polytechnic where she met Albert Einstein. Mileva was the only women out of a group of six students for a physics-teaching course.

Initially, Mileva did well in her course but ended up failing the final teaching diploma exam because of the math part. Mileva worked harder and planned to retake the test but found out she was pregnant with Einstein’s baby. Three months into her pregnancy, she failed the exam again without any improvement to her score. Mileva ended up abandoning her studies and little is known about this daughter, Liserl. It is though the child died or was given up for adoption.

Albert and Mileva married in Swtizerland at a simple ceremony only witnessed by the original members of the Olympia Academy, Maurice Solovine and Conrad Habicht. The pair went on to have two sons but ended up divorcing after about 15 years. As part of their settlement, Mileva received all Albert’s Nobel Prize money and invested it in real estate.

However, throughout their marriage Mileva remained an asset to Albert. She discussed his papers with him and possibly contributed to many of his theories. There is a lot of controversy surrounding how much Mileva actually worked with Albert to develop his famous works. Was she truly a part of the process? Or was she just a wife supporting her husband? Scholars have speculated this for years and continue to examine their correspondence and relationship. Whether she directly contributed or not, Mileva and Albert both shared a deep love of physics and math. They must have bounced around ideas with each other and she probably influenced some of his ideas.  She was a very smart woman who might just have gotten too caught up in love to complete her degree, but I think she deserves a lot of credit. Perhaps she had the ability to do more but was caught in her husband’s shadow.

More about Einstein’s first wife:

http://bnrc.berkeley.edu/Famous-Women-in-Physical-Sciences-and-Engineering/mileva-maric-einstein.html

http://www.biography.com/people/mileva-einstein-maric-282676#divorce

http://www.teslasociety.com/Mileva.htm

http://www.einstein-website.de/biographies/einsteinmileva_content.html

Why do I love STEM?

I think this blog has been around long enough to address a pretty fundamental issue…why I love STEM. To provide some insight, here is my answer to an application question about what interests me about STEM:

STEM is the way of the future. I was interested in the STEM fields way before “STEM” was a buzzword. Ever since I could remember, my mother would buy me various science kits from the local education store because I have always had in interest in learning how things work and performing different experiments. As I have gotten older, I have learned that there is much more to STEM than making geodes or building circuits. I am interested in STEM not only because it is our key to understanding human life but it is also our way to improving human life. Countless new discoveries are being made in STEM fields every day. With STEM, the soldier that lost his leg fighting for the freedom of his country is given a bionic leg (printed on a 3-D printer) to finish the New York City marathon. If predictions come true, that same soldier can live comfortably in a lunar village. With STEM, the possibilities are endless and that is one of the things that entices me. I want to be part of this innovation. I know that the dedication and passion I have makes me a perfect fit to discover a cure or create a new invention. STEM gives us the power to change the world and shows me that there is nothing stopping me from being the next Stephen Hawking or Marie Curie.

Career Corner: Biomedical Engineering

Biomedical engineering: What is it? How do I get involved? Why is it so popular? If these questions have been on your mind lately about the field referred to as BME, you are not alone. I have the same questions and so do a lot of other people.  So, why not have a blog post to discuss it?images-2

Biomedical engineering combines engineering with biological sciences to create devices, software, and equipment to use in medicine. For example, pacemakers and joint replacements are products of biomedical engineering, as well as different systems used to deliver drugs. Biomedical engineers are responsible for researching, testing, and implementing new tools and devices to combat health issues.

What makes BME different than other engineering disciplines is that it puts a big emphasis on life sciences. It is a true combination of science and mathematics, therefore, you need to be strong in those fields. For success in the BME field, you need to truly love both science and math and be adept in both.

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Many schools have started to offer BME programs for undergraduates. Unlike other majors, most colleges have BME students apply for the BME program at the same time as applying for the school itself, because the program is so rigorous and students need all four years (or even more) to get everything done. Also, because BME has become so popular, it is difficult to transfer into a program.

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BME is an engineering field dedicated to improving human health. Biomedical engineers work every day testing and implementing new procedures and medical equipment for use in labs, hospitals, doctors’ offices, and other healthcare places. The field is continuing to grow each day with new advancement. Who knows? Maybe you or I will be the next BME superstar.

Sources:

http://www.bls.gov/ooh/architecture-and-engineering/biomedical-engineers.htm

http://biomedical.cua.edu/overview/whatdo.cfm

http://www.engr.iupui.edu/departments/bme/about/is-biomedical-engineering-right-for-me.php

http://www.mtu.edu/biomedical/department/what-is/

Scientist Spotlight: Hyaptia

This blog post is going back in time, all the way to the 300s A.D. That’s right, I am going to be talking about Hypatia, “the Egyptian wise woman.” Born to Theon of Alexandria, a well-known scholar and one of the last members of the Library Alexandria, she learned a lot from her father. He instilled in her the importance of Greek culture and, being a mathematician and astronomer himself, placed a special emphasis on the mathematical and astronomical traditions.

Living in Alexandria allowed Hypatia to be surround herself with intellectuals. She worked with her father on theories about the solar system and she created a new version of the hydrometer.

Like her father who preserved Euclid’s Elements and commented on Ptolemy’s Almagest and Handy Tables, Hypatia gave commentaries on Apollonius of Perga’s Conics (geometry, Diophantus of Alexandria’s Arithmetic (number theory), and an astronomical table. Unfortunately, her commentaries have been lost, though people have tried to reconstruct pieces of them.

Hypatia was on of the first recorded women to teach and study math. People traveled from all around to hear her lectures. One aspects of her teaching was Neoplatonism, a “pagan” view. I don’t want to get into the aspects of the philosophy here, but due to the strong tensions between Christians, Jews, and Pagans at the time, Hypatia was killed by a group of extreme Christians.

During Hypatia’s life, she was the world’s leading mathematician and astronomer. She is pictured in Raphael’s famous work “The School of Athens” and was mentioned in an ancient encyclopedia called the Suda. She has become a symbol for both the Enlightenment and Feminism.

800px-raffaello_scuola_di_atene_numbered-svg

In this numbered picture of “The School of Athens”, Hypatia is #9

Women in Science: 50 Fearless Pioneers Who Have Changed the World, Rachel Ignotofsky

http://www-groups.dcs.st-and.ac.uk/history/Biographies/Hypatia.html

https://www.britannica.com/biography/Hypatia

Scientist Spotlight: Cori Bargmann

Cori Bragmann, born on New Year’s Day in 1961, grew up in Georgia. Her parents were both translators at the Nuremburg Trials. Her father went to graduate school in the United States and became a professor at the University of Georgia after working at IBM. Cori grew up in “an academic household.” Her family was always reading, writing, or playing music.

In junior high and high school, Cori’s favorite class was always science. Instead of going to the pep rallies, she would spend her time in the chemistry lab.  When she was 17, Cori worked in a laboratory making fly food.  The lab director took a liking to her and introduced Cori to Sidney Kushner in the Genetics Department. Cori ended up working in Kushner’s laboratory and studied bacterial genetics and RNA metabolism. She also learned about molecular biology. The work she did in the laboratory gave her a base for her future research.

Cori attended the University of Georgia and received her undergraduate degree in biochemistry before heading to the Massachusetts Institute of Technology (MIT) for graduate school. She entered MIT in 1981, just “as molecule genetics was exploding.” It was at MIT that Cori studied cancer cells in Bob Weinberg’s lab and was part of some big innovations in the field. Some of Cori’s research led to developments in the treatment of breast cancer.

In 1987 Cori received her Ph.D. from the Department of Biology and stayed at MIT to do some postdoctoral research. She started to do some work with the human nervous system. In 1991, Cori travelled cross-country to work in the Department of Anatomy at the University of California, San Francisco. She learned neuroscience here and studied worms. Though worms seem unhelpful to the study of human genetics, Cori is using them to analyze how the correlation between genes and behavior. Her work is leading her to discover the root causes of diseases like Alzheimer’s and autism.

Cori currently works is the Torsten N. Wiesel Professor in the Lulu and Anthony Wang Laboratory of Neural Circuits and Behavior at Rockefeller University. She has won the Breakthrough Prize in Life Sciences and Franklin Institute Awards. Cori also began the Brain Research Advancing Innovative Neurotechnologies Initiative which is attempting to uncover what causes things like Alzheimer’s, autism, and depression.

To learn more about Cori:

http://www.pnas.org/content/102/9/3181.full

http://www.kavliprize.org/sites/default/files/Cornelia_Bargmann_Biography.pdf

Scientist Spotlight: Kira Larson

In June 2016 I attended the New Jersey Hugh O’Brien Youth Leadership Conference and one of the guest speakers was a bridge engineer by the name of Kira Larson. Kira’s talk captivated me and I saw a lot of her in myself, so I wrote her a thank you note at the end of the conference. Later, I connected with her on LinkedIn and we have been in contact ever since. She was even kind enough to let me visit her engineering firm, HNTB. I got to sit in on a meeting and get a glimpse of what a bridge engineer does. It was a very educational experience and made me seriously think of engineering as a future career path for myself.

I am currently taking a course called Principles of Engineering and one of our assignments was to interview an engineer. I chose to interview Kira and, being an editor on the school paper, I have to say she was an awesome interviewee! With her permission, I decided to publish the interview so all of you can read about her!

What is your specific degree and how does it relate to your current position? 

I have a Bachelor of Science in Civil and Environmental Engineering from Princeton (in 2008), and a Master of Science in Civil Engineering with an Emphasis on Structural Engineering from Columbia University (in 2009).  My position now is Structural Engineer at HNTB Corporation in Parsippany, NJ.  My degree is directly related to my work; structural engineering is really all based on physics and the forces in members, which was largely what my courses were about.  At both schools there was a big focus on designing structures to be efficient, economical and elegant, and I try to remember that every day at my job!

Pease explain your particular engineering field, your current job title, and your duties. 

My field of structural engineering is bridges; I design and detail new bridges and work to rehabilitate existing bridges.  My job title is Structural Engineer II, and I am responsible for performing calculations and choosing the materials and sizes of members needed to make a bridge stand up.  For a given project, I will work under what’s called a Project Manager, who manages the project as a whole, and I will supervise more junior engineers, who will check a lot of my work and perform smaller design tasks.  When we design a bridge, first we look at the geometry – e.g. how long does it need to be, is it straight or curved or skewed, how high does it need to be, and how much room do we have to build.  Then we design each member from the top down, starting with the beams and the deck, to the abutments that the beams sit on, to the foundations that hold the structure up below ground.  (If you remember my speech!) to make sure they will not fail when loaded by cars, trucks, impact from a vehicle accident, wind, earthquake, extreme temperatures, and more.  If you look under a typical NJ bridge, you’ll likely see a concrete deck sitting on steel beams, with smaller steel members called diaphragms spanning between the beams.  Every dimension of concrete and every piece of steel – from the width and depth and thickness of the beams, to the number of bolts connecting the diaphragms to the beams, to the amount of rebar inside the deck, is calculated by the engineer.  Once the design is complete, we put together a set of plans, which tells the contractor all of these sizes we’ve designed, and shows them how the bridge is supposed to be put together.  We also put together an estimate of all the materials used in the bridge, and how much it will cost, so that our client (some of our larger ones are the NJ Department of Transportation or the NJ Turnpike Association), can properly estimate how much the bridge will cost.  All these pieces come together in our submission, and then the project can be built!

 What is your average work schedule, what does your day look like?

The average schedule at my office is 8am to 5pm, with an hour for lunch, but the start and end times can vary.  Since my daughter was born a couple years ago, I’ve been lucky enough to be able to work part-time here, and spend more time with her at home.  I typically work 24 hours a week (Mon – Thurs from 9-3), but sometimes more as needed (like this week!).  My day is typically defined by a to-do list of items for the various projects I’m working on.  When a project first starts, it is largely about running calculations to get all the sizes we need.  Today, as I mentioned, we are working on finalizing our plan set for the bridges on I-80 and the designs are already complete.  So we are finishing drawing up different pieces of the bridges in CAD and making sure everything is shown in a way that a contractor will be able to use our plans and fully understand how to build every part of the structures.

 Starting with high school, please describe your educational background chronologically:

Ramsey High School, 2004

Princeton University, BS, 2008

Columbia University, MS, 2009

 Would you do anything differently if you had to start over?

I wouldn’t!  From a young age I loved math and loved problem-solving.  Today I get to do that every day at my job!  Because I was always passionate about those topics, I was able to enjoy the whole journey. 

 Finally, what advice would you give to me as someone interested in pursuing a career path similar to yours?  

The best advice I can give will sound familiar to you from HOBY – find your passion and start building that foundation!  So if you feel passionate about a career in engineering, start soaking up information, job shadow, and learn more about the field.  And also learn more about yourself, what do you love to do and in what setting do you do your best work (StrengthsFinder2.0 is a book I love for this!).   You don’t have to know all the answers today of what you want to do, but if you make decisions day by day that honor your passions, you will end up in the right place.  At first my major at Princeton was Mechanical and Aerospace Engineering, but I realized that I wasn’t excited about my courses, so I switched to Civil Engineering, and loved it.  Don’t feel stressed like you have to have it all figured out – wherever you go to school, if you make decisions with both your heart AND your mind, it will lead you to where you were meant to be.

I received a “Road Map to Success” from one of the Corporate leaders of my firm that I have hanging in my cubicle and has really inspired me, and I’d love to share it with you:

  1. Act with integrity ALWAYS
  • Be the same person at work, school, or home
  1. Be willing to do anything, anytime anywhere
  • Have a can-do attitude and never stop trying to discover and learn, choose every day to be a happy person as people will always want to be around you!
  1. Find and emulate successful people
  • Be a sponge
  1. Get involved in your community
  • Help others and begin building your relationship network
  1. Always be a hero at home
  • Spend quality time with family and keep your commitments
  1. Focus your career on creating value NOT money
  • Creates a strong work ethic and a success-oriented mindset
  1. Always read for self-improvement and growth
  • Expands your thinking and gives you great talking points
  1. Take responsibility for your career development
  • Find mentors, go after your goals, and do not expect others to be responsible
  1. Get outside your comfort zone
  • Challenge yourself
  1. Become a detailed note taker
  • Ability to repeat spoken information is powerful

 

 

Scientist Spotlight: Sylvia Earle

The ocean is something that has fascinated many, including Sylvia Earle. Sylvia  was born August 30, 1935 in New Jersey. At age 13 her family moved to Florida and she received scholarships to Florida State University. Sylvia learned how to scuba dive and began studying botany to better understand marine ecosystems.

Sylvia received both her M.S. and PhD. from Duke University. Many scientists were impressed with the amount of detail Sylvia used in detailing aquatic plant life for her dissertation as no one had ever been so specific before. Since this detailed feat, Sylvia has made it her lifelong goal to document every species of plant found in the Gulf of Mexico.

Sylvia has spent over 7,000 hours underwater and even lived in a structure 50 feet underwater for two weeks. This underwater stay gained her fame and even a ticker-tape parade and a reception at the White House.

She has explored the ocean in all shapes and forms from photographing shipwrecks to walking the ocean floor at “a lower depth than any human before or since.” She most recently set a record for also diving at a depth of 1,00 meters. Keep in mind this was in 2012 when Sylvia was seventy-seven years old.

Sylvia has served as the Chief Scientist of National Oceanic and Atmospheric Administration and has over 22 honorary degrees. She founded Deep Ocean Exploration and Research, Inc., Mission Blue and SEAlliance, and served as chair of the Advisory Councils of the Harte Research Institute and the Ocean in Google Earth. Sylvia has led hundreds of ocean expeditions and was named the 2014 Glamour Woman of the Year along with many other honors such as the International Seakeepers Award and the 209 TED Prize.

Sylvia’s work in ocean and marine vegetation has been some of the most impressive in her field. Though her work may not be in the typical laboratory, Sylvia’s impact on the scientific community will be making waves for years to come.

 

To learn more about Sylvia and her ocean adventures:

http://www.achievement.org/autodoc/page/ear0bio-1

http://www.nationalgeographic.com/explorers/bios/sylvia-earle/