Advanced Knowledge Problem of the Week 1-5-17

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Problem of the Week 1-3-17

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Problem of the Week 1-17-17

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Problem of the Week 1-10-17

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Advanced Knowledge Problem of the Week 12-29-16

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Advanced Knowledge Problem of the Week 1-19-17

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Problem of the Week 12-27-16

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Advanced Knowledge Problem of the Week 1-12-17

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Advanced Knowledge Problem of the Week 1-26-17

Hello followers! This is going to be my last Advanced Knowledge Problem of the Week, so I decided to give you something special. Read to the end of the solution transcript for some extra, fun problems. I will be referencing a lot of material I've covered in my last AKPoTWs, but not to worry if you haven't seen those.

I hope you've enjoyed all my content. Thank you for checking this out! :)

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Problem of the Week 1-24-17

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Advanced Knowledge Problem of the Week

Check out this week's Winter-themed Advanced Knowledge Problem of the Week! Let us know how you did in the comments!

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Problem of the Week

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The Holiday Math Gift Guide: Best Gifts for the Math Enthusiast in Your Life! (Part 3)

In accordance with Center of Math tradition, we bring you a holiday gift guide for your mathematician friend part III! If you want to check out previous posts like this one, you can find part I here, and part II here. Everything on this list gets the WCoM seal of approval, and we hope you'll enjoy our choices too. Happy holidays from the Center of Math!

Advanced Knowledge Problem of the Week

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Problem of the Week

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Celebrity STEM Stars

Did you know your favorite television star might have co-proved a theorem? Or that your favorite sports star may be pursuing a PhD in math at MIT? Many great celebrities love STEM and are not shy about sharing their passion with you!

Keep on reading to learn about how many people who are famous for sports, film, and TV are also well-known for their role in the world of STEM!

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Problem of the Week

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Advanced Knowledge Problem of the Week

Happy Thanksgiving! Check out this week's Advanced Knowledge Problem of the Week! Let us know if you think infinity is cool in the comments!

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Problem of the Week

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Advanced Knowledge Problem of the Week

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Math Minds: Pablo Portilla

Pablo Portilla is a PhD student at Instituto de Ciencias Matemáticas and is currently visiting Northeastern University. This Friday, he will give a talk on Tête-à-tête graphs and Seifert manifolds which you can find more information on here. Ben and Kelsey interviewed Pablo about his research and interests. 

What research are you doing and why did you choose it?

When I was an undergraduate student I didn't have that much "margin of action". When I finished my bachelor's degree I had a very narrow perspective of all the different kinds of mathematics being researched so as to say that I could actually "choose". I knew I liked topology and geometry, and I really enjoyed a course on differential topology that my current PhD advisor (Javier Fernández de Bobadilla) gave during my master's degree. It turned out that he works on singularity theory but he usually works more from the algebraic point of view. The good thing about singularity theory is that it intersects many different areas of mathematics. So he could propose to me a problem that, within singularity theory, is completely topological, and I was happy with that.

What would you say is your mathematical specialty?

As I said, I work on singularity theory from a differential topology viewpoint. I study things that happen in the space near the places where "abrupt changes" occur, that is singularities. More concretely I am trying to understand some mathematical objects associated to singularities from a combinatorial viewpoint. Hopefully this will be useful for computing invariants of singularities that are difficult to compute now or it will provide tools to attack other problems in mathematics.

Do you have a favorite mathematician, living or deceased?

If I had to choose I would choose René Thom (1923 - 2002). He made the bulk of his career in differentiable topology with very valuable contributions in the theory of characteristic classes and cobordism theory which are now essential to many branches of geometry. Then he settled the foundations of what is called "catastrophe theory" which could be understood as a part of singularity theory. He dedicated the last 20 years of his career to write philosophy and epistemology by "revisiting" much of the work of Aristotle (of who he considers himself a descendant). This last part is very often not valued by mathematicians which tend to see work outside mathematics as a waste of time. Nevertheless, I find inspiration in a man that had not only a great mathematical mind but also a huge interest for other areas of knowledge.

When did you first become interested in math? Was there a specific moment when you knew you wanted to pursue this field? 

I remember that being a kid I used to think of studying computer engineering. Then, at some point in my very early teens, I decided I was going to pursue a career in mathematics. In the beginning I was moved by a platonic idea about mathematics thinking they provide a "path to the truth" (or something like that) and I also liked how the "arguments from authority" just didn't work in mathematics. Then I realized that the kind of truth mathematics talks about is not the kind of truth I was thinking of in the first place. I also realized that since mathematics is done by people, "arguments from authority" are done sometimes at seminars or talks and personal relations influence the publishing (or not-publishing) of a work. I guess in the end, people enjoy doing things they are good at doing, and you don't have to find deep motivations to do anything. I just feel that making a living from doing research will make me happy. 

Is there anyone in particular that you would credit with guiding you to mathematics?

I have to give particular credit to a couple of teachers that I had in high-school: Mercedes was my mathematics teacher when I was 14 or 15. She was also involved in a program that "trained" young students to participate in the mathematical olympiads. I think she was very good at taking care of the individual needs as well as to boost the potential she found in some students. It was definitely very motivating to have her around. I also remember very kindly Luismi, a physics and chemistry teacher I had in high-school. He always put reasoning over knowledge and you could tell he really enjoyed his job. I think he transmitted to me his passion for science and discovery.

What was your favorite upper-level math course that you’ve ever taken, and why was it your favorite?

My favorite upper-level math course was the one I said before that my current advisor gave during my master's degree. It was a course on differential topology, and the goal was to prove a central theorem in this area which is known as "The h-cobobordism theorem" (originally proved by Smale). I really liked it because we started basically from scratch, defining the notion of differentiable manifold and we ended up proving highly non-trivial facts about manifolds in higher dimensions. The core of the proof relies on a result called Whitney's trick that tells you that you can "untangle" spheres of complementary dimension when the ambient space in which they lie has dimension big enough (for instance greater than 4). The implications of this theorem are deep, in particular it tell us that spaces of dimensions 3 and 4 are in some sense much more complicated than spaces in higher dimensions.

If you could attend a class taught by any math professor living or deceased, whose class would it be and why?

I think I would pick any class by John Milnor. I watch some famous recorded lectures he gave on differentiable manifolds at Cornell University [https://www.youtube.com/watch?v=1LwkljjLBns]. He starts from the definition of smooth function and ends up stating precise deep results in differentiable topology. It is just delightful to hear him speak. He goes at the right pace making the right remarks and emphasizing the important parts.

Do you have any general advice for students looking to pursue a degree in mathematics or a career in the field?

Mathematics can be very arid sometimes, but it is really rewarding to understand things, and much more rewarding to prove new results so... keep up the good work! Because it is worth it.

________________________________________________________________________________

Thank you very much for meeting with us, Pablo! We look forward to hearing you talk at the Center! 

Problem of the Week

Happy Election Season! Check out our problem of the week about the 1948 Presidential election! Let us know how you did in the comments, and make sure to vote!

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Happy Halloween! We won't "force" you to check out our problem of the week, but we certainly hope you will! Let us know how you did in the comments.

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Problem of the Week

Happy Halloween! Check out our problem of the week about cardioids pumpkins! Let us know how you did in the comments, and enjoy the holiday!

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Math Minds: Farid Tari

Last week we had Professor Farid Tari of Instituto de Ciências Matemáticas e de Computação visit the Center to give a talk about umbilic points. Professor Tari was born in El-Kseur, a small town 20km south of Bejaia. He has many years of math experience as both a researcher and professor, working in Denmark, the United Kingdom, and Brazil during his career. Co-ops Ben and Kelsey interviewed him shortly after the talk which can be found on YouTube here.

What would you say is your mathematical specialty?

I work in singularity theory and its applications to differential geometry and differential equations.

What research are you doing and why did you choose it?

If you look at the surface of full cup of coffee or tea, you will see that the reflection of light on the surface of the liquid form a curve. The curve has some sharp turning points called singular points. Some singular points of curves split in several other singular points or disappear completely as we deform the curve. Right now I am trying to understand how these singular curves deform but making sure that the deformations  keep some properties of the the shape of the curve. The problem is part of an ongoing research activity by various people on the differential geometry of  singular submanifolds of Euclidean spaces and of other spaces such as Minkowski spaces.

Do you have a favorite mathematician, living or deceased?

Not one but several. I cannot name only one as they are my friends. Mathematicians are human beings and my favorite are humble geniuses.

When did you first become interested in math? Was there a specific moment when you knew you wanted to pursue this field?

When I was at school, about 13 years old in a small village in North Africa and I managed 

to solve a hard problem that my teacher set for the class. After that I tried to solve all the problems in the textbooks.

Is there anyone in particular that you would credit with guiding you to mathematics?

My school teacher Mrs. Thomas. I hope she is still alive and well. She went back to her country 

after she taught me for one year. She was the teacher who gave us the hard problem that I managed to solve. She was full of praises and I didn't want to let her down after that, so I started doing all the exercises in the textbook. Mrs Thomas always found time to check my solutions and made encouraging remarks. Now a teacher myself, I learned from her how important positive feedback is as a tool for student learning.

What was your favorite upper-level math course that you’ve ever taken, and why was it your favorite?

I did my undergraduate studies at the University of Science and Technology Houary Boumedian, Algies, Algeria. The syllabus then was very much influenced by the Bourbaki school (too abstract!). Nevertheless, I enjoyed most of the courses. In particular, the courses that are still relevant to me are those on Differentiable Manifolds, Topology and Group Theory. I also took some heavy courses on Functional Analysis that I enjoyed then but do not use much now, except that they help me follow talks in seminars and general conferences on the subject.

If you could attend a class taught by any math professor living or deceased, whose class would it be and why?

There is this professor at Durham University (United Kingdom) named John Bolton.  We were colleagues when I used to work there (now I work at the University of Sao Paulo in  Brasil). John was the star professor and got the best feedback (questionnaires) from the students. I observed some of his lectures. John has the ability to make the students comfortable  with learning new material. He magically conveys the key points of the lecture without being bogged down by difficult mathematical language and notation. When I started my job at Durham University I was given a course to teach in the second term.  As it happened, the course was an annual one and was taught by John Bolton in the first term. When I got the end of the year questionnaires from the students, one of them wrote "Bring back John Bolton"!

Do you have any general advice for students looking to pursue a degree in mathematics or a career in the field?

My general advice to students is to do what you like and give your best to the task. That way you will get more out of your experience at university. If you like mathematics,  then do it! There is a wide choice of career for you after you graduate as you will be equipped with transferable skills.

________________________________________________________________________________

Thank you for the wonderful talk, Farid! We hope to see you again in the future! 

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Never Fear: ACT and SAT Help!

Standardized testing. 

Those are THE two words faced by countless high school students every year. The SATs, in particular, constantly hover above juniors and seniors once the school year starts. College applications are important, and as competition amongst students increases, it is becoming increasingly difficult for students to gain acceptance into their top choices. While extracurricular activities and GPA are important factors in adding substance to your college application, SAT scores are also a very significant part of the mix. No high school student wakes up on a Saturday morning yearning to take a 6 hour exam, but for those applying for college, the test is basically inevitable. 

One may expect that students who are successful in high school math classes would also perform well on the math portion of the SAT. Surprisingly however, this isn’t always the case. Students who excel in high level math courses are often discouraged and frustrated when their SAT scores fail to align with their school performance. Why does this disparity occur so rampantly? The focus of math classes is largely centered on method based thinking and displaying the correct work that led to the solution. This logical way of thinking is great for grasping complex concepts, but it does not match up with the format of the SAT. The multiple choice questions of the SAT do not allow for partial credit; only the correct answer gives the student points. Furthermore, SAT math questions are based on the fundamentals of mathematics. Even students in AP or high level math classes begin to shy away from the basics as they advance in courses or turn to their calculator. It is important for all students to review basic concepts and practice them throughout their SAT prep. 

Here at the Center of Math, we have a fair amount of combined experience in standardized testing. With these tips, we hope to increase your chances of a success as much as possible! 

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Reimagining Calculus Education -- 1st Annual Conference

Friday, October 28, 2016 Stevens Institute of Technology, Hoboken, NJ Build Student Retention and Critical Thinking Knowledge Featured Experts Deborah Hughes Hallett Harvard University, U. of Arizona Alexei Miasnikov Stevens Institute of Technology Jan Reimann Pennsylvania State University Adrian Sannier Arizona State University Bart Snapp Ohio State University Stephen Wang Rice University Objective Improving the success rates of calculus students through innovative teaching and learning strategies. Learn To Teach using math educational technology Deliver personalized education Keep students engaged Leverage student online literacies Create new options for delivering quality math content Pinpoint areas of mastery, strength and weakness for each student

Early Registration Savings Until October 7.

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