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Last year one of our most popular sets of lectures were on Calculus.  Take this opportunity to hear, Dr. Branislav Kisačanin, introduce even our younger students to this beautiful topic.  Here is a description of the talk in his own words:

In this session we will look at calculus and try to dispel the mystery that often surrounds it. We will begin by looking at examples of limiting processes, and show for example that as x approaches 0, the value of \frac{\sin x}{x} approaches 1. Based on several other examples of limits, we will be able to determine line equations for tangents of various curves. This will bring us to the doorstep of the first derivative.

We will look at other interpretations of the first derivative and also look at how it is applied to maximization and minimization, Newton’s method of tangents for solving equations, etc. In the second hour we will look at another major part of calculus, integration, and will show how integration is used to compute areas and volumes. We will also look at the methods used by Archimedes to compute the volumes of solid spheres, which are remarkably similar to modern integration. Of course, there is much more to calculus than we can learn in one day, but this will be a good start!

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Following his very successful lecture on October 1, Dr. Kisačanin will continue his introduction to calculus.  Students who have already studied some calculus will gain a deeper insight into this beautiful and useful tool.  Those who have not yet studied calculus should not be put off, however, as Dr. Kisačanin is very skilled at explaining mathematical concepts so that they can be appreciated by a broad audience.

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Many of our students have started taking Calculus or are curious about what it’s all about.  Take this opportunity to hear one of our favorite lecturers, Dr. Branislav Kisačanin, introduce even our younger students to this beautiful topic.  Here is a description of the talk in his own words:

 

In this session we will look at calculus and try to dispell the mistery that often surrounds it. We will begin by looking at examples of limiting processes, and show for example that as x approaches 0, the value of \frac{\sin x}{x} approaches 1. Based on several other examples of limits, we will be able to determine line equations for tangets of various curves. This will bring us to the doorstep of the first derivative.

We will look at other interpretations of the first derivative and also look at how it is applied to maximization and minimization, Newton’s method of tangents for solving equations, etc. In the second hour we will look at another major part of calculus, integration, and will show how integration is used to compute areas and volumes. We will also look at the methods used by Archimedes to compute the volumes of solid spheres, which are remarkably similar to modern integration. Of course, there is much more to caclulus than we can learn in one day, but this will be a good start!

 

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A good friend of the Metroplex Math Circle, Dr. Arthur Benjamin, is a popular speaker at the world famous TED conference.  Recently, he offered his own idea for fundamentally changing math education in our country.  Like Richard Rusczyk, he sees the singular focus on Calculus as insufficient and distracting from a full math education.

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As we prepare for our first lecture of the year by Richard Rusczyk, we will share links to some articles that show his excellent observations on problem solving, education and their role in a full life. One of these outstanding articles is The Calculus Trap which begins with the following:

You love math and want to learn more. But you’re in ninth grade and you’ve already taken nearly all the math classes your school offers. They were all pretty easy for you and you’re ready for a greater challenge. What now? You’ll probably go to the local community college or university and take the next class in the core college curriculum. Chances are, you’ve just stepped in the calculus trap.

For an avid student with great skill in mathematics, rushing through the standard curriculum is not the best answer. That student who breezed unchallenged through algebra, geometry, and trigonometry, will breeze through calculus, too. This is not to say that high school students should not learn calculus – they should. But more importantly, the gifted, interested student should be exposed to mathematics outside the core curriculum, because the standard curriculum is not designed for the top students. This is even, if not especially, true for the core calculus curriculum found at most high schools, community colleges, and universities…

Please visit the Art of Problem Solving site to continue reading this and other articles by Richard and his colleagues.

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