I am not an all technology all the time kind of girl. I don’t believe in calculators on exams, or being in contact with my students via email 24 hours a day.

But I LOVE iClickers. IClickers are a student response system, like Wii-motes, that allow students to answer multiple choice questions in class, in real time, and be graded on their answer immediately.

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Not too long ago, while in line for a coffee, the customer in front of me remarked that many people nowadays are so distracted by all these technological gadgets. Apparently, he was looking at a passerby in the street outside who almost got hit by a car because he was texting while crossing an intersection. Guessing that he wanted someone to say something, I quickly said: “It seems so.” My short comment, instead of signaling a close to a conversation, seemed to encourage him to expound on this rather peculiar contemporary phenomenon. I figured I had no choice but to be listening. Our conversation quickly turned to education, and I found out he was a math teacher. He was rather skeptical with all these fancy gadgets installed in classrooms to supposedly improve learning. So, this led to the question: do we really need computers and all the online world that comes with them to learn mathematics? My interlocutor, quite radical in his answer, thinks all those things are not needed; he is afraid that all this “tech clotting” that many people have been convinced to think helpful is the result of marketing hype.

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My summer reading, , follows the mathematical discoveries and subsequent works of Joseph Lagrange, Leonhard Euler, Adrien Legendre, and Carl Gauss. My goal in mathematics is to make the kinds of significant discoveries that these mathematicians made.

Euler lived in the 18th century; he proved some theorems about primes of the form which had been conjectured in the 17th century by another famous mathematician, Pierre de Fermat. Lagrange, who succeeded Euler as the director of the Prussian Academy of Sciences, and Legendre both studied quadratic forms and their applications to Euler’s work. One of the applications of the theory of quadratic forms is to generalize Euler’s proofs. However, Legendre developed the theory in a much more modern and natural way. In addition, he made significant developments in the theory of quadratic reciprocity. Finally, Gauss synthesized all of the above ideas. He is widely considered to be the finest mathematician ever. Continue reading →