What I studied in my (math) life

Not all the mathematics that I studied until today made a sign in me. Many books and articles come and go and just a few things remain.

I’d like to list here some of the things that somehow had an impact in my personal and professional life:

  • some books about recreational mathematics that I read when I was at the elementary school (mostly from Martin Gardner): at the time I was following the suggestions by my uncle Marcello (that was obsessed by prime numbers);
  • some classes in high school with relative manuals and exercises: I was bad in analytic geometry but I think I understood well calculus (that we called analysis at the time);
  • logic at university [Negri, Elementi di logica (several chapters); Odifreddi, Classical recursion theory (few sections), Chung-Keisler, Model theory (few sections), …]: I applied a sort of pattern-recognition to formulas without really understanding (the problem was that we never asked to do exercises) but this material had a deep impact on me;
  • abstract algebra at university: I don’t remember which books I used and I complemented with some tutorials online on group theory; unfortunately I didn’t perform so well at the final exams but group theory is one of the best things I’ve never seen;
  • Sergei Treil, Linear Algebra done wrong: for the very first time I tried, with this book, to really understand proofs, without skimming through them; I think I retained several parts of the book and linear algebra is the branch of mathematics that I know better today;
  • MIT online courses on calculus and linear algebra: I understood pretty well while following them and I believe that every professor should watch Gilbert Strang to learn how to teach;
  • [1999-now] self study in signal processing [some tutorials online, parts of Lyon’s book on DSP, parts of Ripples in mathematics (wavelets), some chapters of Smith’s Mathematics of the DFT, sections of Mallat’s book, …]: I believe I understood some linear algebra, something about filters, something about Fourier, something about wavelets and convolution;
  • selected parts in some analysis textbooks.

There are probably several other books or articles that I read about mathematics (especially during my PhD in… mathematical logic or my post-doc at École normale supérieure in Paris) but probably they didn’t mean too much for me.

I believe, anyway, that the part that one needs more when doing mathematics is exactly doing it. Lack of practice is always an issue.

Author: CarmineCella

Carmine-Emanuele Cella is a weekend-pilot; he wanted to be a mathematician but he ended up in writing music that nobody understands. Freud would say about him that he received too much love during his infancy but his psychologist just says that he should accept himself as he is. He loves life and he teaches at the University of California, Berkeley.

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