[Gianluca Gorni's home page]

Lecture Notes (in Italian)

• Using your fingers to count in base 16 (42K).
• The Greek alphabet, for use in mathematics and computer science (69K).
• Cardano's solution to the third degree equation (140K).
• The induction principle (100K)
• Set theory (229K).
• Set-theoretic relations (120K).
• Peano's axioms (153K).
• Infinite cardinalities (116K).
• The square root of 2 (442K).
• Uniform continuity in dimension 1 (164K).
• Iterating functions of one variable (118K).
• Some "pathological" functions of one variable (188K).
• Limit points of a sequence of real numbers (104K).
• The sequence of the powers of a complex number (138K).
• Some different ways of making R^2 a normed space (89K).
• Cantor's set and Peano's curve (237K). See also the companion Mathematica notebook and Peano's curve QuickTime Movie (700K).
• Van der Waerden's nowhere differentiable function (256K); see also the companion Mathematica notebook.
• Some aspects of the complex exponential function explained through pictures (248K).
• An elementary proof of the fundamental theorem of Algebra (95K).
• An introduction to the integral using the gauge integral approach. Also: printable text summary.
• A pictorial introduction to functions of two variables (2.9 MB). See also a java live 3D version of one of the graphs.
• Double integrals through pictures (16MB). You can view it with the free Wolfram CDF Player.
• Some examples of integration in two variables (7MB).
• A videogame to illustrate the definition of limit (32K). You can view it with the free Wolfram CDF Player.
• A collection of animations to introduce the concept of limit (69K). You can view it with the free Wolfram CDF Player.
• A summary of indeterminate limits, with final quiz (32K). You can view it with the free Wolfram CDF Player.
• A tutorial introduction to the derivative using the concept of zoom. You can view it with the free Wolfram CDF Player).
• A tutorial on the mean value theorems by Rolle, Lagrange and Cauchy. You can view it with the free Wolfram CDF Player). There is also a cloud-based version.
• Animations to visualize real-valued functions on the unit circle, to set the stage for Fourier analysis. (You can view the cdf with the free Wolfram CDF Player)
• Animations to visualize the complex powers on the unit circle
• Pictures to illustrate trigonometric Fourier series: pdf version (633K) and cdf version with animations (37M).
• The convolutions of functions explained with pictures.
• Fourier approximants visualized as composition of uniform circular motions.
• The Hahn-Banach theorem illustrated (290K) (You can view the cdf with the free Wolfram CDF Player)
• Semiintegrable and measurable functions (160K).
• Illustrations on Taylor polynomials in pdf format and in cdf format.
• Construction of Lebesgue measure in Euclidean space.
• Vitali-Lebesgue's theorem on the relation between Riemann and Lebesgue integration.
• Lusin's theorem on the approximations of a measurable function with continuous functions.
• The orthogonal projection onto the closed subspace generated by an orthonormal system in a Hilbert space.