- Lecture notes on Hilbert spaces and compact operators (2.7MB).
- 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.