General ressources on mathematics

• A course on complex analysis (introduction, in French): http://www-irma.u-strasbg.fr/~maudin/analysecomp.pdf
• Many ressources from MIT, undergraduate and graduate level: http://ocw.mit.edu/OcwWeb/Mathematics/index.htm

Ressources on measure theory, probability

• probability.net, a set of tutorials on measure theory and probability. The strong point of this webpage is that all proofs are done through exercices, and there is almost no requirements beside really basic mathematics (you will need some practice in mathematics, but you don't need any background on topology or measure theory for the proofs: any point used in a proof is proved before)
• The book "Probability, Random Processes, and Ergodic Properties", by R. Gray. This is a great introduction to the fundamentals of statistical signal processing. Of interest is a proof of the famous Kolmogorov Extension theorem. Can be found there: http://ee.stanford.edu/~gray/arp.html.
• The same R. Gray wrote a introduction book on stochastic processes which I find better written than the often cited Papoulis reference. This book is much less oriented towards rigourous proofs compared to "Probability, Random Processes, and Ergodic Properties" by the same author (it does not require any knowledge of measure theory), and as such, is much easier to read for people without the need for strong mathematics behind the theory of stochastic signal processing. Available online here: http://ee.stanford.edu/~gray/sp.html.

Ressources on machine learning