MA3105 Advanced real analysis, Spring 2014
10.04 The date of the oral examination is May 28 from 10.15 to 12.15 send me an email to get your time slot. We meet on Monday May 19, 10.15 in room 734 for questions. The final list of topics for the exam is below
20.01 Lecture on Tuesday is at 10.15, usual room
15.01 This week we discuss the laws of large numbers, lecture tomorrow is at 12.15 in 734.
08.01 We started yesterday with Borel-Cantelli lemmas and Infinite Monkey Theorem (ch.5.1 in McDonald, Weiss). Next lecture is on Thursday 12.15 room 734 SB II.
20.12 First lecture will be given on January 7th, Tuesday, room R81 (10.15)
We discuss schedule and the course and start our topic for the week which is foundation of probability theory from analytical point of view. We will learn the zero-one law and prepare the ground for the law of large numbers scheduled for the next week.
Tuesday 10.15-12.00, R81
Thursday 12.15-14.00, to be announced
Lecturer: Eugenia Malinnikova
room 948, Sentralbygg II
e-mail eugenia [at] math [dot] ntnu [dot] no
Signed measures and the Radon-Nykodym theorem.
Riesz-Markov theorem, the dual of C(X).
Mathematical model of probability, The Law of Large Numbers.
Dynamical systems and Ergodic Theorem.
Hausdorff measures and dimension
Fourier transform and applications.
We will mostly use the textbook:
McDonald, Weiss, A course in Real Analysis, Academic press.
More detailed plan of the lectures and final list of topics: List of topics
Lecture notes (updated)
week 2 LN 1 : Foundations of the probability theory, zero-one law
week 3-4 LN 2: Laws of large numbers, Shannon's theorem
week 5 LN 3: Signed measures
week 6 LN 4: Radon-Nykodim theorem; representation theorem
week 7 LN 5: Hausdorff measures and self-similar sets
week 8 Riesz Representation theorem
week 9 LN 6: Central Limit Theorem
weeks 9-10 Probabilistic number theory, slides
week 11 LN 7: Dynamical systems, Ergodicity
week 12-13 LN 8: Entropy of a dynamical system, Kolmogorov-Sinai theorem